Full text of "The determination of hydrogen ions; an elementary treatise on the hydrogen electrode, indicator and supplementary methods, with an indexed bibliography on applications"

See other formats

,A &&••

To
Fellow Workers in the Biological Sciences,

Architects of Progress,
Who Hew the Stone to Build Where Unseen Spires Shall Stand

6? D

CONTENTS

PREFACE TO THE THIRD EDITION ix

PREFACE TO THE FIRST EDITION xiii

CHAPTER I

INTRODUCTION AND THE SIMPLER EQUILIBRIUM EQUATIONS FOR ACIDS
AND BASES 1

CHAPTER II
SOME SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 35

CHAPTER III
OUTLINE OF A COLORIMETRIC METHOD 62

CHAPTER IV
CHOICE OF INDICATORS 67

CHAPTER V
THEORY OF INDICATORS 99

CHAPTER VI

APPROXIMATE DETERMINATIONS WITH INDICATORS 119

CHAPTER VII
THE APPLICATION OF SPECTROPHOTOMETRY, COLORIMETRY, ETC 141

CHAPTER VIII
SOURCES OF ERROR IN COLORIMETRIC DETERMINATIONS 177

CHAPTER IX
STANDARD BUFFER SOLUTIONS 192

CHAPTER X

OUTLINE OF THE "HYDROGEN-ELECTRODE" METHOD 221

CHAPTER XI

ON CHANGES OF FREE-ENERGY 230

CHAPTER XII

THEORY OF THE HYDROGEN-ELECTRODE 251

CHAPTER XIII

POTENTIAL DIFFERENCES AT LIQUID JUNCTIONS 264

VI CONTENTS

CHAPTER XIV
HYDROGEN HALF-CELLS 281

CHAPTER XV

CALOMEL AND OTHER STANDARD HALF-CELLS 303

CHAPTER XVI

THE POTENTIOMETER, NULL-POINT INSTRUMENTS AND ACCESSORY
EQUIPMENT 317

CHAPTER XVII

HYDROGEN GENERATORS, WIRING, INSULATION, SHIELDING, TEMPERA-
TURE CONTROL, PURIFICATION OF MERCURY 350

CHAPTER XVIII

OXIDATION-REDUCTION POTENTIALS 367

CHAPTER XIX

THE QUINHYDRONE AND SIMILAR HALF-CELLS 404

CHAPTER XX

METAL-OXIDE ELECTRODES. THE GLASS ELECTRODE. THE OXYGEN
ELECTRODE 423

CHAPTER XXI
SOURCES OF ERROR IN ELECTROMETRIC MEASUREMENTS 434

CHAPTER XXII

TEMPERATURE COEFFICIENTS 448

CHAPTER XXIII

STANDARDIZATION OF PH-MEASUREMENTS. 461

CHAPTER XXIV

STANDARD SOLUTIONS FOR THE ROUTINE CHECKING OF HYDROGEN
ELECTRODE MEASUREMENTS 483

CHAPTER XXV
THE THEORY OF DEBYE AND HUCKEL 489

CHAPTER XXVI
SUPPLEMENTARY METHODS 513

CHAPTER XXVII
AN ALTERNATE METHOD OF FORMULATING ACID-BASE EQUILIBRIA 519

CONTENTS

Vll

CHAPTER XXVIII
ELEMENTARY THEORY OF TITRATION 530

CHAPTER XXIX
NON-AQUEOUS SOLUTIONS 539

CHAPTER XXX

APPLICATIONS 549

BIBLIOGRAPHY 587

APPENDICES

TABLE A. ARBITRARILY STANDARDIZED VALUES FOR HALF-CELLS .... 672

TABLE B. RELATION OF [H+] TO pH ' 673

TABLE C. FACTORS FOR CONCENTRATION CELLS 0°C. TO 70°C 674

TABLE D. CORRECTION OF BAROMETER READING FOR TEMPERATURE. . 675

TABLE E. BAROMETRIC CORRECTIONS FOR H-ELECTRODE POTENTIALS . 676

a. a

TABLE F. VALUES OF LOG AND OF LOG MULTIPLIED BY

1 - a. I - a

THE TEMPERATURE FACTORS FOR CONCENTRATION CELLS. 677

TABLE G. DISSOCIATION EXPONENTS OF ACIDS 678

TABLE H. DISSOCIATION CONSTANTS AND ASSOCIATION EXPONENTS

OF BASES 679

TABLE I. DISSOCIATION EXPONENTS AND ASSOCIATION EXPONENTS

OF AMINO ACIDS 680

TABLE J. HALF TRANSFORMATION POINTS OF ALKALOIDS 681

TABLE K. RELATION OF PERCENTAGE REDUCTION TO POTENTIAL

AT CONSTANT pH 682

TABLE L. E'0 VALUES FOR SEVERAL OXIDATION REDUCTION INDI-
CATORS AT 30°C 683

TABLE M. SYMBOLS AND CONVENIENT FORMULAS 684

TABLE N. DEFINITIONS FOR THE MOST PART NOT INCLUDED IN THE

TEXT 684

TABLE O. TABLE OF LOGARITHMS 690

INDEX OF AUTHORS 693

INDEX OF SUBJECTS . . . . •. 703

PREFACE TO THE THIRD EDITION

Within the past twenty years methods of determining hydrion
concentration have served well in the exploration of many and
divers subjects. But the period of general exploration is drawing
to a close and long ago there were begun exact studies of equilibria,
or of kinetic events in which hydrions participate. Refinement
of technique, variety of method and elegance of formulation are
in greater demand. Accordingly there have been added in this
edition chapters or sections bearing upon each of these aspects,
and the old text has been almost entirely rewritten to conform
to the revised presentation. There results a superficial appear-
ance as of a more exhaustive treatment. However, the require-
ments of a new age have far outrun the range of subject and the
depth of treatment that can be encompassed with adherence to
the more or less discoursive style of presentation which it has
seemed best to use. Consequently this enlarged edition remains
more elementary in relation to the needs of today than was the
first edition in relation to the needs of its period.

The expansion has not led to a wholly satisfactory product.
For the faults of comprehension or of exposition I need ask no
charity.- It cannot, or should not, be given in such matters. But
I feel compelled to shift to the times some responsibility for one
or two of the major faults of this book.

So varied and extensive are the applications of the methods,
the details of technique and the special forms of theory that it is
become about as ridiculous to attempt to recount all aspects
within one text as it would be to note all the uses of the thermom-
eter, all types of data to which is affixed the symbol °C. and at
the same time to exhaust the theory of thermometry. But,
having set out to glean from the literature important informa-
tion which I think is still desired in one text, I believe the reader
will be interested in a survey incidental to this task and de-
scribed by the accompanying chart.

The data were compiled as follows. The number of papers
for each of the years from 1910 to 1920 was taken from the bibli-

PREFACE TO THIRD EDITION

ography of the second edition. Estimates for each of the subse-
quent years were made as follows. Several numbers of Chemical
Abstracts for each year were taken at random and carefully
searched in all sections for papers which seemed to conform to
the types included in the bibliography of the second edition.
From the number of pages searched and the number of pages for
the year the number of such articles for that year was calculated.
Of course, a serious question of personal judgment enters. This
need not be discussed, for I trust the reader to recognize in the
chart what he himself must have felt is happening in his own
specialty.

1500

1400

1300

1200

to 1100

£ 1000

£ 90°

**" 800

0 700
K 600
<n 500

1 400
Z 300

200
100

frrr

YEAR

The situation has made obsolete some of the old ideals of
scholarship. It has made trivial all available facilities of library,
abstract and review. It has made the monograph almost futile.
It has made ridiculous him who claims to combine thorough
investigation with thorough re-search.

Undoubtedly the mediaeval scholar felt oppressed by the mag-
nitude of his specialty in his time and looked forward with mis-
giving to the "impossible" tasks of the future; and yet, with no
vacation such as Sir Ernest Rutherford whimsically prays for
as a need of the present, scholarship survived then and doubtless
will now. However, there was one disease of mediaeval times
that had to be cured before the intellect came to renewed health
and to vigor adequate for enlarged tasks. I fear that we may be

PREFACE TO THIRD EDITION XI

reinfected. It was the pursuit of "vanishing particulars" and
the employment of conveniences suited to a purpose. A new age
has brought new purposes and an equal sincerity of a new type
that makes us sometimes scorn the old; but amid the abundance
of our learning the instinct of mastery has driven us to take
refuge in specialization wherein we are at liberty to make our
neighbors the victims of our conveniences. They are the con-
veniences of special terminologies suited to the immediate need of
the specialist but barriers to earnest seekers of the contents of
the specialty. They are the conveniences of special formulations
suited to the immediate needs of the case but barriers to the
widespread use of the meaning of the case. While I have tried
to avoid, so far as possible, discussion of the less significant in-
stances, I conceive it to be the function of this book to tell about
a few of the more important matters in terms agreeing essentially
with those which the reader will have to know in his study of
the literature. Partly because the literature is what it is, the
subject is not here presented as I conceive some genius will some
day present it — with brilliant simplicity and, withal, rigidly.

To those who, in philosophic mood, would question what I
mean by simplicity and rigidity I will answer that the pro-
nouncements of genius determine this, that we recognize it when
it comes and dream of it before it comes. And come it must if
those who labor with life chemistry are ever to apply effectively
all the pertinent information being gathered, often with lack of
systematic thoroughness and being recorded with ever increasing
inavailability.

In undertaking the difficult task of revision I have sought and
have been generously given the aid of many friends and authori-
ties. Since none of these has seen the manuscript in final form
I shall not note the subjects on which advice was given, lest, per-
chance, the mishandling of the advice reflect upon the giver.
I hope that this will not seem to detract from the gratitude I
have or from the credit due to :

Mr. C. E. Abromavich Dr. Lloyd Felton

Mr. Alan Bernstein Dr. F. Fenwick

Dr. William Blum Dr. H. D. Gibbs

Dr. Barnett Cohen Dr. A. Grollman

Dr. N. Ernest Dorsey Dr. Louis J. Gillespie

Xll PREFACE TO THIRD EDITION

Dr. A. Baird Hastings Dr. W. A. Perlzweig

Dr. Leslie Hellerman Dr. A. H. Pfund

Dr. Morris Kharasch Dr. Julius Sendroy, Jr.

Dr. H. R. Kraybill Dr. George Scatchard

• Dr. Victor K. LaMer Dr. S. E. Sheppard

Dr. E. K. Marshall, Jr. Dr. Edgar T. Wherry

Dr. George Morey Dr. D. D. Van Slyke

Dr. Leonor Michaelis Dr. G. W. Vinal

and

the publishers.

Needless to say I have drawn freely upon the literature. I hope
that I have given adequate credit at the proper places in the text.
Baltimore, Maryland
Easter Sunday, 1928

PREFACE TO THE FIRST EDITION

Poincare* in The Foundations of Science remarks, ( 'There are
facts common to several sciences, which seem the common source
of streams diverging in all directions and which are comparable
to that knoll of Saint Gothard whence spring waters which fer-
tilize four different valleys."

Such are the essential facts of electrolytic dissociation.

Among the numerous developments of the theory announced
by Arrhenius in 1887 none is of more general practical importance
than the resolution of "acidity" into two components — the con-
centration of the hydrogen ions, and the quantity of acid capable
of furnishing this ionized hydrogen. For two reasons the hydro-
gen ion occupies a unique place in the esteem of students of
ionization. First, it is a dissociation product of the great majority
of compounds of biochemical importance. Second, it is the ion
for which methods of determination have been best developed.
Its importance and its mensurability have thus conspired to make
it a center of interest. The consequent grouping of phenomena
about the activity of the hydrogen ion is unfortunate when it
confers undue weight upon a subordinate aspect of a problem or
when it tends to obscure possibilities of broader generalization.
Nevertheless, such grouping is often convenient, often of im-
mediate value and frequently illuminating. Especially in the
field of biochemistry it has coordinated a vast amount of material.
It has placed us at a point of vantage from which we must look
with admiration upon the intuition of men like Pasteur, who,
without the aid of the precise conceptions which guide us, handled
"acidity" with so few mistakes.

In the charming descriptions of his experimental work Pasteur
has given us glimpses of his discernment of some of the effects of
"acidity" in biochemical processes. In the opening chapter of
Studies on Fermentation he noted that the relatively high acidity
of must favors a natural alcoholic fermentation in wine, while the
low acidity of wort induces difficulties in the brewing of beer.
He recognized the importance of acidity for the cultivation of

xiii

XIV PREFACE TO FIRST EDITION

the bacteria which he discovered and was quick to see the lack of
such an appreciation in his opponents. In describing that process
which has come to bear his name Pasteur remarks, "It is easy
to show that these differences in temperature which are required
to secure organic liquids from ultimate change depend exclusively
upon the state of the liquids, their nature and above all upon the
conditions which affect their neutrality whether towards acids or
bases." The italics, which are ours, emphasize language which
indicates that Pasteur was aware of difficulties which were not
removed till recently. Had Pasteur, and doubtless others of like
discernment, relied exclusively upon volumetric determination of
acidity they would certainly have fallen into the pitfalls which
at a later date injured the faith of the bacteriologist in the meth-
ods of the chemist. Was it reliance upon litmus which aided
him? Perhaps the time factor involved in the use of litmus
paper, which is now held as a grave objection, enabled Pasteur
to judge between extremes of reaction which the range of litmus
as an indicator in equilibrium does not cover. At all events he
recognized distinctions which we now attribute to hydrogen ion
concentrations. Over half a century later we find some of
Pasteur's suggestions correlated with a marvelous development
in biochemistry. The strongest stimulus to this development
can doubtless be traced to the work of S0rensen at the Carlsberg
Laboratory in Copenhagen and not so much to his admirable
exposition of the effect of the hydrogen ion upon the activity of
enzymes as to his development of methods. At about the same
time Henderson of Harvard, by setting forth clearly the equilibria
among the acids and bases of the blood, indicated what could be
done in the realm of physiology and stimulated those researches
which have become one of the most beautiful chapters in this
science.

Today we find new indicators or improved hydrogen electrode
methods in the physiological laboratory, in the media room of the
bacteriologist, serving the analyst in niceties of separation and
the manufacturer in the control of processes. The material
which was admirably summarized by Michaelis in 1914, and to
which Michaelis himself had contributed very extensively, pre-
sents a picture whose significance he who runs may read. There
is a vast field of usefulness for methods of determining the hydro-

PREFACE TO FIRST EDITION XV

gen ion. There is real significance in the fruits so far won.
There remain many territories to explore and to cultivate. We
are only at the frontier.

In the meantime it will not be forgotten that our knowledge of
the hydrogen ion is an integral part of a conception which has
been under academic study for many years and that the time has
come when the limitations as well as certain defects are plainly
apparent. While there is now no tendency nor any good ground
to discredit the theory of electrolytic dissociation in its essential
aspects, there is dissatisfaction with some of the quantitative
relationships and a demand for broader conceptions. It requires
no divination to perceive that while we remain without a clear
conception of why an electrolyte should in the first instance
dissociate, we have not reached a generalization which can cover
all the points now in doubt. Perhaps the new developments in
physics will furnish the key. When and how the door will open
cannot be foreseen ; but it is well to be aware of the imminence of
new developments that we may keep our data as pure as is con-
venient and emphasize the experimental material of permanent
value. We may look forward to continued accumulation of
important data under the guidance of present conceptions, to
distinguished services which these conceptions can render to
various sciences and to the critical examination of the material
gathered under the present regime for the elements of permanent
value. These elements will be found in the data of direct experi-
mentation, in those incontrovertible measurements which, though
they be but approximations, have immediate pragmatic value
and promise to furnish the bone and sinew of future theory. In
the gathering of such data guiding hypotheses and coordinating
theories are necessary but experimental methods are vital.

The time seems to have come when little of importance is to
be accomplished by assembling under one title the details of
the manifold applications of hydrogen electrode and indicator
methods. It would be pleasing to have in English a work com-
parable in scope with MichaehV Die Wasserstoffionenkonzentra-
tion; but even in the short years since the publication of this
monograph the developments in special subjects have reached
such detail that they must be redispersed among the several sci-
ences, and made an integral part of these rather than an unco-

XVI PREFACE TO FIRST EDITION

ordinated treatise by themselves. There remains the need for a
detailed exposition, under one cover, of the two methods which
are in use daily by workers in several distinct branches of bio-
logical science. It is not because the author feels especially
qualified to make such an exposition that this book is written,
but rather because, after waiting in vain for such a book to
appear, he has responded sympathetically to appeals, knowing
full well from his own experience how widely scattered is the
information under daily requisition by scores of fellow workers.

For the benefit of those to whom the subject may be new
there is given in the last chapter a running summary of some of
the principal applications of the methods. This is written in
the form of an index to the bibliography, a bibliography which
is admittedly incomplete for several topics and unbalanced in
others, but which, it is believed, contains numerous nuclei for
the assembling of literature on various topics.

The author welcomes this opportunity to express his apprecia-
tion of the broad policy of research established in the Dairy Divi-
sion Laboratories of the Department of Agriculture under the
immediate administration of Mr. Rawl and Mr. Rogers. Their
kindness and encouragement have made possible studies which
extend beyond the range of the specialized problems to which
research might have been confined and it is hoped that the bread
upon the waters may return. To Dr. H. A. Lubs is due the credit
for studies on the synthesis of sulfonphthalein indicators which
made possible their immediate application in bacteriological
researches which have emanated from this laboratory. Acknowl-
edgment is hereby made of the free use of quotations taken
from the paper The Colorimetric Determination of Hydrogen Ion
Concentration and Its Applications in Bacteriology published in
the Journal of Bacteriology under the joint authorship of Clark
and Lubs.

The author thanks his wife, his mother, Dr. H. W. Fowle and
Dr. H. Connet for aid in the correction of manuscript and proof,
and Dr. Paul Klopsteg for valuable suggestions.

It is a pleasure to know that the publication of the photograph
of Professor S. P. L. S0rensen of the Carlsberg Laboratory in
Copenhagen will be welcomed by American biochemists all of
whom admire his work.

Chevy Chase, Maryland
March 17, 1920

CHAPTER I

INTRODUCTION

AND
THE SIMPLER EQUILIBRIUM EQUATIONS FOR ACIDS AND BASES

In a country rich in gold observant wayfarers may find nuggets on
their path, but only systematic mining can provide the currency
of nations. — SIR FREDERICK HOPKINS.

INTRODUCTION

"Acid" still means sour, like vinegar. This common meaning
preserves the ancient flavor of the word and recalls the fact that
the modern highly technical meaning had its origin in the grouping
of substances by type. In this there is a resemblance to the pro-
cedure of the botanist who in the last analysis determines a
species by reference to a type specimen. But once we pass beyond
the mere origin of the modern meaning we may trace persistent
searches among the sour or vinegar-like substances for the nature
of that community of properties which came to be regarded as of
much more fundamental interest than the classification itself.
Each attempt bears the imprint of its age. By Paracelsus the
community of properties was supposed to reside in the Acidum
primogenium. By Lavoisier, the discoverer of the true nature of
oxygen, it was associated with oxygen. Mills, in philosophic
mood, called it a function. In the age of structural and atomic
chemistry it was hydrogen so placed in a compound as to be
replaceable by a metal. Fortunately no categorical distinction
between property, function, substance, etc., deterred the searchers.

Among the properties common to the sour or acid substances
is their submission to the "killing"1 effect of alkalies. "Alkali"

1 The word "kill," taken from the vernacular discussion of the phenom-
enon in question, is much more appropriate to this stage of the discussion
than certain other words like "neutralize" which, in the parlance of the
laboratory, have acquired meanings so specialized and at the same time so
diverse as to obscure meaning very successfully.

2 THE DETERMINATION OF HYDROGEN IONS

is said to originate in an Arabic word meaning the ashes of plants.
From this origin has arisen a variety of meanings illustrating ad-
mirably another search for an account of another community of
properties. From wood ashes has been isolated potassium, a metal
having properties in common with lithium, sodium, etc. This
series is now known as that of the "alkali metals." To a certain
degree their properties extend to the group of metals known as
the "alkaline earths." Metals of either group act vigorously
upon water and the resulting solutions have preeminently a
property in common with the leachings of wood ashes. They
"kill" the acidity of acid solutions. They are "alkaline."

An alkali upon interacting with an acid forms a salt, for example
caustic potash and hydrochloric acid form the salt potassium
chloride. In a chemistry which elevated the importance of the
metals, the potassium in potassium chloride held the center of
interest. It was considered the base of the salt. But "base" in
this sense is going out of common usage. Again a property, the
basic property, has been abstracted and "base" is now the pre-
ferred word with which to denote all substances, organic as well
as inorganic, which act like the leachings of wood ashes in killing
acids.

There are many evidences of the mutual destruction (complete
or partial) of properties of the two groups, when acids and bases
interact. Attempts to systematize these evidences have had their
important part in developing a classification of specific substances
into acidic and basic compounds. Some of the systems of
classification have extended far beyond the bounds of their con-
crete origin. We need not recreate for ourselves the perplexities
which arose during attempts to make the classification of acids
and bases scientifically definite. But in passing we may recall
that the older theories were reduced by the "practical" chemist
to meet his demand that an acid solution turn litmus red and an
alkaline solution turn litmus blue. The ghost of this delight-
fully simple basis still lingers about the laboratory, although the
litmus test is now recognized as hopelessly inadequate for analysis,
for organic synthesis, for biochemistry, and for a host of industrial
processes. If we ignore the older classifications, it is not be-
cause there is any occasion to disclaim our debt to the early in-
vestigators. They provided the foundations of our far-reaching

I ACIDS AND BASES 3

subject. From these foundations have arisen some concepts and
some specific data of such importance as to merit our entire
attention. The purely historical we shall leave to the historian.

We need only note that the process of abstraction has progressed
until a property common to wood ashes, alkali carbonates, hy-
droxides in general and a host of organic compounds has been
elevated to unique distinction. A similar abstraction has occurred
in the treatment of acids; and at last we associate properties with
material entities again. The entities appear in the following
definitions, and their associations with properties appear in those
manifold consequences which will be touched upon throughout
this book.

For present purposes we may define an acid as any substance
which is capable of supplying to its solution, or to another sub-
stance, hydrogen bearing a positive electric charge. An instance
is hydrogen chloride, HC1, which splits to form_H+ and Cl~.

Likewise we may define a base as any substance which is
capable of supplying to its solution or to another substance the
electronegative group OH~. An instance is sodium hydroxide,
NaOH, which splits to form Na+ and OH~.

Like the Greeks who personified the virtues, we, having em-
bodied the acidic and the basic properties, have lifted to our
Olympus the hydrogen and the hydroxyl ions, H+ and OH~.
Furthermore the current conception of the nature of acids and
bases bears the imprint of the age of electricity.

Having touched upon the electrical aspect we might be tempted
to carry the theme forward into the whirl of current concepts
regarding the electrical nature of matter. Some of these con-
cepts will be used in later chapters; but, for the most part, they
will not be essential to our present theme. Without necessarily
losing sight of adjacent subjects, we may, (as we are entitled
to do) establish a province for our own subject. We may draw
from the adjacent subject helpful pictures; but as our theme pro-
gresses it will be perceived that our task is to formulate a set of
phenomena, that the organization of the material within the chosen
province is our subject and that any reconstruction of the physical
meaning of the terms will affect but little the essential organiza-
tion with which we are concerned.

THE DETERMINATION OF HYDROGEN IONS

All too briefly we shall touch first upon the adjacent subject.

According to current conceptions, the atom of hydrogen, the simplest
of the chemical elements, concentrates the greater part of its mass in a
nucleus having unit, positive, electrical charge. (See figure 1, a.) Fre-
quently this nucleus is called the proton. About this rotates an electron,
the unit, negative, electric charge. This apposition of the unit charges of
opposite sign renders the atom as a whole electrically neutral.

( \

v_y H

C e

d ®

e 0(61)3 e

/JT\ © «/j«iiQ © /Ci
'C' © »vo*j« e (jy

® CH4

. °l@l* •

e e

e e° CI

ee HCI

S9 se cr

FIG. 1. SCHEMATA OP ELEMENTS, MOLECULES AND IONS
Nuclei with + charges; electrons with — charges, a, hydrogen atom;
6, hydrogen molecule; c, carbon atom; d, methane molecule; e, chlorine
atom; /, hydrogen chloride molecule; g, hydrogen ion; h, chloride ion.

Atoms of other elements are built of nuclei having several excess positive
electrical charges and of extra-nuclear, planet-like electrons, the total
number of which in the electrically neutral atom must be equal to the net,
nuclear, positive charge. (See figure 1, c and e.) This number is the
.so-called atomic number of the element. For example the atomic number
of carbon is 6 and of chlorine 17.

It is profitable to assume that the essential, structural aspect
of compound formation is a sharing of the outer electron orbits

I ELECTRONIC STRUCTURE 5

of the component atoms such that not only is the compound as a
whole electrically neutral but that an element such as carbon or
chlorine completes a stable octet of electrons in its outer shell.
Thus the structure of methane is suggested by the formalistic,
static diagram in one plane shown in figure 1, d. Since the outer
electron orbits are considered all-important in the formation of
such compounds, all parts of carbon except the outer electrons

can be represented by C, atomic carbon itself by -O and methane,

H
for example, by H:C:H. Likewise hydrochloric acid is repre-

sented by :C1:H, and the chlorine molecule by :C1:C1:. The

hydrogen molecule, being stable with a pair of electrons shared by
the two protons, is represented by H:H. The hydrogen ion
appears as a proton stripped of electrons.

Physical theory demands rotation of the planet-like electrons, while
chemical theory demands some sort of resultant effect which will account
both for the positions of elements relative to one another when in chemical
combination and for that curiously vague yet definite something called
valence. Pending the results of attempts to meet both demands, it has
become the custom to picture the spatial and valence aspect by repre-
sentations such as those of figure 1 or their abbreviations given above; but
it should be remembered that the apparently implied static positions of
the electrons merely represent effects which come within the range of ele-
mentary chemical demands.

The picture given above and in figure 1 will be found elaborated upon in
Valence by G. N. Lewis, 1923. It is critically discussed by Andrade (1927)
in whose popular book The Structure of the Atom will be found references
to the more important papers on the subject. The chief success of the
theory in the field with which we are concerned has been an attractive,
orderly redescription of well known fact with a few predictions of minor
importance. The student should be very careful to use the picture as a
convenience, subject to radical change if required when the gap between
the demands of chemistry and physics is bridged.

In some of the compounds of hydrogen the sharing of electrons
may be so complete as to make difficult the detachment of the
hydrogen nucleus ; in other compounds the electron of the hydro-
gen atom may occasionally be captured and the proton be left
free to escape; in some cases the capture may be complete and

6 THE DETERMINATION OF HYDROGEN IONS

decisive. In the last case it would appear that only the electro-
static attraction of the oppositely charged parts might keep the
compound intact and that an environment tending for any
reason to favor dispersion would favor complete dissociation.
Thus the dissociation of HC1 (fig. 1, f) would furnish H+ (fig. 1, g)
and Cl~ (fig. 1, h) in high degree.

Whether all or only a very few of the hydrogen nuclei (protons)
in a mass of a given compound escape, those which do escape act
as discrete entities contributing their part to the osmotic pressure of
a solution and to all the other so-called colligati ve (bound together)
properties of a solution such as the lowering of the freezing point,
rise in the boiling point, etc. These effects are discussed in all
texts of physical chemistry and need not be reviewed here. In
aqueous solution the escaped hydrogen nucleus may combine
with water molecules; but the charge is preserved. Therefore,
under the stress of an electric field, the particle will travel toward
the cathode.2 Hence it is called an ion (traveler), more specifi-
cally a cation, and quite specifically it is called the hydrogen ion
or hydrion.3

In cases rarely encountered, for instance in the compound LiH,
the hydrogen nucleus not only tends to hold its own electron but
may take the lithium valence electron from the environment of
the lithium nucleus. On dissociation of this compound there is
formed the negative hydrogen ion.4 In gaseous form molecules of
hydrogen (H2) may become charged and thus become gaseous ions.
Neither of these two types is to be considered. It will be under-
stood that the term hydrogen ion or hydrion as used in this text
refers to the species H+. When using this symbol we ignore the
water of hydration. (See page 540.)

It is suspected that the development of this subject may show

2 Frequently there will be occasion to introduce a technical term the
meaning of which is understood by the majority of readers. To interrupt
the exposition by introducing definitions of all the technical terms which
will be used would not be practical. It might prove distracting to the
novice and irritating to the more advanced student. As an imperfect
compromise there are assembled in appendix N definitions of the more im-
portant technical terms used in this book and not defined in the text.

3 The two terms will be used without discrimination in order to make the
reader familiar with each as they occur in current literature.

4 See Klemenc (1921) on negative hydrion.

I IONIZATION 7

that such a readily dissociable compound as hydrogen chloride
has a structure radically distinct in type from that of so stable a
compound as methane. The latter must suffer drastic treat-
ment before it yields evidence of dissociation. Nevertheless the
tendency of compounds to throw off or surrender hydrions, as
measured in terms presently to be described, grades without any
serious discontinuity5 from that high degree displayed by hydro-
gen chloride, through the comparatively weak yet very distinct
tendencies displayed by many carboxylated compounds (e.g.,
acetic acid), on to the barely measurable tendencies in certain
alcohols. Even beyond the measurable lie cases for which the
presumption of ionizable hydrogen is often useful.

In dealing with these matters we shall find ourselves fully
occupied with the laws governing dissociation in mass and we
shall not be concerned with the architecture and the electronic
structure of the individual molecule. We must circumscribe our
subject matter and we may begin its exposition either with the
acceptance of the evidences for ionization or by introducing the
fundamental concepts as pure postulates. Indeed it is significant
that many modern authors go to no trouble to justify these con-
cepts before introducing them in a manner which would lead the
logician to the conclusion that they are pure postulates. The
reason is simple. The best evidences of the realities to be con-
sidered are found in those quantitative relations which can hardly
be appreciated before the method of formulation is developed.

Let it be said here most emphatically that our first formulation
will be as a map drawn for a locality. If extended far it will
need to be drawn with additional devices comparable with
Mercator's projection for the use of navigators. Like the map
of a locality, our map is good for restricted conditions. Like the
projection of Mercator, the corrected map is good for distant
voyages even if it distort reality. It is of more importance to
indicate how certain experimental devices yield results which
appear to be in substantial agreement locally and in conflict
extralocally. This is because these devices operate in ways as
distinctly different as the sextant and the compass. Surveys

5 There have been several expressions of the opinion that a statistical
study would show a more or less distinct "break" between the frequencies
of occurrence of "strong" and "weak" acids.

8 THE DETERMINATION OF HYDROGEN IONS

by sextant or compass can be made from the same base line ; and
either map, without correction to the terms of the other, is valid
locally. Difficulties arise if the distinctly different natures of
the two methods are not recognized when the traveler is on dis-
tant voyages, or in the presence of local perturbations.

THE CONCEPT OF EQUILIBRIUM

Reversibility

Imagine an acid of the type HA dissociating into the cation
H+ and the anion A~.

HA ^ H+ + A- (1)

Arrows in place of an equation sign were introduced by van't
Hoff to indicate not only the ^equivalence expressed by the usual
equation sign but reversibility. In other words there occur among
the large number of anions and cations, present in any ordinary
aqueous solution of the acid, recombinations of the ions the while
some of the HA molecules are dissociating.

This conception of a "reaction" as labile, continuous and re-
versible is of profound importance. So long as analysts are con-
tent to balance the two sides of such a written form for the purpose
of expressing stoichiometrical relations of ordinary analytical
importance the equation sign suffices and the implications sym-
bolized by the arrows may be neglected. But as a matter of fact
it is of particular importance to analysis to regard reactions as
not necessarily going to completion in one direction. The con-
cept of reversibility6 is particularly applicable to the ionization of
acids and bases and to many reactions in which acids and bases
take part. So, in terms of reversible reactions, the geologist
describes the laying of the limestone stratum and the return of
the "everlasting hills" to the "eternal drift."

Our modern views of chemical reversibility supplement the
ancient views of mechanical reversibility which Mallock7 has
paraphrased.

6 This is not to be confused with reversibility in a strict thermodynamic
sense.

7 Mallock, hu$retius on Life and Death.

I EQUILIBRIUM

No single thing abides, but all things flow,
Fragment to fragment clings; the things thus grow

Until we know and name them. By degrees
They melt, and are no more the things we know.

Nothing abides. Thy seas in delicate haze
Go off; those mooned sands forsake their place;
And where they are shall other seas in turn
Mow with their scythes of whiteness other bays.

As if playing a joke on Fate, Life seems to have seized upon
delicate balances in just such processes as determine the destiny
of mountains and, unlike the Inanimate, has made these balances
the internal environment of its potentially immortal cells.

In the ceaseless interplay of the components of a given, re-
versible reaction, the following situation may occur. The reac-
tion may proceed no faster in one direction than in the other. An
indication of this state is the absence of change in the quantities
of the components of the system. Statistically the system is at
rest. This is the state of equilibrium.

THE EQUILIBRIUM EQUATION FOR ACID DISSOCIATION

At the start let there be no attempt to describe all the factors
which increasingly refined technique forces into view. Let there
be imagined an ideally simple system in which each component
represented in equation (1), while free, behaves as if it were un-
affected by the presence of the other solutes. Let a variation of
the concentration of any component not affect the imagined
constancy of the environment.

Let brackets about a symbol indicate concentration of the
species which the symbol represents and let concentration be ex-
pressed in moles per liter of solution. Trra»-[HA] represents x
moles of residual undissociated apid, HA, per liter.

We need not enquire concerning the forces or the circumstances
which occasion the ionization of the individual, acid molecule.
We need only assume that occasionally the molecule acquires the
ability to ionize and does ionize. Then, since enormous numbers
of molecules are present in solutions even of high dilution, we
may trt u the subject in a crude, statistical way and imagine that
each m 1<> has, on the statistical average, the same span of

10 THE DETERMINATION OF HYDROGEN IONS

life. Then the velocity, Vi, with which the concentration of HA
is decreasing at any instant, is proportional to the concentration
[HA] at that instant.

Vl = ki[HA] (2)

In (2) ki is a proportionality factor. Its value, as we shall see
presently, need not be determinable.

The velocity of the reverse reaction, wherein ions combine to
reconstruct HA, is likewise dependent on the concentrations
[H+] and [A~] and in the following manner.

Suppose, to begin with, that there were equal numbers of
>ydrions and anions. Then imagine that the number of hydrions
in a given volume were tripled. The number of collisions be-
tween hydrions and anions would be tripled. If the original
number of hydrions remained and the number of anions were
tripled the number of collisions would be tripled. But if the
hydrions were tripled and the anions were tripled simultaneously,
the number of collisions would be nine times the original. Thus
the number of collisions is proportional to the product of the con-
centrations. Combination may not necessarily be determined by
collision alone. A favorable orientation during collision may be
necessary. A heightened energy may be necessary. But, if we
idealize the situation, we may suppose that successful combination
is that constant fraction of collisions which is determined by a
particular environment and by the specific natures of the ions
concerned. Then in equation (3) the proportionality factor k2
expresses not only proportionality of combination to collisions but
proportionality to other factors which are idealized as constant.

We have then for the velocity of combination

V2 = k2 [A-] [H+] (3)

Having already defined the state of equilibrium as that at
which the velocity of phange in one direction equals the velocity
in the opposite direction, we let Vi and v2 be those velocities which
occur at the attainment of equilibrium and accordingly we equate
the two. Whence from (2) and (3) there is obtained (4).

^ = T = K» ^

[HA] k2

DISSOCIATION CONSTANT

e ratio of two constants in (4) there is substituted the
one constant Ka, which is properly called the equilibrium con-
stant. It will be noted that the ion concentrations are placed
in the numerator of (4). Had they been placed in the denomi-
nator the equilibrium constant would be the reciprocal of Ka.
When the convention used in (4) is followed, the constant (i.e.,

Ka) is called the dissociation constant. Its reciprocal, ^-, is

J\a

called the association constant.

The dissociation constant is sometimes described as a measure
of the "strength" of an acid. Thus the following comparison
may be made.

CLASS

COMPOUND

I\2 (APPROXIMATE)

Strong acid

HC1

About 10+7

Moderately strong acid

Dichlor acetic acid

About 5. X 10~2

Weak acid

Acetic acid

1 8 X 10~B

Very weak acid

Phenol

1.0 X 10-10

Extremely weak acid

Glucose

4 X 10 ~13

Vanishingly weak acid

Methane

Approaches 0

For tables of dissociation constants see appendix tables G, H,
I, and J.

To indicate that a dissociation constant, as used in these ap-
proximate equations, applies to a limited set of conditions, it is
frequently written K'. K is then reserved for the "true" disso-
ciation constant, which can be estimated by the method of
Chapter XXV.

It is readily perceived that, when actual numerical values are
given to the concentrations of the several "species" occurring in
the equilibrium equation, care must be taken to use a consistent
unit of concentration. If grams per liter in one case, moles per
liter of solution in another, moles per 1000 grams of solvent in
another and millimoles per liter of solution in another case were
used, the equilibrium constants, while well defined in each case
separately, would not be comparable.

Of course, if there be reason to believe that an acid like HC1, or a salt
like NaCl, is ionize ' )st completely in dilute solutions, there is little
point in attempts to apply to experiment the treatment which follows the

12 THE DETERMINATION OF HYDROGEN IONS

derivation given. As noted later, the application of the type equilibrium
equation to a case like

[Na+] [C1-] [H+] [C1-]

INaClJ [HC1] Ka

has no practical value. In the first place, if the quantity in the denomi-
nator of the type equation should approach an infinitesimal, the most ex-
treme accuracy would be required to satisfy the equation experimentally.
Furthermore the simple equation is founded upon an idealization, and
in the case specified the utmost accuracy would be required to detect and
to measure the several factors which might interfere with the applicability
of the ideal equation. But, in the second place, the introduction of a
concentration of a molecule like NaCl or HC1 would be to confess one's
ignorance of the fact that the evidence is against the existence of the
molecule NaCl and (for aqueous solutions) against the existence of the
molecule HC1. (See page 58.) A dilute solution of hydrochloric acid
may be regarded as one extreme. A solution of methane is a case at the
other extreme. In the first case Ka approaches infinity; in the second
Ka approaches zero. In either circumstance the type equation has little
practical value.

APPLICATION TO A SIMPLE ACID SOLUTION

Since the concentrations of the various "species" are treated
like the x, y, z of any ordinary algebraic equation, it may be
interesting to note at this point a special application of equation
(4) which will involve some simple algebra.

Consider a solution containing the acid as the only solute and
neglect the ions which may come from water. The simple acid
HA partially dissociates into equal parts of H+ and A~. Hence

[H+] = [A-]

Let the concentration of total acid [S] be defined by
[S] = [HA] + [A-],

i.e., the sum of the concentrations of undissociated and dissociated
acid. Equation (4) may now be written as follows

fTTJIO

= K. (5)

[S] - [H+]

Equation (5) may be solved for [H+] by the usual process of
"completing a square." There is thus obtained

(6)

I EQUILIBRIA IN MIXTURES 13

When Ka is small in relation to [S]

[H+] ^ -\/Ka [S] (7)

Example: Given Ka = 1 X 10~5; calculate [H+] when [S] = 0.1
molar.

(H} (10-0
Approximately:

[H+] = V 10-6 = 10-3 = 0.001 normal

Application of (6) to the case of the acid having the value 10~5
for Ka will show that the approximation of (7) introduces a sig-
nificant error when [S] is less than 0.001 normal. For dilute
solutions and for solutions of very weak acids, account must be
taken of the hydrions coming from the water as will appear
presently.

GENERAL EXTENSION OF THE EQUILIBRIUM EQUATION TO MIXTURES

When an anion originates by the dissociation of the acid HA
or by the dissociation of some admixed salt, such as NaA, it may
combine with any hydrion irrespective of the source of this
hydrion. Therefore equation (4) holds even in mixtures, — with
the qualification that the actual value of Ka may vary some-
what even in solutions of the same solvent and of the same tem-
perature, if the components of the system vary sufficiently in
concentration to alter appreciably the environment. This, in
our idealization, we demanded should be constant.

To embrace the situation to be considered when salts of the
acid are present, let [S], the concentration of total material con-
taining the acid's main group in the form of ions or ionogens, be
defined by

[S] = [A-] + [HA] + [«] (8)

Here [s] represents the sum of the concentrations of all those
salts of the acid which are in an undissociated state.

14 THE DETERMINATION OF HYDROGEN IONS

Equations (4) and (8) yield (9)8

[S] Ka + [H+] IB]

It can be said at once that if (9) be applied to experimental data
it will appear as if [s] should be considered a variable of significant
magnitude. On the other hand there are frequently good reasons
for believing a salt to be practically completely ionized and in
these cases it is permissible to let [s] = 0. Indeed, effects which
might be attributable to the formation of undissociated salt
molecules are now attributed to the attraction between its charged
ions and are dealt with by the special methods of Chapter XXV.

It should not be assumed that there are no cases in which there
is undissociated salt. However, we shall continue as if for cases
in which it can be assumed that the concentration of undisso-
ciated salt is so small as to be negligible. Then [s] in equation
(9) is considered zero and (9) reduces to (10)

[S] K. + [H+]

[A~1

In either case the ratio -7^7- is called the fraction of dissociation

LbJ

or degree of dissociation. This refers not to the acid alone but
to all the ionogens capable of supplying to the solution the specific
ion A~~. This ratio is so frequently used that it is a convenience
to give it the symbol a. Percentage dissociation = lOOa.
Then (10) is written:

-irniFi (10a)

Equation (lOa) emphasizes, in a very direct way, the fact that
changes in the hydrion concentration of a solution indicate altera-
tion of a, the degree of dissociation, — that is, the degree to which
the specific acid under consideration is present in the dissociated
state. This is the key equation unlocking the door to most of
the reasons for interest in methods of determining hydrion con-
centrations. For, since [H+] indicates or in a specific case, [H+]

8 Since the term (1 — ~) in (9) is to be eliminated the student is advised

[SJ
to develop the simpler equation (10) by neglecting [s] in equation (8).

I LOGARITHMIC EQUATION 15

indicates the degree to which properties associated with the anion
or properties associated with the undissociated residue will be
manifest in mass.

This simple equation sums up the main feature of most that
follows. However, it is more convenient in logarithmic form.

LOGARITHMIC FORMS OF THE FUNDAMENTAL EQUATIONS

Because the values of [H+] may vary so greatly that charting
on a linear scale is impracticable and because of other better
reasons, it is both convenient and logical to use a logarithmic

function of [H+]. That chosen is logio yg^j. To this is given

the symbol pH (see page 36).

For the sake of simplicity continue with the assumption that
M in equation (9) is so small that it may be considered zero.
Equation (lOa) is then applicable and may be transformed to (11)

[H+]-K.^^ (11)

Taking the logarithm of the reciprocal of each side of (11) we
have (12) which is merely another form of the key equation
(lOa) and is the most generally useful of all the equations with
which we shall deal. The greater part of the subject can be
developed with the aid of this equation.

Analogous to the expression pH = log j^j-p: is the expression
pKa = log — • Since the current literature cannot be under-

stood without an appreciation of the meaning of pKa9 we shall
not hesitate to adopt this symbol. Then (12) may be written:

pH = PKa + log ~- (12a)10

1 — a

9 Bjerrum (1923) calls pKa the dissociation exponent.

10 This is the most important equation of the book. The student is
advised to calculate pH with any given value of pKa and values of a
ranging from 0.1 to 0.9 at intervals of 0.1, and to chart the results as in
figure 2.

THE DETERMINATION OF HYDROGEN IONS

It will be remembered that a is the degree of dissociation. If
we can assume that a mixture of equivalents of acid and base
forms a salt which dissociates completely, a should be 1 for such
a mixture. If the acid is so very weak that its dissociation is
negligible compared with that of the salt, we can assume (as an
approximation) that a is approximately the same as the corre-
sponding degree of "neutralization"11 i.e., salt formation. In

2
3
4
5
6
7
8
9

12
pH
13

13
12
11
10
9
6
7
6
5

^^^

3
'pOH

0.2 0.4 0.6 0.6 1.0 0.2 0.4 . 0.6 QA 1.0
a. Acid dissociation o.o a. Base dissociation

FIG. 2. (A) RELATION BETWEEN pH AND THE DEGREE, a, OF THE

DISSOCIATION OF ACIDS; (B) RELATION BETWEEN pH AND THE

DEGREE, a, OF THE DISSOCIATION OF BASES

other words the curve relating a to pH may, under the specified
conditions, be closely comparable with the curve relating degree
of neutralization to pH. Equation (12a) may then be written
in approximate form as:

*H--*+i*S (i2b)

This equation will be derived again later.

11 "Neutralization" is here used in the loose sense that each equivalent
of base destroys the acidic nature of one equivalent of acid.

I BASES 17

The geometry corresponding to equation (12) or (12a) is
shown by figure 2 A. All the curves are identical in form. The
position of any one is det ermine (Tby the value o£j)Ka, for, since
[H+] = Ka when a = 0.5, the midpoint of the curve is deter-
mined by pKa.

BASES

Before dwelling more at length upon equation (12) and upon
the corresponding geometry, there will be considered the funda-
mental equation for the equilibrium state in the dissociation of a
base.

It has been customary to regard oxides such as K20, which on
solution in water give tests for alkalinity, as if they became
hydrated to compounds of the type BOH (e.g., K2O + H20-»
2KOH). The alkalinity of the solution is then assumed to be
due to the ionization of BOH to furnish some definite concentra-
tion of the hydroxyl ion, OH~.

For the reversible reaction :

BOH ^± B+ + OH-

there may be written the equilibrium equation:
[B+] [OH-

[BOH]

= Kb (13)

Equation (13) is to be regarded as the type equation. It is not
applied in practice to a base such as KOH which is practically
completely dissociated in dilute solution. Such a case is best
treated in another manner. (Compare page 12.)

Applying to (13) the same sort of mathematical treatment
accorded (4) we reach in turn (14), (15), and (15a).

pOH = pKb + log ~— (15a)

1 — a.

18 THE DETERMINATION OF HYDROGEN IONS

In the latter cases pOH symbolizes log rrvc, , and pKb =

[(Jti. \

log ib

The geometry of (15a) is illustrated by the curves of figure 2 B.
Again this equation gives a family of curves. Any one curve is
fixed in its position by the value of pKb.

For a reason presently to become clear, values of pOH in
figure 2 B are plotted in a direction opposite to the direction of
increasing values of pH.

THE WATER EQUILIBRIUM

Up to this point no relation has been shown between the acid
systems and the base systems nor between pH and pOH. If we
confine our attention to aqueous solutions we may now introduce
the fact that water yields both hydrions and hydroxyl ions in
accordance with

HOH ^± H+ + OH-

For the equilibrium state of this reaction write :

[H+] [OH-]
[HOH]

Anticipating a conclusion to be mentioned in Chapter II, we
may state that water is so little dissociated that no serious error
will be made in regarding the concentration of the undissociated
residue, [HOH], to be equal to that of the total water. Further-
more this may be considered constant for limited ranges of dilute
solutions. Hence:

[H+] [OH-] = Kw (16)

Properly Kw is an ionic product, but it is commonly called
the dissociation constant of water. Like all the other so-called
equilibrium constants, it is only a constant by grace of the main-
tenance of a constant environment. Its value is subject to
change with change of temperature, salt concentration, etc. For
descriptive purposes Kw may be considered to have the rounded
value 10~14.

I WATER EQUILIBRIUM 19

From (16) there is readily derived the following;

pH + pOH = pKw (17)

and, since the value of Kw may be rounded off to 10~14,

pH + pOH = 14 (17a)

It is this relation which was used in aligning the pH and pOH
values of figure 2.

MORE DETAILED EQUATIONS

It is unnecessary for purposes of general treatment to develop
separate equations for acid systems and for base systems. This
will be shown in Chapter II. Therefore, we shall confine atten-
tion to the equations for acid systems in a discussion of more
detailed equations.

In considering the following treatment the student is advised
to pay little attention to the mathematical derivations of equa-
tion (19) or (20). They are stated in their elaborate form for
convenience of discussion. In this discussion there will be shown,
by one numerical example, conditions under which certain of
the quantities as they occur in the equation can be neglected.
This will aid in the justification of the useful approximation to
follow in the next section.

In the derivation of equation (12) there were introduced — in
addition to the idealistic assumptions at the very origin — two
approximations. One, the neglect of the undissociated salt [s],
we have already mentioned. The other was the neglect of the
hydrions and hydroxyl ions coming from the solvent, water.

In addition to the familiar equation

[HA]

and the summation (8) which is

[S] = [A-]>[[HA] + [«]

20 THE DETERMINATION OF HYDROGEN IONS

it now becomes itecessary to employ equation (18) which will
automatically take account of the hydroxyl and hydrions arising
from the water.

[H+] + [B+] = [A-] + [OH-] (18)

This new equation expresses the electro-neutrality of the solution
as a whole, it being required that the total number of positive
charges of whatever source (ions from water included) must equal
the total number of negative charges. [B+] is the concentration
of the cation of the salt, for example [K+] in a solution of potas-
sium acetate. [OH~] can be eliminated from expressed inclusion
in the equations by using the equation for the water equilibrium,

[H+] [OH-] = Kw or [OH-]

[H+]

These equations can be combined to yield (19) which, in loga-
rithmic form, is (20)

Ka = - ~~ (19)

[S] - [B+] - [H+] + ^ - W

[S] - [B+] - [H+] + -=- _ [8]

pKa = pH + log - (20)

DH + [H+] -

Let equation (20) now be applied in a specific case in order that
the relative importance of each term may be shown numerically.
We shall use the data of Walpole (1914) for mixtures of acetic
acid and sodium acetate. The compositions of the solutions and
the measured values of pH which Walpole gives are found in
table 1. Lest false interpretations of the treatment be made, it
should be emphatically stated that the values called pH are

not strictly those of log - . Partly for this reason and partly

[H+]

for the reason described in Chapter XI the constants as calcu-
lated should not be expected to be exactly the same for all ratios

ACETATE SYSTEM

of acetate to acetic acid. In Chapter XXV corrections will be
discussed. With this caution we may proceed as if the cited
values truly represent hydrion concentrations.

Again we- shall proceed with the assumption that the con-
centration of undissociated salt, [s], in this instance [sodium
acetate], is negligible. This at once simplifies the treatment, be-
cause it not only eliminates this specific term but it also makes it

TABLE i

Calculation of pKafrom Walpole's data for mixtures of acetic acid
and sodium acetate

(1)

NaAc

MOLAR

(2)
HAc

MOLAR

(3)
pH

(4)
[H+]

(5)
[B+] + [H+]
X

(6)

'^T'-

(7)
X

LOGY

(8)
PKa

(9)
pKa

BY AP-
PROXI-
MATION

0.000

0.200

2.696

0.00201

0.198

-1.994

4.690

0.005

0.195

3.147

0.00071

0.00571

0.1943

-1.532

4.679

4.739

0.01

0.19

3.416

0.00038

0.01038

0.1896

-1.262

4.678

4.695

0.02

0.18

3.723

0.00019

,0.02019

0.1798

-0.950

4.673

4.677

0.04

0.16

4.047

0.00009

0.04009

0.1599

-0.601

4.648

4.649

0.06

0.14

4.270

0.00005

0.06005

0.1399

-0.367

4.637

4.638

0.08

0.12

4.454

0.00004

0.08004

0.12

-0.176

4.630

0.10

4.626

0.00002

0.10002

0.10

0.000

4.626

0.12

0.08

4.802

0.000016

0.12

0.08

0.176

4.626

0.14

0.06

4.990

etc.

0.14

0.06

0.368

4.622

0.16

0.04

5.227

0.16

0.04

0.602-

4.625

0.18

0.02

5.574

0.18

0.02

0.954

4.620

0.1925

0.0075

6.024

0.1925

0.0075

1.409

4.615

0.1975

0.0025

6.518

0.1975

0.0025

1.898

4.620

possible to consider [B+] equal to the concentration of total
sodium acetate.12 Therefore the values of [B+] -f- [H+], found in
column 5 of table 1, are readily calculated from the experimentally
determined values of [H+], column 4, and the values for total
sodium acetate, column 1.

The reader may readily calculate, by using the value 10~14

T£"

for Kw, that the values of TTpr are so small as to be negligible in

12 No undissociated base, NaOH, is supposed to remain.

22 THE DETERMINATION OF HYDROGEN IONS

the sum in equation (20). Equation (20) now reduces prac-
tically to (21)

~ ,, [S] - [B+] - [H+] ( .

With this there are made the remaining calculations, which are
summarized in table 1 and which lead to the values of pKa
found in column 8.

There are cases in which values for rTT ,, are significant while

[H+J

those for [H+] are insignificant (alkaline solutions). In rare cases
both terms have to be considered. The latter occur when the
measurements are near "neutrality."

It will be noted in table 1 that values for [H+] in the lower part
of the table affect the magnitude of the sum [B+] + [H+] so little
that the effect is there negligible. We can readily imagine two
cases in which this neglect would be serious. One case would
be that of a stronger acid maintaining, during the course of its
treatment with a base, values of [H+] large in relation to [B+].
Another case would be a solution so extremely dilute that [B+]
would approach the magnitude of [H+].

A USEFUL APPROXIMATION

If we confine attention to the cases like that illustrated in
table 1 we may, for purposes of approximation, neglect [H+] as
it occurs in the sum [B+] + [H+]. Then equation (21) is further
simplified to equation (22).

pKa = pH + log [S] "^ (22)

which may be rewritten

pH = pKa + log _ (22a)

This is virtually ,

pH = PV+log — ^L (23)

[residual acidj

This is frequently called the Henderson-Hasselbalch equation.
Compare (23) with (J2b) on page 16 and see column 9, table 1.

I a-CURVES AND TITRATION CURVES 23

We might return to the complete equation (20) and discuss in
the general language of algebra the effects to be expected if
probable values for the concentration of possibly undissociated
salt [s] were introduced. The danger of this is two-fold. We
would be discussing quantities which are experimentally evaluated
with such difficulty and uncertainty that we would find the
mere algebraic discussion rather academic. In the second place
we might be led to emphasize a method of treating salts which is
less profitable than that which will be discussed in later chapters.

DISTINCTION BETWEEN ^-CURVES AND TITRATION CURVES

Equation (12a) is

PH = pKa + log

1 - a

The "approximate equation" developed in a preceding sec-
tion is

It has been shown in the case of acetic acid that, for a given
set of conditions, there is a fair degree of agreement in the applica-
tion of these two equations. However, if a be considered zero
before any alkali has been added to an acetic acid solution in
the course of its titration, it is obvious that the dissociation of
the acetic acid is being neglected. No correspondence between
the atrcurve and the actual titration curve should be expected
near the beginning of the titration.

This lack of correspondence becomes more and more emphasized
as the "strength" of the acid being titrated increases. The case
of hydrochloric acid is the extreme. In this case it is advisable
to regard the acid as practically completely dissociated in dilute
solution, and to be gradually eliminated as acid during the
course of the titration.

This matter could be gone over again in detail with the aid of
the equations discussed in previous sections. However, the
student will probably find it more profitable at this point to
compare the a-curves of figure 2 and figure 11 (page 47) with the
titration curves of figure 92 (page 531).

THE DETERMINATION OF HYDROGEN IONS

AN EXAMPLE OF DILUTION

There may now be considered another aspect of the acetic acid-
sodium acetate mixtures. In table 2 are tabulated Walpole's
data for various dilutions of a solution equimolecular with respect
to both the sodium acetate and the acetic acid used in construct-
ing the mixtures.

By the approximation formula (23) an observed value of pH

should equal pKa, since the ratio

[salt]
— rr:

is fixed and is equal to 1.

In the calculations of pKa shown in the table there has been
used the more nearly complete formula (21). Its use in place of

TABLE 2

The apparent change of pKa with dilution of a solution equimolecular1 with

respect to both acetic acid and sodium acetate

(Data from Walpole (1914))

TOTAL,
ACETATE

NaAc

HAc

[H+]

xio*

[B+] + [H+]
X10*

[S] - [B+] -
[H+]
X 105

LOG Y

pKa

0.4

0.2

4.606

2.48

20,000+

20,000-

0.000+

4.606

0.2

0.1

4.623

2.38

10,000+

10,000-

0.000+

4.623

0.08

0.04

4.646

2.26

4002.0

3998.0

0.000+

4.646

0.04

0.02

4.663

2.17

2002.0

1998.0

0.001

4.662

0.032

0.016

4.673

2.12

1602.0

1598.0

0.001

4.672

0.02

0.010

4.684

2.07

1002.1

997.9

0.001

4.683

0.01

0.005

4.706

1.97

502.0

498.0

0.003

4.703

0.004

0.002

4.737

1.83

201.8

198.2

0.008

4.729

0.002

0.001

4.758

1.75

101.75

98.25

0.015

4.743

the first approximation (equation (23)) is not significant in this
instance, except for the higher dilutions. Even then its use pro-
duces little improvement in the constancy of the "constant" pKa.
In general it is well, when dealing with highly dilute solutions, and
especially with acids of low pKa values, to consider the more
complete formula. However, there remains a strong suggestion
that account should be taken of the undissociated salt. We shall
see in Chapter XXV that this question is now being dealt with
by unique methods and that, starting with the postulate of
practically complete dissociation of salts, the effect we now have

DILUTION

in mind is accounted for by interionic forces. This is sometimes
described as a force which produces an ionic clustering. These
only remotely resemble true salt molecules. Therefore, we had
best not try to get the complete answer to our problem from the
elaboration of an equation which was established in the first in-
stance on simplifying assumptions and in ignorance of the de-
tailed nature of specific solutions.

8 10

FIG. 3. TEN CUBIC CENTIMETERS 0.2 N ACETIC ACID TITRATED WITH

0.2 N NaOH

Experimental data shown by centers of circles (hydrogen electrode).
Type curve is shown centered at pH = 4.73 the ideal position as corrected
for solutions of zero ionic strength. See page 507.

Equation (23) may be considered a first approximation useful
for the treatment of weak acids. Equation (21) may be con-
sidered a first approximation useful when [H+] becomes of appre-
ciable magnitude relative to [S] and [B+].

Figure 3 shows the experimental data for 0.2 N acetate mix-
tures and also, in a displaced position, the type curve drawn with
the aid of equation (21). The placement of this type curve was
made with a value of pKa taken from conductivity data for

26 THE DETERMINATION OF HYDROGEN IONS

the dissociation constant of acetic acid. As indicated in table 2,
the value of pKa, varies with the dilution. We shall also see that
it varies with the salt content and with the standard of reference
chosen. However, the general form of the curve and its ap-
proximate position are now our chief interests.

ACIDS WITH MORE THAN ONE REPLACEABLE HYDROGEN

Since it is not within the province of this book to outline all
types of acid-base equilibria which are met in the application of
methods for determining hydrion concentrations, the main princi-
ples have been illustrated by considerations of simple acids and
.bases. The outline is easily extended to acids with more than
one replaceable hydrogen and also to those compounds which
contain both acidic and basic groups and which are called "ampho-
teric ionogens" or more usually "amphoteric electrolytes'7 or
"ampholytes." The extension will be illustrated graphically ; but,
to indicate the manner in which equations corresponding to the
geometry are handled, one simple example will be given.

Assume an acid of type HAH dissociating stepwise to HA~
and A.

HAH ^ HA + H+
HA ^ A + H+

The equilibrium equations are :

First step = Kl (24)

Second step ^ = K2 (25)

LrlAJ

If secondary considerations discussed during the treatment of the
simple systems are neglected, there is need to employ only one
additional fundamental equation, namely that giving the sum
[S] of the concentrations of all species.

[S] = [HAH] + [HA] + [A] (26)

I MULTIVALENT ACIDS 27

By defining the degree of the first step of ionization by

^itF = ai (27)

and the degree of the second step by

[A--;

[8] * (28)

there are derived from the above the following :

K! [H+]

Oil

iK, + K! [H+] + [H+p

(29)

i2 . .

" K.K2 + Ki [H+] + [H+P

The degree of total ionization, at, is evidently

Cti + 0(2

Inspection of equations (29) and (30) shows that, since their
denominators are the same, the relative values of Ki[H+] and of
KiK2 determine whether, at a given value of [H+], oti or 1 + az shall
be the targer proportion of at.

The effects of varying the difference between KI and K2 can
be shown best indirectly by resorting again to logarithmic rela-
tions expressed graphically. However, actual calculations are
performed most easily with the equations given above. In figures
4 to 6 are charted the curves for three, multivalent acids. Differ-
ences between the pKa values are such as to show in figure 4 no
serious deviations from the picture which three independent acids
would give. In figures 5 and 6 are indicated "overlappings" to
different degrees.

AMPHOLYTES

For amphoteric electrolytes (i.e., electrolytes containing acidic
and basic groups) a relation of great importance may be illus-

THE DETERMINATION OF HYDROGEN IONS

KH2P

KJHP

C.C.

100

ISO

FIG. 4. TITKATION CURVE OF PHOSPHORIC ACID

Fifty cubic centimeters of M/10 H3PO4 titrated with N/10 KOH. Shows
step-wise "neutralization" of three hydrogens.

C.C.

FlG. 5. TlTRATION OF THE "DlBASIC" AdD, PffTHALIC AdD, WITH KOH

Shows step-wise neutralization but "overlapping" of titration curves

AMPHOLYTES

strated by the conduct of the simple ampholyte, p-amino benzole
acid. The acid dissociation constant Ka is 6.8 X 10~6 and the
basic dissociation constant Kb is 2.3 X 10~12 (Scudder). Trans-
lating these into the corresponding pK values we have 5.17 and

3
4
5
6

"Ns

.. x

-->s

'N;

_ 2.. «

Equivalents of NaoH

FlG. 6. TlTRATION OF THE "TRIBASIC" AdD, ClTRIC AdD

Shows that the pKa values are sufficiently close to obscure the curvatures
of the idealized curves for each step. (After Hastings and Van Slyke
(1922).)

2.36. 1S If we regard the compound as if it were made up of an
acid and a base with the above dissociation constants and each

NHS

p-amino benzoic acid

Cation
in acid solutions

COO

Anion
in alkaline solutions

independent of the other, we can plot the dissociation curves
of each with the aid of equations (12a) and (15a). In each case
the dissociation-residue curves are the complements. These are
plotted in figure 7 with heavy lines. It is seen that they cross
at pH 3.77. This means that at pH 3.77 there is a maximum
of undissociated residue. Now if the salts are more soluble
18 See page 48.

THE DETERMINATION OF HYDROGEN IONS

than the free compound itself, there should be a minimum
solubility at pH 3.77. Michaelis and Davidsohn (1910) found a
minimum solubility at pH 3.80.

FIG. 7. DISSOCIATION CURVES, A AND B, AND DISSOCIATION-RESIDUE

CURVES, A' AND B', FOR P-AMINO BENZOIC ACID

Treated as if this amphoteric ionogen were composed of an acid with
pKa value of 5.17 and a base of pKb value denned by pKb = pKw — 2.36.

Turning to the light lines A and B of figure 7, we see that their
intersection is at a point where the percentage of the compound
ionized as an anion is equal to the percentage ionized as a cation.
In other words the amount carrying a negative charge is equal to
the amount carrying a positive charge. Because of this equality
the point where it occurs is called the isoelectric point.

If we still maintain the simple conditions postulated in this
elementary treatment, we can calculate the isoelectric point from
the dissociation constants of an amphoteric electrolyte.

Consider an amphoteric electrolyte of the type HROH for
which we have the following equilibrium equations :

[HR+] [OH-]
[HROH]

IROH-] [H+]

[HROH]

(31)

(32)

I ISOELECTRIC POINT 31

When [HR+] = [ROH~] (isoelectric condition)
[HROH] [HROHI

KbloiT KaliTfT

Hence [H+] = / Kw (34)

In the case cited above [H+] = i/ 2 3 x KJ-H 10~"

or pH = log = 3.77

Furthermore from equations (31) and (32)

If we let [HR+] -f [ROH~] = X, X becomes a minimum when

/K
= 0, a condition fulfilled when [H+] = A/ -~ Kw

r -*-*•!>

In other words the sum of the anion and cation concentrations
is a minimum at the isoelectric point.

Only in case Ka = Kb will the isoelectric point correspond with
the ' 'neutral point," pH 7.0.

It is at once evident that the isoelectric point of an amphoteric
electrolyte is a point at or near which there should tend to occur
maximal or minimal properties of its solution. Indeed at such
points have been found to occur minimum solubilities, minimum
viscosities, minimum swelling, optimum agglutinations, etc.

Lest this exposition obscure matters of importance to the
treatment of complex ampholytes, the reader should consult such
papers as that of S0rensen and Linderstr0m-Lang (1927).

See Levene and Simms (1923) on calculation of isoelectric
points.

In figure 7 the treatment is as if for two distinct substances, one
an acid and the other a base. Actually the acidic group and the

THE DETERMINATION OF HYDROGEN IONS

basic group are in the same molecule. When the simultaneous
equations are solved for the identical dissociation residue and this
is charted, its curve will follow B' and A' for 'the most part but
will pass from B' to A' a little below the intersection of B' and A'.

Figure 8 gives another set of cases.

It will be noted that this elementary outline of the subject of
ampholytes has been presented with the aid of a specific case in
which the ion formed is probably the univalent anion or the
univalent cation according to the pH .value of the solution.
Many ampholytes probably ionize in such a way as to form
"hybrid"14 ions of the type +NH3-R-COO- These are called in
the German Zwitter-Ionen, signifying hermaphroditic ions. They

2 3 4 5 6 7 8 9 10 11 12 13 14

FIG. 8. REPRESENTATION OF THE DISSOCIATION CURVES OF HEXONE BASES
(After Foster and Schmidt (1923))

are often called ampholyte ions with the implication of the above
special significance of opposite gender or of hybrid nature.
Perlzweig (1926) uses the term "amphoteric ion."

As previously suggested, experimental methods do not always
show clearly whether an acid or a base is being handled; and by
the same token it is often uncertain whether an ionization constant
assigned to an ampholyte from the measurements has been
properly formulated as an acid constant or should be reformu-
lated as a basic constant. Thus the reformulation of the so-called
acid and basic constants of certain amino acids will depict these

*4Kolthoff and Furman (1926, p. 49), use the term "hybrid ion."

STRONG ACIDS

compounds as existing as hybrid ions at the isoelectric point
instead of as undissociated molecules. For a more detailed dis-
cussion of this matter see Bjerrum (1923).

It should be emphasized that the foregoing relationships have
been developed from very simple conditions. When these con-
ditions have been approached, experimental verification has been
found. The insight thus gained has led to a better understanding
of complex ampholytes, the complete equilibria of which can be
seen only in broad outline.

0 10 20 30 40 50 GO 70 80 90 100
^Neutralization

FlG. 9. TlTRATION _CURVES OP HYDROCHLORIC AdD AND POTASSIUM

HYDROXIDE

"STRONG" ACIDS AND BASES AND THEIR SALTS

Many acids like hydrogen chloride (and bases like sodium
hydroxide) are so near complete dissociation in dilute solution that
a first approximation in their treatment can be accomplished by
assuming complete dissociation. The hydrion concentration is
then assumed equal to the concentration of the substance. If a
solution of hydrogen chloride is under consideration and is pro-
gressively undergoing "neutralization" by potassium hydroxide,
there is obtained actually a picture of the relation of pH to
degree of "neutralization" similar to one or the other of the

34 THE DETERMINATION OF HYDROGEN IONS

curves in figure 9. These curves were calculated on the assump-
tion that [H+] = ["unneutralized" HC1]. A similar curve for the
titration of KOH is also shown in figure 9.

However, if the solution vary in its initial content of one or
another neutral salt, or vary, as it actually does during titration,
in the proportion of neutral salt, a distinctly appreciable de-
parture from the approximately calculated relations noted above
will be found when_jbhejiydrogen electrode method of measure-
ment is used. FundamentaTIy~tKe etfecT^s^olTve'ry different
from the "residual error" already noted when hydrogen electrode
measurements are carried into the elementary treatment of a
mixture of a weak acid and its salt. But in the present instance
we are dealing with a strongly dissociating acid and in respect to
the high degree of dissociation the acid is like salts such as KC1.
The high concentration of the acid's charged ions produces an
effect as truly as the highly dissociating salts produce their
effects. Therefore, the displacement of the actual curve from
that approximately calculated cannot be ascribed solely to a
"salt-effect." Rather should it be called an evidence of the con-
duct of strong electrolytes in general.

This is a subject which has stimulated many investigations
and has led to still incomplete but very illuminating results.
The modern treatment is unique but a discussion of it must
be postponed. However, we need not be troubled for the
time being. Although we have introduced simplifying assump-
tions restricting too free and generalized application of the
equations, these serve admirably to outline the main features of
the subject. To only a little less degree are we safe in outlining
the conduct of solutions of strong acids and bases by the assump-
tion of complete dissociation. Later we shall return to detail.

CHAPTER II

SOME SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA
Words are the footsteps of reason. — FRANCIS BACON.

Many relations implicit in the general equations of acid-base
equilibria do not appear vivid and do not find their way into
everyday practice until they are reargued, reformulated and
named. A consequence is a special terminology which must be
understood if the literature is to be followed intelligently; for
sometimes a whole subdivision of our subject is summed up in
a single expression.

THE pH SCALE

As a normal solution of an acid has been defined as one con-
taining in 1 liter of solution the equivalent of 1.008 grams of
acidic hydrogen, so the normal solution of the hydrogen ion was
defined to be one containing in 1 liter of solution 1.008 grams
of hydrogen ions.

Thus an acid solution may be described in terms of its normal-
ity with respect to total acid or in terms of its normality with
respect to hydrions.

To distinguish between these two components with their com-
mon unit it has been suggested that we call "normality" in its
older sense the quantity factor of "acidity" and the hydrogen
ion concentration the intensity factor. This may serve to em-
phasize a distinction, but the suggested analogy with the quantity
and intensity factors of energy is confusing when we retain for
each a unit of the same category. Nevertheless the two com-
ponents remain in a restricted sense the quantity and intensity
factors of "acidity." The one is the total quantity of available
acid. The second, the concentration of the hydrogen ions, repre-
sents the real intensity of "acidity" whenever it is the hydrogen
ion which is the more directly active participant in a reaction.
This is admirably expressed when we use for hydrogen ion con-
centrations a mode of expression which links it with the potential

36 THE DETERMINATION OF HYDROGEN IONS

of a hydrogen electrode. It so happens that in determining the
hydrogen ion concentration with the hydrogen electrode the
potential of this electrode is put into an equation which reduces
to the form :

Potential 1

= log

numerical factor [H+]

Later we shall see that this potential, expressed in volts, is the
intensity factor in the free-energy change involved in the trans-
port of hydrions from a concentration of one normal to another

given value of [H+]. Thus the expression log - - is a linear

function of an intensity factor of energy-change and in this sense
it can be called an index to acid intensity.

On the other hand the association of the words "potenz" and
"puissance" with pH arose in a totally different manner. In his
original article S0rensen (1909) says:

. . . . , la grandeur de la concentration des ions hydrogene s'exprime
par le facteur de normalite de la solution par rapport aux ions hydrogene,
facteur indique sous la forme d'une puissance1 negative de 10.

Dans tons les cas traites dans le present memoire ....

. . . . le facteur de normalite de la solution sous le rapport des ions
hydrogene ou, en d'autres termes, le nombre d'atomes-grammes d'ions
hydrogene par litre est plus petit que 1 et peut etre pos6 egal a 10~p, ou
pour le nombre p je propose le nom d'exposant des ions hydrogene et la
designation pH. Par exposant des ions hydrogene (pj) d'une solution, nous
entendons done le logarithm Brigg de la valeur reciproque du facteur de
normalite de la solution relativement aux ions hydrogene.

Comme il n'est d'ordinaire pas question de solutions d'ions hydrogene
plus fortes qu'une solution normale, j'ai choisi la definition ci-dessus de
1'exposant des ions hydrogene, qui par suite sera generalement un nombre
positif; il ne sera negatif que dans les cas bien rares ou Ton a affaire &
des solutions plus fortes que la normale.

Thus PH is denned by the relation:

As a matter of typographical convenience we shall use pH in
place of the original p^ and PH.

1 "Potenz" in the German translation, i.e., power (mathematical).

pH-SCALE

If we follow S0rensen's original suggestion, pH may be called
the hydrogen ion exponent. Its numerical magnitudes have
been called "S0rensen values," "reaction numbers," etc. The
term exponent (puissance, Potenz, power) is employed because
the relation

pH = logic

[H+]

pH = - logw [H+]

may be written [H+] = 10~pH. Here — pH appears as an ex-
ponent.

TABLE 3

Relation of [H+] to pH

[H+]

10+1

-1

io-»

10±0

10~8

8 '

10-1

10~9

10~2

lO-io

io-«

10-"

io-<

10-u

10-'

etc.

io-«

A caution may now be noted. A difference of sign occurs
between a given value of pH and the exponent found when the
normality of the corresponding hydrogen ion concentration is
written in the usual way. For example, —7 is the exponent in
10~7; but the pH value corresponding to [H+] = 10~7N is +7.

The gross relation of [H+] to pH is shown in table 3. See also
table B, appendix (page 673).

The convenience of pH over [H+] is manifest when we compare
the numerical values encountered in chemical and physiological
studies. For instance, one enzyme may operate most actively at
a hydrogen ion concentration of 0.01 normal while another is
most active at 0.000,000,001 normal. While convenient abbre-
viations of such unwieldy values are 1 X 10~2 and 1 X 10~9,
there remains the difficulty of plotting such values on ordinary

38 THE DETERMINATION OF HYDROGEN IONS

cross-section paper. If the difference between 0.000,000,001 and
0.000,000,002 is given a length of one millimeter, the difference
0.01 to 0.02 when plotted on the same scale would be ten kilo-
meters, ten kilometers distant. Evidently the logarithmic
spacing should be followed and fortunately it is the logarithmic
plotting of hydrogen ion concentration (in terms of pH) which
correctly depicts the fact that the difference between 1 X 10~9
and 2 X 10~9 may be as important to one set of equilibria as the
enormously greater difference between 1 X 10~2 and 2 X 10~2 is
to another set of equilibria. This is revealed in the charts on
previous and subsequent pages.

Thus both convenience and the nature of the physical facts
invite us directly or indirectly to operate with some logarithmic
function of [H+j.

It is unfortunate that a mode of expression so well adapted to the treat-
ment of various relations should conflict with a mental habit. [H+]
represents the hydrogen ion concentration, the quantity usually thought
of in conversation when we speak of increases or decreases in acidity.
pH varies inversely as [H+]. This is confusing.

The normality mode of expression has historical priority and conse-
quently conventional force. Since there is a hydrogen ion concentration
for each hydroxyl ion concentration it became the custom, following
Friedenthal (1904), to express both acidities and alkalinities in terms of
[H+]. This gave a scale of one denomination and the meaning of "higher"
and of "lower" became firmly fixed. Later we meet the new scale with
its direction reversed. The inconvenience is unquestionable and partly
because of this the pH scale has been criticized.

Wherry2 (1919, 1927) and others have proposed changes of one kind or
another which they believe introduce greater simplicity or convenience.
Wherry (1927) in particular has urged the use of his "active acidity"
[antilog (7.0 — pH)] and the descriptive terms: super acid (pH3to4),raecfo'acid
.(pH 4 to 5), subacid (pH 5 to 6), minimacid (pH 6 to 7), neutral (pH 7),
minimalkaline (pH 7 to 8), etc. His purpose is admirable and his case well
stated. It is, in short, an attempt to "humanize" the statement of acidity
for the benefit particularly of botanists.

It will presently be indicated that we are not denying the excellence of
the purpose if we classify Wherry's proposal with others. We may pass
over the fact that the functions offered are arbitrary and artificial. The
same may be said of pH. We may pass over the fact that one or the other

2 Compare Wherry and Adams (1921) with reply by Clark (1921). See
also Giribaldo (1925), Derrien andFontes (1925), Guillaumin (1926), Richter
(1926), Kolthoff (1926), Lambling.

II SUBSTITUTES FOR pH 39

of these newer functions, offered as a convenience, would entail the extreme
inconvenience of recasting in a new mold a vast amount of accumulated
data now recorded in terms of pH. The fundamental difficulties with all
the new functions so far proposed are these. Some of them involve a new
basis of reference when we are having difficulty enough with the con-
ventional basis (see Chapter XXIII) . It might be said that the choice, for
instance, of "neutrality" as a reference point is made without involving
those refinements which acquaint us with the shifts of the "neutral point"
and is made for purposes of approximate descriptions only. As in all
matters of definition the- choice is permissible. However, its proposal is
as much as to say that the proposer has no anticipation that his follower
will see farther than he sees and will have no need to reestablish contact
with the refinements he has ignored. Those substitutes for pH, which
have been proposed so far, employ so many unacknowledged complexities
and tacit assumptions that they have not commanded assent.

If simplicity be desired, it were better to ignore the special meanings of
pH, [H+], aH, etc., which these various authors have used in deriving their
new functions; it were better to ignore the almost useless "neutral point,"
and to develop the themes of Chapters XI and XXVII. It would probably
not satisfy the novice merely to tell him that a pH value is to be used as
an arbitrary number representing the state of acids in solution but if he
will use indicators as type acids he can visualize something of what the
numbers mean. He would then be relieved of the puzzling question of
how a concentration of 1,000,000 N can so profoundly affect the things he
deals with and he might consent to use the numbers with the conventional
name of pH. Because the subject is important too much effort cannot
be spent upon making the presentation direct, simple and at the same
time representative of actuality. This is certainly not accomplished by
piling one convention upon another, one mathematical function upon
another, one difficulty upon another. Until a really fundamental and
simple change is proposed, attempts to alter what has become established
convention should be vigorously opposed and the convenience of pH should
be preserved.

In passing it may be noted that occasionally a mind is found which
honestly distrusts the use of a logarithmic function of [H+] because it is
logarithmic. Apparently it demands [H+] itself from a sense of absolutism.
One possessed of this obsession might profitably consider the innumerable
phenomena which are most vividly described by use of logarithmic func-
tions. See, for example, the absorption of light by an indicator solution
as described in Chapter VII. But see in particular Chapter XXVII.

A new symbol, paH, has been suggested by S0rensen and Linderstr0m-
Lang (1924) to indicate a function of hydrion activity in contrast to pH
which is a function of hydrion concentration. This will be discussed on
page 479.

While discussing "pH" we may note that a symbolization originating
in S0rensen's pH is coming into wide use. In Chapter I it is noted that,

40 THE DETERMINATION OF HYDROGEN IONS

when a dissociation constant occurs in an equation in the form log — ,

it has become the custom to write log — as pKa. So also the custom is

l^a

spreading to similar functions and we find, for instance, pl~, indicating the
logarithm of the reciprocal of iodide ion concentration.

THE EFFECT OF DILUTION

The effect of dilution upon the hydrogen ion concentration of a
solution may be briefly generalized by some approximations.

Consider an acid of the type HA for the dissociation of which
we have the equilibrium equation:

[H+] X [A-]
[HA]

If Ka is small there must obviously be a large reserve of undis-
sociated acid so long as the concentration of total acid is high.
As the solution is diluted this reserve dissociates to keep Ka
constant; but there is a readjustment of all components which can
be conveniently followed only by means of the simple algebraic
equation expressing the equilibrium condition.

If the acid alone is present in the solution we may assume that
[A-] = [H+]. Also if [Sa] = the total acid, [HA] == [SJ - [H+].

Substituting these in the above equation and solving for [H+]
we have:

[H
When Ka is small in relation to [Sa]

[H+] ^

Compare the equation on page 13. On these assumptions the
hydrogen ion concentration should vary with dilution of the
solution (diminution of Sa) only as the square root of Ka[Sa].

If there is present a salt of the acid we can apply the equation
derived on page 22 which shows that the hydrogen ion concen-
tration of a mixture of a weak acid and its highly dissociated salt

DILUTION

is determined approximately by the ratio of acid to salt. Since
dilution does not change the ratio, such a mixture should not suf-
fer a change of hydrogen ion concentration beyond the limits set
by the approximate treatment with which this relation was
derived.

Therefore, except for solutions of high hydrogen ion concentra-
tion induced by the presence of unneutralized strong acids, the
hydrogen ion concentration should vary with dilution somewhere
between the zero change indicated by the last approximation and
the square root relation first indicated.

If an acid be one which, in pure solution, is completely disso-
ciated, the hydrion concentration is equal to the analytical or
stoichiometrical normality of the acid. This will not be shown
precisely by the hydrogen electrode method of measurement since
this device measures energy changes which are not strictly propor-
tional to concentration changes. This appears in a striking way
when a solution of hydrochloric acid is concentrated. At some
dilutions the hydrion concentration, as calculated with the aid
of the uncorrected formula for the concentration cell, will appear
to be higher than that of the available acid. This aspect will
be discussed later.

In the case of mixtures of weak acids and their salts, dilution
may in many instances produce changes in hydrion concentra-
tion too small to be detected by any but refined methods. Ad-
vantage of this is taken in the dilution of solutions otherwise too
dense optically for the application of the indicator method.

The effect of dilution should be reconsidered after reading the
last part of Chapter XXV.

TABLE 4

Effect of dilution

MOLKCULAK CONCEN-
TRATION OF GLY-
COCOLL

MOLECULAR CONCEN-
TRATION OP A8PAR-
AOINE

1.0

6.089

1.0

2.954

0.1

6.096

0.1

2.973

0.01

6.155

0.01

3.110

0.001

6.413

0.001

3.521

0.0001

6.782

0.0001

4.166

42 THE DETERMINATION OF HYDROGEN IONS

For bases and amphoteric electrolytes relations similar to those
discussed above may be deduced.

One or two actual cases may be of interest. S0rensen has
given the accompanying table (table 4) of the pH values of dif-
ferent dilutions of asparagine and glycocoll.

The dilution here is ten-fold at each step, yet the increase in
pH is very small while the solutions are between l.OandO.Ol M.

Walpole (1914) besides giving data on the hydrogen electrode
potentials of various dilutions of acetic acid and "standard ace-
tate," has determined the effect of a twenty-fold dilution of
various acetic acid-sodium acetate mixtures. The change of pH
on twenty-fold dilution of standard acetate is about 0.08 pH;
and for mixtures of acetic acid and sodium acetate which lie on
the flat part of the curve the change of pH is of the same order

of magnitude. When the ratio acetlc acid reaches 19/1 the

sodium acetate

change is about 0.3 pH.

See Cohn (1927) and page 509 on the dilution of phosphate
solutions.

The brief outline given above takes no account of changes of
equilibrium which sometimes occur in colloidal solutions.

"NEUTRALITY" AND VALUES OP Kw

It was shown in Chapter I that, under ideal conditions, the
product of the hydrogen ion concentration and the hydroxyl ion
concentration of an aqueous solution is constant

[H+] [OH-] = Kw

Therefore, aqueous solutions, even those containing large excess
of hydrogen ions (i.e. strongly acid solutions) must contain
sufficient hydroxyl ions to maintain the constant relation shown
above. Likewise aqueous solutions, even those containing large
excess of hydroxyl ions (i.e. strongly alkaline solutions), must
contain sufficient hydrogen ions to maintain the constant rela-
tion shown above. Obviously, there will be one point at which
the concentration of hydrogen ions will equal the concentration
of the hydroxyl ions, that is [H+] = [OH~]. Using for Kw the
rounded value 10~14, we find this point as follows.

[H+]2 = [OH-]2 = 10~14 or [H+] = [OH~] = 10~7

NEUTRALITY 43

In other words, equality of hydrion and hydroxyl ion concentra-
tions occurs at pH = 7. This is, as stated, an approximation.
Here no account has been taken of the variation of the value of
Kw with variation of temperature, salt-content of the solution,
etc., nor of the precise meaning of the values called Kw as they
are derived from experimental measurements of very different
types.

Considerable confusion will be avoided if there is maintained a
categorical as well as an obviously numerical distinction between
Kw and the pH value called "neutrality."

The pH value. 7.0 is a convenient reference point with which to
differentiate "acid" from "alkaline" solutions in ordinary, crude
descriptions. Otherwise, it is of little practical significance. To
be sure, it is the pH value of pure water and, therefore, an interest-
ing value to calculate as a derivation from water's characteristic
constant, Kw. But pure water itself has seldom been seen and is
of little use. Its hydrogen ion concentration has no general
relation to the hydrogen ion concentration at the equivalence point
sought in the "neutralization" of an aqueous solution of an acid
by an aqueous solution of a base. This will be made plain in
the discussion of the theory of titration (Chapter XXVIII) but it
also appears in several of the figures of Chapter I. "Neutrality"
is also of no interest whatever in the study of ampholytes. See
Chapter I.

In contrast to the pH-value 7, Kw, the ionic product of water,
is frequently employed when formulations of equilibria involve
both hydroxyl and hydrogen ions. The relation [H+] [OH~] =
Kw enables one to eliminate either [OH~] or [H+] when desired.
Usually the necessity of this transformation may be avoided as
will be shown in the discussion starting on page 46.

Kw has been determined by a variety of methods and with
substantial agreement. The following are some instances.

Kohlrausch and Heydweiller (1894) determined the electrical
conductivity of water approaching very near to purity. On the
assumption that the conductance is proportional to the numbers
and mobilities of the hydrogen and hydroxyl ions, that these are
present in equal concentrations and that the mobilities of the
hydrogen and hydroxyl ions are known, there can be calculated
the value of Kw. Wijs (1893) used the results of a study of the

THE DETERMINATION OF HYDROGEN IONS

relative rates of hydrolysis of methyl acetate by hydrions and
hydroxyl ions and applied these data to the case of the hydrolysis
of methyl acetate by water. There have also been studies of the
hydrolysis of salts, studies on the hydrogen potential in acid and
alkaline solutions (e.g., Lewis, Brighton and Sebastian (1917)) and
many other studies leading to substantially the same order of
magnitude for Kw.

Kolthoff (1921) has compiled the following table 5 showing the
"dissociation" constant of water at different temperatures as
given by different authors. Lewis, Brighton and Sebastian
(1917) found Kw = 1.012 X 10~14 at 25°C. Hence, [H+] = 1.006

TABLE 5

Ion-product (dissociation constant} of water at different temperatures
(After Kolthoff and Furman (1926))

TEMPER-
ATURE

AUTHORITIES

0.12 X 10-"

0.14 X 10-"

0.089 X 10-"

0.59 X 10~"

0.72 X 10-"

0.74 X 10-"

0.46 X 10-"

1.04 X 10-"

1.22 X 10-"

1.27 X 10-"

0.82 X 10-"

5.66 X 10-"

8.7 X 10-"

100

58.20 X 10-"

74.0 X 10-"

48.0 X 10-"

1. Kohlrausch and Heydweiller (recalculated by Heydweiller) (1909).
2>. Lorenz and Bohi (1909).

3. Michaelis (1914), p. 8,.

4. Various investigators.

X 10~7 (practically, pH = 7.0). Lewis and Kandall (1923)
give Kw = 1.005 X 10~14 at 25°C.

The following values of pKw (log — ) given by Michaelis

(1922) (see table 6) were obtained on a basis somewhat different
from that used by Lewis, Brighton and Sebastian.

Here it may be said that Kw appears as a constant because, in
its derivation, there was introduced at the very beginning the
postulate that the environment is to be constant. If the solu-
tion be altered, as by the addition of a certain quantity of neutral
salt, there is the possibility that Kw will have a new value under

IONIC PRODUCT OF WATER

the new conditions. It is only on the expectation that the altera-
tion will be slight in ordinary changes of composition that we are
justified in neglecting the corrections which modern theoretical
methods have brought to light. However figure 10 will illustrate

TABLE 6

Interpolated values of — log Kw
(After Michaelis (1922))

TEMPERATURE

LOO^r-

pH OF NEUTRAL POINT

•c.

14.200

7.10

14.165

7.08

14.130

7.07

14.100

7.05

14.065

7.03

14.030

7.02

13.995

7.00

13.960

6.98

13.925

6.96

13.895

6.95

13.860

6.93

13.825

6.91

13.790

6.90

13.755

6.88

13.725

6.86

13.690

6.85'

13.660

6.83

13.630

6.82

13.600

6.80

13.567

6.78

13.535

6.77

13.505

6.75

13.475

6.74

13.445

6.72

13.420

6.71

what is to be expected. Note the specific effects of salts so similar
as are sodium chloride and potassium chloride.

At this point it is appropriate to remark that, since in exact
treatments of equilibria a correction term for Kw (or varying
activity coefficient for water, see later chapters) must be taken
into consideration, it will be well to formulate the elementary

THE DETERMINATION OF HYDROGEN IONS

aspects of our subject by avoiding forms which include Kw
wherever that is feasible. This will be our policy in dealing with
bases, although the classical equations will also be shown. The
variation of Kw constitutes one of very many reasons for avoiding
several of the schemes which have been suggested as substitutes
for the pH scale (see p. 39) and which involve Kw in their
derivations.

Although a correction term must be applied in refined formula-
tion and although this correction term varies with every change
in the composition of the solution, the rounded values of Kw as
given by Michaelis (1922) and shown in table 6 may be used for
ordinary, approximate calculations.

1.6

1.5

1.4

"2 ,.3

1.2

1.0

0.5 1.0 1.5

SQUARE ROOT OF CONCENTRATION

FIG. 10. VARIATION OF V Kw WITH CONCENTRATION OF SALT

FORMULATION OF EQUILIBRIA IN SOLUTIONS OF BASES WITH
AVOIDANCE OF THE USE OF [OH~] AND Kw

In Chapter I figure 2 was constructed by first formulating the
equilibria of acids and of bases separately and then aligning the
two sets of curves by use of the relation

pH + pOH = pKw^14

In such a system of formulation the transformation of a given
value of pOH to a corresponding value of pH (or vice versa) may
be made whenever desired by use of that numerical value of pKw
which is applicable to the specific conditions. Therefore, it is
convenient in general discussion to neglect pOH and to use pH
uniformly.

FORMULATION WITHOUT [OH"

Now consider figure 11 in conjunction with figure 2 (page 16).
In figure 11 there is shown by curve C the relation between pH
and percentage dissociation-residue for an acid having the
dissociation curve B. Obviously curve C has the form of the
dissociation curve for a base. Its position on the pH scale is
made evident by the legend of figure 11.

Thus, if it suits our convenience, we may proceed to deal with
the cation of a base as if we were dealing with the dissociation

pH3 4 5 6 78 9 10

FIG. 11. DISSOCIATION CURVES AND DISSOCIATION RESIDUE CURVES

A. Dissociation curve for acid, pKa = 8.0.

B. Dissociation curve for acid, pKa = 4.8.

C. Dissociation curve for base, pKb = 14 - 4.8 = 9.2 or dissociation-
residue curve for acid pKa = 4.8.

residue of an acid. Likewise we may deal with the dissociation
residue of a base as if we were dealing with the anion of an acid.
Likewise if our knowledge of a compound tells us nothing of its
acidic or basic nature and if a series of measurements can be
formulated by equation (12a) or by equation (15a) we shall not
be able to tell by these measurements and their formulation
whether we are dealing with an acid or a base.

However, there is a more direct way of arriving at a uniform
method of formulation. Consider, for instance, equilibria in
solutions of ammonia.

Ammonia, NH3, is usually considered the parent of the base

48 THE DETERMINATION OF HYDROGEN IONS

NH4OH, a hypothetical substance supposed to be formed by the
hydration

NH3 + H20 -> NH4OH
A basic dissociation constant could be defined by

[NH4+] [OH-]
[NH4OH]

If this were used, we would proceed in the classical manner.
Ammonia systems may equally well be treated in accordance
with the following formulation3

[NHS] [H+]
[NHt]

3 It is instructive to note the following:
For the hydration equilibrium:

[NHJ [H.O]

[NH4OH]
For the dissociation equilibrium:

[NHt] [OH-]
[NH4OH]

Combine these two equations to yield:

[NHJ [H20]

= Kh

[NHJ] [OH-] Kb
Introduce [H+] [OH~] = Kw

[NHJ [H+] Kh Kw

[NHJ] Kb [H20]
If [H2O] is regarded as a constant

[NHJ [H+] _
[NHt]

II FORMULATION OF BASES 49

There are many amino compounds which are substituted
ammonias, — primary, secondary and tertiary ammonias. These
may be considered to add hydrions and the equilibrium equation
can be formulated as is done in the last equation above. We have
also to consider the quaternary ion, R^RsRiN^. In this case
it would seem more logical to formulate the basic dissociation
as follows

[R1R2R3R4N+] [OH-]
[RiR2R3R4NOH]

But the quarternary ammonium hydroxides are exceedingly
strong bases. Frequently they are so strong that complete dis-
sociation may be assumed as it is in the case of sodium and
potassium hydroxides. Under such circumstances equations of
the ordinary type are of little practical value as stated on page
12. The majority of the weak organic bases may be treated as
the ammonia system is above and the equilibrium equation may
be written

[RiR2R3N+H]

Thereby one avoids the necessity of considering either [OH~]
or Kw.

The important point is that in general either mode of treat-
ment can be adapted to convenience. When a more comprehensive
formulation capable of extension to all sorts of non-aqueous
solutions is desired, those presented by Br0nsted (1923) and by
Lewis in Valence will be found useful. See also Lowry (1924).

This is the equation given in the text where Ka is substituted for the
constant

KhKw

Kb [H20]

This way of avoiding an account of the changing properties of the
solvent is, in a sense, only a "dodge."

50 THE DETERMINATION OF HYDROGEN IONS

BUFFER ACTION

If we were to add to 1 liter of perfectly pure water of pH 7.0,
1 cc. of O.OlN HC1, the resulting solution would be about pH 5.0
and very toxic to many bacteria. If, on the other hand, we
were to add this same amount of acid to a liter of a standard
beef infusion medium of pH 7.0, the resulting change in pH would
be hardly appreciable. This power of certain solutions to resist
change in reaction was commented upon by Fernbach and
Hubert (1900) who likened the resistance of phosphate solutions
to a "tampon." The word was adopted by S0rensen (1909) and
in the German rendition of his paper it became "Puffer" and
thence the English "buffer." There has been some objection4
to this word so applied, but it now possesses a clear technical
meaning and is very widely used. By buffer action is meant the
resistance to change of pH exhibited by a solution when it is sub-
jected to gain or loss of acid or alkali. The elementary theory of
buffer action is already clear if the implications of the simple
equations of Chapter I are understood.

Returning to figures 4 to 6 we see that along the flat portion of a
titration curve considerable alkali has to be added to produce
much change in pH. Conversely, the addition of a strong acid
would not have anywhere near the effect at this flat portion of the
curve that it would have near either end. Thus it is evident that
a mixture of an acid and its salt will tend to stabilize the pH
of the solution only within certain narrow zones having vague
boundaries. Mixtures buffering the solution within such a pH
zone are often referred to as "regulator mixtures." They are of
very great value to the analyst and the physiological chemist in
that they furnish a means of stabilizing the hydrogen ion con-
centration within a predetermined zone. The middle point of
this zone, where the strongest buffer action is exerted, is deter-
mined approximately as shown on page 17 by the dissociation
constant of the acid or base concerned. Other things being
equal, the choice of mixtures is thus revealed in a table of disso-
ciation constants.

* "Moderator" is sometimes preferred. Moore, Roaf and Whitley were
employing the concept as early as 1905 under the term "balanced-
neutrality."

BUFFERS

Henderson (1908) and Washburn (1908) simultaneously utilized
the principle that an equimolecular mixture of an acid and its
salt will stabilize the hydrion concentration of a solution.

Emphasis may be placed upon one or another aspect of buffer
action by means of the following examples.

A 1 per cent solution of Witte peptone was found to have a
pH value of 6.87. To equal portions of the solution were added

—

•

42024
C.C.

FIG. 12. TITEATION CURVES OF 1 PER CENT ANDJ> PER CENT PEPTONE

SOLUTIONS yjjj

Ten cubic centimeters of peptone solution titrated with 0.1 N lactic
acid (to right) and with 0.1 N NaOH (to left).

successively increasing amounts of O.!N lactic acid and the result-
ing pH was measured in each case. There were also added to
equal portions of the solution successively increasing amounts of
O.!N NaOH and the resulting pH was measured in each case.
The pH values were then plotted on cross section paper as ordi-
nates against the amount of acid or alkali added in each case as
abscissas. This gave curve 1 shown in figure 12. The other
curve shown in this figure was constructed with data obtained
with a 5 per cent solution of Witte peptone.

THE DETERMINATION OF HYDROGEN IONS

Figure 12 shows that the buffer action of a solution is dependent
upon the concentration of the constituents. The 5 per cent solu-
tion is much more resistant to change in pH than the 1 per cent
solution.

It will also be noticed that in either case the buffer action is
not the same at all points in the curve. In other words the buffer
action can not be expressed by a constant but must be determined
for each region of pH. This is illustrated even more clearly by
the titration curve for phosphoric acid (fig. 4, page 28). At
the point where the solution contains only the primary phosphate

c.c.

FIG. 13. TITRATION OF A BEEF-INFUSION CULTURE MEDIUM
One hundred cubic centimeters of medium titrated with 0.2 N HC1
solution in one case and with 0.2 N lactic acid solution in the other case.

and again where it contains only the secondary phosphate there
is very little buffer effect indeed.

Furthermore the buffer action of a solution may not be due
entirely to the nature of the initial constituents titrated but also
to the nature of the substance with which it is titrated. This
point may be illustrated by titrating a beef infusion medium in
the one case with hydrochloric acid and in the other case with
lactic acid, both of the same normality (see fig. 13). It will be
seen. that at first the two curves are identical. As the region is
approached where the dissociation of the lactic acid (a weak acid)
is itself suppressed because of the accumulation of lactate ions
(and the hydrogen ions) further addition of this acid has com-

II BUFFERS 53

paratively little effect. The "strong" acid, hydrochloric, on the
other hand continues to be effective in changing pH until at high
hydrion concentrations the logarithmic function suffers less
change. As already noted in Chapter I, hydrochloric acid may
be considered in approximate treatments as completely disso-
ciated. The flattening of the titration curve, of which pH is the
ordinate, is therefore inherent in the nature of the case; but it
must not be presumed that a mere mathematical limitation
obscures the reality of a physically significant buffer effect.
Imagine an acid which is not totally dissociated but which has a
high dissociation constant. The degree of its dissociation remains
a function of pH and if we are to suppress its dissociation com-
pletely we might have to run the pH value of the solution into
negative values by adding high concentrations of very strong
acids. Ultimately we reach a limit in the "strength" of the acids
available and can use only higher total concentrations of those
acids which approach complete dissociation in dilute solution.5

These examples will suffice to make it evident that the buffer
action of a solution is dependent upon the nature and the con-
centration of the constituents, upon the pH region where the
buffer action is measured and upon the -nature of the acid or
alkali added.

The main aspect of the subject is summed up in the relation

that, so long as the ratio does

rr rrrr ,

[HAJ [M J L-tlAJ

not depart far from unity, [H+] cannot depart far from the
constant Ka.

Buffer action, that is resistance to change of pH upon addition
or loss of acid or alkali, cannot always be so easily formulated.
For instance, suppose that there is present in a solid phase some
material which adsorbs from the solution a component of the
solution's acid-base equilibrium. That substance, by reason of its
ability to take up or give off the adsorbed component according
to the concentration of the component in the liquid phase, may
act as a buffer. Henderson (1909) called attention to this. Bovie
(1915) and others have shown the buffering effect of charcoal.

5 Later we shall encounter the case of an acid dye which behaves as if
it has a dissociation exponent, pK = 1.5. To obtain what appeared to be
complete dissociation there was used 36 per cent HC1 solution!

THE DETERMINATION OF HYDROGEN IONS

When a component of the acid-base equilibrium of a solution
reaches such a concentration that it precipitates and forms a
solid phase in equilibrium with the liquid phase, the zone of pH,
within which buffer action would be expected from the relations
for homogeneous solutions, may be considerably altered. The
direction which the treatment then takes is outlined on page 582

Since the types of such cases are numerous, we shall not pause
to discuss the detail; but it should be noted that the subject
is of fundamental importance to many problems of physiology,
analysis, etc.

There are occasions when a more elegant definition of buffer
action leads to very useful formulas. Thus Van Slyke (1922),

FIG. 14. BUFFER ACTION
Change of pH on addition of base

in an independent development of a treatment first attempted
by Koppel and Spiro (1914) (cf. Lehmann, 1922, and Michaelis
and Perlzweig, p. 106) proposes the following.

Let there be charted as in figure 14 the relation between pH
and the equivalents of base per liter added to a given solution.

Between the points A and C the ratio -TT-^T gives the slope of

the line AC. This is only a rough indication of the order of
magnitude of the slope of a tangent to the curve in this region.
The slope of the tangent obviously changes between its position
at A and its position at C. To obtain the slope at any point
use is made of the infinitesimals dB and d(pH).

II BUFFER INDEX 55

Van Slyke then describes a unit for the buffer effect. "The

JT> «^V**'

unit adopted is the differential ratio -,. T,.? expressing the rela-

tionship between the increment (in gram equivalents per liter)
of strong base B added to a buffer solution and the resultant
increment in pH. Increment of strong acid is equivalent to a
negative increment of base, or — dB. In these terms a solution
has a buffer value of 1 when a liter will take up 1 gram equivalent
of strong acid or alkali per unit change in pH. If base is added
to a solution, pH is increased, so that both dB and d(pH) are
positive. If acid is added both dB and d(pH) are negative.

The ratio ,, is, therefore, always a positive numerical value."

To summarize Van Slyke 's treatment we shall proceed as follows :
For the convenience of the mathematical treatment equation

(12a) of Chapter I, namely,

/—•-£*•

pH = pKa + log

is rewritten with natural logarithm as (1)

pH = pKa + 0.4343 In — — (1)

1 — a

The derivative is

= 0.4343 — d -— (2)

a \l - a)

Whence

= 2.303 a(l - a) (3)

da
When a — 0.5, , = 0.576. This value is the maximum ob-

tained by a univalent acid.

56 THE DETERMINATION OF HYDROGEN IONS

Now under limited conditions, explained in Chapter I,

_ Base added _ [B] d[B]

Total acid := [S] J '' [S]

Hence

^r = 2.303 «(1 - «) [S] (4)

Also

Ka + [H+]
Hence

For brevity ,/ J. is called /3 by Van Slyke. In figure 15 equa-
a(pJti)

tion (5) is used to obtain part of the curve showing the relation
of /3 to pH in the cases of 0.1 M and 0.2 M acetic acid. Equation
(5) gives that part of each curve shown in the figure by the
central, peaked portion and continued as dotted curves near
pH 2 to 3.5. In the region lower than pH 3.5 correction must be
made for the buffer effect of the strong acid. Likewise beyond
pH 10 the effect of a strong base should be considered.

These additional buffer effects are calculated as follows.

Consider a strong base added to water. Assume that the base
is completely dissociated. Then d[B] = d[OH~] and

4B] dIOH-]

d(pH) d log [OH-]
Likewise for the case of a strong acid added to water we have :

d[E] = 2.303 [H+] (7)

BUFFER INDEX

The buffer effect in strong acid or alkaline solutions is the sum of
these two effects; i.e.,

d[B]

rf(pH)

= 2.303 ([H+] + [OH-])

(8)

This is illustrated in figure 15.

Between pH 2 and pH 3.5 a resultant of the /5 of the acetate
system and the (3 of the strong acid prevents the buffer index
from falling to zero.

0.12

0.10

0.08

0.06

0.04

0.02

0.00

0.2 IT acet.c acid

M \\\

0.1 M ace

tic acid

/9-duetofel

1 2 3 4 5 6 7 8 9 10 11 12 13

FIG. 15. VALUES OF OR /3 FOR MIXTURES OF ACETIC ACID AND ACETATE

dpH

(After Van Slyke (1922))

For further details see the original articles by Van Slyke (1922),
Koppel and Spiro (1914) and Taufel and Wagner (1926).

One very distinct advantage in the use of Van Slyke's buffer
values arises from the fact that the buffer values of various com-
ponent systems of a complex system are additive. When the
individual values of component systems can be precisely formu-
lated, much can be predicted of complex systems.

A FURTHER REMARK ON STRONG ELECTROLYTES

The reader who is seeking an outline of our subject will doubt-
less be willing to proceed with the approximate treatment which

THE DETERMINATION OF HYDROGEN IONS

was accorded strong acids at the close of Chapter I (page 34)
and to postpone a reconsideration of the effects of those highly
dissociating salts formed by the addition of strong bases to weak
acids. Since it has been intimated that the simple relations pre-
sented so far are inapplicable to strong acids and bases, an addi-
tional remark on strong electrolytes may be appropriate here,
pending the development in later chapters of more suitable
methods of approach and formulation.

In the introductory section of Chapter I brief mention was
made of the electronic architecture of atoms and molecules.
There it was stated that certain compounds behave as if one of

FIG. 16. REPRESENTATION OP A PORTION OF A CRYSTAL OF SODIUM

CHLORIDE

Sodium ion represented by dots; chloride ion by circles

the component atoms has completely captured the valence elec-
tron or electrons of the other component with the result that the
compound is virtually an association of ions. For example, it is
believed that, whatever may be the orbits of the electrons in
sodium chloride, the chlorine there found has captured an elec-
tron to complete its own octet, while the sodium has lost an elec-
tron. Consequently the sodium chloride molecule might be
represented by (Na+, Cl~)x. Indeed x-ray analysis of the crystal
suggests this. An interpretation of the x-ray "reflection spectrum"
of sodium chloride crystals yields the conclusion that the sodium
and the chloride ions are arranged as shown in figure 16. In this
picture there is no indication of the molecule NaCl or of any
"molecule" short of the crystal as a whole. There is only evi-
dence of a spatial arrangement which can reasonably be accounted

STRONG ELECTROLYTES 59

for by the assumption that chloride and sodium ions are each
attracting the ions of opposite charge with no exclusive, one-to-
one pairing. A variety of data supports this view.

When the components of the crystal are dispersed, as in water
solution, it would certainly be expected that the only discrete
particles persisting as individuals would be the sodium and the
chloride ions (undoubtedly combined with water molecules).
Indeed evidence has been molding opinion to this view until it
is rather widely although not universally accepted. Thus many
treatises start with the assumption of the "complete dissociation
of strong electrolytes."

This view by no means excludes the persistence of the attractive
force which is so strongly manifest in the crystal. The operation
of this force, theoretically, can not become completely negligible
until the thermal agitation becomes exceedingly great (infinite
temperature) or the dispersion by the solvent becomes exceed-
ingly great (infinite dilution). In short, it must be supposed that
at any given concentration of the sodium chloride solution, and
notwithstanding the thermal agitation, there occur situations in
which a sodium ion is surrounded by more chloride ions than by
sodium ions or a chloride ion is surrounded by more sodium ions
than chloride ions. This is to be regarded as an expression of
the orienting force.

Thus there should exist, statistically, groupings very different
in nature from the sodium chloride molecule specified in the
classical equation:

[Na+] [C1-]
[NaCl]

If one is convinced of this, he might say that an attempt to apply
the above equilibrium equation proceeds in ignorance of the
nature of sodium chloride and is no test whatever of the mass law.
With this interpretation of the data on crystal structure and
with the support of various other types of evidence it is con-
venient to regard salts such as sodium chloride, and also acids
such as HC1, as completely ionized in solution and to take account
of the constantly changing associations of the ions by methods
quite different from those which are employed in treating the
cases where true molecules are probably formed.

60 THE DETERMINATION OF HYDROGEN IONS

We owe to Milner and particularly to Debye and Hiickel the
way in which statistical mechanics may be applied to this situa-
tion. The theory is outlined in Chapter XXV. However, it
should be well understood that Debye and Hiickel attempt to
take account only of the effect of the electrical forces between the
oppositely charged ions and that their theory has nothing to say
about several other factors which may interfere with the applica-
tion of the postulates entering the derivation of the simple, ideal,
equilibrium equation. Since these factors are many and varied,
it may be said that the student has the choice of attempting the
impracticably rigid all at once or of setting up an ideal as a guiding
principle in some such way as that which we have here attempted.

There is, however, another way of approaching the subject.
We shall see that some of the methods to be described, notably
that of the hydrogen electrode, are methods which measure
energy changes. It is sometimes assumed that there is some
definite relation between two concentrations of hydrions and the
energy necessary to bring a mole of hydrions from one of the
given concentrations to the other. In this assumption trouble
begins. It could be avoided if we were content not only to leave
the results of the measurement in terms of energy changes but
also to formulate equilibrium conditions in these same terms and
to eschew the employment of equations cast in terms of concentra-
tion. Since current thought is not yet wholly receptive to the
extreme of this method of formulation we have the rather interest-
ing situation that the so-called rigid formulations of the day are
fundamentally those of the energy changes, but there is introduced
a term, called the activity, which has been rather inaccurately
described as a sort of corrected concentration.

In place of the equation

[HA]

where [] represents concentration, there is used the equation

(H+) (A~)
(HA)

where () represents "activity."

Then the equations reduce to the forms we have been using

II SIGNIFICANCE OF pH 61

but with "activity" replacing "concentration." Formulation by
"activity" is a defined application of rigid thermodynamics but
the value of the activity of a substance varies with every change
of condition and practically makes concrete knowledge of the
details largely empirical. Formulation by concentration is an
idealistic application of molecular theory but then the equilibrium
"constant" varies with every change of condition and again the
detail remains largely a matter of empiricism.

We shall proceed with "concentrations" and molecular theory
and shall return in due time to a consideration of energy changes.

THE SIGNIFICANCE OF CERTAIN pH VALUES

There is no hesitation in attributing a significance of actuality
to hydrion concentrations arising from the dissociation of strong
acids. There is little disposition to question the essential reality
of hydrion concentrations arising from the dissociation of moder-
ately weak acids. However, there is good reason to doubt the
physical significance of hydrion concentrations said to be of the
magnitude of 10~7N, 10~13N, etc.

We shall postpone a discussion of this very pertinent question
to a later chapter because there will then be an opportunity to
include material discussed in the intervening chapters. We may
here state that if the questioned values be considered as numbers,
they serve admirably and conveniently as indices to states of
equilibrium among relatively large quantities of materials. If
the doubting reader is not content to accept this for the moment
as a dogma, he should at once read the first part of Chapter
XXVII.

CHAPTER III

OUTLINE OF A COLORIMETRIC METHOD

In a short time you will improve, my friend,
When of scholastic forms you learn the use;
And how by method all things to reduce.

Mephistopheles to the Student in Goethe's Faust.

While the word "indicator" can have various meanings, — as
current indicator, pressure indicator, etc., — we shall use it as a
generic name for substances which "change color" when the pH
values of their solutions change.

We shall postpone to a later chapter a closer analysis of what
is meant by "change of color" and shall use the expression as it is
commonly understood.

Each indicator exhibits color-change within a characteristic
zone of pH. We shall consider here only those indicators which
have one, or at most two, characteristic zones. Beyond one
indefinite edge of such a zone one characteristic color appears.
Beyond the other indefinite edge the other characteristic color
appears. Within the zone, the color may be treated as if it were
a mixture of the two characteristic colors. Because the edges of
the zone are indefinite the color or color mixture in the center of
the pH-zone constitutes a useful point of reference. The value
of pH at the 50 per cent transformation is called the indicator's
pK value. This originates in the use of the equation

and in the treatment of the indicator as a simple acid.

The color chart is useful as a crude representation of the colors
of various indicators at various values of pH. The pK values
are indicated.

The color chart exhibits only intermediate colors. When the
pH value of a solution containing any one indicator is lower than
the pK value by about 2 units pH, what is conveniently called

Ill OUTLINE OF COLORIMETRIC METHOD 63

the "acid color" appears. When the pH value of the solution is
greater than the pK value of the indicator by about 2 units pH,
what is conveniently called the "alkaline color" appears. "Acid"
and "alkaline" used in this sense have no reference to a line of
demarkation between "acid" and "alkaline" solutions. Theory
associates the "acid color" with the "acid-form" and the "alkaline-
color" with the "alkaline-form" of the indicator substance.
These terms are conveniences.

In ordinary titrations (see Chapter XXVIII) conditions are
so chosen that when the "end-point" of the titration is reached
the pH, value of the solution plunges through the entire range of
the indicator's color transformation. A pronounced change of
color occurs on the addition of a very small amount of acid or
alkali. The intermediate colors even if observed are not em-
phasized. However, the intermediate colors are important to
our present purpose.

They can be maintained by buffer solutions which maintain
constant values of pH. Thereby reference standards may be
prepared. Standard buffer solutions are described in Chapter IX.
In their use it is essential to remember that the buffer solution
controls only the ratio1 between the concentrations of "acid"
and the "alkaline" color-forms of the indicator. Therefore the
preparation of a standard color tube to be judged by eye includes
the use of a definite concentration of indicator substance and ob-
servation through a definite depth of solution.

Suppose that the phosphate-buffers are employed in the range
pH 6.0 to pH 7.0 with the indicator brom thymol blue. If these
standards are to be used in comparison with an unknown solution
it is essential, not that any particular amount2 of indicator be
used, but that the same concentration be used in both standard
and unknown. It is furthermore essential that standard and un-
known be observed through equal depths of solution. It is then

1 If instead of the ratio for the two color forms we use the ratio of the
concentration of the alkaline color-form to the concentration of total
indicator we may call this a and use the equation

pH = pKa + log — - —

1 — OL

8 The amount becomes very important in studying poorly buffered solu-
tions. See page 190.

64 THE DETERMINATION OF HYDROGEN IONS

clear that, if standard and unknown have produced the same ratio
of the two color-forms of the indicator, the appearance of the
two tubes will match. The first approximation of the theory
concerned is that equal ratios of the two indicator forms will be
produced by solutions of the same pH value. Therefore, if the
color of the unknown match that of standard "pH 6.6" it is pre-
sumed that the pH value of the unknown is 6.6.

In case the approximate value of the unknown is undetermined
a preliminary test may be made as follows. The indicator brom
thymol blue will differentiate solutions having pH values greater
or less than 7.0. If then, a drop or two of brom thymol blue
gives a distinctly yellow color one knows that the solution has a
pH value less than about 5.6. Imagine that brom cresol green
is next tried and that there is found an intermediate color suggest-
ing to the memory pH 4.4 or 4.6. Standards for this range are
set up with phthalate buffers (table 35) or citrate buffers (table 39)
and brom cresol green. The standards are compared with the
unknown. It is remembered that equality of concentrations and
views through equal depths are essentials. Suppose color match
is not perfect at "4.4" or at "4.6" but that the unknown appears
as if it would match an intermediate between standard "4.4"
and "4.6." Unless extreme accuracy is desired 4.5 may be said
to be the value for the solution under measurement.

In case an extensive set of standards is set up it is well to
employ volumes, etc., systematically. Thus, 10 cc. of each buffer
are added seriatim to each of a set of uniform test tubes and to
each of these are added 5 drops of a stock solution of the proper
indicator. Mixing should, of course, be insured. Now when an
unknown is to be compared, 10 cc. of this solution are placed in
a tube of the same bore as those of the standards and 5 drops of
the stock indicator solution are added and mixed. Change of
stock solution is obviously inadvisable.

When one is familiar with the colors of the indicators at known
pH values, very fair estimations may be made without the aid
of the standards; but there is no way as satisfactory as the
setting up of the standards for the establishment of a correct
impression of the relations of the various indicators on the pH
scale. On the other hand; the author has discovered in his

Ill COLOR CHART 65

conversations that there are many investigators who would like
to use indicators for the occasional rough measurement of pH
but who are discouraged by a pressure of work which prevents
them from taking the time to carefully prepare the standard
solutions. To furnish such investigators with a demonstration of
the general relations of the various indicators and to furnish
rough standards the attempt has been made to reproduce the
colors in figure 17.

It must be remembered, however, that in undertaking a repro-
duction by means of the printer's art the publishers are to be
commended for their courage and are not to be held responsible
for the inadequacy of the result. Aside from the inherent dif-
ficulty in freeing a printed color from the effect of the vehicle,
there remains the utter impossibility of reproducing with paper
and ink the effect observed in a liquid solution. The funda-
mental phenomena are quantitatively very different in the two
cases. Therefore, the user of the chart of colors will have to
use discretion and some imagination. If he does not attempt
to .make the reproductions take the place of the standards he
should find them useful for class room demonstrations, for refresh-
ing the memory and for rough standards.

For class-room work it is advantageous to show the position
of the several indicators on the pH scale by cutting the chart and
relining each series so that corresponding pH values overlap.

Many users of the color chart have not only failed to note the
warning given above in previous editions of this book but have
failed to realize how the best use may be made of the chart.
By certain mechanical improvements in the art of production the
gradation of the color has been improved. This feature serves
as a very helpful guide. Too much emphasis should not be
placed upon the color quality. These brief reminders give re-
lease to the exercise of judgment which is all that the chart can aid.

In each case the colors were designed to match standards in
tubes 16 mm. internal diameter containing 10 cc. of buffer solu-
tions and the following proportions of indicators.

Thymol blue (T.B. ac) 1.0 cc. 0.04 per cent solution
Brom phenol blue (B.P.B.) 0.5 cc. 0.04 per cent solution
Brom cresol green (B.C.G.) 0.5 cc. 0.04 per cent solution

66 THE DETERMINATION OF HYDROGEN IONS

Chlor phenol red (C.P.R.) 0.5 cc. 0.04 per cent solution
Brom cresol purple (B.C.P.) 0.5 cc. 0.04 per cent solution
Brom thymol blue (B.T.B.) 0.5 cc. 0.04 per cent solution
Phenol red (P.R.) 0.5 cc. 0.02 per cent solution

Cresol red (C.R.) 0.5 cc. 0.02 per cent solution

Meta cresol purple (M.C.P.) 0.5 cc. 0.04 per cent solution
Thymol blue (T.B.) 0.5 cc. 0.04 per cent solution

CHAPTER IV

CHOICE OF INDICATOKS

We are now forced to increase the number of compounds, not merely
in order to prepare new substances, but to discover natural laws. —
R. FITTIG.

From the enormous number of colored compounds found in
nature and among the products of the laboratory many have
been called into use as acidimetric-alkalimetric indicators. Few
have been chosen. Among indicators of plant origin litmus and
alizarine are the more familiar. One indicator of animal origin,
cochineal, an extract of an insect, was formerly used to some ex-
tent. Walpole's (1913) treatment of litmus, Walbum's (1913)
study of the coloring matter of the red cabbage and some of the
more recent work, have given us some data on properties of plant
and animal pigments which are applicable to hydrogen ion deter-
minations. But for the most part indicators of natural origin
have been neglected for the study of "synthetic" compounds.

Litmus has played so important a role in acidimetry that it is
worthy of brief, special mention.

litmus is obtained by the oxidation in the presence of ammonia
of the orcin contained in lichens, generally of the species Roccella
and Lecanora. The material which comes upon the market is
frequently in the form of cubes composed of gypsum or similar
material and comparatively little of the coloring matter. The
coloring matter is a complex from which there have been isolated
many compounds, chief among which are azolitmin, erythrolitmin,
erythrolei'n and spaniolitmin. Of these the azolitmin is the
most important. Scheitz (1910) found the azolitmin of com-
merce to be of uncertain composition and it may well be so now,
for the composition of the crude material varies with the source
and with the extent of the complex action of air and alkali on the
original materials.

The following method of preparing a sensitive litmus solu-
tion is taken from Morse (1905).

68 THE DETERMINATION OF HYDROGEN IONS

The crushed commercial litmus is repeatedly extracted with fresh quan-
tities of 85 per cent alcohol for the purpose of removing a violet coloring
matter which is colored by acids but not made blue by alkalies. The resi-
due, consisting mainly of calcium carbonate, carbonates of the alkalies
and the material to be isolated, is washed with more hot alcohol upon a
filter and then digested for several hours with cold distilled water. The
filtered aqueous extract has a pure blue color and contains an excess of
alkali, a part of which is in the form of carbonate and a part in combination
with litmus. To remove the alkaline reaction the solution is heated to
the boiling point and cautiously treated with very dilute sulfuric acid
until it becomes very distinctly and permanently red. Boil till all CO2
is dispelled. Treat with a dilute solution of barium hydroxide until the
color changes to a violet. Filter, evaporate to a small volume and pre-
cipitate the litmus with strong alcohol. Wash with alcohol and dry.

Dr. P. Rupp (private communication) prefers to make a final
washing with water which removes much of the salt at the expense
of some dye.

"Synthetic" indicators have for the most part displaced those
of natural origin until litmus and alizarin, turmeric and cochineal
are becoming more and more unfamiliar in the chemical labora-
tory. Indeed Bjerrum (1914) states that the two synthetic indi-
cators, methyl red and phenolphthalein, particularly because of
the zones of hydrogen ion concentration within which they change
color, are sufficient for most titrimetric purposes.

But the two indicators mentioned above cover but a very lim-
ited range of hydrogen ion concentration so that they are insuf-
ficient for the purpose we now have under consideration. A sur-
vey of indicators suitable for hydrogen ion determinations was
opened in Nernst's laboratory in 1904 by Salessky. This survey
was extended in the same year by Friedenthal, by Fels and by
Salm and the results were summarized in Salm's famous table
(cf. Z. physik. Chem., 57, 471).

Then came the classic work of S0rensen (1909) of the Carlsberg
laboratory in Copenhagen. The array of available indicators had
become so large as to be burdensome. S0rensen in an extensive
investigation of the correspondence between colorimetric and
electrometric determinations of hydrogen ion concentrations re-
vealed discrepancies which were attributed mainly to the in-
fluence of protein and salts. He chose those indicators which
were relatively free from the so-called protein aiid salt errors,
constructed solutions of known and reproducible hydrogen ion con-

IV INDICATOR HISTORY 69

centrations and thus furnished the biochemist with selected tools
of beautiful simplicity. It is well to emphasize the labor of
elimination which S0rensen performed because without it we
might still be consulting such tables as that published by Thiel
(1911), or the ponderous table 8, pages 76-86, and be bewildered
by the very extensive array.

S0rensen's work, coupled as it was with a most important con-
tribution to en'zyme chemistry, gave great impetus to the use of
indicators in biochemistry. His selection was, therefore, soon
enlarged by additions of new indicators which fulfilled the criteria
of reliability which he had laid down. Alpha naphthol phthalein,
a compound first synthesized by Grabowski (1871), was shown by
S0rensen and Palitzsch (1910) to have a range of pH 7-9 and was
found useful in biological fluids. Methyl red (Rupp and Loose,
1908) was given its very useful place by the investigations of
Palitzsch (1911). Henderson and Forbes (1910) introduced 2-5
dinitrohydroquinone as an indicator possessing several steps of
color change and therefore useful over a wide range of pH.
Walpole (1914) called attention to several indicators of potential
value. Hottinger (1914) recommended "lacmosol," a constituent
of lacmoid, and Bogert and Scatchard (1916) advocated the use
of dinitrobenzoylene urea.

Lund (1927) and Kolthoff (1927) report some data obtained
with certain very interesting indicators of the triphenyl methane
series. These indicators are colored in acid solution and color-
less in alkaline solution. They are numbers 99a, 99b and 102a
of table 8. No. 102a is described as requiring a time interval for
the color change. The others are described as useful for a variety
of purposes. Their unique color changes should be of service
in some cases.

Additions continue to be made every little while; sometimes
with accompanying data of value to our subject. Only the cases
for which pH measurements of some kind are available can be
included in the following tables. For this reason the tables do
not include those vast arrays of material waiting to be explored.

In 1915 Levy, Rowntree and Marriott, without applying the
tests of reliability which S0rensen had employed, used phenol
sulphonphthalein in determining the pH of the dialyzate of
blood. This compound, first synthesized in Remsen's laboratory

70 THE DETERMINATION OF HYDROGEN IONS

by Sohon (1898), received considerable attention from Acree and
his co-workers because it furnished excellent material for the
quinone-phenolate theory of indicators. To further such studies
Acree and White had synthesized new derivatives of phenol
sulphonphthalein at the time when the work of Levy, Rowntree
and Marriott attracted the attention of Clark and Lubs. The
latter were looking for more brilliant indicators for use in bacterial
culture media and were attracted by the well known brilliance
of phenol sulphonphthalein. Through the courtesy of Professor
Acree some of the derivatives which White had prepared were
obtained. Many new homologs were synthesized by Lubs.
There was then undertaken an extensive study of the applica-
bility of these and numerous other indicators to the study of
biological fluids and of bacterial culture media in particular. See
Clark and Lubs (1916-1917). They finally selected a series of
indicators which, for the most part, was made up of sulfon-
phthaleins. Two azo compounds were included, methyl red
(cf. Palitzsch, 1911) and propyl red (Clark and Lubs, 1915).
Propyl red precipitates too easily from buffer solutions and was
soon discarded. Methyl red continued in the series until the
work of Cohen (1922) [see especially Cohen's paper of 1927] made
available several new sulfonphthaleins.

In the course of their investigations Clark and Lubs resurrected
ortho cresol phthalein (Baeyer and Fraude, 1880), found it quite
as reliable as phenolphthalein and more brilliant with a color
better adapted to titrations in artificial light.

In spite of the fact that S0rensen rejected the greater number
of the indicators which he studied and that Clark and Lubs, after
a resurvey of the subject and the preparation of many new com-
pounds, listed but few indicators as reliable, there has recently
appeared a tendency to resurrect the rejects. Many of these
are useful in special cases and undoubtedly there is an occasional
individual to be found in the lists which has been insufficiently
studied and unjustly rejected. Nevertheless, the indiscriminate
use of miscellaneous indicators may lead to gross errors or at
least to such a diversity of data that their correlation will become
complex during the coming period when the specific salt-effects
and general conduct of the individual indicators are still being
determined.

IV SELECTED INDICATORS 71

It is, therefore, advisable to use the more thoroughly studied
indicators. Three lists of these are given (tables 10, 11, and 12).
The indicators therein listed should suffice for all ordinary needs.
S0rensen's list is given in table 10 and to this are appended S0ren-
sen's comments. For general purposes the indicators named
in table 11 will be found the most satisfactory especially because
of their brilliancy. Each of these, however, has its own special
limitations as every indicator has. For the study of colorless
solutions where salt errors are to be reduced the nitrophenols
listed in table 12 should be valuable.

In table 8 are a few indicators which are undoubtedly reliable
but little used, a few which are definitely unreliable though often
used, and very many of uncertain character and for the most part
bearing the stamp of disapproval by competent judges. Since
the indicators in tables 10, 11 and 12 cover all ordinary require-
ments it seems hardly worth while to venture upon an analysis
of table 8 except to note by a star one or another compound
which seems promising or has received more or less careful study.

TYPE STRUCTURES

Since it is impractical to give structural formulas for all the
indicators of the general list (table 8), a few typical structures
will be given as guides. The grouping in table 7 is that of table 8
and the numbers are the index numbers of table 8.

COMMENTS ON THE GENERAL LIST

Table 8 is taken from International Critical Tables, Clark (1926) .
A few additions have been made. The lists on which it is based
were originally compiled with the aid of Dr. Barnett Cohen and
Dr. Elias Elvove with several purposes in view. In the first
place there exist in the older literature a great many observations
recorded in terms of the color of a given indicator. These data
can often be translated into modern terms if the pH range of the
given indicator is known. In the second place there are circum-
stances when, for one reason or another, it becomes necessary
to draw upon the list of miscellany. It should therefore be avail-
able. Lastly, and perhaps most important, our review of the
literature and of indicator labeling has shown that there is great
confusion; and an initial step in the clarification of the subject

TABLE 7
Type structures shown by examples

EXAMPLES

GE NERAL STRUCTURE

Nitro group

12.

p-Nitro phenol

HO^ ^>NO2

16.

Nitramine ;
2,4, 6-trinitrophenyl-
methyl-nitroamine

O,N<^ ^>N( J

Mono-azo group

44. Methyl orange;

p-benzenesulfonic acid-
azo-dimethylaniline

59. Methyl red;

o-carboxybenzene-azo-
dimethylaniline

<( )>-N=N-<( ^>
C02H

Dis-azo-group

87. Congo red;

Diphenyl-disazo-bis-o:-
naphthylamine-4-sul-
fonic acid

-<^ ^>N=

Triphenylmethane group

97. Methyl violet 6B (penta-
methyl constituent)

TABLE 7— Continued

GENERAL STRUCTURE

Phthalein group

120. Phenol phthalein;

dihydroxyphthalophenone

•o

Sulfonphthalein group

142. Phenol red

Quinoline group

151. Quinoline blue;

1 , 1 '-di-iso-amyl-4, 4'-
quinocyanine iodide

-N =C- N—

Indophenol group

152. Indophenol;

Benzenone-indo-phenol

Azine group

158. Neutral red;

Amino-dimethylamino-
toluphenazonium
chloride

H3C

N(CH3)2C1

Oxaiiine group

160. Alizarine green B;

Dihydroxy-dinaphthaz-
oxonium sulfonate

THE DETERMINATION OF HYDROGEN IONS
TABLE 7— Concluded

GENERAL STRUCTURES

Anthraquinone group

H OH

166. Alizarin;

/v Y>H

1 , 2-dihydroxy-anthra-

quinone ;

SA A/

Indigo group

168. Indigo carmine;
Indigotin-5,5' disulfonic

C
HOsS^V \

/C\/\SO,H

acid

U\ /c~c"

\ / V

N
H

will be taken if there is available a tabulation of existing data to
serve as a basis for revision.

In examining a large collection of indicators the labeling was
found to be insufficient in a large percentage of cases. On study-
ing the literature we find evidence that others have encountered
the same difficulty without stating so, for in many instances the
indicator names given were evidently provided by one or another
dealer who cared so little for the scientific uses of his commodity
that he left from the label the designation essential to its identifica-
tion. This habit had become more or less prevalent. In some
instances our own uncertainty may be due to an arbitrary ad-
herence to the nomenclature found in various editions of Schultz.
For instance when we see the indicator croce'ine listed and refer
to Schultz (1914) we find four croce'ines with various distinguish-
ing marks and seven other compounds for the names of which
"croce'ine" is used in one or another combination. Eut Schultz
lists no croce'ine. We are not helped in going back to the lists
of Schultz and Julius (1902). Now we might assume that

IV INDICATOR LABELING 75

"croceme" was used in Salm's table as a term having a definite
meaning outside the dye industry. On this principle we should
find that "helianthine" has been employed in accordance with
scientific usage. However we find that an old sample of helian-
thine from Salm's dealer is not the helianthine of methyl orange
but corresponds in pH-range to Salm's Helianthine I, which,
together with Salm's Helianthine II we have not identified.

There are other difficulties such as are illustrated by the case
of Tropaeolin OOO No. 1 and Tropaeolin 000 No. 2. No. 1 is
prepared from p-sulfanilic acid and a-naphthol. No. 2 is prepared
from p-sulfanilic acid and (3-naphthol. In this there is agreement
by Schultz and Julius 1902, Green 1904 and Beilstein (third edition).
In accord with this, S0rensen describes his a-naphthol prepara-
tion as Tropaeolin 000 No. 1. In the second edition of Indi-
cators and Test Papers, Cohn (1914) has given synonyms for the
a and 0 compounds which agree with Green, but has reversed
the No. 1 and No. 2 at the headings of his descriptions and uses
"No. 1" and "No. 2" inconsistently in the text, Prideaux (1917)
has called the /3 compound Tropaeolin 000 and gives the range
as 7.6-8.9, which looks suspiciously like S0rensen's 7.6-8.9 for
the a compound. Prideaux uses the synonym Orange II for the
j8 compound in harmony with Green; but on the next page de-
scribes the a compound as Orange II. The identity of Salm's
Tropaeolin 000 is not clear. It was evidently different from
the Tropaeolin 000 No. 1 used by S0rensen. We find that an
old sample with the label "Tropaeolin 000" agrees with neither
S0rensen's nor Salm's data.

Many other instances might be cited to show the confused
state of the subject. Because it is serious the reader will have to
use the following tables with caution, and he need not be sur-
prised if a sample of indicator which he tests does not give a
pH range corresponding to that recorded. Since the publication
of the list in the second edition only one person has called our
attention to a correction. In this case the information was oral
and unverified and hence is not applied. Established corrections
will be welcome.

TABLE 8

General list of indicators
After Clark (1926)

The following list of indicators includes all those for which data on the
pH-ranges have been found. Many of the data of this table are to be
regarded with caution, because in some cases the names proposed are
inadequate for complete ^identification, and in other cases names have
been given to materials of uncertain composition.

The Schultz (S ) and Rowe (R....) numbers are taken from the

1923 and 1924 editions, respectively, of these works. Delicate shades of
meaning in the color nomenclature have been avoided, as data regarding
the purity of the compounds have often been lacking. The abbreviations
used are as follows: b, blue; br, brown; c, colorless; f, fades; fl, fluorescent;
g, green; o, orange; p, pink; pu, purple; r, red; v, violet; y, yellow. pK
is the pH at which there is an apparent half-transformation of the indicator.
* indicates that the indicator has been studied in sufficient detail to be
used in supplementing the lists of tables 10, 11 and 12.

INDEX

NUM-
BER

INDICATOR

COLOR AND USEFUL
RANGE pH

LITERATURE

Nitro compounds

2,4,6-trinitrophenol; Picric acid
[S 5; R 7]

c 0 0- 1 3 y

C15 21)

2
3

2,6-dinitrophenol [Michaelis' ft] . .
2,4-dinitro-a-naphthol; Man-
chester vellow [S. 6; R. 9] ...

c 2.0- 4.0y
v 2 0- 4 0 v

(15, 20, 21)
(3a)

2, 4-dinitrophenol [Michaelis' a] ...
4,6-dinitroguaiacol

c 2.6-4.4y
pK = 3 4

(17, 20, 21)
(10 17)

Dinitrohydroquinol

3-10

m26)

Nitrohydroquinol

3-11

(26)

3,5-dinitrocatechol .. . .

[ pKi = 3.25

L (17)

7
8
8a

2,3-dinitrophenol [Michaelis' «]...
2,5-dinitrophenol [Michaelis' 7]...
2 , 4-dinitroresorcinol

\ pK2 = 10.39
c 3.9- 5.9 y
c 4.0- 5.8y
pK = 4 22

(15, 20, 21)
(15, 20, 21)

(17)

2,6-dinitro-4-aminophenol; Iso-
picramic acid

p 4 1- 5 6 v

(36)

10
11

3, 4-dinitrophenol [Michaelis' 5]...
4-nitro-6-aminoguaiacol

c 4.3- 6.3y
y 4.5- 8.0 r

(20, 21)
(18)

p-nitrophenol

c 5.6-7.6y

(15, 20, 21, 32)

o-nitrophenol ... . ...

c 5 0- 7 0 y

(26)

13a

2-nitroresorcinol

pK2 = 6.47

(17)

*Dinitrobenzoylene urea

c 6.0- 8.0 y

(2, 10)

m-nitrophenol

c 6 8- 8 6 y

(15, 20, 21)

2,4, 6-trinitrophenyl-methyl-
nitroamine ; Nitramine ....

c 10.8-13 0 br

(15)

sym.-trinitrobenzene

c 12.0-14.0o;f

(10, 29)

2, 4, 6- trinitrotoluene

p 11.5-14.0 o

(3a)

IV INDICATOR LIST 77
TABLE 8— Continued

INDEX

NUM-
BER

INDICATOR

COLOR AND USEFUL
RANGE pH

LITERATURE

Mono-azo compounds

19
20

22
23

24
25

26
27

28
29

30
31
32
33

34
35

37
38
39

p-toluene-azo-phenyl-aniline . . .

1.0-2.0
r 1.0- 3.0 y

1.1- 1.9
p 1.2-2.1y

r 1.2-2.3y
v 1.4^2.6o

r 1.4r-2.6y
1.4-2.9

1.6-2.6
1.6-2.8

1.9-2.9
y 1.9- 3.3y
r 1.9-3.3y
r 1.9- 3.3y

r 2.0- 4.0y
p 2.3- 3.3 y

r 2.6- 4.0y

r 2.6- 4.6y
r 2.9- 4.0 y
r 2.9- 5.8y
mid-point 2. 9

(31, 32)
(3, 33)

(31, 32)
(32)

(32)
(31, 32)

(32, 33)
(31, 32)

(31, 32)
(31, 32)

(31, 32)
(31, 32, 33)
(31, 32, 33)
(32, 33)

(3b)
(32)

(32, 33)

(3a)
(32, 33)
(34)
(33)

p-carboxybenzene-azo-dimethyl-
aniline; Para methyl red

p-toluene-azo-phenyl-a-naph-
thylamine

Benzene-azo-diphenylamine
m-benzenesulfonic acid-azo-
diphenylamine ; Metanil yellow
[S. 134; R. 138J

Benzene-azo-phenyl-a-naphthyl-
amine

p-benzenesulfonic acid-azo-di-
phenylamine; Tropaeolin OO
[S. 139; R. 143]

o-tuluene-azo-o-toluidine ; Spirit
yellow R [S. 68; R 17]

p-toluene-azo-benzyl-o!-naphthyl-
amine

p-toluene-azo-benzyl-aniline

Benzene-azo-benzyl-a-naphthyl-
amine

Benzene-azo-aniline; amino-azo-
benzene [S. 31 ; R. 15]
p-benzenesulfonic aeid-azo-ani-
line

p-benzenesulfonic acid-azo-ben-
zylaniline - .

m-carboxybenzene-azo-dimethyl-
aniline

Benzene-azo-benzylaniline
p-benzenesulfonic acid-azo-m-
chlorodiethylaniline

m-nitrobenzene-azo-^-naphthol-
3,6-disulfonic acid; Orange III
[S. 47; R. 39] . .

Benzene-azo-dimethylaniline ;
Topfer's indicator [S. 32; R. 19].
o-carboxybenzene-azo-a-naph-
thylamine

p-benzenesulfonic acid-azo-o-
toluidine

THE DETERMINATION OF HYDROGEN IONS

TABLE 8— Continued

INDEX

NUM-
BEB

INDICATOR

COLOR AND USEFUL
RANGE pH

LITERATURE

Mono-azo compounds — Continued

p-benzenesulfonic acid-azo-m-
xylidine

mid-point 2 9

(33)

o-carboxybenzene-azo-diphenyl-
amine

p 3 0- 4 6 y

(3b)

42
43

p-benzenesulfonic acid-azo-
methylaniline
p-benzenesulfonic acid-azo-ethyl
aniline

r 3.1- 4.2y
r 3 1- 4 4 y

(31, 32, 33)
(31 32 33)

p-benzenesulfonic acid-azo-di-
methylaniline ; Methyl orange
[S. 138; R. 142]

r 3 1- 4 4 y

(32, 33)

45
46

p-benzenesulfonic acid-azo-di-
ethylaniline ; Ethyl orange
o-benzenesulfonic acid-azo-
dimethylaniline

r 3.5- 4.5y
mid-point 3.5

(31, 32, 33)

(33)

p-benzenesulfonic acid-azo-m-
toluidine

mid-point 3.5

(33)

p-benzenesulfonic acid-azo-p-
xylidine

mid-point 3 6

(33)

49
50

* p-sulfo-o-methoxybenzene-azo-
dimethyl-a-naphthylamine
p-benzenesulfonic acid-azo-a-
naphthylamine

b 3.5- 4.9 o
r 3.5- 5.7 y

(23)
(32, 34)

p-benzenesulfonic acid-azo-
phenyl-«-naphthylaniine

v 3.5- 6.5 o

(34)

o-carboxybenzene-azo-phenyl-a-
naphthylamine

v 3.5- 6.5 o

(34)

53
54
55

Benzene-azo-a-naphthylamine ....
p-toluene-azo-a-naphthylamine. . .
o-carboxybenzene-azo-methyl-
aniline

r 3.7- 5.0 y
3.7- 5.0

r 4.0- 6.0 y

(32, 34)
(31, 32)

(3b)

56
57

Benzene-azo-m-phenylenedi-
amine ; Chrysoidine [S. 33 ; R. 20] .
o-carboxybenzene-azo-ethylani-
line

o 4.0- 7.0 y
r 4 2- 6 2 y

(3a)
(3b)

58
59
60

o-carboxybenzene-azo-n-propyl-
aniline
o-carboxybenzene-azo-dimethyl-
aniline; Methyl red [R. 211]. . . .
o-carboxybenzene-azo-diethyl-
aniline ; Ethyl red

r 4.2- 6.2y
r 4.2- 6.3y
r 4.4- 6.2y

(3b)
(4, 32, 33)
(3b, 33)

INDICATOR LIST

TABLE 8— Continued

INDEX
NUM-
BER

COLOR AND USEFUL
RANGE pH

LITERAtCRE

Mono-azo compounds — Continued

* o-carboxybenzene-azo-di-n-
propylaniline ; Propyl red.. ..

r 4 6- 6 6 y

(3b)

o-carboxybenzene-azo-m-
phenylenediamine

o 4 fr- 7 6 y

(3a)

Benzene-azo-dimethyl-a-naph-
thvlamine

48-55

(31 32)

p-benzenesulfonic acid-azo-di-
methyl-a-naphthylamine

r 5 0-5 7 o

(31, 32, 34)

o-carboxybenzene-azo-a-
naphthlyamine

p 5 6- 7 0 y

(3b)

o-carboxybenzene-azo-(di or
mono?)-amyl aniline

o 5 6- 7 6 y

(3b)

o-carboxybenzene-azo-dimethyl-
a-naphthylamine

r 5 6- 7 6 o

(4 34)

4-sulfo-a-naphthalene-azo-o:-naph-
thol; Naphthylamine brown [S.
160; R. 175]

o 6 0- 8 4 p

(3a)

Tropaeolin?

y 7 0- 9 o r

(29)
^)

6-sulfo-a-naphthol-l-azo-m-
hydroxybenzoic acid

f o 7.0- 8. Ob
\ v 12 -13 r

| (36)

Curcumine?

y 7 4- 8 6 b

(15)

p-benzenesulfonic acid-azo-a-
naphthol; Tropaeolin OOO No. 1
[S. 144; R. 150]

y 7 &- 8 9 p

(32)

p-benzenesulfonic acid-azo-/9-
naphthol; Tropaeolin OOO No. 2
IS. 145; R. 151]

76-8 9(?)

(25)

m-nitrobenzene-azo-salicylic acid ;
Alizarin yellow GG [S. 48; R.
36]

c(?) 10 0-12 0 y

(20, 21)

75
76

p-nitrobenzene-azo-salicylic acid ;
Alizarin yellow R [S. 58; R. 40].
a-naphthylaminosulfonicacid-azo-
0-naphthol;RedI[S. 161; R. 176].
a-naphthalene-azo-/8-naphthol-
3,6-disulfonic acid; Bordeaux
B [S. 112; R. 88]

y 10.0-12.1 y
10.5-12.1

p 10.5-12 5 o

(32)
(31, 32)

(3a)

77a

Isonitrosoacetyl-p-amino-azo-
benzene

see p 583

(24)

p-benzenesulfonic acid-azo-re-
sorcinol; Tropaeolin O [S. 143;
R. 148]

y 11 1-12 7 o

(32)

THE DETERMINATION OF HYDROGEN IONS

TABLE 8— Continued

INDEX
NUM-
BER

COLOR AND USEFUL
RANGE pH

Mono-azo compounds — Continued

Benzene-azo-/?-naphthol-6, 8-di-
sulfonic acid; Orange GG (S.
38; R. 27]

y 11 5-14 0 p

(3a)

Crocein?

p 12 0-14 0 v

C291

80a

Isonitroso-p-toluazo-p-
toluidine

see p 583

(24)

Helianthin (Griibler)?

o 11 0-12 0 r

(3a)

Helianthin 1?

o 11 0-13 0 r

(29)

Helianthin II?

y 13 0-14 0 v

(29)

Curcumein?

f o 0.0- 1.0 y

J (29)

| yl3.0-15.0g

Dis-azo compounds

85
86
87
88

Ditolyl-disazo-bis-/3-naphthyl-
amine-6-sulfonic acid; Benzo-
purpurin B [S. 365; R. 450]
Ditolyl-disazo-bis-a-naphthyl-
amine-4-sulfonic acid; Benzo-
purpurin 4B [S. 363; R. 448]. . . .
Diphenyl-disazo-bis-a-naphthy!-
amine-4-sulfonic acid; Congo red
[S. 307; R 370] . . .

[ b 0.3- 1.0 v
v 1.0- 5.0 y
[ y 12. 0-14. Or

v 1.3- 4. Or
b 3.0- 5. Or

v 10. 5-11. 5 p
f mid-point 7. 3
\ mid-point 7. 6

(29)

(15)
(29)

(3a)
(28)
(9)

Ditolyl-disazo-bis-a-naphthol-4-
sulfonic acid; Azo blue [S. 377;
R. 463]

CurcuminW [probably Rowe, 364].

Triphenylmethane derivatives

90
91

92
93

Methylated pararosaniline ; Crys-
tal violet [S. 516; R. 681]
p, p'-tetramethyldiamino-tri-
phenylcarbinol; Malachite green
[S 495- R 657]

g 0.0- 2. Ob

I y 0.0-2.0g
b 11. 5-14. Of

g 0.0- 2. Ob
y 0.0-2.6g

(3a)
(29)

(3a)
(3a)

Hofmann's violet; methylated
rosanilines and pararosanilines
[S 514* R 679]

Tetraethyl-diamino-triphenyl-
carbinol; Brilliant green [S. 499;
R 662]

IV INDICATOR LIST 81
TABLE 8— Continued

INDEX

NUM-
BER

INDICATOR

COLOR AND USEFUL
RANGE pH

LITERATURE

Triphenylmethane derivatives—Continued

94
95
96
97

98
99

99a
99b
100

101
102

102a
103
104
105

106
107

Heptamethylrosaniline; Iodine
green [R 686]

y 0.0-2.6b
y 0.0- 3.6b
y 0.3-2. Ob

yO.15- 3.2 v
0.4-2.7

pu 1.2- 3. Of
v 1.2- 3.2c
p 2.6- 4.6c

p 3.6- 6.0 c
o 3.8- 6.5 v

b 4.7-7.0c
r 5.0-7.0c
br 6.9- 8. Or
v 9.4r-14.0 p

b 10. 0-13. Op
b 11. 0-13. Or

r 12. 0-14. Of

(3a)
(3a)
(15)

(32)
(31, 32)

(3a)
(16)
(16)

(3a)
(15)

(3ft)

(16)
(32)
(3a)

(3a)
(3a)

(29)

Hexaethylpararosaniline; Ethyl
violet [S. 518; R. 682]
Ethyl-hexamethyl-pararosaniline;
Ethyl green [R 685]

Methyl violet 6B; benzylated
tetra- and pentamethyl-para-
rosaniline [S. 517; R. 683]

Gentian violet; mixture

Aniline red; rosaniline and para-
rosaniline [S. 512; R. 677]
2,4,2',4',2"-pentamethoxytri-
phenylcarbinol

2,4,2',4',2",4"-hexamethoxytri-
phenylcarbinol

Red violet 5RS; di- and tri-sul-
fonate of ethylrosaniline [S. 525;
R. 693]

Resazurin [R. 727 note] .

China blue [S. 539; R. 707]; mix-
ture

2,4,6,2',4',2",4"-heptamethoxy-
triphenyl carbinol

Rosolic acid [S. 555; R. 724]; mix-
ture

Alkali blue 4B [S. 536; R. 704];
mixture ...

XL soluble blue [S. 538; R. 706];
mixture

Poirrier's blue

Acid fuchsin; di- and tri-sulfonic
acids of rosaniline and para-
rosaniline [S 524; R 692]

Phthaleins and related compounds (see also Thiel and Diehl, 1927)

108

Diethyl-m-amino-phenolphtha-
lein; Rhodamine B [S. 573; R.
749]

o 0.1- 1.2 p

(3a)

109

Pyrogallol-phthalein; Galle'in [S.
599; R. 781] ...

variable 0—14

(29)

THE DETERMINATION OF HYDROGEN lONg

TABLE 8— Continued

INDEX

NUM-
BER

INDICATOR

COLOR AND USEFUL
RANGE pH

LITERATURE

Phthaleins and related compounds — Continued

110
111

112
113

114
115
116
117
118
119
120
120a

121
121a
122
123

124

125
126

Tetrabromofluorescein; Eosine
Y S [S. 587; R. 768]

y 0 -3.0fl

o 0.0- 3.6fl
p 1.4r- 3.6r

y 3.6- 5.6fl
y 4.0- 6.6fl
y 8.9-9.5g(f)
y 7.0- 9. Ob
c 8.0-9.0v
c 8.5- 9.0 pu
c 8.2- 9.8r
c 8. 3-10. Or

c 8.4r- 8.8b
c 8. 9-10. 2 b
c 9. 2-10. Ob
c 9.3-10.5b(f)

p 10. 5-14. Oy
c 8.4r-10.0v

c 8.6- 9.8 v
c 9.0-lO.Ov

(3a)

(3a)
(3a)

(3a)
(3a)
(8)
(32)
(25)
(1, 14)
(3b)
(20, 21, 32)

(7)
(8)
(7)
(32)

(3a)
(12)

(12)
(12)

Erythrosin (iodeosin); di- or
tetra fluorescein [S. 591, 592?
R. 772, 773?]

Phloxin red B.H. (Griibler)?

Dihydroxyfluoran; Uranin (fluo-
rescein) [S. 585; R. 766]

Dichlorofluorescein

o-a-naphthol phthalein .

p-a-naphthol phthalein

Tetrabromophenol phthalein
o-cresoltetrachlorophthalein
o-cresolphthalein

Phenolphthalein [R. 764]

Dibromothymoltetrachloro-
phthalein

* 1,2,3-xylenolphthalein

Thymol tetrachlorophthalein

Thymolphthalein

Dibromo-dinitrofluorescein; Eosin
BN [S. 590; R. 771]

R= SCH3 ^^ /<CZy>OH
R=SC4HJ/N \ [\^ ^>OH
R=SC6H60 = C— 0 R

Sulfonphthaleins

127

Catecholsulf onphthalein

f p. 0.2- 0.8o
\ y 4.0- 7.0 g

[ (22)

128

m-cresolsulfonphthalein; Meta-
cresol purple

v 8.5-10.2 b

f r 1.2- 2. 8 y
1 y 7.4-9.0pu

} (5)

129

Thymolsulf onphthalein ; Thymol
blue

f r 1.2- 2. 8 y
\ y 8.0- 9 6b

} (3b).

130
131

Tetranitrophenolsulf onphthalein.
Tetrabromophenolsulf onphtha-
lein; Bromphenol blue

y 2.8- 3.8r
y 3 0- 4 6 b

(3b)
(3b)

132

* Tetrachlorophenolsulfonphtha-
lein

y 3 0- 4 6 b

(3b)

INDICATOR LIST

TABLE 8— Continued

INDEX
NUM-
BER

INDICATOR

COLOR AND USEFUL
RANGE pH

LITERATURE

Sulfonphthaleins — Continued

133

* Dichloro-dibromo-phenol-sul-
f onphthalein; Brom-chlorphenol
blue

y 3 0- 4.6 b

(5)

134
134a

Tetrabromo-m-cresolsulfon-
phthalein; Bromcresol green —
Tetrachloro-m-cresolsulfon-
phthalein . .

y 3.8- 5.4b
y 4 0- 5 6 b

(5)
(5)

135
136

Dichlorophenolsulf onphthalein ;
Chlorphenol red
Dibromo-o-cresolsulf onphthalein;
Bromcresol purple

y 4.8- 6.4 r
y 52-68 pu

(5)
(3b)

137

138
139

Dibromophenolsulf onphthalein ;
Bromphenol red
* Diiodophenolsulf onphthalein . . .
Dibromothymolsulf onphthalein ;
Bromthymol blue

y 5.2- 6.8r
y 5.7- 7.3 pu

y 6 0- 7 6 b

(5)
(3a)

(3b)

140

* Brom xylenol blue, dibrom-
inated No 145

y 6 0- 7 6 b

(5)

141
142

Phenol-nitrosulf onphthalein
Phenolsulf onphthalein; Phenol
red

y 6.6 8.4pu

y 6 8- 8.4 r

(3b)
(3b)

143

144

o-cresolsulf onphthalein; Cresol red
Salicylsulf onphthalein

y 7.2- 8.8r
y 7.2- 9.2 p

(3b)
(3a)

145

* 1.4-dimethyl-5-hydroxyben-
zenesulf onphthalein; Xylenol
blue

y 8.0- 9.6 b

(4)

146

a-naphtholsulf onphthalein

y 7 5- 9.0 b

(3b)

147

Carvacrolsulf onphthalein

y 7.8- 9.6 b

(3b)

148

Orcinsulfonphthalein .

y 8.6-lO.Ofl

(3b)

149

Nitro-thymolsulf onphthalein

v 9. 2-11. 5 y

(3b)

Quinoline compounds

150

a- (p-dimethylaminophenylethyl-

ene)-quinoline ethiodide; Quin-

aldine red. Eastman Kodak

Co. No. 1361

C, 1.0-2.0 r

' (18)

150a

Pinacyanol [R. 808]

pK = 3.7

(10, 18)

150b

Ortho-chrom-T [R 807]

pK = 6 7

(10, 18)

151

Quinoline blue (cyanin); 1,1'

di-iso-amyl-4, 4'-quinocyanine

iodide IS. 611; R. 806]

c 7.0- 8.0 v

(31, 32)

THE DETERMINATION OF HYDROGEN IONS

TABLE &— Continued

Index no. 152 Indophenols (6)

Color changes: from brownish or clear red in acid to deep blue in alkali.
All indophenols are somewhat unstable

5' 6' 56

HO/ ^N = <T I^> = 0
\ / \ /

3' 2' 32

Indophenol

SUBSTITUENT8

2,6,3' tribromo- 5.1

2,6-dibromo-3'-chloro- 5.4

2,6-dibromo-3'-methyl- 5.4

2,6-dichloro-3'-chloro- 5.8

2, 6-dichloro-3'-methyl- 5.5

2,6-dibromo-3/-methoxy- 5.6

2,6-dichloro- 5.7

2,6-dibromo- 5.7

2, 6-dibromo-2 '-methyl- 5.9

2, 6-dibromo-2'-bromo- 6.3

2-chloro- 7.0

2-bromo- 7.1

3-bromo- 7.8

Indophenol 8.1

2-methyl- 8.4

3-methyl- 8.6

2-methoxy- 8.7

2-isopropyl-5-methyl- 8.8

2-methyl-5-isopropyl 8.9

5' 6'

3' 2'

Orthoindophenol

SUBSTITUENTS

3' bromo-

Orthoindophenol .
2'-methyl-

7.1
8.4
8.8

INDICATOR LIST

TABLE 8— Continued

H03S 5 6

H0<^ ~^>N = \ / = 0

/ S 3 2

Indonaphthol-3'-sulfonic acid

8UBSTITUENT8

2,6di
Indon
2-metl

chloro-

6.1

8.7
9.0

aphthol-3'-sulfonic acid

tivl-

INDEX
NUM-
BER

INDICATOR

COLOR AND USEFUL
RANGE pH

LITERATURE

Azines

153
154

155
156

157

158

159

Safranine (which?) ....

b-0.3- l.Or

pu 0.0- 1.2 v
0.1- 2.9

p 3.0- 4. On
b 5.6- 7.0 v

r 6.8- 8.0y
9.3-10.2

(29)

(3a)
(32)

(29)
(3a)

(32)
(31, 32)

Amino-dimethylamino-phenyl-
diphenazonium chloride; Meth-
ylene violet B.N. [S. 680; R.
842]

Amino-phenylamino-p-tolyl-ditol-
azonium sulphate; Mauve [S.
688; R. 846]...:

Magdala red; mixture amino- and
diamino-naphthyl-dinaphth-
azonium chlorides [S. 694; R. 857]
Induline, spirit soluble [S. 697;
R. 860]; mixture
Amino-dimethylamino-toluphen-
azonium chloride; Neutral red
[S. 670; R. 825]

Dimethylamino-phenyl-naphtho-
phenazonium chloride; Neutral
blue [S. 676; R. 832] . .

Oxazine compounds

160

Dihydroxy-dinaphthazoxonium
sulfonate; Alizarin green B [S.
657; R 918]

f v-0.3- 1.0 p
\ y 12 0-14 0 br

N 9

| (33)

161
162

Diethylamino-benzylamino-
naphtho-phenazoxonium chlo-
ride; Nile blue 2B [S. 654; R. 914].
Diethylamino-aminonaphtho-
phenazoxonium sulfate ; Nile
blue A [S. 653; R. 913]. .........

b 7.2- 8. 6 p.
b 10. 2-13. Op

(3a)
(3a)

THE DETERMINATION OF HYDROGEN IONS

TABLE 8— Continued

INDEX

NUM-
BEK

INDICATOR

COLOR AND USEFUL
RANGE pH

LITERATURE

Anthraquinones

163

164
165
166
167

1 , 2-dihy droxy-anthraquinone-0-
quinoline; Alizarin blue ABI
[S. 803; R. 1066]

[ p 0.0- 1.6y

1 y 6.0- 7. 6 g
f y 0.0- 4.0 o
\ o 4.0- 8. Op

y 3.7-4.2p
f y 5.5- 6.8r
1 vlO.l-12.lpu
various 6-14

[ (3a)
} (3a)

(36)
} (.31,32)
(25)

1,2, 4-trihydroxy-anthraquinone ;
Purpurin [S. 783; R. 1037]

Alizarin sulfonic acid; Alizarin
red S [S. 780; R 1034]

1 , 2-dihy droxy-anthraquinone ;
Alizarin [S. 778; R. 1027]

Alizarin blue S

Indigos

168

Indigo disulf onate ; Indigo carmine
[S. 877; R. 1180] ..

b 11. 6-14. Oy

(3a)

Miscellaneous and natural indicators

169
170

171
171a

172

173

174

175
176
177
178
179
180
181,

182
183

184
185

Echtrot?....

y 0 - l.Or
various 0-14
r 2.4r4.5g
various 2-11

c 2.7- 3.7 pu

o 2.8- 3.9 y
( y 3.0- 6. Or
\ rlO.O-13.0c
r 4.4- 5.5b
r 4.4- 6.2 b
r 4.5- 8.3b
y 4.8- 6.2 v
p 5.6-7.6v
c 6.0- 8.0 p

y 7.3-8.7g
7.7-9.6

y 7.8- 9.2br

8.3-10.0
y 8.5-9.8g

(29)
(25)
(35)
(19)

(36)

(36)
} (25)

(13)
(31, 32)
(31, 32)
(31, 32)
(3a)
(3a)

(36)

(32)

(15)

(31, 32)
(31, 32)

Logwood [S. 938; R. 1246]

* Red cabbage extract

Blue cabbage extract

1-oxynaphtho-quinomethane ;
Nierenstein's indicator
Troger and Hille's indicator,
CuHisNiSOsH

Phenacetolin

Lacmosol

Lacmoid [R. 908 note]

Azolitmin (litmus) [R 1242]

Cochineal [S. 932; R. 1239]
Archil (orchil) [S. 934; R. 1242]...
Brazilein [S. 935; R. 1243]

Di-o-hydroxy-styryl ketone ;
Lygosine

Mimosa flower extract

Turmeric (curcuma) [S. 927; R.
1238]

Alkannin [R. 1240, note] cf.
alizarin

a-naphtholbenzein

IV INDICATOR NAMES 87

TABLE 8— Concluded

(1) Arnold (1924). (18) McClendon (1924).

(2) Bogert and Scatchard (1916). (19) Milobedzki and Jajte (1926).
(3a) Clark, Cohen and Elvove (see (20) Michaelis and Gyemant (1920).

text, page 71). (21) Michaelis and Kr tiger (1921).

(3b) Clark and Lubs (1915-1917). (22) Moir (1920).

(4) Cohen, A. (1923). (23) Moir (1923).

(5) Cohen, B. (1927). (24) Naegeli (1926).

(6) Cohen, Gibbs and Clark (1924). (25) Prideaux (1917).

(7) Cornwell and Esselstyn (1927). (26) Prideaux (1924).

(8) Csanyi (1921). (27) Rowe (1924).

(9) Fels (1904). (28) Salessky (1904).

(10) Hegge (1925). (29) Salm (1906).

(11) Henderson and Forbes (1910). (30) Schultz (1923).

(12) Holt and Reid (1924). (31) S0rensen (1909).

(13) Hottinger (1914). (32) S0rensen (1912).

(14) Hundley and McClendon (33) Thiel Dassler. and Wiilfkin

(1925). (1924).

(15) Kolthoff (1923). (34) Thiel and Wulfkin (1924).

(16) Kolthoff (1927). (35) Walbum (1913).

(17) Laxton, Prideaux and Rad- (36) Walpole (1914).

ford (1925).

TABLE 9
Common synonyms of indicators

Among synonyms given in this table are several which apply to dyes
which are not listed in preceding table or which have been applied to two
or more of the indicators listed. Such cases are indicated by*. Num-
bers are index numbers of table 8.

Acid bordeaux, 77 Alkanet, 184

Acid brown R,* 68 Alkalin, Alkannin, 184

Acid fuchsin,* 107 Alphanaphtholbenzein, 185

Acid magenta II, 107 Alphanaphtholphthalein,* 116

Acid roseine, 107 Amido-azo-benzol, 30

Alizarin, 166 Amido-azo-toluol, 26

Alizarin blue ABI, 163 Amino-azo-benzene, 30

Alizarin blue S, 167 Amino-azo-toluene, 26

Alizarin blue X, 163 Amyl red, 66

Alizarin carmine, 165 Anchusin, 184

Alizarin green B, 160 Aniline orange,* 31

Alizarin red S, 165 Aniline red, 99

Alizarin sulfonate or S, 165 Aniline yellow,* 3, 25, 30

Alizarin yellow GG, 74 Archil, 179

Alizarin yellow R, 75 Aurin, 103

Alkali blue 4B, 104 Azo-blue, 88

THE DETERMINATION OF HYDROGEN IONS

TABLE 9— Continued

Azolitmin, 177

Azoresorcin, 101

Benzopurpurin B, 85

Benzopurpurin 4B, 86

Benzyl violet, 97

Beta naphthol orange, 73

Bitter almond oil green, 91

Blauholz, 170

Boettger's indicator, 184

Bordeaux B, 77

Brasilein, brasilin, brazilin, 180

Brazil wood, 180

Brilliant green, 93

Brilliant yellow,* 89

Brom-chlor-phenol blue, 133

Brom cresol green, 134

Brom cresol purple, 136

Brom phenol blue, 131

Brom phenol red, 137

Brom thymol blue, 139

Brom xylenol blue, 140

Butter yellow,* 26, 37

Cabbage red, 171

Campeachy wood, 170

Carmine, 178

Carminic acid, 178

Catechol sulphonphthalein, 127

China blue, 102

Chlor phenol red, 135

Chrome printing orange R, 75

Chrome printing yellow G, 74

Chrysoidine, * 56

Chrysoine, 78

Coccus, 178

Cochenille, cochineal, 178

Congo, 87

Congo red, 87

Corallin, 103

Cresol red, 143

Cresolphthalein,* 119

Cresolsulphonphthalein, * 143

Crismer's indicator, 101

Crocein,* 80

Crystal violet, 90

Curcuma, 183

Curcumein,* 84

Curcumin,* 183

Curcumin W, 89

Curcummin,* 183

Cyanin, 151

Dechan's indicator, 109

Degener's indicator, 174

Dianil red,* 87

Dichlorofluorescein, 114

Diethylaniline orange, 45

Dihydroxyanthraquinone, 166

Dimethylaniline orange, 44

Dimethyl orange, 44

Dimethyl yellow, 37

Dinitroaminophenol, 9

Dinitrohydroquinone, 5

Echtrot,* 169

Echtrot A, 76

Echtrot B, 77

Eosine, 110

Eosine BN, 123

Eosine YS, 110

Erythrosine, * 111

Ethyl green,* 96

Ethyl orange, 45

Ethyl red,* 60

Ethyl violet, 95

Fast red A, 76

Fast red B,* 77

Fluorescein, 113

Formanek's indicator, 160

Fuchsia, 154

Fuchsin,* 99

Fuchsin S, 107

Galeine, 109

Gallein, 109

Gentian violet, 98

Golden orange, 44

Haematein,*1 170

Haematoxylin,*1 haematoxylon,*

170

Helianthine,* 44, 81, 82, 83
Hematein,*1 hematine,*1 170

1 Haematoxylin is the leuco-compound of Haematein or Hematine as
obtained from logwood although the name is sometimes givon to the oxi-
dized form. Haematein or Hematine should not be confused with Hem-
atin of the blood pigment.

INDICATOR NAMES

TABLE 9— Continued

Hematoxylin,*1 170
Henderson & Forbes' indicator, 5
Heptamethoxy red, 102a
Herzberg's indicator, 87
Hexamethoxy red, 99b
Hofmann's violet, 92
Holt & Reid's indicators, 124-126
Indigo carmine, 168
Indigo disulphonate, 168
Indophenols, 152
Induline spirit-soluble, 157
lodeosine,* 111
Isopicramic acid, 9
Iodine green, 94
Kosmos red, 87
Kroupa's indicator, 99
Kriiger's indicator, 113
Lackmoid, lacmoid, 176
Lacmosol, 175
Lacmus, 177
Litmus, 177
Logwood, 170
Luck's indicator, 120
Lunge's indicator, 44
Lygosine, 181
McClendon's indicator, 11
Magdala red, 156
Magenta,* 99
Malachite green, 91
Manchester yellow, 3
Martius yellow, 3
Mauve, mauveine, 155
Mellet's indicator, 70
Meta cresol purple, 128
Meta methyl red, 33
Metanil yellow, 23
Metanitrophenol, 15
Methyl blue,* 105
Methylene violet BN, 154
Methyl green,* 96
Methyl orange, 44
Methyl red, 59
Methyl violet 5B or 6B, 97
Methyl yellow, 37
Michaelis' nitro indicators, 1, 2, 4,
7, 8, 10, 12, 15

Mimosa flower extract, 182

Moir's "Improved methyl orange,"

149

Moir's polychromatic indicator, 127
Monobenzyl orange, 32
Monoethyl orange, 43
Monoethyl red, 57
Monomethyl orange, 42
Monomethyl red, 55
Monopropyl red, 58
Naphthol benzein, 185
Naphthol orange, 72
Naphtholphthalein,* 115, 116
Naphthylamine brown, 68
Neutral blue, 159
Neutral red, 158
Nierenstein's indicator, 172
Nile blue A, 162
Nile blue B, 161
Nitramine, 16
Nitroaminoguaiacol, 11
Nitrobenzene (tri), 17
Nitrobenzoylene urea, 14
Nitronaphthol, 3
Nitrotoluene, 18
Oil yellow,* 37
Oil yellow B, 30
Orange G,* 79
Orange GG, 79
Orange I, 72
Orange II, 73
Orange III,* 36, 44
Orange IV, 25
Orchil, 179
Orseille, 179
Ortho-chrom-T, 150b
Parahelianthine, 44
Para methyl red, 20
Paranitrophenol, 12
Paraphthalein, 120
Pentamethoxy red, 99a
Pernambuco, 180
Phenacetolin, 174
Phenol red, 142
Phenolphthalein, 120
Phenolsulphonphthalein, 142

THE DETERMINATION OF HYDROGEN IONS

TABLE 9— Concluded

Phloxin red BH, 112
Phosphine substitute, 78
Picric acid, 1
Pinacyanol, 150a
Poirrier's blue C4B, 106
Poirrier's orange III, 44
Propyl red, 61
Purpurin, 164
Pyrogallol phthalein, 109
Quinaldine red, 150
Quinoline blue, 151
Red I, 76

Red cabbage extract, 171
Red violet 5R,* 92
Red violet 5RS, 100
Red wood, 180
Resazurin, 101
Resorcin blue,* 176
Resorcin phthalein, 113
Resorcin yellow, 78
Rhodamine B, 108
RiegePs indicator, 87
Rosaniline, 99
Roseine, 99
Rose magdala, 156
Rosolane, 155
Rosolic acid, 103
Rotholz, 180
Rubine S, 107
Safranine,* 153
Salicyl yellow,* 74
Schaal's indicator, 166
Soluble blue 3M, 2R, 102
Soluble red woods, 180
Spirit yellow, 30

Spirit yellow G, 30

Spirit yellow R, 26

Tetra brom fluorescein, 110

T. N. T. 18

Thymol blue, 129

Thymolphthalein, 122

Toluidine orange* (ortho), 39

Toluidine orange* (meta), 47

Toluylene red,* 158

Topfer's reagent, 37

Tournesol, 177

Troger and Hille's indicator, 173

Tropaeolin*,? 69

Tropaeolin D, 44

Tropaeolin G,* 23, 72

Tropaeolin O, 78

Tropaeolin OO, 25

Tropaeolin OOO No. 1, 72

Tropaeolin OOO No. 2, 73

Tropaeolin R, 7

Turmeric, 183

Turnsole, 177

Uranin, 113

von Miiller's indicator?, 25

Weselsky's indicator, 101

Water blue, 102

XL Soluble blue, 105

Xylenol blue, 145

Xylenol phthalein,* 121

Xylidine orange* (meta), 40

Xylidine orange* (para), 48

Yellow B, 37

Yellow T, 78

Zellner's indicator, 113

SELECTED INDICATORS

Table 10 is S0rensen's list,
sen remarks:

Concerning these indicators S0ren-

Not all these indicators furnish equally well defined virages and above
all they are not of equal applicability under all circumstances. In the
choice of an indicator from among those which we have been led to recom-
mend it is necessary to use judicious care and especially to take into con-
sideration the following facts;

rv S^RENSEN'S INDICATORS 91

a. The indicators of the methyl violet group (nos. 1 and 2) (see table 10)
are especially sensitive to the action of neutral salts; furthermore the
intensity of color changes on standing and the change is the more rapid
the more acid the medium.

6. The basic indicators (nos. 3, 6, 9, 11, 14) are soluble in toluene and in
chloroform. The first four separate partially on prolonged standing of
the experimental solution.

c. In the presence of high percentages of natural proteins most of the
indicators are useless although certain of them are still serviceable; nos.
1, 2, 13, 16, 17, 18.

d. In the presence of protein decomposition products even in considera-
ble proportions the entire series of indicators may render real service.
Yet even in these conditions some of the acid azo indicators may give
notable errors (nos. 4, 5, 7, 8, 10) in which case one should resort to the
corresponding basic indicators.

e. When only small percentages of protein or their decomposition prod-
ucts are concerned the acid azo indicators are more often preferable to
the basic for they are not influenced by toluene or chloroform and do not
separate from solution on standing.

/. In all doubtful cases — for example in the colorimetric measurement
of solutions whose manner of reaction with the indicator is not known,
the electrometric measurement as a standard method should be used.
Then the worth of the indicator will be determined by electrometric
measurement with colorimetric comparison.

In table 11 will be found the selection of Clark and Lubs, modi-
fied by the rejection of methyl red and the inclusion of Cohen's
contributions. These indicators are marketed both in the form
of the dry powder and in stock solutions. In cases where the
acidity of the free acid dye does not interfere with accuracy and
when alcohol is not objectionable the alcoholic solutions of the
dyes may be used. Clark and Lubs prefer to use aqueous solu-
tions of the alkali salts in concentrations which may be con-
veniently kept as stock solutions. These are diluted for the test
solutions used in the dropping bottles.

For the preparation of these stock solutions one decigram (0.1
gram) of the dry powder is ground in an agate mortar with the
quantities of NaOH shown in column A and footnote in table 11.

If there be no particular reason to maintain exact equivalents
it may be found easier to dissolve the dyes in 1.1 equivalents of
alkali instead of one equivalent as indicated above. See page 190.

To place the dyes upon a comparable basis the final dilution
should be nearly the same when calculated upon a molar basis

THE DETERMINATION OF HYDROGEN IONS

§i

3 3

e^onpoad jo 'ouoo q3ijj

3 § § §

3 §D

^vaxaaN ox

o o o o

CO O O

lid

W fe

8 11*

Oi 03 cj ^

+ 1 g.s

3 -

51 3

^ ? o

^ S *
«+ §

I 1^ ill

a a o a M P

ooo
odo

o o
o o

•3*3

ES
§

a> H CD w ^3 .3

O£ja £ 0 £ >>•$ S>

0^6 -3S3^4 n

.3 1 3 SgS^S 2

'S^i G'^fl'Si O

SC^RENSEN'S INDICATORS

.2 »

jl §:3

c3 M d ^

7 o "* "3
I o B ...

TJ £ 8 .2 T3 T3

8 « "2 * 0 §

a 48 g g

9 Q

02 02

-2 5 -2

I I

1 I

^ a ja

o os r*»

06 06 06

ct coco

CO 4. JH

8 8

888
§ § g

8 8 8 § 8 S S
«§§§"§§§

•a -s -s 1« .s .s

a s a ° 'S s s

s ™ I g I

<o o cs

! 1
1 I

1-a

o o

O C=>

5*2

THE DETERMINATION OF HYDROGEN IONS

0 K
tc <J

CHANGE
LKALINE

§ fl
8 8

•s -a

a I!** s-s

•5 g •£ | a s

ill!!!

'I s la^8
g ^&^^5

II q II II ^ W

* two^c5
c2 W

IV SULFONPHTHALEINS 95

and, by reason of the great change in molecular weight caused
by the introduction of bromine and other group substituents,
equal molecular concentrations will be very far apart in per-
centage concentration. For all ordinary purposes, however, this
may be neglected and solutions of a concentration of 0.04 per
cent will be found satisfactory for use in testing 10 cc. of a solu-
tion with about five drops of indicator.

From various sources have come complaints that the method
outlined above for the preparation of the aqueous alkali salt
solution of brom cresol purple1 leads to a solution of much lower
tinctorial power than when the same material is taken up directly
in alcohol. No such difficulty was experienced with the material
described by Lubs and Clark but it has appeared not infrequently
since. The source of the difficulty is not yet definitely traced,
but is suspected to be due to impurities. If so it should be
avoided by purchasing the highly purified material which is now
made specially.

Since the range of an indicator depends to a considerable extent
upon the manner in which the indicator is used, it is of interest
to note the ranges assigned by Saunders (1923) on the basis of
his ability to detect changes of 0.02 pH unit.

Brom cresol purple 5.8 -6.4

Brom thymol blue 6.4 -7.2

Phenol red 7.1 -7.9

Cresol red 7.65-8.45

Thymol blue 8.4 -9.2

Phenolphthalein, or orthocresolphthalein, and methyl red,
which are valuable indicators for titrations, may be used for this
purpose in alcoholic solution unless exacting requirements are to
be met.

Since the requirements of titration are so varied no separate
lists for this process have been compiled. The theory of titration
is outlined in Chapter XXVIII. There reference will be made to
the color chart (page 65) for the selection of various end-point

1 The effect of excess alkali on sulfonphthaleins is still more or less
uncertain. See, however, Hubbard and Meeker (1924), Brown (1923),
Brightman,Hopfield andJMeacham and Acree (1918) . AJsp search the papers
of Orndorff ,

96 THE DETERMINATION OF HYDROGEN IONS

colors to be used in conjunction with figures 93 and 94 (page 535).
There, also, reference is made to the indicator constants of
table 11 which are used for more refined work.

Michaelis' selection of "one-color" indicators is given in table
12. Discussion will be found in Chapter VI.

TABLE 12

Michaelis' indicators and their ranges as used in the method of Michaelis and
Gyemant (see Chapter VI)

Picric acid colorless 0.0- 1.3 yellow

2, 4-dinitro phenol colorless 2.0- 4.7 yellow

a dinitro phenol

2, 6-dinitro phenol colorless 1.7- 4.4 yellow

0 dinitro phenol

2, 5-dinitro phenol colorless 4.0- 6.0 yellow

y-dinitro phenol

m-nitro phenol colorless 6.3- 9.0 yellow

p-nitro phenol colorless 4.7- 7.9 yellow

Phenolphthalein colorless 8.5-10.5 red

Alizarin yellow GG colorless 10.0-12.0 yellow

Salicyl yellow

MIXED INDICATORS

Mixtures of indicators are used for two purposes. The modifica-
tion of color is discussed in Chapter VII. In that chapter will
be found, in terms of absorption spectra, an example of the re-
sultant effect of pH-change upon the simultaneous changes in
degree of dissociation of each component. The more usual pur-
pose of a mixture is to extend the pH range which can be covered
by one test solution.

In one sense indicator mixtures are comparable with those
indicators which have several ionizations each associated with a
color change. Henderson and Forbes' (1910) employment of
dinitrohydroquinone provided one of the earlier instances in
which use was made of a compound of several stages of dissocia-
tion. With this one indicator they were able to cover roughly
the range pH 3 to pH 9.

Prideaux and Ward (1924) describe the "universal indicator' '

MIXED INDICATORS 97

put out by the British Drug Houses as having the following
color changes:

pH 4.2 4.8 5.4 6.8

color red yellow- orange yellowish

ish red yellow green

pH 7.3 9.1 10.3 11.5

color sap greenish violet reddish

green blue violet

Bogen (1927) describes a mixture with a range of from pH 1 to
pH 10. His receipt is as follows.

Phenol phthalein, 100 mgm.; methyl red, 200 mgm.; dimethylaminoazo-
benzene, 300 mgm.; bromthymol blue, 400 mgm.; thymol blue, 500 mgm.
Dissolve in 500 cc. of absolute alcohol. Add tenth normal sodium hy-
droxide solution until the red disappears and the solution becomes yel-
low (pH 6.0).

The colors produced resemble those of the spectrum, thus:
Red indicates about pH 2.0 (very strongly acid)
Orange indicates about pH 4.0 (strongly acid)
Yellow indicates about pH 6.0 (weakly acid)
Green indicates about pH 8.0 (weakly alkaline)
Blue indicates about pH 10.0 (strongly alkaline)

Moir (1917) is cited as using a mixture of methyl red, naphthol
phthalein and phenolphthalein. To this Carr (1922) adds brom
thymol blue or cresol phthalein, or cresol red.

Niklas and Hock (1924) are cited as employing the following
mixture: one volume 0.04 per cent brom cresol purple, 4 volumes
0.04 per cent brom phenol blue, 6 volumes 0.02 per cent methyl
red and 4 volumes 0.04 per cent brom thymol blue. Range pH
3.5 to 7.6.

Felton (1921) used equal parts of methyl red and brom thymol
blue for the range 4.6 to 7.6 (unsatisfactory between 5.6 and 6.2) ;
methyl red and brom cresol purple 4.6 to 7.0; methyl red and
thymol blue (rough) 1.2 to 9.0.

Lizius and Evers (1922) cite the following:

THE DETEEMINATION OF HYDROGEN IONS

ARBITRARY NAME

COMPONENTS

pH RANGE

COLOR

Methyl-thymol blue

Methyl red (1 part),

4^10

red-yellow-greenish

thymol blue (3

blue

parts)

Phenol violet

Phenolphthalein (1

8-10

yellow-blue-violet

part), thymol blue

(6 parts)

Phenol-thymol

Phenol phthalein (1

8.3-11

Colorless-pink-

phthalein

part), thymol

violet

phthalein (6 parts)

Thymol violet

TropaeolinO (1 part),

9-13

Yellow-green-blue-

thymolphtnalein

violet

(4 parts)

See also A. Cohen (1922), Lizius (1921) and Kolthoff (1927) on mixed
indicators.

INORGANIC INDICATORS

Grunberg (1924) notes that complex platinum compounds
behave as acid-base indicators. A number of other inorganic
systems have been used either as involving a species precipitated
within a certain zone of pH or as involving a color change. See
Houben (1919), Daniel (1927).

CHAPTER V

THEORY OF INDICATORS

It requires a long-necked observer to see the whole firmament out
of one window. — J. ARTHUR THOMSON.

INTRODUCTION

Indicator theory is a cross-roads. Here the organic chemist
fetches structural formulas, group names, and correlations be-
tween molecular architecture and "color." The physicist brings
his account of the radiant energy absorbed, methods for its
measurement, and schemes for its translation into color. The
psychologist pauses here to philosophize on color and to reflect
upon the eye as a differentiating instrument. The physical
chemist has called the cross-roads his own for he has tried to
bridge the gap between the knowledge supplied by chemistry and
that supplied by physics; but his sole outstanding contribution
has been to formulate what can be formulated by equilibrium
equations. The colloid chemist has occasionally tried to direct
the traffic. He possesses valuable information the submission
of which is welcomed as a service. The botanist has left on the
roadside the historically important indicators and the entomologist
has furnished cochineal. The bacteriologist has brought some of
the first records of dye reduction and has asked of the plant physiol-
ogist what part acidity and what part reduction plays in the
beauty of the autumn landscape. The analyst has camped here
to acquire for his daily use the information that comes this way.
And he who has imagined the chemistry to come, illustrated with
electron orbits, seeks in the passing throng the bearer of the
Rosetta stone that will translate speculative ideas concerning the
electronic nature of organic reactions into reasonable certainties.
Beside him stand the biochemist and pharmacologist, awaiting
the formulation of what neither structural chemistry alone nor
physical measurement alone seems to suggest half so well as the
imagination which has been fired by the contributions of all.
For the indicator has been shown to be a labile thing, responsive

100 THE DETERMINATION OF HYDROGEN IONS

to radiant energy and to the pressures of protons and electrons,
subject to structural changes and physical changes in delicate
response to changes in the environment. It is the embodiment of
sets of phenomena having an " all-togetherness" with which our
intellectual methods have hardly attained the power to cope.
The indicator reminds the biochemist of many things in the chem-
istry of life that exhibit an analogous "togetherness." He hopes
that a complete mastery of indicator theory may take its part in
the understanding of the unity and lability of life -chemistry.

But our present task is limited and commonplace. We must
separate and assign to another chapter the physical phenomena
of light absorption. We must relegate to the treatises on organic
chemistry details of structure and the proofs thereof which the
thoughtful student will require. We must pass over the fascinat-
ing story of indicator history with its contributions to theory.
In short we must select only that which is essential to the use of
indicators for the measurement of hydrion concentration. Hence
there will be found in this chapter little of what is sometimes
called indicator theory.

OSTWALD'S THEORY

Let us deal first with the simple theory of Ostwald which was
constructed on the primd facie evidence that indicators do behave
as acids or bases, the molecules of which have abilities to absorb
radiant energy of one spectral band, and the ions of which have
abilities to absorb radiant energy of another spectral band.

If we start with this as a postulate, it is evident that the "color"
of an indicator should change with the pH of a solution exactly
as depicted by one of the dissociation curves*<iescribed in Chapter
I. If, for instance, the indicator is an acid, colorless in the un-
dissociated form, but colored when dissociated as an anion, then
the change of color with the hydrogen ion concentration should
conform to the equation:

where Ka is the dissociation constant of the acid indicator and
a. is the degree of dissociation. Assuming that such a relation

OSTWALD'S THEORY

101

does hold, let us determine Ka for a series of indicators in the
following way.

From the above equation when a = J, Ka = [H+]. That is,
at a hydrogen ion concentration corresponding numerically to the
dissociation constant, the acid is half dissociated. At such a
hydrogen ion concentration a colorless-to-red indicator, such as
phenolphthalein, should show half the available color; and a
yellow-to-red indicator, such as phenol red, should show the half-
yellow, half -red state. We can match the half-way state of this
first solution by superimposing two solutions each of a depth
equal to the first, if we have in one of the superimposed solutions
only the yellow form and in the other only the red form, each
concentration equaling half the concentration in the first solution.
Such an arrangement is shown diagraphically in the following
figure :

Alkaline solution
(full red) 5 drops
indicator

Known pH stand-
ard 10 drops
indicator

Acid solution (full
yellow) 5 drops
indicator

Water blank

We may not know at the beginning at what pH the half trans-
formation may occur, so we vary the pH of the standard solution
until a match with our superimposed solutions does occur. Then
we have found, presumably, the hydrogen ion concentration the
numerical value of which is that of the dissociation constant of the
indicator. Values so obtained by Clark and Lubs (1917) are
given in table 13.

This is the method of Salm (1906).

Of course it is not necessary to confine attention to the case
where each of the superimposed tubes at the left in the diagram

102 THE DETERMINATION OF HYDROGEN IONS

contains the same quantity of the indicator. Various divisions
between the solutions inducing the full "alkaline color" and the
full "acid color" may be made; and in each instance a color-
match may be made by adjusting the standard buffer until the
ratio of the "acid form" to the "alkaline form" is that of the
artificial division between the acid and the alkaline solutions.

TABLE 13
Approximate apparent dissociation constants of indicators

INDICATOR

Phenol sulf on phthalein

1.2 X 10-

7.9

o-Cresol sulfon phthalein

5 0 X 10-

8 3

Thymol sulfon phthalein

1.2 X 10-

8.9

Carvacrol sulfon phthalein . . .

1 0 X 10"

9 0

a-Naphthol sulfon phthalein

5.3 X 10"

8.2

Tetra bromo phenol sulfon phthalein

7 9 X 10~§

4 1

Di bromo o-cresol sulfon phthalein

5.0 X 10~7

6.3

Di bromo thymol sulfon phthalein

1.0 X 10~T

7.0

Phenol phthalein

2.0 X 10~10

9.7

o-Cresol phthalein

4.0 X 10~10

9.4

a-Naphthol phthalein

4.0 X 10~9

8.4

Methyl red

7 9 X 10"6

5 1

Ethyl red

4.0 X 10~6

5.4

Propyl red

4.0 X 10~e

5.4

Thymol sulfon phthalein (acid range)

2.0 X 10~2

1.7

Thus it is possible to determine various values of a and, by means
of equation (1) or (la), to determine whether the simple require-

pH = pK + log

1 - a

(la)

ments of the Ostwald theory are met formally. Figure 18 shows
some examples. In this figure the experimental points are shown
lying on or very near type curves drawn to correspond to equa-
tion (la) and placed with reference to the pH axis by using the
average value of pK calculated from the known pH- values of the
buffers and the measured values of a.

As indicated in Chapter I the determination of the dissociation
curve, or of the half transformation point, does not tell us whether
we are dealing with the dissociation curve of an acid or the disso-

INDICATOR CONSTANTS

103

elation-residue curve of a base or vice versa. Thus methyl red
is treated in table 13 as an acid and plotted in figure 19 as if the
color were associated with the undissociated form. Methyl red
however could be treated as a base.

Figure 19 shows at a glance that an indicator of the simple type
we have assumed has no appreciable dissociation and consequently
exists in only one colored form at pH values beginning about 2
points below the half transformation point, while at the same
distance above this point the indicator is completely dissociated
and exists only in its second form. Between these limits the

Pep cent dissociation
ooSSSSSc^Sg

•~

•%?•

38^,

:^'

~vf

' *^>

jj/

£d

«?

" Broro-cpcsol orccn'aL 38*
• Brom-cpesol 6re«nal 20*
• Chlop-phcnol pcd it 38*
o Chlop-phenol red at 20*
* 6rom-cr>csol purple &L 38*
+ Bronocpcsol pupplc &t 20*
o Phenol red at 36'zuid20*

*"'

16 3.8 4.0 42 4.4 46 W SO U S.4 5.6 5.J 6D 62 &4 66 tt TO 12 T4 16 T8 S0 82 S.4 8.6 8.8 9.0 92 9.4

FIG. 18. CALCULATED AND OBSERVED DISSOCIATION CURVES FOR INDICA-
TORS, USED IN URINE pH DETERMINATION
(After Hastings, Sendroy and Robson (1925))

color changes may be observed. The useful range of such an
indicator is far less than 4 pH units for optical reasons which will
be discussed in Chapter VII.

The illustration (fig. 19) will show how in choosing a set of indi-
cators it is advantageous to include a sufficient number, if reli-
able indicators can be found, so that their ranges overlap. It
shows that each of the indicators, when considered to be of the
simple type we have assumed, has an equal range. It also shows
that the half transformation point of each indicator occurs nearer
one end of the useful range, the useful range being indicated by
the shaded part of the curve, This aspect will be discussed later.

VlO MCI

AS?ERGILL0S
LIMIT

B.PARA TYPHI

B.TYPHI AOOL.
B.COLI4.WIT
PWEUHOCOCCOS A&CL.

BLOOD

NH4OH

100

FIG. 19. INDICATOR CURVES AND SIGNIFICANT pH VALUES

Shading indicates useful range

104

V TAUTOMERISM 105

It is evident that if the actual color change of an indicator
varied with pH in accordance with a curve such as those in fig-
ure 19, and if the true dissociation constant were accurately known,
then the hydrogen ion concentration of a solution could be deter-
mined by finding the per cent transformation induced in the
indicator. Indeed the dissociation constants of some few indi-
cators have been determined with sufficient accuracy to permit
the use of this method when the proper means of determining the
color intensities are used. This will be discussed in Chapters

VI and VII.

TAUTOMERISM

The following sketch of tautomerism is purposely made brief.
Its consideration leads to equations which reduce to the forms
used with the Ostwald theory. Further consideration would lead
to very many points of interest but these are involved in the use
of indicators which are ordinarily rejected.

Without following the detail of the reasoning we may say that
certain reactions of isatin suggest the formula

C6H4 C=0

\ /
N
H

while other reactions of isatin suggest the formula

C6H4 C— OH

Since the study of this case there have been found many com-
pounds which act now in one way and 'again in another, according
to the conditions used and the reagents with which they are
attacked. To account for a case like that of isatin it has been

106 THE DETERMINATION OF HYDROGEN IONS

assumed that a hydrogen atom moves from one position to the
other, that the two forms are in dynamic equilibrium and that
when a reagent attacks one form the other rearranges to main-
tain the dynamic equilibrium and thus maintain a supply of the
reacting form.

Among the types are those with the lactam and lactim struc-
tures and those with the keto and enol structures.

— C=0 — C— OH — O=0 — C— OH

I II I II

— NH — N — CH — C—

I
Lactam Lactim Keto Enol

From one and the same compound have been formed derivatives
corresponding to the enolic or to the ketonic structure. The
two forms of the original substance are isomers; but to emphasize
their labile nature Laar (1885) called them tautomers. To denote
each and every shade of meaning in explanations which differ, we
now find more terms than we can afford space to define. We
shall use the word tautomerism to denote labile isomeric changes
of whatever nature.

Frequently tautomeric rearrangements are associated with
change of color. The argument is as follows. In those beautiful
and often very elaborate series of syntheses by means of which
the organic chemist attains an orderly view of structures, it is
noted that color is associated with various, particular structures.
When a colorless ionogen is converted into an ion, a colorless
ion might be expected. But the fact that the ion is colored is
the occasion for believing that a rearrangement takes place with
the production of one or another of those structures which have
been associated with color production. Groups which, by their
presence, "produce" color are called chromophores. Important
chromophores are:

>C=0;> C=S;> C=N— ;— NO;— N02;— N=N— ;=

TAUTOMERISM

107

Of particular importance to our subject are groups such as
— NH2, —OH, etc., which are not chromophores per se but which
may have a profound influence upon the calling forth or the
suppression of the appearance of color.

Now consider the case of crystal violet. The "free base" will
be represented by formula I. It contains no chromophore. It
is colorless. However it contains substituted amino groups and
a hydroxyl group. Therefore it is an ionogen, potentially, at
least. Imagine that the free base is brought into a solution
containing hydrogen ions at a concentration just sufficient to
convert one of the groups, and one only, to an ion. Perhaps the
first result will be the addition of a hydrion to one of the three
symmetrically placed dimethyl amino groups as represented by
formula Ha. Or perhaps the first result will be the stripping of
the hydroxyl group from the carbon to leave the ion lib. Either
ion could rearrange to form the ion He, the first by elimination
of water and shift of electrons; the second by shift of electrons
alone. Now He contains the chromophore group, the quinone
group, which "accounts for" the color of the ion. It is therefore
the preferred way of representing the ion.

We may now note a matter of considerable importance. If in
fact there be a rearrangement which resembles the transformation
of Ha or lib into He, the rearrangement is spontaneous and repre-
sents the persistance of the more stable form. Its direct control
is often beyond our power, although it may be possible by taking
advantage of the slowness of rearrangement in a rare instance to

(CH3)2N

N(CH3).

C— OH (CH3)2N

H+

N(CH3)2

(CH3)S

N(CH3)S

108

THE DETERMINATION OF HYDROGEN IONS

N(CH3)2

(CH

form a derivative which rearranges less readily than the original
tautomer. On the other hand the first step, whereby the ion is
formed, appears to be under control by the hydrion concentration
of the solution. It must not be assumed that a measurement of
the "ionization constant" evaluates the primary ionization alone.
The rearrangement, being spontaneous, leads to the formation of
the more stable tautomer and the process of rearrangement is an
integral part of the whole process of which the initial and final
steps are only parts. Later we shall see that an ionization con-
stant is a function of ionization energy. In the case at hand there
may be energy involved in the rearrangement. Our measurements

V TAUTOMERISM 109

are incapable of separating the two energies, and we shall find
ourselves describing the total energy change between I and He
as if it were that of an ionization of I directly to He.

Of course we must assume that any one of the forms shown is
capable of existence, in small amounts at least, under any con-
ditions. It is assumed that acetic acid molecules, for instance,
occur in minute amounts in very alkaline solutions of acetate.
Nevertheless there remains a radical distinction between the
ionogen and any one of the ions depicted above. The latter are
true tautomers, the dominance of any one of which is determined
by the stability of the internal configuration. The ionogen or a
tautomer thereof differs from the ion or a tautomer thereof by
the energy involved.

There may now be noted a rather interesting matter. By
following the elementary principles for the writing of formulas
as given for instance in Valence (G. N. Lewis, 1923), we arrive at
the following configuration for the group attached to the quinone
ring of He.

H + H
H:C:N:C:H

ii :: ii

:C:

The nitrogen and each carbon are surrounded by octets of elec-
trons. However, carbon has a charge of -f- four to be neutralized,
nitrogen has a charge of + five to be neutralized and hydrogen a
charge of + one to be neutralized. Not only does this group
lack one electron required to fulfil these neutralizations but the
ion as a whole lacks one electron required to complete the neutral-
ization at all points. Therefore lib and He differ only in the
positions of the electron pairs and of the odd electron. If one
is willing to place any significance in this rather crude way of
depicting the situation, he has already accepted some degree of
shift of an electron, if lib and He are to be called tautomers in
dynamic equilibrium.

There have been attempts to relate such electron shifts, which
might be oscillations capable of resonating with radiant energy,
to color. The modern spectroscopist would doubtless not consent

110 THE DETERMINATION OF HYDROGEN IONS

to this for various reasons. Indeed the gap between the in-
formation supplied by structural chemistry and that demanded
for a solution of the problem in terms of spectroscopy is so large
that it would be inappropriate to our present purposes to enter
the discussion and recount the many partial theoretical ad-
vances. However it would appear that a structural formula for
a "tautomer" may be merely an expression of a limiting state, a
state which perhaps represents crudely a main feature important
to the rationalization of chemical reactions but nevertheless a
state which is perhaps of no particular importance to our present
purpose. We shall detect a hint of this in a further treatment
of the equations.

In the meanwhile let us proceed as if the molecule or ion re-
adjusts in large jumps to those configurations which are usually
described.

Consider the case of crystal violet further. Assume that
further increase in the hydrogen ion concentration will drive
hydrions upon the comparatively weak, substituted amino groups
forming successively the ions III and IV. Adams and Rosen-
stein (1914), by an analysis of the absorption bands, correlate
the changes of color with the stepwise addition of hydrions to
the dimethyl amino groups.

To indicate more specifically the structures assigned to particular
systems we may deal briefly, with a few of the other important
indicators.

The case of phenolphthalein is often represented as follows:

OH OH

— C—0 f \COOH ( \COO

V TAUTOMERISM 111

The lactone form V is a tautomer of VI which may undergo
primary ionization at the carboxyl or phenolic group. The
resulting ion can be represented as rearranging in several ways.
A probable form is VII. This or its tautomer can then suffer
secondary ionization and if the primary ion is VII the result is
VIII

o- o-

coo /\- coo

VIII

If this is rewritten with the extra electrons situated as far as possible
from the center, carbon is left positive and is satisfied by addition
of hydroxyl. Hence IX is sometimes used to represent the color-
less carbinol found in very alkaline solutions.

According to Acree and his students (Acree, 1908) (Acree and
Slagle, 1908) (Lubs and Acree, 1916) the chief color change in
phenolphthalein is associated with the presence of a quinone
group and with the ionization of one of the phenol groups. In
the sulfon phthalein series of indicators Acree and his students
(White, 1915, and White and Acree, 1918) have found much the
same sort of condition.

In the sulfonphthalein group of indicators we have to deal
with poly-acids; but as Acree has shown, the dissociation con-
stant of the strong sulfonic acid group is so very much greater
than that of the weak phenolic group, with which the principal
color change is associated, that there is no serious interference.
As shown in Chapter I we may, therefore, plot the curve for the
chief "color-change" as if we were dealing with a univalent acid.

112 THE DETERMINATION OF HYDROGEN IONS

The structures of all the sulfon phthaleins are analogous to
that of phenol sulfon phthalein (phenol red) whose various tau-
tomers are given by Lubs and Acree (1916) in the following
scheme :

C6H4OH
I
C6H4— C(C6H4OH)2 -> C6H4— C— C6H4OK -> C6H4— C(C8H4OK) ,

I II II

S02 — 0 S02 — O S02 — 0

A colorless B colorless C colorless

C6H4OH C6H4OH C6H4OH

I I I

C6H4— C:C6H4:0 -> C6H4— C:CCH4:O -> C6H4— C:C6H4:0

I I 'I

S02— OH S020- + H+ S020- + K+

D slightly colored E slightly colored F slightly colored

C6H4O- K+ C6H40- + K+

I I I
C6H4— C:CcH4:0 C6H4— C:C6H4:0

I I

S020- + K+ < — > S020- + K+

H deeply colored G deeply colored

Of course such a table represents possibilities (some of them
remote) and says nothing about the relative probability of any
specific form. This must be very carefully argued by a series of
analogies and by all the manifold devices of organic chemistry.

In the case of an azo indicator such as methyl orange, X, in
alkaline solution,

s ^ / \

we find the chromophore group — N = N— associated with a
yellow color. On driving a hydrion into this structure (by
decrease of pH) there would be expected XI

TAUTOMERIC EQUILIBRIA 113

N(CH3)2 H+ XI

which may rearrange to XII

H , x +

s— N— N=< > N(CH3)2 XII

with quinoid structure and red color. See Stieglitz (1903).

The question now is this. Given these tautomers, will their
inclusion in the equilibrium equation affect the end result of the
Ostwald theory?

EQUATIONS INVOLVING TAUTOMERS

In a previous section it was assumed that the theory of indicators
may be treated in the simple manner outlined by Ostwald. His
theory does not embrace the possibility of a radical change in
structure with distinctive properties pertaining to each structure.
In the section immediately preceding this, the concept of
tautomerism was briefly and inadequately outlined. There we
found that the ionization of one group may be followed by a
rearrangement of the molecule. If the tautomer is a distinct
entity there may be ascribed to any ionogenic group that it may
contain a distinctive ionization constant. Let us therefore formu-
late the acid-base equilibria of these systems by including the
ionization constants of the separate tautomers and follow the
consequences to the rather curious end.

Merely to illustrate a principle in outline assume two tautomers
HTi and HT2 and let HTi alone ionize as an acid. The equilib-
rium state for the ionization is described by

[THIH+]

lirT" a

For the equilibrium of the tautomers

[HTl! K to)

[HTJ= KT
The combination of (2) and (3) gives:

[HT21 K° KT = K "

114 THE DETERMINATION OF HYDROGEN IONS

Now suppose that Tf furnishes one color and either HT\ or
HT2 another color. Since (4) has the form of the ordinary equa-
tion (K'a replacing the ordinary Ka) it is obvious that the color-
change will depend on [H+j in the manner already described.
Regarding the matter from another point of view we perceive
that a determination of the equilibrium constant from the data
for the color-change would not reveal whether this constant is a
simple acid dissociation constant (Ka of 2) or a complex constant
(K'. of 4).

In one sense this situation is not unlike that which obtains in
the case of an ' 'ordinary" acid. There may be no occasion to
ascribe a tautomeric form to one of these "ordinary" acids but it
would require considerable skill to demonstrate that there are no
tautomeric forms. There is every reason to believe that dif-
ferent states of hydration occur and a complete equation should
contain the equilibrium constants for the hydration. We simply
agree to ignore this as we agree to ignore the hydration of the
hydrion in ordinary formulations. See also page 561 for a dis-
cussion of the use of the sum of the concentrations of HaCOa and
COs in formulating carbonate equilibria.

The too simple treatment given above must now be elaborated ;
for the ionization of the second tautomer was neglected and may
modify the conclusion. With slight changes of notation we shall
follow the treatment given by Noyes (1910).

The three fundamental equations are:
Ionization of tautomer 1;

[TT1 [H+]

Kal

= Ka2 (6)

Ionization of tautomer 2 :

[T2~]

[HT2]
Tautomerism :

[HT2]
[HTJ

V TAUTOMERIC EQUILIBRIA 115

Multiply (6) by (7), add (5) to the product and for [HTJ in the
denominator of the resulting equation substitute its equivalent
[HTJ + [HT2] which can be obtained from 7> There resultg

[H+] ([17] + [IT]) = K.. + K., KT =
[HTJ + [HTJ 1 + KT

Now if [T~] represents the sum [Tr] + [Tr] and if [HT] repre-
sents the sum [HT:] + [HT2], we have;

[T-] [H+] _ , ,

Again we have in (8) an equation of the usual form. Applying
to it the derivation given on page 14 we find

K' + [H+]

where a is now the ratio

[T-] + [HT] [Tr] + [TTJ + [HTJ + [HT,]
or

sum of all ions

a =

sum of all forms

The ordinary dissociation curve will then represent the degree
of color- transformation only when the sum [Ti~] + [T2~] is prac-
tically equal to either [Ti~] or [T2~], according to which tautomer
is associated with the color. A suggested explanation of the
fact that such curves do represent closely the color degree in
certain instances is that KT is very large or very small. Formal-
istically, at least, an equally good suggestion is that [Ti~] +
[Tj~] or [HTi] + [HTJ is merely an expression of a formal sum
of two limiting states the shift between which is only a part, but
nevertheless an integral part, of a phenomenon with which there
may be associated absorption of radiant energy.

Assuming the first and more usual suggestion, we then find

116 THE DETERMINATION OF HYDROGEN IONS

that the consideration of the tautomeric equilibria only modifies
the original Ostwald treatment to this extent : the found dissocia-
tion constant is a function of the several equilibrium and ioniza-
tion constants involving the different tautomers. It is what
Acree calls the "total affinity constant," or what Noyes calls the
"apparent dissociation constant." As Stieglitz (1903) and others
have pointed out, it is the state of these compounds, their exist-
ence in a dissociated or undissociated condition, which determines
the stability of any one form.

But there remains a view of the together-ness of the whole
set of phenomena which cannot be well formulated when we start
with the assumption of independent entities having independent
ionization constants. The simpler view is perhaps the better in
that it permits us to conceive of the departure of the hydrion and
the rearrangement as a unified process and the hydrion associa-
tion and re-rearrangement as a unified process. Then the energy
of ionization is linked inseparately with, or rather is, an integral
part of any energy change involved in the rearrangement of the
molecule. Because of this together-ness we appear to be dealing
with a most simple case of a simple dissociation when we measure,
by the means described above, the apparent ionization constant.

MULTIVALENT INDICATORS

Many indicators will not conform to the treatment of a uni-
valent acid because there are two or more distinctive groups which
may ionize either near the same level of pH or at different levels
of pH.

An instance of the first is phenolphthalein. It was shown by
Acree (1908) and by Wegscheider (1908) that the dissociations of
the carboxyl and of a phenolic group occur near together. The
proper equations to apply in such a case were developed by Acree
(1907, 1908) and by Wegscheider (1908, 1915).

In the case of a sulphonphthalein the "strong" sulfonic acid
group is already ionized when the phenolic group undergoes its
transformation. The "spread" between the dissociation curves
is then sufficient to permit the drawing of the curve of chief color
change as if of a univalent acid, the undissociated portion of
which is, however, the sulfonate ion.

There are also indicators with two or more basic groups, e.g.

V TIME CHANGES 117

crystal violet; and indicators of amphoteric nature, e.g. methyl
orange.

In case any two ionization constants, expressed in comparable
terms, have values of the same order of magnitude, it is necessary
to use the complete equation and to avoid the inevitable error
that would be involved in a treatment as if of a univalent acid
or base.

MORE COMPLEX EQUILIBRIA

A displacement of the position of and an alteration of the form
of a dissociation curve occurs when one of the components of a
system precipitates. The precipitate is a special case of an aggre-
gate which may remain in suspension. Imagine then an indicator
of high molecular weight tending to form aggregates which bring
its "solutions" within the category of colloidal "solutions."
The presence of the aggregate per se interferes with simple formu-
lation. In addition there may occur surface phenomena and
various types of adsorption. These effects will be superimposed
upon the basic equilibrium relations in an inseparable way and
with the failure of a simple quantitative formulation the flood-
gates of speculation open. Many indicators such as congo red
must be turned over to the students of colloid chemistry before
a full account of their conduct can be given.1 Until that account
is clear these indicators and partial accounts of their conduct
had best be studiously avoided except as objects of research.

THE TIME FACTOR

In the application of indicators we take advantage of the accom-
modating way in which they adjust their equilibria practically
instantaneously and it hardly ever occurs to us to imagine the
embarrassing predicament we would be in if they did not adjust
instantaneously. Yet there are such indicators and one must be
on his guard if the occasion arises in which they are put to use.
S0rensen has one or two in his list. "China Blue" used by
Bronfenbrenner (1918) is another, and a disconcerting indicator
it is found to be when the very different rates of transformation of
different commercial samples are compared. Equilibrium equa-

1 See also Zsigmondy (1924) on the degree of dispersion of some dyes
which have been used as indicators.

118 THE DETERMINATION OF HYDROGEN IONS

tions are inadequate to deal with this "time effect" and equilib-
rium studies are easily put in jeopardy by the use of such indi-
cators. For discussion of the time changes we refer the reader
to the very numerous papers of Hantzsch and his co-workers.
Indicators involving a time adjustment are most frequently en-
countered among the triphenylmethane dyes.

CHAPTER VI
APPKOXIMATE DETERMINATIONS WITH INDICATORS

// you can measure that of which you speak, and can express it by a
number, you know something of your subject; but if you cannot
measure it, your knowledge is meagre and unsatisfactory. — LORD
KELVIN.

The distinctive advantages of the indicator method are the
ease and the rapidity with which the approximate hydrogen ion
concentration of a solution may be measured. The introduction
of improved indicators, the charting of their pH ranges, better
definition of degree in "acidity" or "alkalinity," and the illumina-
tion of the theory of acid-base equilibria have developed among
scientific men in general an appreciation of how indefinite were
those old, favorite terms — "slightly acid," "distinctly alkaline,"
"neutral," etc. There is now a clear recognition of the distinct
difference between quantity and intensity of acidity; and for
each aspect there may be given numerical values admitting no
misunderstanding.

Furthermore the clarification of the subject has brought a
perspective which may show where accuracy is unnecessary and
where fair approximation is desirable. In such a case the in-
vestigator turns to the indicator method knowing that even if his
results are rough they can still be expressed in numerical values
having a definite meaning to others.

A very good approximation may be attained by color memory
and without the aid of the standard buffer solutions or of the
systems presently to be described in which the standard buffer
solutions are dispensed with.

An excellent procedure for rough measurements is to utilize
the colors of indicators with overlapping ranges. For instance,
Cohen (1923) gives the following table.

119

120

THE DETERMINATION OF HYDROGEN IONS

INDICATOR

COLOR AT pH—

4.5

5.0

5.5

6.0

6.5

Methyl red

red
yellow
yellow
yellow

red
green
yellow
yellow

orange
blue
yellow
yellow

yellow
blue
orange
yellow

yellow
blue
red
green

Brom cresol green

Brom phenol red

Brom thymol blue

The reader may elaborate such a table by use of the color
chart (page 65).

To establish a color memory, as well as to refresh it, a set of
"permanent" standards is convenient. These may be prepared
with the standard buffer solutions in the ordinary way, protected
against mold growth by means of a drop of toluol, and sealed
by drawing off the test tubes in a flame or by corking with the
cork protected by tinfoil or paraffin. For temporary exhibition
purposes long homeopathic vials make very good and uniform
containers. They may be filled almost to the brim and a cork
inserted, if a slit is made for the escape of excess air and liquid.
The slit may then be sealed with paraffin. A hook of spring-
brass snapped about the neck makes a support by which the vial
may be fastened to an exhibition board. A neater container is
the so-called typhoid-vaccine ampoule which is easily sealed in
the flame. Standards having considerable permanency are made
by sealing buffer-indicator mixtures in Pyrex glass tubes and steril-
izing them by the ordinary intermittent method.

If one of a series of standards so prepared should alter, the
change can generally be detected. But if all in a series should
change, it may be necessary to compare the old with new stand-
ards. Because such changes do occur, "permanent" standards
are to be used with caution. The sulfonphthalein indicators
make fairly permanent standards but methyl red which is
an important member of the series of indicators recommended by
Clark and Lubs (1917) often deteriorates within a short time.

As an aid to memory the dissociation curves of the indicators
are helpful even when used alone. The color chart shown in
Chapter III is a still better aid to memory and within the limita-
tions mentioned the colors may be used as rough standards.

VI GILLESPIE METHOD 121

COLORIMETRIC DETERMINATION OF HYDROGEN ION CONCENTRATION
WITHOUT THE USE OF STANDARD BUFFER SOLUTIONS

We have already seen that if an indicator is an acid, its degree
of dissociation, a, is related to the hydrogen ion concentration of
the solution by the equatkm

1 -a

[H+] = Ka

We have also seen that if Ka, the true dissociation constant is
replaced by the so-called apparent dissociation constant, K'a,
which is a function of Ka and of the constants of tautomeric
equilibria, then a represents the degree of color transformation.
We then have

K'a — —

or the more convenient form

PH - PK'a + log -- (1)

1 — a

where a may now be considered as the degree of color transforma-
tion. If, for instance, an indicator conducts itself as a simple
acid having the apparent dissociation constant 1 X 10~6 (pK'a
= 6.0), we can construct the dissociation curve with its central
point at pH = 6.0. Then there can be read from the curve, or
calculated from the corresponding equation, the percentage color
transformation at any given value of pH. Proceeding with these
simple and sometimes unjustifiable assumptions we can now
devise a very simple way of measuring the degree of color trans-
formation. The following is quoted from Gillespie (1920).

We may assume that light is absorbed independently by the two forms
of the indicator, and hence that the absorption, and in consequence of this
the residual color emerging, will be the same whether the two forms are
present together in the same solution or whether the forms are separated
for convenience in two different vessels and the light passes through one
vessel after the other. Therefore, if we know what these percentages are
for a given indicator in a given buffer mixture, we can imitate the color
shown in the buffer mixture by dividing the indicator in the proper pro-
portion between two vessels, and putting part of it into the acid form with
excess of acid, the rest into the alkaline form with excess of alkali.

122

THE DETERMINATION OF HYDROGEN IONS

Gillespie sets up in the comparator (see page 171) two tubes,
one of which contains, for example, three drops of a given indicator
fully transformed into the acid form, and the other of which con-
tains seven drops of the indicator fully transformed into the alka-
line form. The drop ratio 3:7 should correspond to the ratio of
the concentrations of acid and alkaline forms of ten drops of the
indicator in a solution of that pH which is shown by the disso-
ciation curve of the indicator to induce a seventy per cent trans-
formation. If then the two comparison tubes and the tested

TABLE 14

Gillespie's table of pH values corresponding to various drop-ratios

DROP-RATIO

BROM-
PHENOL
BLUE

METHYL
RED

BROM-
CRE80L
PURPLE

BROM--
THTMOL
BLUE

PHENOL
RED

CRESOL RED

THTMOL

BLUB

1:9

3.1

4.05

5.3

6.15

6.75

7.15

7.85

1.5:8.5

3.3

4.25

5.5

6.35

6.95

7.35

8.05

2:8

3.5

4.4

5.7

6.5

7.1

7.5

8.2

3:7

3.7

4.6

5.9

6.7

7.3

7.7

8.4

4:6

3.9

4.8

6.1

6.9

7.5

7.9

8.6

5:5

4.1

5.0

6.3

7.1

7.7

8.1

8.8

6:4

4.3

5.2

6.5

7.3

7 9

8.3

9.0

7:3

4.5

5.4

6.7

7.5

8.1

8.5

9.2

8:2

4.7

5.6

6.9

7.7

8.3

8.7

9.4

8.5:1.5

4.8

5.75

7.0

7.85

8.45

8.85

9.55

9:1

5.0

5.95

7.2

8.05

8.65

9.05

9.75

Produce
acid color <
with

1 cc. of
0.05M
HC1

1 drop
of
0.05M
HCJ

1 drop
of
0.05M
HC1

1 drop of
2 per cent
H2KPO4

solution are kept at the same volume, and the view is through
equal depths of each, the two superposed comparison tubes should
match the tested solution.

Barnett and Chapman (1918) applied this method with one
indicator, phenol red, but without using the dissociation curve.
Gillespie (1920) extended the procedure to several other indicators
and -made use of the dissociation curves so that he was able to
smooth out to more probable values the experimental data re-
lating drop ratios to pH. This is important because the experi-
mental error in judging color is not inconsiderable and if the

VI GILLESPIE METHOD 123

purely empirical data he made the sole basic standardization of
the method there may be involved a systematic error, which,
added to the error of the individual measurement may make the
cumulative error unnecessarily large. That this had already
occurred was indicated by Gillespie's comparison of the values
for the drop ratios of phenol red given by Barnett and Chapman
on the one hand and the report of the bacteriologists' committee
(Conn, et al, 1919) on the other hand.

Gillespie found the correspondence between the experimental
and the theoretical results predicted on the basis of the simpli-
fying assumptions mentioned above to be very good for the sul-
fonphthaleins, doubtless because of the reasons mentioned in
Chapter V. He also showed good correspondence in the case of
methyl red but reiterated the fact that phenolphthalein cannot
be treated by means of the simple dissociation curve for a mono-
acidic acid, as was mentioned in Chapter V.

In table 14 are given the pH values corresponding to various
drop ratios of seven indicators as determined by Gillespie. At
the bottom of the table are shown the quantities of acid used to
obtain the acid color in each case. Acid phosphate instead of
hydrochloric acid is used in two cases because the stronger acid
might transform the indicator into that red form which occurs
with all the sulfonphthalein indicators at very high acidities.
The 0.05 M HC1 is prepared with sufficient accuracy by diluting
1 cc. concentrated hydrochloric acid (specific gravity 1.19) to
240 cc.

The alkaline form of the indicator is obtained in each case
with a drop of alkali (two drops in the case of thymol blue).
The alkali solution used for this purpose may be prepared with
sufficient accuracy by making a 0.2 per cent solution with
ordinary stick NaOH. The indicator solutions may be made up
as described on page 91. Gillespie prefers the alcoholic solution
in the case of methyl red and specifies it for soil work.

Gillespie proceeds as follows:

Test tubes 1.5 cm. external diameter and 15 cm. long are suitable for
the comparator1 and for the strengths given for the indicator solutions.

1 See page 171.

124 THE DETERMINATION OF HYDROGEN IONS

It is advisable to select from a stock of tubes a sufficient number of uni-
form tubes by running into each 10 cc. water and retaining those which are
filled nearly to the same height. A variation of 3 to 4 mm. in a height of
8 cm. is permissible. Test tubes without flanges are preferable. The
tubes may be held together in pairs by means of one rubber band per pair,
which is wound about the tubes in the form of two figure 8's.

It is convenient to use metal test tube racks, one for each indicator,
each rack holding two rows of tubes, accommodating one tube of each
pair in front and one in back. For any desired indicator a set of color
standards is prepared by placing from 1 to 9 drops of the indicator solu-
tion in the 9 front tubes of the pairs and from 9 to 1 drops in the back row
of tubes. A drop of alkali is then added to each of the tubes in the
front row (2 drops in the case of thymol blue), sufficient to develop the
full alkaline color and a quantity of acid is added to each of the tubes in
the back row to develop the full acid color without causing a secondary

change of color (see table 14 for quantities) The volume is at

once made up in all the tubes to a constant height (within about one drop)
with distilled water, the height corresponding to 5 cc.

These pairs are used in the comparator and matched with the
tested solution. This tested solution is added to ten drops of the
proper indicator until a volume of 5 cc. is attained and the tube
is then placed in the comparator backed by a water blank.

Gillespie describes the use of the comparator (page 171) and a
modification for the accommodation of sets of three tubes used
when colored solutions have to be compared. He also discusses
a number of minor points and cautions against the indiscriminate
comparison of measurements taken at different temperatures.
For the details the original papers should be consulted. Were it
not that the writer has seen evidence that the method has been
applied with neglect of volume or concentration relations called
for by the theory involved and carefully specified by Gillespie,
it would seem unnecessaiy to advise that the principles be under-
stood before the method is used. Certain other misconceptions
of theory and practice found in a treatment of the method by
Medalia (1920) have been corrected by Gillespie (1921).

A very judicious appraisal of the value of the method was given
by Gillespie in these words:

The method should be of especial use in orienting experiments, or in
occasional experiments involving hydrogen ion exponent measurements,
either where it is unnecessary to push to the highest degree of precision
obtainable, or where the investigator may be content to carry out his

BICOLOR STANDARDS

125

measurements to his limit of precision and to record his results in such a
form that they may be more closely interpreted when a more precise study
of indicators shall have been completed.

For the elaboration of certain manipulative details see Van
Alstine (1920).

TABLE 15
Table for preparation of bicolor standards with 0.016 per cent brom cresol

green, 0.002 N HCl, and 0.001 N NaOH

Brom cresol green. pK' = 4.72 at 38° and 20°

(After Hastings, Sendroy and Robson, 1925)

PH38° and 20°

ALKALI TUBE

ACID TUBE

Dye

Alkali

Dye

Acid

cc.

4.00

0.40

24.60

2.10

22.90

4.10

0.49

24.51

2.01

22.99

4.20

0.58

24.42

1.92

23.08

4.30

0.69

24.31

1.81

23.19

4.40

0.81

24.19

1.69

23.31

4.50

0.94

24.06

1.56

23.44

4.60

1.08

23.92

1.42

23.58

4.70

1.23

23.77

1.27

23.73

4.80

1.38

23.62

1.12

23.88

4.90

1.51

23.49

0.99

24.01

5.00

1.64

23.36

0.86

24.14

5.10

1.77

23.23

0.73

24.27

5.20

1.88

23.12

0.62

24.38

5.30

1.98

23.02

0.52

24.48

5.40

2.07

22.93

0.43

24.57

5.50

2.14

22.86

0.36

24.64

5.60

2.21

22.79

0.29

24.71

5.70

2.26

22.74

0.24

24.76

5.80

2.31

22.69

0.19

24.81

Hastings, Sendroy and Robson (1925) have systematized the
Gillespie method as follows. The indicator solution specified in
each of the following tables (15 to 18) are added to each tube from
a micro burette. Then either 0.001 N HCl, 0.01 N or 0.001 N
NaOH solution is added to bring the volume to 25 cc. "The
tubes are stoppered or sealed and kept in a dark cupboard. When
sealed, the solutions are stable for several months."

126

THE DETERMINATION OF HYDROGEN IONS

The stock indicator solution (0.1 per cent) are prepared by the
procedure noted on page 91. These are diluted as follows.

FINAL
CONCENTRATION

STOCK SOLUTION
DILUTED TO
200 CC.

Phenol red

per cent

0.0075

cc.

Brom cresol purple

0.008

Chlor phenol red

0 010

Brom cresol green

0.016

TABLE 16

Table for preparation of bicolor standards with 0.01 per cent chlor phenol

red, 0.001 N HCl, and 0.01 N NaOH

Chlor phenol red. pK' = 5.93 at 38°, and 6.02 at 20°

(After Hastings, Sendroy and Robson, 1925)

pH38o

ALKALI TUBE

ACID TUBE

pH20°

Dye

Alkali

Dye

Acid

cc.

5.00

0.26

24.74

2.24

22.76

5.09

5.10

0.32

24.68

2.18

22.82

5.19

5.20

0.39

24.61

2.11

22.89

5.29

5.30

0.48

24.52

2.02

22.98

5.39

5.40

0.57

24.43

1.93

23.07

5.49

5.50

0.68

24.32

1.82

23.18

5.59

5.60

0.80

24.20

1.70

23.30

5.69

5.70

0.93

24.07

1.57

23.43

5.79

5.80

1.07

23.93

1.43

23.57

5.89

5.90

1.20

23.80

1.30

23.70

5.99

6.00

1.35

23.65

1.15

23.85

6.09

6.10

1.50

23.50

1.00

24.00

6.19

6.20

1.63

23.37

0.87

24.13

6.29

6.30

1.75

23.25

0.75

24.25

6.39

USE OF

INDICATORS

If an indicator has only one color, for instance if it is yellow
in the alkaline form and colorless in the acid form, it is evident
that the method employed by Gillespie may be used with the
elimination of one of the sets of tubes. Thus if 10 cc. of a tested
solution containing 1 cc. of para nitrophenol matches 10 cc. of

BICOLOR STANDARDS

127

an alkaline solution containing 0.2 cc. of the same solution of the
same indicator, it is known that the tested solution has induced
a 20 per cent transformation of the indicator. Then a is 0.2.
If now K'a has been determined, and if it has been shown that
the simple dissociation formula holds for the indicator in use, the
following equation may be solved for pH.

PH == pK'a + log

1 -a

TABLE 17
Table for preparation of bicolor standards with 0.008 per cent brom cresol

purple, 0.002 N HCl, and 0.01 N NaOH

Brom cresol purple. pK' = 6.09 at 38°, and 6.19 at 20°

(After Hastings, Sendroy and Robson, 1925)

pH38o

ALKALI TUBE

ACID TUBE

pH20o

Dye

Alkali

Dye

Acid

cc.

5.60

0.61

24.39

1.89

23.11

5.70

0.72

24.28

1.78

23.22

5.80

0.85

24.15

1.65

23.35

5.90

0.99

24.01

1.51

23.49

6.00

1.12

23.88

1.38

23.62

6.10

1.26

23.74

1.24

23.76

6.20

1.40

23.60

1.10

23.90

6.30

1.55

23.45

0.95

24.05

6.40

1.68

23.32

0.82

24.18

6.50

'1.80

23.20

0.70

24.30

6.60

1.91

23.09

0.59

24.41

6.70

2.01

22.99

0.49

24.51

6.80

2.09

22.91

0.41

24.59

6.90

2.16

22.84

0.34

24.66

7.00

This procedure has been developed by Michaelis and co workers;
Biochem. Z. (1920) 109, 165; Biochem. Z. (1921) 119, 307; Deut.
med. Wochenschr. (1920) 46, 1238; 47, 465, 673; Z. Nahr. Genussm.
(1921) 42, 75; Z. Immumtatsf. (1921) 32, 194; Wochenschrift
Brau. (1921) 38, 107.

The following revisions of their tables are taken from the 1926
edition of Praktikum der Physikalischen Chemie by Michaelis.

In the cases of phenolphthalein and Alizarine Yellow GG the

128

THE DETERMINATION OF HYDEOGEN IONS

TABLE 18
Table for preparation of bicolor standards with 0.0075 per cent phenol red,

0,001 N HCl, and 0.01 N NaOH

Phenol red. pK' = 7.65 at 38°, and 7.78 at 20°

(After Hastings, Sendroy and Robson, 1925)

pH38°

ALKALI TUBE

ACID TUBE

pH20°

Dye

Alkali

Dye

Acid

cc.

6.70

0.25

24.75

2.25

22.75

6.83

6.80

0.31

24.69

2.19

22.81

6.93

6.90

0.38

24.62

2.12

22.88

7.03

7.00

0.46

24.54

2.04

22.96

7.13

7.10

0.55

24.45

1.95

23.05

7.23

7.20

0.65

24.35

1.85

23.15

7.33

7.30

0.77

24.23

1.73

23.27

7.43

7.40

0.90

24.10

1.60

23.40

7.53

7.50

1.04

23.96

1.46

23.54

7.63

7.60

1.18

23.82

1.32

23.68

7.73

7.70

1.32

23.68

1.18

23.82

7.83

7.80

.46

23.54

1.04

23.96

7.93

7.90

.60

23.40

0.90

24.10

8.03

8.00

.73

23.27

0.77

24.23

8.13

8.10

.85

23.15

0.65

24.35

8.23

8.20

.95

23.05

0.55

24.45

8.33

TABLE 19

One-color" indicators

COMMON NAME

CHEMICAL NAME

COLOR

pKAT

18°

RANGE

SOLUTION

j8-dinitrophenol

l-oxy-2, 6-dinitroben-

yellow

3.69

2.2-4.0

0.1 gram in 300 cc.

zene

water

a-dinitrophenol

l-oxy-2, 3-di nitroben-

yellow

4.06

2.8-4.5

0.1 gram in 200 cc.

zene

water

y-dinitrophenol

l-oxy-2, 5-di nitroben-

yellow

5.15

4.0- 5.5

0.1 gram in 200 cc.

zene

water

p-nitrophenol

l-oxy-4-nitrobenzene

yellow

7.18

5.2- 7.0

0.1 gram in 100 cc.

water

m-nitrophenol

l-oxy-3-nitrobenzene

yellow

8.33

6.7- 8.4

0.3 gram in 100 cc.

water

Phenol phthalein . . .

phenol phthalein

red

(9.73)

8.4-10.5

0.04 gram in 30 cc. al-

cohol + 70 cc. water

Alizarin yellow GG

•

(salicyl yellow) . . .

m-nitrobenzene-azo-

yellow

(11.16)

10.0-12.0

0.05 gram in 50 cc. al-

salicylic acid

cohol + 30 cc. water

ONE-COLOR INDICATORS

129

TABLE 20
pK values of " one-color" indicators at different temperatures

TEMPERATURE

/3-DINITRO-
PHENOL

(1:2:6)

a-DINITRO-
PHENOL

(1:2:4)

7-DINITRO-
PHENOL

(1:2:5)

P-NITRO-
PHENOL

1:4

m-NITRO-
PHENOL

1:3

3.70

4.16

5.24

7.39

8.47

3.76

4.13

5.21

.7.33

8.43

3.74

4.11

5.18

7.27

8.39

3.71

4.08

5.16

7.22

8.35

3.69

4.06

5.15

7.18

8.33

3.68

4.05

5.14

7.16

8.31

3.65

4.02

5.11

7.10

8.27

3.62

3.99

5.09

7.04

8.22

3.59

3.96

5.07

6.98

8.18

3.56

3.93

5.04

6.93

8.15

3.54

3.91

5.02

6.87

8.11

3.51

3.88

4.99

6.81

8.07

TABLE 21

Relation of apparent degree of color, a, to pH
Phenolphthalein

0.01

8.45

0.16

9.10

0.55

9.80

0.014

8.50

0.21

9.20

0.60

9.90

0.030

8.60

0.27

9.30

0.65

10.00

0.047

8.70

0.34

9.40

0.70

10.1

0.069

8.80

0.40

9.50

0.75

10.2

0.090

8.90

0.45

9.60

0.80

10.3

0.120

9.00

0.50

9.70

TABLE 22

Relation of apparent degree of color, a, to pH
Alizarin yellow GG

0.13

10.00

0.56

11.20

0.16

10.20

0.66

11.40

0.22

10.40

0.75

11.60

0.29

10.60

0.83

11.80

0.36

10.80

0.88

12.00

0.46

11.00

130

THE DETERMINATION OF HYDROGEN IONS

color-change does not follow the type a-curve for a univalent
acid. Tables 21 and 22 give the empirical values for a for
use with the ideal equation.

Calculations are aided by the use of a table relating a to

log

Such a table, somewhat more elaborate than that

1 - a

required for this special purpose, will be found on page 677 of
the Appendix.

TABLE 23

Composition of color standard
m-nitrophenol

Tube number

Cubic centimeters of indicator. .
pH..

5.2

8 4

4.2

8 ?

3.0

8 0

2.3

7 8

1.5

7 6

1.0

7 4

0.66
7 ?,

0.43
7 0

0.27
6 8

p-nitrophenol

Tube number

Cubic centimeters of indicator. .
pH

4.05

7 0

3.0

6 8

2.0
6 6

1.4
6 4

0.94

6 ?,

0.63
6 0

0.4
5 8

0.25
5 6

0.16
5 4

2, 5-dinitro phenol (7 dinitro phenol)

Tube number

?,0

?,1

?,2

Cubic centimeters of indicator .

6 6

5 5

4 5

3 4

?, 4

1 65

1 1

0 74

pH .

5 4

5 ?,

5 0

4 8

4 6

4.4

4.2

4.0

2, 4-dinitro phenol (a dinitro phenol)

Tube number

27
6.7
4.4

28
5.7
4.2

29
4.6
4.0

30
3.4

3.8

2.5
3.6

32
1.74
3.4

1.20
3.2

0.78
3.0

0.51

2.8

Cubic centimeters of indicator. .
pH

With these data we are now prepared to measure pH values
without the use of standard buffer solutions.

Test tubes must be of equal bore. A measured amount of the
solution to be tested (e.g. 10 cc.) is mixed with the proper indicator
in such amount that a rather weak color is developed. To a
second test tube containing 9 cc. 0.1 M Na2C03 (for nitro phenols
only) there is added such a volume of the indicator solution that
the color developed approximately matches that of the first tube.
The volume of the second tube is now made up to the volume of
the first. If the two tubes do not match in color, another trial

MICHAELIS' METHOD 131

is made with more or less indicator until a color match is obtained.
The amount of fully transformed indicator in the second tube then
corresponds to that amount of indicator in the first tube which
has been transformed to the colored tautomer. Let us assume
that 1.0 cc. was added to the tested solution and that a color match
occurs when 0.1 cc. of the same indicator solution was placed in
the second alkaline tube and made up to the volume of the first.
Then the percentage color transformation induced by the tested
solution was 10.

Hence a = 0.1 and log —2— = - 0.95.
1 — a

If the indicator used was p-nitrophenol and the temperature
was 20°C. pH = 7.16 - 0.95 = 6.21 (6.2).

For routine work in the range pH 2.8 to 8.4 Michaelis (1921)
recommends the following system. See table 23.

To uniform test tubes are added seriatim the volumes of
indicator solution given in table 23, the indicator solution
being prepared by diluting the stock solutions (page 128) ten
times with 0.1 M Na^COs solution. Each tube is now filled to
a 7 cc. mark with the soda solution. (In the original paper
Michaelis and Gyemant describe dilutions with N/100 NaOH
solution.)

The test tubes are sealed and when not in use are protected
from the light.

To test a solution for its pH value, 6 cc. are taken and 1 cc.
indicator solution added. The solution is then compared with
the standards in a comparator, see page 171, figure 29.

Empirically, Michaelis finds that if there be placed over the
comparator holes a ground glass and a glass of cobalt blue, the
color quality of two tubes will be very different when there is no
match. This increases the differentiating ability of the eye and
makes the use of the nitrophenols with colored solutions, such as
urine, much more satisfactory. The glass of cobalt blue should
be selected by trial for a satisfactory density.

For finding the pH values of waters Michaelis (1921) operates
as follows :

A stock solution containing 0.3 gram pure m-nitrophenol in
300 cc. distilled water is diluted before use by adding to 1 cc.
of the stock 9 cc. distilled water. There are used flat bottom

132 THE DETERMINATION OF HYDROGEN IONS

tubes of about 25 cm. height and 14 mm. internal diameter
having such uniformity that 40 cc. of water will stand at a height
of between 22 and 23 cm. To six such tubes are added seriatim
0.25; 0.29; 0.33; 0.38; 0.45 and 0.50 cc. of the diluted m-nitro-
phenol solution. To each tube are added 40 cc. of an approxi-
mately N/50 NaOH solution freshly prepared by dilution of an
approximately normal solution. These are the standards.

To test a water, 40 cc. are added to a tube of correct dimensions
and to this is added sufficient indicator to develop a color within
the range of the standards, preferably near the brighter of the
standards. Comparison is now made as in Nesslerization, after
having waited two minutes for completion of the mixing.

TABLE 24
Effect of salt on pK of m-nitrophenol

MOLECULAR SALT CONTENT

log^I

0-0.01

8.33

0.05

8.28

0.10

8.23

0.15

8.22

0.20

8.18

0.3-0.6

8.17

to 1.0

8.15

The amount of indicator in the alkaline, matching standard
corresponds to the amount transformed to the colored form by
the tested solution. Therefore,fthe cubic centimeters of indica-
tor in the standard divided by the cubic centimeters in the tested
solution is a, the degree of color transformation, or when multi-
plied by 100, the percentage color transformation.

Michaelis and his co-workers have tabulated corrections for
temperature and for salt concentrations. The operator should
determine for himself not only the order of accuracy required in
his problem but his own ability to make readings with that pre-
cision which will make corrections significant. He may then
refer to the original papers for tables giving corrections for salt
effects and for temperature. The order of magnitude of these
corrections may be seen in tables 20 and 24.

For ^m-nitrophenol Michaelis and Kriiger give the values of

VI MICHAELIS' METHOD 133

log — at 17°C. in solutions of the indicated salt concentrations

shown in table 24.

In spite of the fact that the nitro-compounds used by Michaelis
and Gyemant are of wan color and those tried in the survey made
by Clark and Lubs were neglected for this reason, Michaelis and
Gyemant describe the application of their method to colored
solutions. In this use the colored glass is essential.

Advantage is taken of the fact that many solutions are inappre-
ciably altered in pH by diluting five or even ten times (see page
40). For dilution, Michaelis and Gyemant use freshly boiled
NaCl solution of a concentration approximately that of the test
solution. If on dilution the natural color still interferes with
the use of an indicator, the natural color may be duplicated in
the standard by the use of supplementary dyes such as S0rensen
uses. Or, if addition of alkali does not alter the natural color of
the solution under test, the standard may be made up with an
alkaline solution of the tested solution itself. In this case it is
necessary to be on guard against the buffer action and to add
alkali until no increase in the color of the indicator is observed.

Without doubt the preferable procedure to follow when apply-
ing the Michaelis and Gyemant method or any other method to
colored solutions is to use the "comparator" described on page
172 and illustrated in figure 29, page 171. The blue glass (see
page 131) is held before the holes by a pair of clips.

The method of Michaelis and Gyemant is fundamentally the
same as that of Gillespie and should, therefore, be used with the
qualifications which Gillespie has stated. There is a distinct
advantage in the use of the nitrophenols for they have been found
to have relatively small "protein" and salt effects, and do not
show the errors with alkaloids that appear with the use of sulfon-
phthaleins. It is sometimes necessary to use very high con-
centrations of the indicator, and in such circumstances one must
be on guard against the effect of the indicator itself or of im-
purities. Only the purest grades of nitrophenols should be
used. Impure samples are almost useless.

Inasmuch as the method inherently is capable of high accuracy
it may be asked why its description is relegated to a chapter
entitled "approximate determinations." If the reader will reflect

134 THE DETERMINATION OF HYDROGEN IONS

he will remember that any numerical value reached by the ap-
plication of this method depends upon the value of the disso-
ciation constant. There remain larger discrepancies in the values
for some of the indicators than are warranted by the accuracy of
available methods if applied to the same solutions. But, as we
shall see, a dissociation constant formulated by the classical
methods, is subject to some change in value as the nature of the
solution (e.g., salt content) changes. It is therefore preferable
to recast the equations into terms of activities (see Chapter XI)
and when this is done the true dissociation constant may have a
very different numerical value than has the apparent constant
at a given salt content of the solution. As this edition goes to
press the period is just beginning when the characteristic con-
stants of indicators are being redetermined both with the aid of
spectrophotometric accuracy and with the aid of modern re-
formulation. Pending the outcome we must regard the applica-
tion of the method in question, when performed with the data
available, as having been standardized by reference to the standard
buffer method and with all the systematic errors attendant upon
a secondary standardization.

Indicator papers. Although a favorite form of indicator is the
deposit on a strip of paper (for example the familiar litmus paper)
it is to be avoided unless the use of an indicator solution is pre-
cluded. It is to be avoided because the factors involved in the
reaction between solutions and indicator are made complex by
the capillary action of the paper or the material entrained in
these capillaries. On the other hand there are occasions when
an approximate measure of pH is sufficient and when an indicator-
paper is to be preferred. On such occasions it is desirable to
know the difficulties to be encountered.

We are indebted to Walpole (1913) and others and particularly
to Kolthoff (1919, 1921) for investigations on this subject. Kolt-
hoff has given particular attention to the sensitivity of indicator
papers when used in titrations, a situation where there is generally
but little buffer action near the end-point. Under such circum-
stances there are to be regarded a number of details which are
described at length in Kolthoff's papers. Several of these details
will be perceived if we describe some of the more important aspects
of the indicator-paper method of determining pH.

VI INDICATOR PAPER 135

In general one must ride either horn of the following dilemma.
The paper is sized, in which case the buffer action of the tested
solution must be strong enough and allowed time enough to over-
come the buffer action of the sizing. Or the paper has the quali-
ties of filter paper, in which case the solution tested will spread
and leave rings of different composition formed by the adsorp-
tive power of the capillaries.

Kolthoff found that various treatments and selections of filter
paper are of secondary importance, so the choice lies between
sized and unsized paper. Certain coloring matters are adsorbed
by filter paper so that a separation is possible and the clear solu-
tion can be found in a ring about the point of contact between a
tested colored solution and the indicator paper. But beyond this
ring is a much more dilute one and unless one knows the properties
of the system under examination it is not easy to estimate cor-
rectly the pH of the solution from the appearance of the paper.

In any case the paper should be left in contact with the tested
solution a generous length of time, for the establishment of
equilibrium may be very slow (Walpole), and there must be in-
stinctively exercised a mental plotting of the time curve.

If, after having exhausted all other methods, it is found that
the indicator-paper method is the better adapted to a particular
set of circumstances, the procedure should be calibrated to the
purpose at hand rather than forcec} to render accurate pH values.

Rebello (1922) replaces paper by cotton thread which he draws
through the tissue he examines. Wulff (1926) uses transparent
membranes of cellulose derivatives.

See Kolthoff and Furman's book Indicators for further discus-
sion of indicator papers.

Dilution. As indicated in Chapter II a well buffered solution
may often be moderately diluted without seriously altering the pH.

When dealing with complex solutions which are mixtures of
very weakly dissociated acids and bases in the presence of the
salts, and especially when the solution is already near neutrality,
dilution has a very small effect on pH, so that if we are using the
crude colorimetric method of determining pH, a five-fold dilution
of the solution to be tested will not affect the result through the
small change in the actual hydrogen ion concentration. Differ-
ences which may be observed are quite likely to be due to change
in the protein or salt content.

136 THE DETERMINATION OF HYDROGEN IONS

For accurate work with dilutions there should be involved the
principles discussed in Chapter XXV.

The salt content of the standards undoubtedly influences the indi-
cators and should be made as comparable as is convenient with
the salt content of the solutions tested when these are diluted to
obtain a better view of the indicator color.

In the examination of soil extracts colorimetrically little could
be done were the "soil-solution" not diluted. Whatever may be
the effect it is certain that the correlations between the pH values
of such extracts and soil conditions is proving of great value (see
Chapter XXX). Wherry has developed a field kit of the sulfon-
phthalein indicators with which he has found some remarkable
correlations between plant distribution and the pH of the native
soils. This field kit is now on the market.

A good example of the application of the dilution method is
given in a paper by Sharp and Mclnerney (1926). They dilute
milk, whey and cream with as much as nineteen volumes of water
in order to lower the turbidity adequately. They then apply
their statistical study of corrections to be made to bring the
colorimetric readings into conformity with the hydrogen electrode
measurements of the undiluted solution. They tabulate these
corrections for convenience in routine examinations.

The use of indicators in bacteriology. Perhaps no other science
requires such continuous routine use of indicators as does bac-
teriology. This use is chiefly in the adjustment of the reaction
of culture media and in the testing of the direction and limits of
fermentation. While these are but examples, the frequency with
which they become matters of routine warrants a brief outline of
special procedures.

If experience has shown that the pH of the medium may lie
within a zone about 0.5 unit of pH wide, it is sufficient to add un-
standardized acid or alkali, as the case may be, until a portion
of the medium tested with the proper indicator in proper concen-
tration approximately matches that color standard shown in the
color chart of page 65 corresponding to the pH value to be ap-
proximated. This requires experience in overcoming the con-
fusing effect of the natural color of the medium and also a well
established sense of color memory. The beginner should proceed
in some such way as the following.

VI SPECIAL USES OF INDICATORS 137

It is desired, for instance, to adjust a colorless medium to pH
7.5. The medium as prepared is somewhat below the final vol-
ume. A quick, rough test at room temperature shows that the
pH value lies between 6.0 and 6.5. Therefore, alkali must be
added. The alkali solution to be used need not be standardized
but may be about 1 normal. An exact one-in-ten dilution of this
is run into 5 cc. of the medium to which have been added 5 drops
of phenol red solution. Titration is continued until the color
nearly matches 10 cc. of standard buffer "7.5." The tube of
medium is now diluted to 10 cc. so that a color comparison may be
made between test solution and standard, each containing the
same concentration of indicator. The tubes are viewed through
equal depths of solution. If the desired point, 7.5, has been
overstepped, another trial is made. If 7.5 is not reached a
moderate addition of alkali may be made without serious viola-
tion of volume requirements, and a second reading is taken.

After making estimates of the pH values in the two readings
an interpolation is made of the amount of dilute alkali required
to bring the medium to exactly pH 7.5. From this is calculated
the amount of the stronger alkali required for the main portion.
After adding this, a check determination is made. When
finally adjusted the medium is diluted to its final volume Most
culture media suffer alterations of their pH values during sterili-
zation and consequently allowance for this must be made if the
final pH value is to be exact. This allowance will vary with the
medium but can easily be determined for a standard medium
prepared under uniform conditions.

When the color or turbidity of a tested solution interferes with
direct color comparisons proceed as above but make comparisons
by means of the Walpole compensation method described on
page 171.

It need hardly be said that if the requirements of an organism
are such that the desired pH value cannot be obtained with phenol
red a more suitable indicator is selected from table 11 and if the
medium requires the addition of acid an unstandardized acid
solution approximately normal (or stronger) and an exact 1:10
dilution of this are substituted for the alkali solutions mentioned
above.

In testing fermentations it often happens that the final hydro-

138 THE DETERMINATION OF HYDROGEN IONS

gen ion concentration is of more significance than the amount of
acid or alkali formed; but the two distinct types of data are not
to be confused to the complete displacement of either.

It is sometimes convenient to incorporate the indicator with the
medium, provided the indicator is not reduced or destroyed by
the bacterial action. The sulfonphthaleins are particularly use-
ful for they are not reduced except by the more active anaerobes.
Brom cresol purple replaces litmus in the common milk-fermenta-
tion tests without introducing that confusion which the reduction
of litmus causes. It reveals differences in pH even beyond the
range of its usefulness for ordinary measurements, passing from a
greyish blue in normal milk to more and more brilliant yellows
with the development of acidity, and to a deep blue with the
development of alkalinity. For further details see Clark and
Lubs (1917).

In the method of Clark and Lubs (1915, 1916) for the differenti-
ation of the two main groups of the coli-aerogenes bacteria, as
well as in the similar method of Avery and Cullen (1919) for
separating streptococci, the composition of the medium is so
adjusted to the metabolic powers of the organisms, that the
reaction is left acid to methyl red in one case, and alkaline in the
other. No exact pH measurements are necessary. In cases
where large numbers of cultures falling within the range of one
indicator are to be tested, the cultures may be treated with the
indicator and compared by grouping. A careful determination
made upon one member of a homogeneous group will serve for all.
In this way large numbers of cultures may be tested in a day.

Special uses. While on the subject of approximate determina-
tions with indicators a word may be said about the usefulness of
the quick, rough test.

Almost every investigator has come to realize that among the
mistakes in labeling chemicals the more frequent are cases in
which a basic salt is labeled as an acid salt and vice versa. A
solution of NaaHPO4, for example, has a pH value, which, while
easily displaced (see fig. 4), distinguishes it definitely from a solu-
tion of NaH2P04 or Na3P04. Indeed some idea may be obtained
of the degree of impurity if the pH value of a dilute solution is
displaced definitely from about pH 8.5. Some serious accidents
have occurred in medical practice by the use of solutions purported

VI MICRO METHODS 139

to be neutral and too late found to be acidic. One short, swift
test with an indicator could have revealed the situation, and
averted the accident.

Indeed there are a great many substances solutions of which
have either a buffered and definite pH value, as in the case of
acid potassium phthalate, or else a pH value easily displaced by
impurities from that of the absolutely pure substance but still
falling within limits, as in the case of the primary and secondary
phosphates. When properly defined, such values can be made
part of the specifications for purity. Especially in the case of
drugs which are often used beyond the reach of the assay labora-
tory a simple indicator test should prove helpful as suggested by
Evers (1921) and especially emphasized by Kolthoff (1921).

MICRO COLORIMETRIC METHODS

The majority of micro-methods2 follow the main principles
hitherto described but with greater or lesser reduction in the
dimensions of the vessels. Such are the capillary tubes employed
by Walther and Ulrich (1926), Needham and Rapkine. Rap-
kine's capillary tubes, used for comparison with a single cell
which has been injected with an indicator, are made of varying
diameter in order that there may be selected a portion of the
capillary of the same diameter as the cell.3 Vies (1926) describes
a micro colorimeter for use on the microscope stage.

Spotting. When only small quantities of solution are available
or when highly colored solutions are to be roughly measured, their
examination in drops against a brilliant white background of
"opal" glass is often helpful. In the examination of colorless
solutions comparisons with standards may be made as follows.
A drop of the solution under examination is mixed with a drop
of the proper indicator solution upon a piece of opal glass. About
this are placed drops of standard solutions and with each is mixed
a drop of the indicator solution used with the solution under
examination. Direct comparison is then made. Felton, who
developed details in this method for the examination of small
quantities of solutions used in tissue-culture investigations, found

2 See also Pfeiffer (1927), Vies (1926) and Lindhard (1921) on micro-
colorimetric methods. Cf. Ellis (1925).

3 Personal communication.

140 THE DETERMINATION OF HYDROGEN IONS

mixtures of indicators of particular value for orientation. (See
page 96.) Mixtures are used only as "feelers." The opal glass
or porcelain upon which the tests are to be made should be care-
fully tested for the absence of material seriously affecting the
acid-base equilibria of the material under examination. Errors
due to unequal drops, evaporation and impurity of indicator are
to be watched for. For further details see Felton (1921).

To what extent the mixture of as much as 50 per cent by volume
of indicator solution and tested solution causes an error can only
be judged in the specific case.

From the spot-plate with flat surface and drops of any size
that can be made, we come to the spot-plate with depressions to
hold larger quantities; and then to small glass cells such as Brown
(1923) employs and such as the LaMotte Co. uses in one of their
commercial sets.

PRECIPITATING INDICATORS

Naegeli (1926) employs the principle, briefly noted on page
583, that precipitations may occur within narrow ranges of pH.
He therefore selects organic acids the undissociated forms of
which are very little soluble.

The variation of the precipitation point with the buffer suggests
a restudy in terms of activities. See page 583.

CHAPTER VII

THE APPLICATION OF SPECTROPHOTOMETRY, COLORIMETRY, ETC.

How that element washes the universe with its enchanting waves!
.... 'Tis the last stroke of Nature; beyond color she cannot go.

— EMERSON.

INTRODUCTION

The marvelous color-change of an indicator invites scrutiny of
the internal structure. Why should the mere act of ionization
initiate a radical change in the response to radiation? Theory
relating structure to absorption of radiant energy has not yet
attained the certitude that will doubtless arrive in time. There-
fore, we had best resist the temptation to look into this tantalizing
subject lest our attention be diverted from the present task,
which is to formulate the fact of absorption of radiant energy in
a manner which will contribute to exactitude in measurement of
pH-values.

ABSORPTION

As radiant energy of any wave-length advances through a
material medium it suffers some absorption. Visible radiant
energy is absorbed but little by water and by optical grades of
glass; but in refined measurements absorption by these relatively
"transparent" materials must be taken into account. Usually
absorption by solutions is somewhat selective. Absorption is
both selective and effective in solution of those "dyes" which are
used as indicators. Thus, if an alkaline solution of cresol red is
viewed through a spectroscope, there appears in the spectrum a
dark band, the position of which indicates that the stimuli of the
colors yellow and green have been very effectively obstructed.
So far as relative absorption of the radiant energy is concerned,
this is shown quantitatively by the curves of figure 20 where the
ordinate is a measure of relative absorption and the abscissa
is divided in such a way as to show approximately the relative
positions of lines of various wave-length as distributed in the

141

142

THE DETERMINATION OF HYDROGEN IONS

spectrum of a prism instrument. From this curve it is evident
that, in addition !to Relatively great absorption centered at the
wave-length (X)1 of mju = 572, there is appreciable absorption by

... 650 700
Violet Blue Green Yellow 01-41136 Red

FIG. 20. ABSORPTION CURVES OF INDICATORS

cresol red within the range m/* 450 to m^ 610. Quantitative
measurement of absorption and the charting of the absorption

1 X = general symbol for wave-length, m/x
X 10~9. One m/i = 10 Angstrom units.

milli micron = meters

VII ABSORPTION 143

band provides data for identification of an indicator and for tests
of purity. A special application of the data to the determination
of pH values will presently be outlined.

Neglect for the moment absorption by the solvent and by the
glass walls of the container. Consider the absorption which occurs
when radiant energy of one definite wave-length, X, passes through
a homogeneous solution of some absorbing substance contained
in a cell the end-plates of which are plane-parallel, the propagation
through the cell and solution being rectilinear.

In advancing through an infinitesimal length, dl, of the solu-
tion, the radiant energy of the given wave-length suffers the loss
of some certain fraction of its power,2 P. Within the next in-
finitesimal length the remaining power is reduced by the same
fraction. Accordingly, the decrease of power per element of
length is proportional to the power of the radiant energy in this
length.

Now let the power incident at the first surface of the solution be
PI and that emergent at the second surface be P2. When these
limits are used in the integration of equation (1) there is obtained
equation (2)

-Zn|2 = k'l (2)

-tl

In this equation In (logarithmus naturalis) symbolizes (natural)
logarithms to the base e.

The decline of radiant power within any infinitesimal length
of the solution should be proportional to the number of absorbing
molecules encountered. This number may be considered propor-
tional to the concentration, c, of the dye under a given set of con-
ditions. Therefore, (1) becomes (3). Integration of (3) between
the limits PI and P2 yields (4)

'T>

= kcP (3)

2 Since ratios of powers are to be used, intensity might be substituted
here for power.

144 THE DETERMINATION OF HYDROGEN IONS

- ln |» = kcl (4)

The ratio ^ is that fraction of the power of the incident radiant

energy which emerges. This ratio is called the transmittance and
is symbolized by T. Introducing T and changing the constants
of (2) and (4) to correspond with the conversion of natural
logarithms to common logarithms we have from (2) and from
(4) equations (5) and (6) respectively.

-logTx=lK'x (Lambert's Law) (5)

-logTx = IcKx (Beer's Law) (6)

The subscript X is used to emphasize the fact that specific values
for the indicated terms depend upon the wave-length (X) of the
radiant energy.

Here it may be noted that any relation between the transmit-
tance at a given wave-length and the wave-length is determined
by the specific properties of the absorbing system. In other
words the position and shape of the absorption curve is charac-
teristic of a given system. With the cause of this, or with the
empirical formulation of a relation between TX and X as X varies, we
are not now concerned. We are concerned only with the accept-
ance of the fact as a specificity to put to our present uses. For a
brief discussion of variation of TX with variation of X see Thiel
and Diehl (1927) page 517 ff. but especially the Report of the
Committee on Spectra and Constitution, 1926, British Asso-
ciation.

Equation (5) is an expression of Lambert's law of absorption and is be-
lieved to be universally applicable. Equation (6), which involves concen-
tration of the absorbing species, must be used with caution; for, although
there will presently be noted cases in which apparent deviation from this
so-called Beer's law is readily explained and indeed put to use, there are
cases in which observed deviations have not been explained.

When the length, 1, and the concentration, c, are each unity

- log T = K

K is called the specific transmissive index. Its value as determined by a
measurement of T at a, given wave-length will of course depend upon the unit
adopted for 1 and c. The unit of length is usually the centimeter; but the

VII EXTINCTION COEFFICIENT 145

unit of concentration is frequently changed to the convenience of special
problems. Were c the concentration of total dye, as it is in the usual state-
ment of Beer's law, and were one mole per liter the unit of concentration, K
would be the molar transmissive index. The term absorption index arises
from the fact that the magnitude of K is a measure of the extent of the

r> ~p

relative absorption. If — - is T, the transmittance, 1 — — ^ may be called

r\ . * i

the absorptance A, a term little used.

The term "extinction coefficient" arises in the following way. Were all
the radiant power incident at the first surface to be absorbed (extinguished)

when the radiation reached the second surface, — would be zero and then,

by equation (5), K' or 1 would have to be infinity. Since K' has a finite
value, the length would have to be infinity. To avoid this difficulty

imagine the value of 1 to baadjustedso that K' equals unity. Then —log
•p I

T = 1 or T = — = — . Under these conditions K' appears as that coeffi-
tr\ 10

cient the value of which determines the distance, 1, within which the radiant
power is one-tenth extinguished, hence, "extinction coefficient."

As specified in their derivation, and as indicated by means of the
subscript X, equations (5) and (6) are applicable only when the
wave-length is specified. In practice very narrow bands of the
spectrum are used. Using these narrow bands and determining
at successive wave-lengths the specific transmissive indices we
can chart so-called absorption curves. (See figs. 20 and 24.)
For regions of the spectrum in which the wave-length is lower
than the wave-length of visible radiant energy photographic
methods are employed. For regions in which the wave-length is
larger than the wave-length of visible radiant energy thermo-
electric methods are used. Undoubtedly the most fundamental
data will be obtained when indicators are examined with radiant
energy of a wide range of wave-length, but the immediate task is
to make use of visible radiant energy.

SPECTROPHOTOMETERS

A brief description of a remarkably direct-reading instrument,
the Keuffel and Esser Color Analyser, will show how the trans-
mittance of a solution may be measured. Figure 21 is a diagram-
matic representation of the instrument. See Keuft'el (1925).

Radiant energy from tungsten lamps, 12, in the "integrating"
sphere, 1, is diffusely reflected from two blocks of magnesia held

146

THE DETERMINATION OF HYDROGEN IONS

at 6 and 7. The two beams of radiant energy pass through the
slit 17 of the collimator, and are brought by the collimator to the
prism 19. The position of this prism, which can be rotated by
the drum with wave-length scale 4, determines the narrow band of
the spectrum in the photometric field at the eye-piece 21. By
means of the biprism 20 placed over the lens 18, there is produced
the photometric field of the type illustrated by 9. The energy
in one -half of this field comes by one of the beams and that in the
other comes by the second beam.

1. Spherical Light Source.

2. Photometer.

3. Spectromter.

4. Wave Length Scale.

5. Photometer Scale.

6. Holder for Standard Sample.

7. Holder for [Reflection Sam-

ples.

ft. Hold erf or Transparent Sam-
ples.

9. Field of View thru Eye Slit.

10. To Vacuum Ventilator.

11. Plug for Vacuum Ventilator
li. 400 Watt Lamps.

13. Lever for Kaising Photo-

meter.

14. Sector Discs.

15. Universal 110 Volt Motor.

16. Speed Control Rheostat.

17. Entrance Slit.

18. Collimator Objectives.

19. Dispersion Prism.

20. Bi-Prism.

21. Eye Slit.

22. Cast Aluminum Base.

Diagram of K A, E COLOR ANALYZER

FIG. 21
(Courtesy of Keuffel and Esser Company)

The one beam passes through the solution which is under ex-
amination and which is held at 8. The other beam passes through
a tube of the same length and similar glass end-plates (also held
at 8) but containing the solvent alone. The power in the given
narrow section of the spectrum as seen at the eye-piece is now cut
down by the rotating sector, 14, until photometric match is ob-
tained. The openings of the sector are controlled in an ingenious
way while the sector is rotating. The drum controlling these
openings is so marked (scale 5) as to indicate directly the per-
centage transmission.

VII

SPECTROPHOTOMETERS

147

Since the transmission by the solvent and by the end-plates are
compensated by placing in the path of the second beam a similar
tube of like length and solvent, the percentage transmission ob-
served is that of the solute, conditioned, of course, by the solvent.

The percentage transmission is one hundred times^the trans-
mitt ance T.

In some instruments the photometric match is obtained by
altering the actual or virtual distances of two sources.

One of the most frequently used devices is the Konig-Martens
photometer, the principal features of which are indicated by
figure 22.

a. .A

D- Ji -O— I

~t* II II "U2 ! "

FIG. 22. (Above) PRINCIPAL FEATURES OF THE KONIG-MARTENS PHO-
TOMETER; (Below) ARRANGEMENT OF TUBES IN PHOTOMETER

Two beams of radiant energy coming through apertures A and
B are to be reduced to equal power at the eye-piece O. The
beams are converged by the biprism C to the collecting lens D and
thence pass through the Wollaston prism W. The Wollaston
prism is a crystal of calcite so cut as to separate the "ordinary"
and "extraordinary" rays of the double refraction and deliver
them polarized in planes mutually perpendicular. Each of the
original beams, a and b, is thus divided into two and each of these
is redivided by the biprism F. Thereby eight images correspond-
ing to the two apertures A and B are formed. The polarization
of each is indicated in the figure. All but one pair of these images is
screened or absorbed by the walls of the instrument. In the pair
selected the polarizations are in planes mutually perpendicular.

148

THE DETERMINATION OF HYDROGEN IONS

At N is a Nicol prism which can be turned. At one position it
reduces to zero the amplitude of vibration in the ray that gives
image A'. At 90° from this position it reduces to zero the
amplitude of vibration in the ray that gives image IV.

If the power at A equals the power at B and there are no inci-
dental polarizations at the surfaces of the optical parts, and if
there is no inequality of absorption in the paths, there will be
photometric match between A' and B' when the Nicol is turned
45° with relation to either of the extinction settings.

But assume that the radiant power at A is not equal to that
at B. The angle at which the Nicol must be turned is related to
the ratio of the powers at A and B as follows:

Suppose beam a is polarized in the direction OA, figure 23. Let
the amplitude of the vibrations be represented by the distance

FIG. 23

OA. If the Nicol be turned so that its optic axis conforms to
OA it will not affect the amplitude. If it be turned 90° from OA
it will reduce the amplitude of vibration in beam a to zero. At
any angle 6 the amplitude of the vibrations in beam a which
will be transmitted by the Nicol will be represented by the dis-
tance OC. Likewise for beam b the amplitude of the vibrations
transmitted by the Nicol will be OD.
Geometrically we have

OC = OA sine B
OD = OB cos 6

OD OB

(7)
(8)

(9)

Again consider figure 22 in which the photometer with aper-
tures A and B is placed in train with the beams a and 6 which pass
through tubes of absorbing solution and solvent respectively.

VII PHOTOMETER EQUATION 149

For purposes of generality we shall assume that the light source,
S, delivers to the absorbing tubes energy of unequal power Pal
and Pbi- For simplicity of exposition we shall imagine that the
solvent and solution are held in like tubes of equal length. Also
we shall imagine that the solute is removed from the solution tube
and placed in a space of the same dimensions.

The various Ps in the figure represent the powers of the
radiant energies at the several points.

The ratio of the powers of two beams equals the ratio of the
squares of the amplitudes.

Therefore,

¥ = = do)

Pb3 ODa

Photometric match is determined by adjustments to the con-
dition that Pa4 = Pbs. Using this relation and equations (9) and
(10) we obtain

L = tan20 (11)

OA2

Since

OA2 Pa3

^-2 = tan2 0 (12)

Pa3

The transmittance of the solute is given by:

T = |^ (13)

The transmittance of the solvent is given by the identities

JL al -Tbl

Combination of equations (12), (13), and (14) yields:

Pbi

tan2 9 (15)

150 THE DETERMINATION OF HYDROGEN IONS

If no absorbents were in the train, (T = 1), photometric match
would be obtained at a new angle 8' of the Nicol in place of 6

P P

of equation (12) and the ratio -^ would be replaced by =£1.

*a3 Pal

Hence for the "zero setting" of the instrument

^ = tan°9' (16)

ial

Substitute this in (15) and obtain:

T = cot2 6 X tan2 tf (17)

If the instrument conformed to the theory given above and if
the light-source were such that Pai = Pbi, (16) would become

1 = tan2 0' (18)

B' = 45°, 135°, 225° or 315°.

If the instrument alter the amplitude of the vibrations in either
ray by slight polarization at glass surfaces, it is equivalent to
altering the relative powers Pal and Pbl. Thus, for example, a
"zero-setting" may occur at 46° instead of 45° even if Pai = PM-

In (17) 0', it will be remembered, is the angle at "zero-setting"
while B is the angle with absorbents in train.

In case the tubes are reversed we have

T = tan2 0 X cot2 0' (19)

According to equation (17) or (19) the transmittance desired
is determined as follows. First make photometric match with
no absorbents in train. Read the angle B'. Second make the
reading with tubes of solvent and solution in train and read the
angle 0. In each case the angle is that at photometric match.

It has been tacitly assumed that energy of one wave length or
narrow spectral band has been used. The spectrometer deliver-
ing this to the eye is usually placed beyond the photometer.
This virtually accomplishes the desired limitation.

For further information on spectrophotometers consult : Walsh
(1926).

VII

ABSORPTION CURVES

151

BROM
PHENOL
BLUE

1=5.0 em.
c-0.02 g. per

THYMOL
BLUE

AC.
1=5.0 cm. I RED

C = 0,04 o. |1 '5.0cm.
per tOO cc. -\c*0.(U5g. \\vs//
per 100

BROM

THYMOL

BLUE

BROM
CRESOL
PURPLE

1 = 5.0 cm.
c = 0.032 g. per
lOOcc

1 = 5.0 cm.
C=0.04£. per

100 cc.

1 = 5.0 cm.

C = 0.016 g. per

100 cc.

1=5.0 cm.

c = 0.032 g. per

1 = 5.0 cm.
c = 0.01a. per

440 480 520 560 600

480 520 560 60O 640

460 520 560 600

WAVE LENGTH. M/AS-MILLIMICRONS^ METERS x io~9

FIG. 24. ABSORPTION CURVES OP SEVEN SULFONPHTHALEINS, METHYL

RED AND PHENOL PHTHALEIN

(After Erode (1924))

152 THE DETERMINATION OF HYDROGEN IONS

ABSORPTION CURVES

By use of a spectrophotometer the value of a transmittance, T,
or the value of —log T at any given wave-length or narrow
section of the spectrum within the range of visibility is deter-
mined. When determinations are made at successive wave-
lengths the results may be charted and a curve drawn through the
points. Such a curve is called an absorption curve or a trans-
mittance curve, according to the manner of charting, or choice.

Typical transmittance curves are shown in figure 24. Each curve
represents the relation of —log T to X, expressed in m/z, when
the indicator was kept in a solution of the pH value indicated by
the number. These curves were determined by Erode (1924).
Each individual curve in figure 24 was determined while the
solution was held at a constant value of pH by means of a buffer
solution. In each instance the pH number is indicated. Any
such curve can be called an "isohydric transmittance curve."
Thiel, Dassler and Wulfken (1924) call them ''isobathmen."

It is evident in figure 24 that the isohydric absorption curve
changes in some regular way when the pH value of the indicator
solution is changed. We naturally ascribe this to the change in
the degree of dissociation of the indicator, and since the curve for
a very low pH value is distinctly different from that for a com-
paratively high pH value we are led to attribute to the ion and
to the undissociated molecule a qualitative difference in their
abilities to absorb radiant energy.

According to equation (6) the effect of doubling the concentra-
tion c can be compensated by halving the length. Therefore,
to make the argument simple, let it be imagined that all the ions
are forced into the first half of the tube, and all the undissociated
molecules into the second half. The final effect will be unchanged
but we may now consider separately the transmission by the
ions and by the undissociated molecules.

Let the radiant power incident at the first surface of the solu-
tion containing the ions be PI and that leaving this solution be
P2. Then up to this surface

VII ABSORPTION CURVES 153

where KI is the molar transmissive index of the ions, c is the con-
centration of the indicator in the undivided solution, 1 is the length
of the whole solution and a is the degree of dissociation. In the
half of the divided solution c has been doubled but 1 has been

halved l-2co; = L

For the second part of the path of the radiant energy let P3
be the radiant power leaving the solution of the undissociated
molecules. Then

where Ku is the molar transmissive index of the undissociated
molecules. The total transmittance equals •*_?. Hence

- log T = lc[«Ki + (1 - a) KJ (20)

If a = 1, — log T = IcKi. Thus, if the pH value of the solution is
such as to cause complete dissociation, the observed transmittance
is that of the ions alone and the measurable value of Ki at a given
wave-length, or the absorption curve relating Ki to X, becomes
characteristic of the ions. Likewise, if a = 0, — log T = lcKu;
and now the isohydric absorption curve becomes characteristic
of the undissociated molecules.

It frequently happens that as the wave-length changes in one
direction the values of Ki and Ku approach and at some one
value of X become equal. Then by equation (20)

- log T = IcKi = lcKu (21)

In (21) the degree of dissociation, a, does not appear. This
means that each isohydric curve should pass through some
common point as most of them are seen to do in figure 24. This
point Thiel, Dassler and Wlilfken (1924) call "der isobestischer
Punkt." Prideaux (1926) adopts "isobestic point."

It may be noted that the isobestic point is not merely a point
of intersection between the curve characteristic of the ions alone
and the curve characteristic of the molecules alone, but that it is
a point of intersection between all isohydric curves whatever the

154 THE DETERMINATION OF HYDROGEN IONS

value of the degree of dissociation. Consequently the probability
of its occurrence is low unless two "colored" components and two
only have some intimate relation as have the ions and undissociated
molecules in our equilibrium equation.

If then the instrumental accuracy of the spectrophotometric
measurements be adequate to establish the actual rather than the
apparent occurrence of an isobestic point, it would be presumptive
proof that two absorbing components of the dye system and two
only are related to the hydrion concentration of the solution,
within the range of pH where the point suffers no displacement.

Not infrequently there are to be observed, in the published
charts and tables of indicator absorption data, indications that
there is a true isobestic point for a limited range of pH values but
that an extreme change of pH throws the absorption curve out of
conformity. This suggests the formation of a new absorbing
species. If so, nonconformity to the isobestic point should be
used as a warning that the argument to follow should be modified,
and that, in the spectrophotometric method of determining pH
values, on isohydric curves that do not conform to the isobestic
point are to be avoided.

SPECTROPHOTOMETRIC DETERMINATION OF DISSOCIATION
CONSTANTS

Let it be assumed that equation (20) is applicable. Let the
pH value of the solution be changed in one direction until the
values of — log T no longer change. It is then to be presumed
that a. has become either 1 or 0, according to the acidic or basic
nature of the indicator and the direction of the change in pH. Let
the pH value of the solution now be changed in the other direc-
tion until the values of — log T no longer change. It is of course
impossible to tell from the spectrophotometric measurements
whether an acidic or a basic indicator is being used but, as indi-
cated in Chapter I, the data in either case can be treated as if
for an acid. Inspection of the absorption curves for the disso-
ciated and undissociated indicator shows whether or not there is
a wave-length at which either KI or Ku, as it appears in equation
(20), is negligible. This wave-length should be as near as prac-
ticable to the peak of the curve for the chosen species, provided
that it does not depart far from the region of good visibility,

VII DETERMINATION OF INDICATOR CONSTANTS 155

presently to be discussed. Let us assume that the ion is the
chosen species and that the wave-length is such that (20) approxi-
mates closely to

- log T = lea Ki (22)

Determine — log T when it is certain that the alkalinity of the
solution is sufficient to make a practically unity. Then — log
Tm = IcKi, at a specific value of X where Tm indicates minimum
transmittance (maximum absorption). Now change the pH value
of the solution till it is within that range where a lies between
0.9 and 0.1; and, having measured the pH value of the well-
buffered solution without the indicator, determine (for the same
wave-length previously used) the new value of — log T. This
will be designated by — log Tx. Then

(23)

— log

In some cases it contributes to accuracy of measurement if the
concentration or the tube length is varied. In that case there
can be used the equivalent of equation (23), namely:

= lm cmKi logT,
lxcxKi logTm

Remembering that we are using one wave-length, we can cancel
KI from equation (24). Also the exact concentrations cm and
cx need not be known if the ratio be known.

The values of a having been determined in a number of cases,
there is used the familiar equation

pH = pK + log

1 - a

pH values being known from the buffers used, pK is now cal-
culated.

Holmes (1924) uses the transmittances of both ion and" undis-
sociated molecules in the following manner. Select two wave-
lengths Xi and X2, preferably in regions of good visibility, one
preferably near the peak of the curve for the ion and the other
preferably near the peak of the curve for the undissociated mole-

156 THE DETERMINATION OF HYDROGEN IONS

cule. If it happens that these wave-lengths are such that in one
case KIM = 0 and in the other case Ku\2 = 0, equation (23) will
apply to the ions and a similar equation will apply to the undis-
sociated molecules. To distinguish the cases the subscripts i\i
and u\2 will be used with obvious meanings.

[log TjjXi , .

= Ri (25)

- a =

= Ru (26)

pK is found directly from the relation :

PH = pK + log|i (27)

As Holmes (1924) notes, the change in the concentrations of the

•p .

ions and the ionogen both contribute to the ratio ^ and con-

sequently the use of this ratio is preferable, where practicable.

In case there cannot be selected a wave-length at which the
absorption is due practically to the ion or the ionogen alone,
equation (20) must be used. The resulting equations for a by
either of the above principles becomes somewhat more com-
plicated (cf. Vies, 1925), but this in itself is not serious. The real
difficulty lies in the accurate estimation of KI and Ku which can
no longer be eliminated. The determination of a transmissive
index requires a pure compound used in known concentration.
If the pure compound is not available the apparent transmissive
indices must be determined.

SPECTROPHOTOMETRIC DETERMINATION OF pH

There is to be used the equation:
pH = pK + log

1 - a

The value of a is to be determined by the ratio . * where

log Tm

Tx is the transmittance of the tested solution containing the

VII

DETERMINATION OF pH

157

indicator partially transformed and Tm is the transmittance of
the indicator fully transformed. Therefore pK must have been
previously determined by the method described in the previous
section and by the use of buffers which now become the standard
of reference. See table 25.

TABLE 25

pK values and absorption maxima of sulfonphthaleins
A. = solution used for full transformation.
Solutions: 1. Between 20 and 36 per cent HC1.

2. M/20 borax.

3. M/2 trisodium phosphate.

Formulas: a. pH = pK — log

b. pH = pK + log

1 - a.

log T,

1 - a log Tm

Standards of reference: Clark and Lubs' buffer solutions.

INDICATOR

WAVE-LENGTH
OF MINIMUM
TRANSM ITT ANCE

FOR-
MULA

m-cresol purple (acid range)

1.51

533 (Cohen)

Thymol blue (acid range)

1 5

544 (Erode)

Brom chlor phenol blue

3 98

596 (Cohen)

Broin phenol blue

4.10

592 (Erode)

Brom cresol green (

4.68

614 (Holmes)

Chlor cresol green

4.67

4.8

617 (Cohen)
612 (Cohen)

Chlor phenol red

5 98

573 (Cohen)

Brom phenol red

6.16

574 (Cohen)

Brom cresol purple

6 3

591 (Erode)

Brom thymol blue

7 0

617 (Erode)

Phenol red

7.9

558 (Erode)

Cresol red

8 3

572 (Erode)

m-cresol purple (alkaline range)

8.32

580 (Cohen)

Thymol blue (alkaline range) . . \

8.91

596 (Holmes)

8.90

596 (Erode)

Establish by trial that strength of the standard indicator solu-
tion which, with the tube length selected, will give a transmit-
tance of 0.2-0.1, when the indicator is fully transformed to the
"alkaline" (or, if preferred, to the "acid") form. Establish
accurately the value of log Tm. Then with the same indicator

158 THE DETERMINATION OF HYDROGEN IONS

solution added in the same proportion to the tested solution deter-
mine log Tx. Introduce the values into the above equation and
with the given value of pK solve for pH. To facilitate such cal-
culations there is given in Appendix F (page 677) values of log

— for various values of a.

I— a

There can be used also the ~ values as discussed in the pre-

vious section.

In table 25 are given the wave-lengths at which maximum ab-
sorption of several indicators are reported. It is well to select
a wave-length near such a "peak." There might have been in-
cluded the extinction coefficients for these stated wave-lengths.
However, extinction coefficients are misleading in practical appli-
cations of the method because, to be of universal significance,
they would have to apply to these rare articles of commerce —
pure indicators. One hundred per cent purity of indicator and
perfection in the construction of a standard solution of known
concentration cannot always be depended upon and, as shown,
are unnecessary to the method when a wave-length can be
selected at which the equations permit the elimination of one or
the other extinction coefficient.

For the production of the full transformation of the indicator
the same precautions must be used that are applied in the Gil-
lespie method. Data for the sulfonphthaleins are found in table
14 (page 122).

A fundamental assumption in the method as described is that
the specific absorptive property of the ion and of the ionogen
are not affected by change in the general composition of the solu-
tion, e.g., alteration of "salt" content by addition of neutral salt
or change in buffer composition. That this assumption is not
justified in strictness is shown by Halban and Ebert (1924).

Of the method, Holmes (1924) remarks:

"With judicious selection of indicators and technique the spectrophoto-
metric method affords the maximum accuracy possible in indicator

methods The phenomena of dichromatism, encountered with

many indicators, introduce no interference. The presence of such degrees
of color and turbidity as are ordinarily met in solutions to be evaluated
does not affect the accuracy with which the ratios may be measured,

VII

DETERMINATION OF pH

159

since the technique of spectrophotometric practice is, or may be made,
such that an exact compensation for their effects is obtained automati-
cally. The difficulties introduced by excessive color or turbidity may be
overcome by increasing the concentration of the indicator and decreasing
the thickness of the layer of solution employed in the measurements.
The resort to thin layers of solution should also render it possible to
determine the ratio of a solution when only a few drops of material may be
available for examination."

A fuller discussion of the effect of turbidity would be welcome.
In passing it is well to note how well the values of a, determined
spectrophotometrically, conform to the type curve corresponding
to the simple equation

URGENT TRANSFORMATION

8* 0> OB 0
O O O O

pH = pK + log -
1 — a

rf^

10 II

FIG. 25. RELATION OF pH TO PER CENT TRANSFORMATION OF BROM CRESOL

GREEN (pK = 4.68) AND OF THYMOL BLUE (pK = 8.91)

(After Holmes and Snyder (1925))

Determinations by Holmes and Snyder (1925) are shown in
figure 25.

Other references to the use of spectroscopy in indicator work are :
Birge and Acree (1919), Baker and Davidson (1922), Brue're
(1925), Henri and Fromageot (1925), Hildebrand (1908), Buch
(1926), Lund (1927), Moir (1916), Morton and Tipping (1925),
Paulus, Hutchinson, and Jones (1915), Prideaux (1925), Siegler-
Soru (1927), Stenstrom and Reinhard (1925), Vies et al. (1922-
1927). Adams and Rosenstein (1914), Brightman et al. (1918-
1920), Hirsch (1925).

160

THE DETERMINATION OF HYDROGEN IONS

EFFECTS OF ABSORPTION ON THE STIMULUS AS IT REACHES THE EYE

•p

Transmittance, is merely the fraction ~, the fraction of the

-t i

power incident at the surface 1 which emerges at the surface 2.
It has been particularly noted that this fraction varies with the

TABLE 26

Relative visibility of radiant energy of different wave length and spectral
distribution of relative radiant energy for standard white light

WAVE
LENGTH

RELATI\ B
VISIBILITY*

RELATIVE
RADIANT
ENERGY —
STANDARD
WHITE LIGHTf

WAVE
LENGTH

RELATIVE
VISIBILITY*

RELATIVE
RADIANT
ENERGY —
STANDARD
WHITE LIGHTf

400

0.0004

53.33

550

0.995

100.95

410

0.0012

60.00

560

0.995

100.00

420

0.0040

66.67

570

0.952

99.05

430

0.0116

69.52

580

0.870

97.14

440

0.023

77.14

590

0.757

95.24

450

0.038

86.19

600

0.631

94.29

460

0.060

92.38

610

0.503

93.33

470

0.091

96.19

620

0.381

92.38

480

0.139

99.05

630

0.265

91.43

490

0.208

100.48

640

0.175

90.48

500

0.323

100.95

650

0.107

89.52

510

0.503

101.43

660

0.061

87.62

520

0.710

100.95

670

0.032

86.19

530

0.862

100.95

680

0.017

84.29

540

0.954

100.95

690

0.0082

82.86

700

0.0041

80.48

* Provisionally adopted by the International Commission on Illumina-
tion, Geneva, July, 1924. See Gibson et al. (1925).

t Average noon sun at Washington. Used as standard white. See
Gibson et al. (1925).

wave-length. It must now be emphasized that the values of the
incident power at different wave-lengths vary with the source.
In table 26 are shown relative intensities at different wave-lengths
of the radiant energy of white light. The values given are
proportional to the relative powers. By means of the relative

VII LUMINOSITY 161

value of PI and the value of the fraction =^ (i.e., T) there can

-T2

now be calculated the value of P? for any wave-length. P2, as
evaluated in relative terms, is the destined stimulus as it leaves
the solution on its way to the eye.

Now the visibility of radiant energy varies greatly with the
wave-length. Standard values of relative visibility provisionally
adopted in 1924 by the International Commission on Illumina-
tion as quoted by Gibson et at. (1925) are shown in table 26.
The product of the relative visibility and the relative value of P2
at a given wave-length is the relative light or the luminosity for
the wave-length under consideration.

At this point attention may be called to our previous avoidance
of the word "light." It is a word which is in such common use
that no committee can ever dictate its good and proper usage.
Yet, in an exposition of such technical matters as those now
under discussion there is a distinct advantage in adhering to the
nomenclature of the Colorimetry Report (Troland, 1922) wherein
the physical aspects of radiation are kept distinct from physio-
logical effects. There it is stated, that light is to be regarded as a
"Psycho-physical" quantity. It is defined "as the product of
absolute power and visibility measures for any given sample of
radiant energy,"

"Relative light quantities are called luminosities.'"

The only immediate concern which we have for luminosity,
in the application of the spedrophotometer is that the luminosity
shall be sufficient to make possible accurate measurements in
which the eye is the detector of inequalities. On the other hand,
further consideration of this quantity reveals relations of con-
siderable importance to the direct visual observation of indicator
solutions. An instance of this will be shown in the next section.

DICHROMATISM

Consider for instance a solution of brom cresol purple which
at pH 7.6 gives the transmittance curve indicated in figure 24.
By means of the data of table 26 and the values of T read from a
large scale drawing of figure 24 there are calculated and plotted
as curve A of figure 26 the variation of luminosity with wave-

162

THE DETERMINATION OF HYDROGEN IONS

length. Now let either the concentration or the length of the
brom cresol purple solution be increased ten times and for the
new condition let there be plotted curve B.

In the first case (low concentration, or short tube), the luminos-
ity is greatest in the "blue" and "blue-green." There is still a
marked luminosity in the "red." The combined effect is "purple."
In concentrated solution or deep layers as shown by curve B there
is very little luminosity for the "blue" and the luminosity for the
"red" is dominant. The effect approaches "red." Thus a change
of concentration or length causes a distinct change of color. This

440 480 520 560 600 640 680
Blue Green Tfetlow Orange Red

FIG. 26. LUMINOSITY CURVES, CALCULATED BY MEANS OF THE TRANS-
MISSION, THE RELATIVE RADIANT ENERGY OF STANDARD WHITE

LIGHT AND THE RELATIVE VISIBILITY

Curve A — brom cresol purple in dilute solution. Curve B — brom cresol
purple in ten times the concentration of case A.

is called "dichromatism." It can readily be observed with the
proper concentration of brom cresol purple by observing it in a
test tube, first side wise and then lengthwise of the tube. It is
of very great importance in the determination of pH values. In
the first place, two solutions of like pH value containing brom
cresol purple will give distinct differences in "color" quality if
there is an error either in the concentration of indicator or in the
depth of view. Secondly, if a solution containing suspended
material be compared with a clear standard, an error may arise
from the fact that in the turbid solution much of the radiant energy
reaching the eye may not have traversed the whole depth but

VII DICHROMATISM 163

may have entered from the side and having been scattered by
the particles may have traversed only a shallow layer of the
solution. Indeed turbid solutions containing this indicator often
appear "bluer" than the standard having the same pH value and
having the same concentration of the indicator. With milk the
red tone of brom cresol purple is almost undetectible unless re-
flected light be screened off.

This effect, dichromatism, is operative to some extent with
most indicators but it becomes distinctly troublesome only with
indicators such as brom cresol purple, and brom phenol blue, the
absorption curves of which are located in such a position that
effective amounts of radiant energy are transmitted in the region
of visible "red" on the one hand and visible "blue" on the other
hand.

Since the luminosity is determined in part by the spectral
distribution of the relative power of the source, the luminosity at
a given wave-length will vary with the source. Artificial illu-
minants, as, for instance, the tungsten lamp furnish radiant energy
the power of which at different wave-lengths is much less uniform
than that of sunlight. Such illuminants are commonly de-
scribed as deficient in "blue" or relatively rich in "red." Thus
a dichromatic indicator appears much "redder" under a tungsten
lamp than in daylight.

In dealing with dichromatic indicators which give trouble in
direct visual observations, it sometimes helps to change the source
of illumination. For instance, it is an appreciable although not
an entirely satisfactory aid in the use of brom cresol purple to
screen off the "blue" in the source of illumination. This can be
done crudely as follows. In an ordinary box of convenient size
are mounted three or four large electric lights. A piece of "tin"
serves are reflector. The box may be lined with asbestos board.
A piece of glass, cut to fit the box, is held in place on one side by
the asbestos lining and on the other by a few tacks. This glass
serves only to protect the screen and is not essential. The screen
is made from translucent paper known to draughtsmen as "Econ-
omy" tracing paper. It is stretched across the open side of the
box and painted with a solution consisting of 5 cc. of 0.6 per cent

phenol red and 5 cc. of — KH2PO4 (stock standard phosphate

164 THE DETERMINATION OF HYDKOGEN IONS

solution). While the paper is wet it is stretched and pinned to
the box with thumb tacks. If a dark-room is not available for
observations, exterior light may be shut off with a photographer's
black cloth.

Blue-yellow indicators which retain a dichromatic red may be
observed by mercury arc. Its emission is poor in "red" but
"yellow," "green" and "blue" lines fall in the spectrum where,
for instance, shifts in the absorption bands of brom phenol blue
occur.

The absorption spectra of all the indicators of the sulfon
phthalein series are such that the appearance of dichromatism
must be expected under certain conditions. It will be observed
with phenol red in illumination relatively poor in "red" and rich
in "blue," for example, that of a mercury arc; and with thymol
blue in illumination relatively poor in "blue" and rich in "red"
for example, ordinary electric light.

OBSERVATIONS BY THE COLOR-BLIND

Curiously enough the author never has heard this problem dis-
cussed until he raised the question himself, a fact which suggests
that few people have such insuperable difficulties with the indi-
cator method that they are conscious of possible personal limita-
tions. It may be said at once that an adequate discussion of
this problem would require a clear recognition of the various types
of color-blindness and that the author is not competent to deal
with the subject except superficially. One aspect is clear. The
physical phenomena are definite. The absorption bands are
usually broad enough so that some alteration with change of pH
occurs at wave-lengths at which eyes of limited deficiencies are
still sensitive. Consequently, changes are detected. It is a
matter of no fundamental importance that the deficiencies lead to
wrong names of colors. The serious aspect is deficient sensitivity
in the region of greatest indicator change. When this occurs
there may be manifest (in certain instances) avoidance of red-
yellow indicators and preferance for blue-yellow indicators or
vice versa (compare Saunders (1923)). Preferences arising from
real physiological deficiencies and not from esthetics deserve more
study. Such problems became important when, as frequently
happens in industrial work, extensive measurements become

VII DIFFERENTIATION BY EYE 165

routine and rapidity, accuracy and ease of measurements should
be encouraged.

DIFFERENTIATION BY EYE

Let us also consider the range of an indicator as it is deter-
mined by the differentiating power of the eye. An approximate
treatment of this is all that will be attempted.

Use the equation :

(

On differentiation the rate of increase in a with increase of pH
is found to be :

-Jfe- 2.3 «(!-*).

d(pH)

When

d*a I

0, a

d(pH)> 2'

In other words the maximum rate of increase in dissociation is at
the half transformation point. This fixes a reference point when
indicators are to be employed in distinguishing differences in pH.
The question now arises whether or not this is the central point
of the optimal conditions for differentiation of pH values. It
may be said at once that it is not, because the eye has not only
to detect differences but also to resolve these differences from the
color already present. Experience shows that the point of maxi-
mum rate of increase in a is near one limit of the useful range and
that this range lies on the side of lower color. Thus, in the case
of the one-color indicator phenolphthalein, the useful zone lies
between about 8.4 and 9.8 instead of being centered at 9.7 which
corresponds with the point of half -transformation. -In the case
of a two-color indicator such as phenol red the same reasoning
holds, because the attention fixes upon the very dominant red.
With other two-color indicators the principle holds except when
there is no very great difference in the command upon the atten-
tion by one or the other color.

It should be mentioned however that these more or less empiri-

166 THE DETERMINATION OF HYDROGEN IONS

cal relations are observed in comparing colors at equal incre-
ments of pH when the indicator concentration is adjusted to
emphasize the differences among the less intensely colored tubes.
By suitable dilution of the indicator the differences among the
tubes having the higher percentage color may be emphasized
and the useful range of the indicator slightly extended. In prac-
tice this is a procedure which requires care for it is easy to be-
come confused when dealing with different concentrations of the
same indicator.

The fixing of the lower pH limit of usefulness of a given indi-
cator involves another factor. There is the question of the total
indicator which may be brought into action. A dilute solution
of phenolphthalein may appear quite colorless at pH 8.4 while
a much stronger solution will show a distinct color which would
permit distinguishing 8.2 from 8.4. But the concentration is
limited by the solubility of the indicator and this must be
taken into consideration. In short there is no basis upon which
to fix definite limits to the pH range of a given indicator, and
those limits which are given must be considered to be arbitrary.
On the other hand the apparent dissociation curve is quite defini-
tive; and were it not for the greater convenience of the "range of
usefulness" it would be preferable to define the characteristics
of an indicator in terms of its apparent dissociation constant.

COLOR

Translation of the data of transmittances into luminosities
requires the data of table 26. But if an attempt is made to carry
the matter further into a description of the psychological affair
called color, additional data are required. This is beyond the
scope of this treatise, and since it is we have taken liberties in
preceding paragraphs and have named stimuli by the names of
the effects, e.g., "red."

In no part of our subject is color quantitatively evaluated. As
we shall see presently the ordinary colorimeter is misnamed.

On the other hand, when we use two-color indicators like the
sulfonphthaleins, and have normal eyes, we undoubtedly utilize
color distinction, which stands us in good stead and often becomes
the sole criterion of distinctions when turbidity and other factors
interfere with the judgment of relative intensities. See also

VII COMPAKATOR 167

page 131 on the utilization of color-quality in observations of
"one-color" indicators.

THE "COLORIMETER," I.E., COMPARATOR
Beer's law is:

- log TX = lcKx

(see page 144) where T is the transmittance at a specified wave-
length, X, 1 is the length of the absorbing layer, c is the concen-
tration of absorbing substance and K\ is a constant characteristic

of the absorbing substance for the specified wave-length X. The

•p

transmittance is the ratio, -=?-, of the power of the radiant energy

Jti

emerging from the solution to the power incident at the first
surface.

Imagine two solutions receiving from a source the same radiant
power Pi at wave-length X and containing a substance character-
ized by the absorption constant K\. Let the length 1 of one solu-
tion or its concentration c, of absorbing material, be adjusted
until the emergent power P2 is equal to that of the second solu-
tion. The transmittances will be equal in each case. Then by
applying the above equation to the two cases, indicated by sub-
scripts 1 and 2, and solving, we have:

- log Tx = lidKx = 12C2KX; whence: lid = I2c2
or

Cj = 1^
C2 li

The ordinary "colorimeter" of the Duboscq type is a device
whereby the length of absorbing layers li and 12 can be varied
and measured, until, by an optical device for bringing the photo-
metric fields into juxtaposition it is seen that the transmittances

are equal. If Ci is known, and the ratio ^ is measured, c2 is

li
determined.

In the treatment given above, it was tacitly assumed that
absorption by the solvent could be neglected. This assumption
is not serious. The specification that there is to be used radiant
energy of one wave-length ("monochromatic light") is, of course,

168

THE DETERMINATION OF HYDROGEN IONS

not usually met. And yet it is essential to the strict applicability
of the laws involved. We need not repeat here the discussion,
given in a previous section, of the variation in "color-quality"
made very evident in solutions of "dichroic" indicators as the
concentration of indicator or the length of absorbing layer is
varied. Suffice it to say, that if a "colorimeter" is used with two-
color indicators, the variation in "color-quality" with variation
in the ratio of tube lengths will be so disconcerting as to make the
use of the ordinary ' ' colorimeter" quite useless for pH measurements .
Gillespie (1921) brought into prominence a principle which
promises to be of considerable value. It is illustrated diagram-
matically by figure 27. The vessels A, B, C and E are of colorless
glass. The bottoms should be optically plane-parallel. A and
C are fixed while B may be moved up or down. The position of

FIG. 27. DIAGRAMMATIC SECTION OF GILLESPIE'S COLOR COMPARATOR

B is indicated on a scale the zero mark of which corresponds to
the position of B when B and C are in contact and the 100 mark
of which corresponds to the position of B when B is in contact
with A. If now there is placed in B a solution of the acid form
of an indicator and in C a solution of the same concentration of
the indicator transformed completely to the alkaline form, it is
obvious that the position of the vessel B will determine the ratio
of the two forms of the indicator which will be within the view.

For comparison a solution to be tested is placed in E together
with that concentration of indicator that occurs in the optical
system B-C. For colored solutions tubes A and D are used as
in the Walpole system, which will presently be described. As
Gillespie has indicated, this "colorimeter" should be useful for
certain general work where the exact principles of color comparison
have often been neglected.

VII

COMPARATOR

169

170 THE DETERMINATION OF HYDROGEN IONS

An instrument embodying the principle which Gillespie used
was described by Mines (1910) under a title concerning the action
of beryllium, etc., on the frog's heart. Wu (1923) and Gerretsen
(1924) have employed the principle. The instrument made by
the Bausch and Lomb Optical Company for Dr. A. B. Hastings
is shown in figure 28. It has the advantage of auxiliary cups H
useful in the compensation of natural colors of solutions.

COLOR-WEDGE

Another principle which has been put to use is embodied in the
"color- wedge" of Bjerrum (1914). This is a long rectangular
box with glass sides and a diagonal glass partition which divides
the interior into two equal wedges. One compartment contains
a solution of the indicator fully transformed into its alkaline
form, the other a like concentration of the indicator transformed
to the acid form. A view through these wedges should imitate
the view of a like depth and concentration of the indicator trans-
formed to that degree which is represented by the ratio of wedge
thicknesses at the point under observation. Compare Barnett
and Barnett (1921) and Myers (1922). Myers apparatus has
been developed commercially and is now on the market. Wherry
has reproduced Bjerrum's color-wedge with celluloid walls
and made of it a very helpful field kit.

McCrae (1926) Kolthoff (1924) have also employed the wedge
principle.

In the use of the wedge the relation between wedge thicknesses
and pH values are determined by the relation

, . thickness 1

pH = pKa + log —T-

thickness 2
provided, of course, the indicator has been properly used.

COMPENSATION FOR NATURAL COLOR OF A SOLUTION

There have been two chief methods of dealing with the interfer-
ing effect of the natural color of solutions. The first method, used
by S0rensen (1909), consists in coloring the standard comparison
solutions until their color matches that of the solution to be
tested, and subsequently adding to each the indicator.

VII

COMPARATOR

171

S0rensen's coloring solutions are the following:

a. Bismarck brown (0.2 gram in 1 liter of water).

b. Helianthin II (0,1 gram in 800 cc. alcohol, 200 cc. water).

c. Tropaeolin O (0.2 gram in 1 liter of water).

d. Tropaeolin OO (0.2 gram in 1 liter of water).

e. Curcumein (0.2 gram in 600 cc. alcohol, 400 cc. water).
/. Methyl violet (0.02 gram in 1 liter of water).

g. Cotton blue (0.1 gram in 1 liter of water).

The second method was introduced by Walpple (1910). It
consists in superimposing a tube of the colored solution over the
standard comparison solution to which the indicator is added,
and comparing this combination with the tested solution plus
indicator superimposed upon a tube of clear water.

THE BLOCK COMPARATOR

A somewhat crude but nevertheless helpful application of Wai-
pole's principle may be made from a block of wood. Six deep
holes just large enough to hold ordinary test tubes are bored
parallel to one another in pairs. Adjacent pairs are placed as
close to one another as can be done without breaking through the
intervening walls. Perpendicular to these holes and running
through each pair are bored smaller holes through which the test
tubes may be viewed. The center pair of test tubes holds first
the solution to be tested plus the indicator and second a water
blank. At either side are placed the standards colored with the
indicator and each backed by a sample of the solution under test.

LIGHT LIGHT

CONTROL O®O CONTROL CONTROL OO
STANDARD O®O STANDARD ACID OO W

£Y£ ALKALINE OO UNKNOWN

EYE

FIG. 29. SIMPLE COMPARATORS

172 THE DETERMINATION OF HYDROGEN IONS

This is the so called "comparator" of Hurwitz, Meyer, and
Ostenberg (1915). Before use it is well to paint the whole block
and especially the holes a non-reflecting black. To produce a
"dead" black use a soft wood and an alcohol wood-stain.

This comparator is shown in two forms in figure 29. Form A is
used with the unknown X + indicator, backed by a water blank,
W, in the center. On either side is placed the standard buffer +
indicator, backed by a tube of the unknown (control) to com-
pensate for the^ natural color or turbidity of the unknown. Form
B is used with the Gillespie method. The unknown + indicator
is backed by two tubes of water. The acid solution of indicator
and the alkaline solution of indicator are backed by a tube of the
untreated unknown (control) to compensate for the natural color
or turbidity of the unknown.

There have been described many elaborations of this simple
device. Several provide mechanical means of rapidly exchanging
tubes in the field of view, see for example Cooledge (1920).

In the operation of this comparator with "one-color" indicators
(nitrophenols) Michaelis uses a screen of blue glass. See page 131.

COMPENSATION FOR TURBIDITY

Turbidity often presents a difficult problem. S0rensen (1909)
has attempted to correct for this effect by the use of a finely
divided precipitate suspended in the comparison solution. This
he accomplishes by forming a precipitate of BaS04 through the
addition of chemically equivalent quantities of BaC^ and Na2S04.
Strictly speaking, this gives an imperfect imitation, but like the
attempt to match color it does very well in many instances. The
Walpole superposition method may be used with turbid solutions
as well as with colored, as experience with the device of Hurwitz,
Meyer and Ostenberg has shown. In passing, attention should
be called to the fact that the view of a turbid solution should be
made through a relatively thin layer. When the comparison is
made in test tubes, for instance, the view should be from the side.

There are some solutions, however, which are so dark or turbid
that they cannot be handled with much precision by any of these
methods. On the other hand a combination of these methods
with moderate and judicious dilution [as was indicated in Chap-
ter II this may not seriously alter the pH of a solution], permits

VII FLUORESCENCE 173

very good estimates with solutions which at first may appear
"impossible." Some of the deepest colored solutions permit reason-
ably good determinations and when sufficiently transparent per-
mit the application of spectrometric devices. Turbidity on the
other hand is sometimes unmanageable. Even in the case of
milk where comparison with a standard is out of the question a
two colored indicator presents a basis for judgment. See also
page 136.

REFLECTIONS

Buckmaster (1923) has suggested using films of tested solution
and of buffer standards. The comparison is to be made by
reflected light. He does not describe the principles. Since they
are rather complex and since the procedure seems not to be of
immediate importance, the citation will suffice.

FLUORESCENT INDICATORS

A number of substances, among them fluorescein, not only
suffer changes in the grosser aspects of their color in solution when
the pH value of the solution passes through a certain range, but
also fluoresce within and above one zone of pH and not below
the zone.

True fluorescence is described as follows. Radiant energy of
one or another wave-length is absorbed by the substance and the
energy is given forth as radiant energy of another wave-length
usually greater than that of the exciting radiation. Fluorescence
is therefore best observed indirectly as if one were considering the
substance the source. An extensive discussion is given by Pring-
sheim (1923) and Wood (1921).

Since, in some cases, there appears to be a direct relation be-
tween the degree of fluorescence and what might be expected to
be the degree of dissociation as controlled by buffer solutions,
measurement of the degree of fluorescence provides a method of
measuring hydrion concentration. In figure 30 is a graph taken
from the work of Desha, Sherrill and Harrison (1926) which shows
the relation between the pH values of the solution and the degree of
fluorescence of 2 naphthol, 3, 6-disulfonic acid. The fluorescence
is very easily influenced by chlorides. Included in the paper
mentioned above are data for other substances such as quinine.

See also Mellet and Bischoff (1926) and Robl (1926).

174

THE DETERMINATION OF HYDROGEN IONS

80 100

40 60

PERCENT
FIG. 30. RELATION OF pH TO PER CENT MAXIMUM FLUORESCENCE OF

2-NAPHTHOL,3,6-DISULFONIC AdD

Center of curve at pH 9.45. (After Desha, Sherrill and Harrison (1926))
ARTIFICIAL COLOR STANDARDS

There is an inherent simplicity in the use of standard buffer
solutions and indicators themselves which would seem to pre-
clude attempts to use artificial standards. And yet there seems
to be an insistent demand for artificial standards. Even color
charts are in demand! See page 65. These should be used
with due precautions.

Grieg-Smith (1924) tells us that he makes his own water color
standards for use with the spot-plate method and that he has seen
similar standards at the Lister Institute. They can be prepared
by a good artist better than by the printer's art. The original
color chart which Professor Max Brodel did in water color for
reproduction in the first edition of this book was a beautiful
piece of work : but it could not be reproduced accurately and was
used only as a guide. The artist's eye is not the eye of the
spectrophotometer or of the camera or of the printer.

In the same category of artificial standards fall the organic
or inorganic solutions such as those proposed or discussed by
Haskins (1919), Kolthoff (1922), Risen (1924), Janke and Kro-
pacsy (1926), Brue*re (1926), Taub (1927), J0rgensen (1927). See
also comments on inorganic standards by Breslau (1925).

Sonden (1921) has used colored glasses (see also Anon. (1927),

VII

MIXED INDICATORS

175

/. Sri. Inst. 4, 327). Incidentally it is interesting to note how the
old Lovibond tintometer with its colored glasses has become quite
out of date.

MIXED INDICATORS

Mixtures of indicators are employed for two very distinct pur-
poses, only one of which justifies their description in this chapter.

0.0

440 480 520 560 600 640 680

WAVE LENGTH

FIG. 31. ABSORPTION CURVES FOR THE MIXED INDICATOR: 0.015 GRAM

METHYL RED + 0.04 GRAM BROM THYMOL BLUE

(After Erode (1924))

Sometimes a rational selection of indicators having different ab-
sorption bands or the admixture of an indicator with a dye which
is not itself an indicator, results in color-changes more easily
distinguished. A case in point is described by Hickman and
Linstead (1922) who use xylene cyanole F F as an "internal light
filter" in conjunction with methyl orange (1 part methyl orange
to 1.4 part cyanole in 500 parts 50 per cent alcohol). The result

176 THE DETERMINATION OF HYDROGEN IONS

at pH 3.8 is a grey intermediate color which, these authors claim,
increases the ease of detecting end-points in titrations. The ab-
sorption bands showing the rationale of the combination are given
in the original paper.

For a very different purpose is admixture of indicators to ex-
tend with one test solution the range of pH values determinable.
While recognizing some advantage in this, the author has never
felt it to be a distinct advantage to ordinary pH measurements.
In certain titrations the ability to detect two or more end-points
widely apart on the pH scale is a distinct advantage of indicator
mixtures.

A spectrophotometric analysis of one mixture is shown in
figure 31. This analysis by Erode (1924) illustrates a mode of
attack which should be profitable in cases where specific results
are to be achieved.

Several references to mixed indicators are given in Chapter IV.

PHOTOELECTRIC CELLS

Now that the photoelectric cell is coming into more general
use it will doubtless be applied in a variety of ways in our subject.
Reimann (1926) describes its use in titrations and Miiller and
Partridge (1927) apply it to the automatic control of titrations.
The selenium cell has been applied by Hjort, Lowey and Black-
wood (1924) in end-point work with indicators absorbing in the
orange and red. In following absorption in the ultra-violet certain
types of photoelectric cell have been very useful. See for instance
Halban and Geigel (1920), Halban and Siedentorff (1922) and
Kaplan (1927). There may be rare instances when minute de-
flections of the galvanometer mirror in potentiometric measure-
ments have to be detected. The photoelectric cell has been used
to amplify such minute deflections.

For a discussion of photoelectric cells as applied to colorimetry
see Campbell and Gardiner (1925) and also the book on spectro-
photometry by Walsh.

CHAPTER VIII

SOURCES OF ERROR IN COLORIMETRIC DETERMINATIONS

A series of judgments, revised without ceasing, goes to make up the
incontestable progress of science. — DUCLAUX.

INTRODUCTION

There are errors of technique, such as incorrect apportionment
of the indicator concentration in tested and standard solution and
the use of unequal depths of solutions through which the colors
are viewed, that may be passed over with only a word of reminder.
Likewise we may refer to certain of the optical effects mentioned
in Chapter VII and then pass on to the more serious difficulties
in the application of the indicator method.

At the very beginning it will be well to emphasize the distinc-
tion which should be maintained between discrepancies attrib-
utable to the neglect of factors which may be evaluated by
some general, if arbitrary, formulation and discrepancies attrib-
utable to the sum of what is ordinarily called "error" and spe-
cific phenomena beyond the range of any convenient formulation.

Up to this point in the development of the subject there has
been used as the fundamental type-equation the following:

[HA]

For convenience of discussion consider separately the constant

[A~]

Ka, the ratio rTJA1 and [H+].
|MAJ

In the derivation of the equation it was assumed that it is
primarily the density of the number of particles in the solution-
space that determines the equilibrium state. As the subject
develops it will be found necessary to introduce appreciable
corrections to this formula because it was deduced on assumptions
far too ideal to meet the varying conditions of actual solutions.
If we then insist on using the above formula, variation of condi-

177

178 THE DETERMINATION OF HYDROGEN IONS

tions will make it appear as if the so-called constant Ka were
subject to appreciable variations. If under one set of conditions
there is used a value of Ka standardized for another set of condi-
tions an error will be introduced.

It is reasonable to assume as a close approximation that the
ratio of the concentrations of two forms of the indicator will be
determined by the "color" as described in Chapter III. However,
see Halban and Ebert (1924). Their objection will now be
neglected. Therefore, and in accordance with the theory of

Chapter V, we use the ratio ;g-rr as it stands uncorrected in

the equation. On the other hand, we shall see, after having
studied the theory of the hydrogen electrode, that there is no
exact relation between the potential of a hydrogen cell and the
hydrogen ion concentrations. However, there is an approximate
relation.

Later there will be used the convenient equation

(H+) (A-) _ [H+] [A-] jrHA_

(HA) [HA] K"7H.7A-

Where () indicates "activity" and y represents the "activity coeffi-
cient." Now it is doubtless a very close approach to fTJA1 that

|rLA|

is measured colorimetrically; it is (H+), or [H+frn+i and not
[H+] that is measured electrometrically and ascribed to the

buffer system; and it is Ka -~ that is determined under one

specific set of conditions and applied rather indiscriminately to
all conditions.

The situation requires careful "unscrambling" which cannot
well be done until the developments in subsequent chapters. In
the meanwhile the interpretation of indicator conduct will be
considered to be standardized by the use of standard comparison
solutions having the pH values assigned in Chapter IX.

Because investigators have been content to proceed with this
system of comparison and have not imposed upon themselves in
all cases the accuracy demanded of the systematic type of study
later to be indicated, most of the more directly applicable tables

VIII SALT EFFECTS 179

of corrections are rather inaccurate. They will be cited to indi-
cate orders of magnitude found by the methods used. The reader
will do well to watch current literature for better systematized
data which will probably be published extensively in the near
future.

In the ordinary method of comparison, discrepancies have often
been traced so clearly to two definite sources that they have been
given categorical distinction. They are the so-called "protein"
and "salt" effects.

From what has already been said in previous pages, it will be
seen that, if there are present in a tested solution bodies which
remove the indicator or its ions from the field of action either by
adsorption, or otherwise, the equilibria which have formed the
basis of our treatment will be disturbed. An indicator in such a
solution may show a color intensity, or even a quality of color,
which is different from that of the same concentration of the indi-
cator in a solution of the same hydrogen ion concentration where
no such disturbance occurs. We could easily be led to attribute
very different hydrogen ion concentrations to the two solutions.
This situation is not uncommon when we are dealing with protein
solutions, for in some instances there is distinctly evident the
removal of the indicator from the field. In other cases the dis-
crepancy between electrometric and colorimetric measurements
is not so clear, nor can it always be attributed solely to the indi-
cator measurement.

If two solutions of inorganic material, each having the same
pH- value, are tested with an indicator, we should expect the same
color to appear. If, however, these two solutions have different
concentrations of salt, it may happen that the indicator colors are
not the same. As S0rensen (1909) and S0rensen and Palitzsch
(1913) demonstrated, this effect of the salt content of a solution
cannot be logically tested by adding the salt to one of two solu-
tions which have previously been brought to the same pH-value.
The added salt, no matter if it be a perfectly neutral salt, will
change the pH-value of the solution. Comparisons had best be
made between solutions of the same pH-value.

So long as hydrogen electrode measurements are made the

180

THE DETERMINATION OF HYDROGEN IONS

standard, it is convenient to throw the burden of the "salt effect"
upon the indicator; but neutral salts are known to displace elec-
trode potential differences from the values estimated from the ex-
pected hydrogen ion concentration.

A standardization procedure may be illustrated as follows. The
pH-value of the unknown is measured potentiometrically. Let it
be 6.73. A portion of the same solution is now treated with the
indicator and a color match is found with a standard buffer
having an electrometrically determined pH-value of 6.70. The
"error" is —0.03 pH unit and the correction necessary to bring
the apparent colorimetric reading to the electrometric is +0.03.

Bjerrum (1914) gives an example of a case where the influence
of the neutral salt is evidently upon the buffer equilibrium rather
than on the indicator. An ammonium-ammonium salt buffer
mixture and a borate buffer mixture are both made up to give
the same color with phenolphthalein. On the addition of sodium
chloride the color of phenolphthalein becomes stronger in the
ammonium mixture and weaker in the borate mixture.

Let it be kept in mind that while neutral salts displace the
electrode equilibrium and lead to different pH values of the
standard, it is the measurement of the particular standard used
that is usually taken as a standard of reference in the colorimetric
comparison. The following illustrates a procedure with solu-
tions of the same general nature. S0rensen and Palitzsch (1910)
were studying the salt effects of indicators in sea water. They
acidified the sea water and passed hydrogen through to displace
carbon dioxid, and then neutralized it to the ranges of various
indicators and buffer mixtures and compared colorimetric with
electrometric measurements. In this way they found the follow-
ing "errors."

INDICATOR

BUFFER

PARTS PER 1000 OF SALTS AND
CORRESPONDING ERRORS

p-Nitrophenol

Phosphate
Phosphate
Borate
Phosphate
Borate

+0.12

-0.10
+0.22
+0.16
+0.21

+0.08
-0.05
-fO.17
+0.11
+0.16

0
+0.03
-0.04
+0.05

0
-0,07
-0.14
-0,03

Neutral red

a-Naphthol phthalein. . .<
Phenolphthalein

TABLE 27

Salt effect of indicators, after Kolthoff

INDICATOR

SALT

SALT
CONCEN-
TRATION

CORREC-
TION

REMARKS

Tropaeolin OO
(Orange IV)

KC1
KC1
KC1
KC1

0.10 N
0.25 N
0.50 N
1.00 N

-0.05
-0.01
+0.06
+0.23

Indicator suitable. NaCl
has about same influence

Methyl orange
Butter yellow

KC1
KC1
KC1
KC1

KC1

0.10 N
0.25 N
0.50 N
1.00 N

0.10 N

-0.08
-0.08
+0.02
+0.23

—0.08

Indicator suitable. NaCl
has about same influence

Same errors as methyl

orange but indicator floc-
culates with salt

Thymol blue (acid

KC1
KC1
KC1

0.10 N
0,20 N
0.50 N

-0.06
-0.06
—0.04

NaCl has same influence

KC1

1.00 N

+0.05

Brom phenol blue..

KC1
KC1
KC1
KC1

0.10 N
0.25 N
0.50 N
1.00 N

-0.05
-0.15
-0.35
-0.35

Corrections large at weaker
concentration of salt

Brom cresol purple . .
Phenol red

NaCl
NaCl

0.50 N
0.50 N

-0.25
—0.15

At small concentrations of

Thymol blue

NaCl

0.50 N

—0,17

salt correction of opposite
sign

Methyl red

NaCl

0.50 N

+0.10

p-Nitrophenol
Azo yellow 3G

NaCl
NaCl

0.50 N
0.50 N

-0.05
0.00

Phenolphthalein

NaCl

0.50 N

-0.17

KC1
KC1

0.10 N
0.25 N

-0.06
-0.12

NaCl has about same influ-
ence

KC1
KC1

0.50 N
1.00 N

-0.10
-0.29

181

182

THE DETERMINATION OF HYDROGEN IONS

If, for example, sea water of about 3.5 per cent salt is matched
against a standard borate solution with phenolphthalein and
appears to be pH 8.43 the real value is pH 8.22. Compare table
44, page 213 and McClendon (1917).

TABLE 28

The salt error of cresol red at salinities from 5 to 85 parts of sea salts per 1000
(After Ramage and Miller)

Salinity

Correction

-0.11

-0.13

-0.14

-0 15

-0 16

-0 17

-0 18

—0 19

Salinity

Correction

-0.20

-0.21

-0.22

-0.23

-0 23

-0 24

Salinity

Correction

-0 24

-0 25

-0 26

Salinity

Correction

-0.26

-0.27

TABLE 29

Salt effects
(After Parsons and Douglas 1926)

1 molar

2 molar

3 molar

Thymol blue (alkaline range)

-0.22

-0.29

-0.34

Cresol red

-0 28

-0 32

—0 37

Phenol red

-0.21

-0 26

-0 29

Brom thymol blue

-0.19

-0.27

-0.29

Brom cresol purple . . .

-0 26

-0.33

-0.31

Brom cresol green

-0.26

-0.31

-0.29

Brom phenol blue

-0 28

-0 37

-0 43

Thymol blue (acid range)

-0.10

-0.13

-0.12

Methvl red. .

-0.04

-0.01

+0.12

CORRKCTION

Such calibration is one of the very best ways to deal with the
salt errors since it tends to bring measurements to a common
experimental system of reference.

The following table taken from Prideaux (1917), illustrates the
order of magnitude of the "salt error" in some instances.

VIII

SALT EFFECTS

183

INDICATOR

BUFFER USED

CHANGE OF pH

IN PRESENCE OF

0.5 N NaCl

p-Benzene sulphonic acid azo naphthylamine —
p-Nitrophenol . .

Phosphate
Phosphate

-0.10

-f 0 15

Alizarin sulphonic acid

Phosphate

+0 26

Neutral red . ....

Phosphate

—0 09

Rosolic acid

Phosphate

+0.06

p-Benzene sulphonic acid azo a-naphthol
Phenolphthalein

Phosphate
Phosphate

+0.12
+0.12

Kolthoff (1922) gives table 27 page 181 showing the correc-
tions to be applied for the "salt error" of various indicators. It
should be noted that Kolthoff includes in this table data obtained
when the hydrogen electrode potentials were taken as standard
and also data in which the pH values were calculated. The two
sets are not strictly comparable and therefore must be used
with caution in theoretical work. We have eliminated from
Kolthoff's table Congo red, Azolitmin, and Tropaeolin 0 (Chry-
soi'n) which Kolthoff describes as having salt errors so large that
these indicators are useless.

Michaelis and his coworkers have determined the salt errors
for a number of the nitrophenols, but, since the corrections are
often intimately related to the constants used in Michaelis'
method of operating, the reader is referred to the original litera-
ture for the details. See Chapter VI.

TABLE 30

Salt effect. New sulfonphthaleins

(After Cohen (1927))

[The values given below are corrections to be added to the colorimetric
pH determinations to bring the values to the electrornetric pH of the corre-
sponding Clark and Lubs' buffers.]

MOLAR
CONCEN-
TRATION
SALT

m-CRESOL PURPLE

. BROM

CRESOL
GREEN

BROM
PHENOL
RED

CHLOR
PHENOL
RED

BROM
CHLOR
PHENOL
BLUE

Acid range

Alkaline
range

1.0

-0.14

-0.29

-0.32

-0.26

-0.33

0.5

-0.09

-0.22

-0.26

-0.22

-0.20

-0.28

0.2

-0.02

-0.16

-0.12

-0.10

-0.16

0.005

+0.11

+0.09

+0.25

+0.23

+0.14

184

THE DETERMINATION OF HYDROGEN IONS

Ramage and Miller (1925) after a comparison of their own and
Wells' (1920) data for cresol red give table 28 for use in the study
of sea water.

Parsons and Douglas (1926) give a table (table 29) for "average"
corrections which they suggest using in order to bring pH measure-
ments of solutions of the indicated concentrations of NaCl to
conformity with the values of Clark and Lubs' standard buffers.

Cohen (1927) publishes table 30.

2 3

Electrometric

FIG. 32. VARIATION OF THE "PROTEIN ERROR," IN THE COLORIMETRIC
DETERMINATION OF pH AS THE pH VALUE OF GELATINE

SOLUTION CHANGES

O = bromphenol blue and 1.0 per cent gelatine. • = Thymol blue
and 1.0 per cent gelatine. + = bromphenol blue and 0.4 per cent gelatine.
X ss Thymol blue and 0.4 per cent gelatine. (After St. Johnston and
Peard (1926).)

EFFECTS

The magnitude of "protein" effects may be roughly judged from
the following tables. The data, which could only be summarized
in this way by neglecting some variation in the salt content of
the solutions, include to some degree a salt effect.

Since it is not often that protein errors are presented in a
systematic way, figure 32 by St. Johnston and Peard (1926) is

TABLE 31

" Protein" effects of indicators
(Data from Sprensen (1909))

Corrections to be added to apparent colorimetric reading to bring read-
ing to the electrometric standard.

INDICATOR

CORRECTIONS

In 2% peptone
0.3 'N salt

In 2% egg-
white 0.07 —
0.3 N salt

Methyl violet

-0.02
-0.04
-0.06
-0.27
-0.30
+0 01
-0.22

-0.41
-0.08
-0.18
-0.02
-0.03
-0.06
+0.13
+0.08
-0.12
-0.01
+0.01

-0.19
-0.19
>-0.90
>-1.40
>-1.40
>-0.80
>-0.80

-0.53

+0.15
-0.04
+0.68
+0.44
+0.10
+0.18
+0.40
+0.29
-0.30

Mauve ... ....

Benzene-azo-diphenyl amine

Tropaeolin OO

Metanil yellow

Benzene-azo-benzylaniline

p-Benzene sulfonic acid-azo-benzylaniline. . . .

p-Benzene-sulfonic acid-azo-w-chlorodiethyl
aniline

Topfer's Indicator . ...

IVIethyl orange

Benzene-azo-a-naphthylamine

p-Benzene sulfonic acid-azo-a-naphthylamine. . .
p-Nitrophenol

Neutral red

Rosolic acid

Tropaeolin OOO no. 1 .

Phenolphthalein

Thymolphthalein

Alizarin yellow R

TroDaeolin O...

TABLE 32

" Protein" effects of indicators
(Data from Clark and Lubs (1917))

Corrections are to be added to colorimetric readings to bring readings
to electrometric standard.

CORRECTIONS

INDICATOR

Peptone-
infusion

10%
gelatine
sol.

2 % egg-
white

Urine

Brom phenol blue

0.05

Methyl red

-0 10

0.24

0.05

Brom cresol purple

0.01

0.04

0.01

Brom thymol blue

0.10

0.04

0.02

Phenol red

0 04

0 20

0.00

Cresol red

0 03

0 20

Thymol blue

6.04

0.20

Cresolphthalein . .

-0.03

0.20

185

186

THE DETERMINATION OF HYDROGEN IONS

TABLE 33
"Protein" effects of indicators

(Data of Cohen (1927))

[The values listed are the corrections to be added to colorimetric pH
readings to bring them to the electrometric.]

INDICATOR

IN 5 PER CENT WITTE
PEPTONE

CLARK AND
LUBS*

Series 1

Series 2

m-Cresol purple (acid)

-0.20
-0.19

-0.28
-0.28
-0.10
+0.09
+0.11
+0.11
+0.34
+0.24
+0.02
+0.03
+0.09

-0.20
-0.20
-0.43
-0.43
-0.13
-0.07
-0.10
-0.10
+0.07
-0.01
-0.03
-0.02
-0.03

+0.05

+0.01
+0.10
+0.04
+0.03

+0.04

Thymol blue (acid)

Brom phenol blue . ...

Brom-chlor phenol blue

Brom cresol green

Chlor phenol red

Brom phenol red

Brom cresol purple

Brom thymol blue . .

Phenol red

Cresol red

m-Cresol purple (alk.)

Thymol blue (alk.)

* In a 1 per cent peptone-beef infusion broth.

TABLE 34

Protein errors with neutral red and with phenol red
(After Lepper and Martin (1927))

NEUTRAL

PHENOL RED

PHENOL

RED

PSEUDO-
GLOBU-
LIN

DEVIA-
TION FROM
ELECTRO-

ALBUMIN

DEVIA-
TION FROM
ELECTRO-

PSEUDO-
GLOBULIN

DEVIATION
FROM
ELECTRO-

ALBU-
MIN

DEVIA-
TION FROM
ELECTRO-

METRIC

„ TT

METRIC

per cent

0.00

0 (7.38) 0.00

0.00

0.17

0.00

0.23

0.00

0.03

0.00

0.33

0.00

0.047 (sic)

0.00

+0.02

0.06

-0.02

0.67

-0.05

0.095 (sic)

+0.10

+0.03

0.13

-0.03

1.35

-0.15

0.19

+0.20

+0.04

2.70

-0.25

0.38

+0.30

0 (7.93) 0.00

4.09

-0.45

0.75

+0.40

1.75

0.00

5.40

-0.60

1.5

+0.51

3.5

+0.02

8.17

-0.73

3.0

+0.58

7.0

+0.09

10.80

-0.83

11.0

+0.12

16.35

-0.85

VIII SYSTEMATIC TKEATMENT 187

rather interesting. The apparent error is lowest near the iso-
electric point of gelatin (4.7). Table 34 shows some cases in
which the effect of the concentration of the protein is evident.

SYSTEMATIC TREATMENT

We owe to Br0nsted (1921) the separation of the several differ-
ent sorts of quantities appearing in the equation

IH+] [A-] 7HA

[HA]

briefly mentioned earlier in this chapter. He applied certain of
his equations for the estimation of the correction terms and ob-
tained in some cases a rather striking agreement between ob-
served salt-effects and calculated salt-effects. A more recent
development will be mentioned in Chapter XXV (see page 511).
There it will appear that salt effects are probably subject to
much more systematic treatment than they have hitherto re-
ceived. It will also appear that specific salt-effects remain. How-
ever, the first order corrections can be estimated by use of the
Debye-Hiickel equation described in Chapter XXV. Also the
principle concerned can be put to good use. For instance,
Hastings and Sendroy (1924) employ 0.154 M NaCl solution
for the dilution of plasmas to be compared colorimetrically with
phosphate standards. The ionic strength,1 /*, of this sodium
chloride solution is

1/2 (0.154 X I2 + 0.154 X I2) = 0.154/1

At 6.8 the ionic strength of the M/15 phosphate buffer is ap-
proximately

1/2 (.0333 X 22 + .0333_X I2 + 0.1 X I2) = 0.1330
HP04 H2P04 Na+

At 7.8 the ionic strength is about 0.190/1. Hence there is not a
great difference between the ionic strengths of the diluted plasma
and the buffer standard and consequently little difference in
"salt error."

1 See pages 490 and 559.

188 THE DETERMINATION OF HYDROGEN IONS

It were much better to begin the systematization of salt-
effects on such a basis than to continue longer with the pure
empiricism which has characterized the data of the past. Un-
fortunately there are available as yet few systematic data and
consequently the older tables are given in the foregoing pages.
But see page 511 and figure 90.

It is not improbable that, even if the protein error cannot be
precisely formulated with the aid of the Debye-Hiickel equation,
its description can be rationalized by the procedure suggested for
the salt effects.

SPECIFIC ERRORS

The "protein" effect and the salt effect have been given prom-
inence in the literature partly because both have to be taken into
consideration in dealing with biological solutions, and partly
because there is to be perceived underlying the salt error a most
interesting phenomenon of rather general theoretical importance.
However, this emphasis should not obscure the fact that there are
specific conditions for each indicator which render that indicator
useless for the determination of pH. For instance alizarin, in
passing from the phosphate to the borate buffer mixtures, exhibits
a sudden transition which has all the appearances of a specific
effect of the borate upon the indicator. And alizarin is not
alone in this peculiarity. This same alizarin in the presence of
aluminium may form a lake and with proper pH control may be
made a useful reagent for aluminium in place of a very poor acid-
base indicator, cf. Williamson (1924). Zoller (1921) has called
attention to the incompatibility between certain dyes and the
phthalate buffers. Kolthoff (1926) notes an especially large
error when methyl orange is used with phthalate buffer. Arndt
and Nachtwey (1926) note errors with pyridine solutions and
Michaelis (1926) states that sulfon phthaleins show errors with
alkaloids that are not observed with nitrophenols.

Some indicators precipitate with certain cations, for instance
Orange IV and Congo with alkali earths.

S0rensen (1909) paid particular attention to the extraction of
an indicator from the aqueous phase by excess of chloroform etc.
used as antiseptics.

Many indicators precipitate more or less slowly from standard

VIII SPECIFIC ERRORS 189

buffer solutions. When this is not noticed immediately it may
lead to deceptions. Propyl red was rejected from Clark and Lubs'
original list for this reason. Some indicators fade in light.2

Other indicators are reduced by suspensions of living cells.
Some of these are useful as oxidation-reduction indicators; but
the two classes should be so sharply distinguished that, when
possible, the one property will not be used under conditions in
which the other operates. In litmus-milk, for instance, the reduc-
tion and the acid-base change of the litmus may occur together
and introduce complexity of interpretation as noted by Clark
and Lubs (1917). They recommend that brom cresol purple be
substituted for litmus in the acid test. Compare Reiss (1926).
There should also be distinguished the reversible oxidation-
reduction indicators and the irreversible. For a discussion of
oxidation-reduction indicators see references found in Chapter
XVIII and Appendix, tables K and L.

Some indicators, especially several of the triphenylmethane
series, undergo some of their color changes slowly. Ignorance of
this may lead to serious error.

Several common indicators, notably Congo, do not form true
solutions and degree of dispersion contributes to the color. These
indicators show abnormally large errors due partly to variations
in degree of dispersion. They should not be expected to follow
the ordinary equations except in a very approximate manner, if
at all.

In short all possibilities must be watched lest the investigator
venturing upon the study of some new solution, be misled by the
mark of reliability placed upon an indicator tried under limited
circumstances.

Wherever possible it is good practice to test doubtful cases
with two indicators of widely different chemical composition.

TEMPERATURE EFFECTS

Let it be supposed that the simple equilibrium equation is
applicable. A condition in its derivation was that the tempera-
ture should remain constant. If the indicator constant is deter-

2 Cullen (1922) reports that color standards may fade in the course of a
week to the extent corresponding to about 0.02-0.04 pH unit.

190 THE DETERMINATION OF HYDROGEN IONS

mined by reference to some standard buffer solution it is implied
not only that the constant found applies only at the temperature
used but that this same temperature was a condition determining
the state of the standard buffer solution. If a new temperature
is used it determines the states of both the buffer and the indi-
cator systems. If now the pH values of the buffer solutions at
different temperatures are to be made the basis for determining
the temperature coefficient of the indicator constant, the method
of comparing pH values at different temperatures becomes of
fundamental importance. Unfortunately it will be found from
the discussion of Chapter XXII that there is considerable con-
fusion in regard to this point. Therefore, we find various methods
of determining so-called temperature coefficients and if in a given
case the specific method is not duplicated, an error is made in the
sense that the specified specifically standardized correction for
temperature has been wrongly applied.

In Chapter VI are found temperature coefficients for nitro-
phenols by means of which the error due to temperature changes
may be estimated when the procedure specified is used. Further
discussion is postponed to Chapter XXII, page 448.

ON MEASUREMENTS OF POORLY BUFFERED SOLUTIONS

The extreme of a poorly buffered solution is a solution of a
strictly "neutral" salt such as KCL Were an indicator added,
the indicator system, however dilute, would function as the buffer
and would "indicate" only its own state of equilibrium.

In the ordinary applications of indicators it is assumed that
the buffer strength of the solution is so great as practically to be
unaffected by the addition of the small quantity of indicator
acid, indicator base, or indicator salt.

Now in the ordinary use of an indicator which is, for instance,
an acid, either a solution of the acid form itself, of one or another
of its salts, of the partially neutralized indicator or of the over-
neutralized indicator is used. In applying such solutions to
poorly buffered solutions there may be extensive interaction and
the indicator color merely represents the position of the new
equilibrium.3 This has been a very troublesome source of error

3 Apparently, and unless 1 misunderstand their treatment. McBain,
Dubois and Hay (1926) have neglected this aspect.

VIII POORLY BUFFERED SOLUTIONS 191

in numerous practical applications of indicators to solutions which,
although poorly buffered, are conveniently characterized by
pH values.

A method frequently applied is as follows. Estimate by par-
tially neutralized indicators the approximate pH value of the
solution to be tested. Then, if the addition of more of the par-
tially neutralized indicator alters the color as compared with a
like well buffered standard, the assumption is that the indicator
solution and unknown had not the same pH value and therefore
reacted upon each other to a new point of equilibrium. If the
displacement of color was toward a greater proportion of the acid
form of the indicator, it is assumed that the tested solution had a
lower pH value than the indicator solution. Accordingly adjust
the indicator solution in this direction and again compare after
adding different amounts of the indicator, in each case comparing
the resulting color with that of a well buffered standard containing
the given quantity of indicator. By this "trial and error"
method there are at last established isohydric solutions which on
admixture in different proportions should not affect the equilib-
rium of either system except in a minor and, for present purposes,
negligible degree. Obviously a salt-effect remains to be con-
sidered, see also Dawson (1925).

CHAPTER IX

STANDARD BUFFER SOLUTIONS FOR COLORIMETRIC COMPARISON

// arithmetic, mensuration and weighing be taken from any art}
that which remains will not be much. — PLATO.

The standard solutions used in the colorimetric method of
determining hydrogen ion concentrations are buffer solutions
with such well defined compositions that they can be accurately
reproduced, and with pH values accurately defined by hydrogen
electrode measurements. They generally consist of mixtures of
some acid and its alkali salt. Several such mixtures have been
carefully studied. An excellent set has been described by S0ren-
sen (1912). This set may be supplemented by the acetic acid —
sodium acetate mixtures most careful measurements of which
have been made by Walpole (1914), and restudied by Cohn,
Heyroth and Menkin (1928). The set may also be supplemented
by Palitzsch's (1915) excellent boric acid-borax mixtures, or by
one or another of the several series of mixtures which have been
described in more recent years. A few of these will be mentioned
but details will be given only for those mixtures which are, in
the writer's limited knowledge, the more widely used.

In assigning values to these buffer solutions different authors
have made somewhat different assumptions. See especially
Chapter XXIII and those sections which deal with the hydrogen
electrode.

Clark and Lubs (1916) have designed a set of standards which
they believe are somewhat more conveniently prepared than
are the S0rensen standards. Their set is composed of the follow-
ing mixtures:

Potassium chlorid + HC1
Acid potassium phthalate + HC1
Acid potassium phthalate + NaOH
Acid potassium phosphate + NaOH
Boric acid, KC1 + NaOH
192

IX STANDARD BUFFERS 193

Clark and Lubs published their data for KC1-HC1 mixtures as
preliminary data. Although these data were retained in previous
editions they have now been rejected and replaced by table 35a.
The pH numbers in table 35a are calculated with the assumption
that 7n+ = 0.84 for these mixtures of constant ionic strength
(/* = 0.1). The assumption is not entirely justified; but, for con-
venience in the comparison of calculations, the third decimal of
the pH numbers is given. The uncertainty affects the second
decimal place.

In table 35 the compositions have been recalculated from the
original data with the elimination of corrections made with the
Bjerrum extrapolation. This should bring the numbers into
conformity with the specifications of Chapter XXIII.

For a discussion of these mixtures, the methods used in deter-
mining their pH values, and the potential measurements we refer
the reader to the original paper (Journal of Biological Chemistry,
1916, 25, no. 3, p. 479). -We may proceed at once to describe the
details of preparation.

The various mixtures are made up from the following stock
solutions: M/5 potassium chlorid (KC1), M/5 acid potassium
phosphate (KH2PO4), M/5 acid potassium phthalate (KHCsH^CX),
M/5 boric acid with M/5 potassium chlorid (H3BO3, KC1), M/5
sodium hydroxid (NaOH), and M/5 hydrochloric acid (HC1).
Although the subsequent mixtures are diluted to M/20 the above
concentrations of the stock solutions are convenient for several
reasons.

The water used in the crystallization of the salts and in the
preparation of the stock solutions and mixtures should be redis-
tilled. So-called "conductivity water," which is distilled first
from acid chromate solution and again from barium hydroxid, is
recommended, but it is not necessary.

M/5 potassium chlorid solution. (This solution will not be
necessary except in the preparation of the most acid series of
mixtures. See table.) The salt should be recrystallized three or
four times and dried in an oven at about 120°C. for two days. The
fifth molecular solution contains 14.912 grams in 1 liter.

M/5 acid potassium phthalate solution. Acid potassium phtha-
late may be prepared by the method of Dodge (1915-1920) modified
as follows. Make up a concentrated potassium hydroxid solu-

194 THE DETERMINATION OF HYDROGEN IONS

tion by dissolving about 60 grams of a high-grade sample in about
400 cc. of water. To this add 50 grams of the commercial re-
sublimed anhydrid of ortho phthalic acid.1 Test a cool portion of
the solution with phenol phthalein. If the solution is still alka-
line, add more phthalic anhydrid; if acid, add more KOH. When
roughly adjusted to a slight pink with phenol phthalein2 add as
much more phthalic anhydrid as the solution contains and heat
till all is dissolved. Filter while hot, and allow the crystalliza-
tion to take place slowly. The crystals should be drained with
suction and recrystallized at least twice from distilled water.

Crystallization should not be allowed to take place below 20°C.,
for Dodge (1920) states:

A saturated solution of the acid phthalate on chilling will deposit
crystals of a more acid salt, having the formula 2KHC8H4O4-C8H6O4.
These crystals are in the form of prismatic needles, easily distinguished
under the microscope from the 6-sided orthorhombic plates of the salt
KHC8H4O4.

Dry the salt at 110°-115°C. to constant weight.
A fifth molecular solution contains 40.836 grams of the salt
in 1 liter of the solution.

M/6 acid potassium phosphate solution? A high-grade com-

1 While phthalic anhydride is now prepared commercially in very high
purity and has become comparatively inexpensive, dealers will sometimes
furnish material which is grossly impure. Among the more serious con-
taminants are benzoic acid, naphthols and possibly quinones. See Conover
and Gibbs (1922). The best method of purification is that of sublimation
in an apparatus of the type invented by Gibbs (1924) . The better grades
of phthalic anhydride are now made in remarkable purity by the vapor
phase, catalytic oxidation of naphthalene; a process discovered by Gibbs
(1918). Unless some purification is made when one has to use the lower
grades of the anhydride, it may be necessary to recrystallize the potassium
salt of the acid ten or more times before a sample is suitable for satis-
factory hydrogen electrode measurements. A great deal of trouble is
avoided by purchase of the highest grade anhydride in the first place.

2 Use a diluted portion for the final test.

3 The original measurements of Clark and Lubs were made with samples
of phosphate which gave no clouding or floes in their dilute solutions.
Since then, and especially within recent years, the writer has had difficulty
in obtaining phosphates, dilute solutions of which will not show this
sign of impurity. No reasonable number of recrystallizations seem to rid
the material of the contaminant. It appears to be an aluminium com-

IX PEEPARATION OF SOLUTIONS 195

mercial sample of the salt is recrystallized at least three times
from distilled water and dried to constant weight at 110-115°C.
A fifth molecular solution should contain 27.232 grams in 1 liter.
The solution should be distinctly red with methyl red and dis-
tinctly blue with brom phenol blue.

M/5 boric acid M/5 potassium chlorid. Boric acid should be
recrystallized several times from distilled water. It should be
air dried4 in thin layers between filter paper and the constancy
of weight established by drying small samples in thin layers in a
desiccator over CaCl2. Purification of KC1 has already been
noted. It is added to the boric acid solution to bring the salt
concentration in the borate mixtures to a point comparable with
that of the phosphate mixtures so that colorimetric checks may
be obtained with the two series where they overlap. One liter
of the solution should contain 12.4048 grams5 of boric acid and •/-
14.912 grams of potassium chlorigL ^ ~f~

M/5 sodium hydroxid solution. This solution is the most diffi-
cult to prepare, since it should be as free as possible from carbon-
ate. A solution of sufficient purity for the present purposes may
be prepared from a high grade sample of the hydroxid in the
following manner. Dissolve 100 grams NaOH in 100 cc. distilled
water in a Jena or Pyrex glass Erlenmeyer flask. Cover the
mouth of the flask with tin foil and allow the solution to stand
over night till the carbonate has settled. Then prepare a filter
as follows. Cut a "hardened" filter paper to fit a Buchner funnel.
Treat it with warm, strong [1:1] NaOH solution. After a few
minutes decant the sodium hydroxid and wash the paper first
with absolute alcohol, then with dilute alcohol, and finally with
large quantities of distilled water. Place the paper on the Buch-
ner funnel and apply gentle suction until the greater part of the

pound. A large sample of phosphoric acid which Dr. Ross prepared for
the writer by the method of Ross, Jones and Durgin (1925) was converted
to acid potassium phosphate. This has been entirely satisfactory.

4 Eoric acid begins to lose "water of constitution" above 50°C.

6 This weight was used on the assumption that the atomic weight of
boron is 11.0. The atomic weight has since been revised and appears as
10.82 in the 1927 International Table of Atomic Weights.

Because the solutions were standardized with the above weight of boric
acid this weight should be used.

196

THE DETERMINATION OF HYDROGEN IONS

water has evaporated; but do not dry so that the paper curls.
Now pour the concentrated alkali upon the middle of the paper,
spread it with a glass rod making sure that the paper, under
gentle suction, adheres well to the funnel, and draw the solution
through with suction. The clear filtrate is now diluted quickly,
after rough calculation, to a solution somewhat more concentrated
than N/l. Withdraw 10 cc. of this dilution and standardize
roughly with an acid solution of known strength, or with a sample
of acid potassium phthalate. From this approximate standardiza-
tion calculate the amount required to furnish an M/5 solution.

FIG. 33. PARAFFINED BOTTLE, WITH ATTACHED BURETTE AND SODA-LIME
TUBES FOR STANDARD ALKALI

Make the required dilution with the least possible exposure, and
pour the solution into a paraffined* bottle to which a calibrated 50
cc. buret and soda-lime guard tubes have been attached. See
figure 33. The solution should now be most carefully standard-
ized. One of the simplest methods of doing this, and one which

6 The author finds that thick coats of paraffin are more satisfactory than
the thin coats sometimes recommended. Thoroughly clean and dry the
bottle, warm it and then pour in the melted paraffin. Roll gently to make
an even coat and just before solidification occurs stand the bottle upright
to allow excess paraffin to drain to the bottom and there form a very sub-
stantial layer.

IX STANDARD ALKALI 197

should always be used in this instance, is the method of Dodge
(1915) in which use is made of the acid potassium phthalate
purified as already described. Weigh out accurately on a chemical
balance with standardized weights several portions of the salt of
about 1.6 gram each. Dissolve in about 20 cc. distilled water
and add 4 drops phenol phthalein. Pass a stream of C02-free
air through the solution and titrate with the alkali till a faint
but distinct pink is developed. It is preferable to use a factor
with the solution rather than attempt adjustment to an exact
M/5 solution.

If one should be fortunate enough to find that the concentrated
sodium hydroxid solution had clarified itself without leaving
suspended carbonate, the clear solution might be carefully pi-
petted from the sediment. Cornog (1921) describes another
method as follows :

Distilled water contained in an Erlenmeyer flask is boiled to remove
any carbon dioxide present, after which, when the water is cooled enough,
ethyl ether is added to form a layer 3 or 4 cm. in depth. Pieces of metallic
sodium, not exceeding about 1 cm. in diameter are then dropped into the
flask. They will fall no further than the ether layer where they remain
suspended. The water contained in the ether layer causes the slow forma-
tion of sodium hydroxid, which readily passes below to the water layer.

Cornog depends upon the evaporation of the ether as a barrier
to CO2. There are various ways in which the protection can be
made more sure, and there are also various ways in which the
aqueous solution may be separated from the ether.

From time to time there appear in the literature suggestions
regarding the use of barium salts to remove the carbonate in
alkali solutions.

In the author's opinion the next step to take, if the separation
of carbonate from very concentrated NaOH solutions is not con-
sidered refined enough for the purpose at hand, is to proceed
directly to the electrolytic preparation of an amalgam. Given
a battery and two platinum electrodes this is a simple process.
A deep layer of redistilled mercury is placed in a conical separa-
tory funnel. The negative pole of the battery is led to this
mercury by a glass-protected platinum wire. Over the mercury
is placed a concentrated solution of recrystallized sodium chlorid
and in this solution is dipped a platinum electrode connected

198 THE DETERMINATION OF HYDROGEN IONS

with the positive pole of the battery. The battery may have a
potential of 4 to 6 volts. Electrolysis is continued with occasional
gentle shaking to break up amalgam crystals forming on the
mercury surface.

Boil the CO2 out of a liter or so of redistilled water, and, while
steam is still escaping, stopper the flask with a cork carrying a
siphon, a soda-lime guard tube and a corked opening for the
separatory funnel.

When the water is cool introduce the delivery tube of the separa-
tory funnel and deliver the amalgam. Allow reaction to take
place till a portion of the solution, when siphoned off to a buret
and standardized, shows that enough hydroxid has been formed.
Then siphon approximately the required amount into a boiled-
out and protected portion of water. Mix thoroughly and
standardize.

M/5 hydrochloric acid solution. Dilute a high grade hydro-
chloric acid solution to about 20 per cent and distill. Dilute the
distillate to approximately M/5 and standardize with the sodium
hydroxid solution previously described. If convenient, it is well
to standardize this solution carefully by the silver chlorid method
and check with the standardized alkali. Standard solutions of
hydrochloric acid are also prepared from constant boiling mix-
tures. See data and references by Foulk and Rollings worth
(1923).

The only solution which it is absolutely necessary to protect
from the C02 of the atmosphere is the sodium hydroxid solution.
Therefore all but this solution may be stored in ordinary bottles
of resistant glass*. The salt solutions, if adjusted to exactly M/5,
may be measured from clean calibrated pipets.

These constitute the stock solutions from which the mixtures
are prepared. The general relationships of these mixtures to
their pH values are shown in figure 34. In this figure pH values
are plotted as ordinates against X cc. of acid or alkali as abscissas.
It will be found advantageous to plot this figure from table 35
with greatly enlarged scale so that it may be used as is S0rensen's
chart (1909). The compositions of the mixtures at even intervals
of 0.2 pH are given in table 35.

In any measurement the apportionment of scale divisions
should accord with the precision. Scale divisions should not be

STANDARD BUFFERS

199

4fe—

X-C.C.

FIG. 34. CLARK AND LUBS' STANDARD MIXTURES

A. Fifty cubic centimeters 0.2 M KHPhthalate + X cc. 0.2 M HC1.
Diluted to 200 cc.

B. Fifty cubic centimeters 0.2 M KHPhthalate + X cc. 0.2 M NaOH.
Diluted to 200 cc.

C. Fifty cubic centimeters 0.2 M KH2PO4 + X cc. 0.2 M NaOH. Diluted
to 200 cc.

D. Fifty cubic centimeters 0.2 M H3BO3, 0.2 M KC1 + X cc, 0.2 M
NaOH. Diluted to 200 cc.

200

THE DETERMINATION OF HYDROGEN IONS

TABLE 35

Composition of mixtures giving pH values at 20°C. at interval of 0.2
Phthalate-HCl mixtures

50 cc. M/5 KHPhthalate

46.60cc. M/5HC1

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

39.60cc. M/5HC1 '

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

33.00cc. M/5HC1

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

26.50cc. M/5HC1

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

20.40cc. M/5HC1

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

14.80cc. M/5HC1

Dilute

to 200

cc.

3.4

50 cc. M/5 KHPhthalate

9.95 cc. M/5 HC1

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

6 00 cc. M/5HC1

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

2.65cc. M/5HC1

Dilute

to 200

cc.

Phthalate-NaOH mixtures

50 cc. M/5 KHPhthalate

0.40cc. M/5NaOH

Dilute

to 200 cc.

4.2

50 cc. M/5 KHPhthalate

3.65cc. M/5NaOH

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

7.35cc. M/5NaOH

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

12 00 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

17.50 cc. M/5 NaOH

Dilute

to 200

cc.

5.0

50 cc. M/5 KHPhthalate

23. 65 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

29. 75 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

35.25cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

39. 70 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

43. 10 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KHPhthalate

45. 40 cc. M/5 NaOH

Dilute

to 200 cc.

50 cc. M/5 KHPhthalate

47.00 cc. M/5 NaOH

Dilute

to 200

cc.

KH2PO4-NaOH mixtures

50 cc. M/5 KH2PO4

3 66 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2PO4

5.64 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2PO4

8.55cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2P04

12.60cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2PO4

17.74 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2PO4

23 60 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2PO4

29. 54 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2PO4

34. 90 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2P04

39.34 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2PO4

42. 74 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2P04

45.17 cc. M/5 NaOH

Dilute

to 200

cc.

50 cc. M/5 KH2P04

46. 85 cc. M/5 NaOH

Dilute

to 200

cc.

STANDARD BUFFERS

201

TABLE 35— Concluded

Boric acid, KCl-NaOH mixtures

7.8 50 cc.
8.0 50 cc.
8.2 50 cc.
8.4 50 cc.
8.6 50 cc.
8.8 50 cc.
9.0 50 cc.
9.2 50 cc.
9.4 50 cc.
9.6 50 cc.
9.8 50 cc.
10.0 50 cc.

M/5 HsBOs,
M/5 H3BO3,
M/5 H3BO3,
M/5 H3B03,
M/5 H3BO3,
M/5 H3BO3,
M/5 H3B03,
M/5 H3BO3,
M/5 H3BO3,
M/5 H3BOS,
M/5 H3B03,
M/5 H3B03,

M/5 KC1
M/5 KC1
M/5 KC1
M/5 KC1
M/5 KC1
M/5 KC1
M/5 KC1
M/5 KC1
M/5 KC1
M/5 KC1
M/5 KC1
M/5 KC1

2.65cc.

4.00 cc.

5.90 cc.

8.55 cc;
12.00 cc.
16.40 cc.
21.40 cc.
26.70cc.
32.00cc.
36.85 cc.
40.80 cc.
43.90 cc.

M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH
M/5 NaOH

Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute
Dilute

to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc.
to 200 cc

It is important to check the consistency of any particular set of these
mixtures by comparing "5.8" and "6.2 phthalate" with "5.8" and "6.2
phosphate" using brom cresol purple. Also "7.8" and "8.0 phosphate"
should be compared with the corresponding borates using cresol red.

TABLE 35a

HC1-KC1 MIXTURES OF CONSTANT IONIC STRENGTH, ju = 0.1
Calculated on assumption that 7H+ = 0.84

KC1

MOLAR

HCl

MOLAR

COMPOSITION FOR 0.1 pH UNIT INCREMENT OF pH

STOCK KC1: 0.2 MOLAR
STOCK HCl: 0.2 MOLAR

KC1

solution

HCl
solution

cc.

0.00

0.10

1.07tfa 0.00 + 59.5

dilute to 100 cc.

(1.0) Gu = 0.119)

0.01

0.09

1.120 ' 2.72 + 47.28

dilute to 100 cc.

1.1

0.02

0.08

1.175 12.45 + 37.55

dilute to 100 cc.

1.2

0.03

0.07

1.231 20.16 + 29.84

dilute to 100 cc.

1.3

0.04

0.06

1.298 1 26.30 + 23.70

dilute to 100 cc.

1.4

0.05

1.377

31.18 + 18.82

dilute to 100 cc.

1.5

0.06

0.04

1.474

35.03 + 14.95

dilute to 100 cc.

1.6

0.03

1.595

38.12 + 11.88

dilute to 100 cc.

1.7

0.01

0.02

1.774

40.57 + 9.43

dilute to 100 cc.

1.8

0.09

0.01

2.07£a

42.51 + 7.49

dilute to 100 cc.

1.9

0.095

0.005

2.377

44.05 + 5.95

dilute to 100 cc.

2.0

0.098

0.002

2.77-5

45.27 + 4.73

dilute to 100 cc.

2.1

0.099

0.001

3.075

46.24 + 3.76

dilute to 100 cc.

2.2

a See page 472.

202 THE DETEKMINATION OF HYDROGEN IONS

The original data for mixtures in table 35 were obtained with a saturated
KC1 calomel electrode as a working standard. This was compared with a
group of tenth-normal KC1 calomel half -cells. In calculating pH values
for previous tables (see earlier editions and compare Clark and Lubs
1916, 1917) there were included Bjerrum extrapolations. These were es-
pecially large in the case of the HC1-KC1 mixtures. The original data
have now been used in recalculations in accord with the specifications of
Chapter XXIII.

so coarse that interpolations tax the judgment nor so fine as to
be ridiculous. What scale divisions are best in the method under
discussion it is difficult to decide, since the precision which may
be attained depends somewhat upon the ability of the individual
eye, and upon the material examined, as well as upon the means
and the judgment used in overcoming certain difficulties which
we shall mention later. S0rensen (1909) has arranged the stand-
ard solutions to differ by even parts of the components, a system
which furnishes uneven increments in pH. Michaelis, (1910) on
the other hand, makes his standards vary by about 0.3 pH so
that the corresponding hydrogen ion concentrations are approxi-
mately doubled at each step. Certain general considerations
lead to the conclusion that for most work estimation of pH values
to the nearest 0.1 division is sufficiently precise, and that this
precision can be obtained when the nature of the medium per-
mits if the comparison standards differ by increments of 0.2 pH.

If smaller increments are desired it is permissible within limits
to interpolate; but see table 43.

It is convenient to prepare 200 cc. of each of the mixtures and
to preserve them in bottles each of which has its own 10 cc.
pipet thrust through the stopper.7 It takes but little more time
to prepare 200 cc. than it does to prepare a 10 cc. portion, and
if the larger volume is prepared there will not only be a sufficient
quantity for a day's work but there will be some on hand for the
occasional test.

Unless electrometric measurements can be used as control, we
urge the most scrupulous care in the preparation and preserva-
tion of the standards. We have specified several recrystalliza-
tions of the salts used because commercial samples are not always
to be relied upon.

7 No serious error will be made if the tips of the pipettes be broken to
permit rapid delivery.

ix S^RENSEN'S STANDARDS 203

S0RENSEN?S STANDARD BUFFER SOLUTIONS

S0rensen's standards are made as follows. The stock solutions
are:

1. A carefully prepared exact tenth normal solution of HC1.

2. A carbonate-free exact tenth normal solution of NaOH.

3. A tenth molecular glycocoll solution containing sodium chlo-
rid, 7.505 grams glycocoll ancL'5.85 grams 'Nad in 1 liter of
solution.

4. An M/15 solution of primary potassium phosphate which
contains 9.078 grams KH2P04 in 1 liter of solution.

5. An M/15 solution of secondary sodium phosphate which
contains 11.1876 grams Na2HP04, 2H2O in 1 liter of solution.

6. A tenth molecular solution of secondary sodium citrate made
from a solution containing 21.008 grams crystallized citric acid
and 200 cc. carbonate-free N/l NaOH diluted to 1 liter.

7. An alkaline borate solution made from 12.404 grams boric
acid dissolved in 100 cc. carbonate-free N/l NaOH and diluted
to 1 liter.

The water shall be boiled, carbon dioxid-free, distilled water,
and the solutions shall be protected against contamination by
C02.

The materials for these solutions are described by S0rensen as
follows.

Glycocoll (glycine)

Two grams glycocoll should give a clear solution in 20 cc.
water and should test practically free of chlorid or sulfate. Five
grams should yield less than 2 mgm. of ash. Five grams should
yield, on distillation with 300 cc. of 5 per cent sodium hydroxid,
less than 1 mgm. of nitrogen as ammonia. The nitrogen content
as determined by the Kjeldahl method should be 18.67 ±0.1 per
cent.

Primary phosphate,

The salt must dissolve clear in water and yield no test for
chlorid or for sulfate. When dried under 20 or 30 mm. pressure
for a day at 100°C. the loss in weight should be less than 0.1 per
cent, and on ignition the loss should be 13.23 ±0.1 per cent.
When compared colorimetrically with citrate mixtures the stock

204 THE DETERMINATION OF HYDROGEN IONS

phosphate solution should lie between "7" and "8 citrate-HCl."
On addition of a drop of tenth-normal alkali or acid to 100 cc.
the color .of this phosphate solution with an indicator should be
widely displaced.

Secondary phosphate NazHPO^, 2 H20

The salt with this content of water of crystallization is pre-
pared by exposing to the ordinary atmosphere the crystals con-
taining twelve moles of water. 8 An exposure of about two weeks
is generally sufficient. The salt should yield a clear solution
and yield no test for chlorid or sulfate. A day of drying under 20
to 30 mm. pressure at 100°C. and then careful ignition to constant
weight, should result in a 25.28 ±0.1 per cent loss. The stock
solution should correspond on colorimetric test with "10 borate-
HC1" and should be displaced beyond "8 borate-HCl" on addi-
tion of a drop of N/10 acid, and beyond "8 borate-NaOH" with
a drop of alkali to 100 cc.

Citric acid, C6HB07, H20

The acid should dissolve clear in water, should yield no test
for chlorid or sulfate and should give practically no ash. The
water of crystallization may be determined by drying under 20
to 30 mm. pressure at 70°C. On drying in this manner the acid
should remain colorless and lose 8.58 ±0.1 per cent. The acidity
of the citric acid solution is determined by titration with 0.2 N
barium hydroxid with phenolphthalein as indicator. Titration is
carried to a distinct red color of the indicator.

8 There have been occasional complaints of the difficulty of preparing
or keeping S0rensen's salt with a definite water content. See for example
Clark and Lubs (1916) and Cohn (1927). Naegeli (1926) has brought
together a number of references and a table of vapor pressures of the
several hydrate systems which indicate that the subject is not yet in a
satisfactory state. Naegeli prefers to make his buffer solutions with
the heptahydrate, solutions of which are standardized gravimetrically.
S0rensen states that he had no difficulty in obtaining the salt by exposure
of the heptahydrate to the dry atmosphere of cold winter days. It should
be noted that S0rensen took his usual care by determining the water con-
tent. This is advisable in variable climates.

Certain samples sold for the preparation of standard buffers and called
"S0rensen's Phosphate" are wrongly labeled Na2HP04.

STANDARD BUFFERS

205

O.C.-A

1098

8 9 10

01 2345
C.C.-B

FIG. 35. S0RENSEN's STANDARD MIXTURES, WALPOLE'S ACETATE SOLU-
TIONS AND PALITZSCH'S BORATE SOLUTIONS
Mixtures of A parts of acid constituent and B parts of basic constituent

206

THE DETERMINATION OF HYDROGEN IONS

"c3 d
> «

CQ '_-j

OOOOOOOSOOiOOOi— (»-H

OOOOO5O5OSOOOrH»— ti— (

(MCOOCOt^i— (

i-HtOT— 1 r*< CO

COCOi— iTt(
OSCOl>r-(

OCOOOSOiOOi— ir-(T-(

§ 55 S §3

lOOOOO^OOSOrHiOOOOO

S0RENSENJS STANDARDS

207

T— iCOOOOOOOS^fCOC^t^-C^CJOOO
t^t>o6oOodoiC5OOOOi-<T-ii— i

l^l-~OOo6o5CiC5OOC>!— i I-H TH i— (
|>Q6o6o6o5O5OiOOOi— I TH i— I T- (
t>.Q6o6oOOiO5O5OOOi-Hi— I r-l r-l
t>«o6o6o6o5O5OOOOi— Ir- li— IrH
t^OOOOQOOiCiOOOi— I rH r-l i— I i-l

0 t>o6coo6o5osoooT-ii— ii— i i— i T-t

QQ .

"** i>c30oooooiO5OOOi— ii— IT-HI— ic^i
GOooodoioiciocJOi-HT-i^Hcicsi

208

THE DETERMINATION OF HYDROGEN IONS

00 00 O TF t^ rH 00
O rH CO rt< CO CO CO

OS OS OS OS OS O rH

CO ^ CM CM 00 00 CM
00 OS O rH CM OS I>

oo* 06 os os os os o'

rH O CM b- rH 00 b-

rH CM CO ^ t^ CO 1>

OS OS OS OS OS O rH

O CM OC
CO O l>

OS O O

s 8 8 g £ s SB

rH rH '

OS O O

OS O rH

o oo oo oo to o i— i

OS OS O rH CO TH OS

00 OO OS OS OS O O

i3^°^Si^S

OS OS OS OS OS CO 0s!

rH rH

00 CO 00
CO rH OS

os 6 o

rH rH

OS O (N

CO rH rH CM O OS "3-
OS O rH CM Tf rH O

OO OS OS OS OS O rH

00 OS CO OS CO rH CO
rH <N T^ IO 00 OS rH

CO CO O

"^ CM rH

i §

Os O) O^ O^ O^ ^^ Ol

rH TH

OS O rH

rH rH

i ^

88S2

t>- to to !>• CO l> l>

OS O rH CM •<*! CM rH

S _ fe;

N-

^SrH

00 OS OS OS OS O rH

* 2 o

(N CO TH CO OS OS <N

^ CO CM

os os os os os co CM

rH rH

OS O rH

rH rH

ii J t

°S

OS O CO

§00 OO rH rH CO OS
O rH CO IO CO CM

OS OS OS OS OS O rH

Ills

CS CO § CO Ol 0 CO

55 ® c^

>- 1 w

""*

O^ O5 O^ O^ O^ T-H C^Q

i— t rH

OS O rH

rH rH

Tfs

O <N IO

O5 T-H Tf

CM rH CM tO CO Tf CM
O rH CM CO tO TT Tfi

OS OS OS OS OS O TH

$ S o

CM CO ^0 ^ 0 rH S3

§ ? ^

-2 W

*~*

OS OS OS OS O rH <N

rH rH rH

OS O rH

rH rH

2 o

O 08

W £

O' rH <N

rH rH rH

°^

tO IO CO O CM CO LQ
O rH CM rfi CO to to

os os os os os o rH

„

O CM Is- CO CO "* "*"

CO rf IO l> O CM CO

•*f l> rH

CO to CO

OS OS OS OS O rH CM

rH rH rH

OS 0 rH

O O O O O O

^ ^ il ll £ ^

rH CM CO Tf tO CO

w w w w w w
o o o o o o

j<5 ^ ^j ^j ^ ^j

rH CM CO Tfl IO CO
| HI || 0

o o o o o o o

O OS 00 t" CO to -^

O O O O O O Q

CO CQ CQ CQ CQ CQ rt^

O OS 00 t^ CO to ^

S0RENSEN'S STANDARDS

209

TABLE 38

Sprensen's borate — HCl mixtures

(Walbum's values)

Borate: 12.404g H3BO3 + 100 cc. N NaOH per 1.
HCl: 0.1 TV

Temperature

10°

20°

30°

40°

50°

60°

70°

8.86

10.0 Borate

9.30

9.23

9.15

9.08

9.00

8.93

9 5 Borate + 05 HCl

9.22

9.15

9.08

9.01

8.94

8.87

8.80

9.0 Borate + 1.0 HCl

9.14

9.07

9.01

8.94

8.87

8.80

8.74

8.5 Borate + 1.5 HCl

9.06

8.99

8.92

8.86

8.80

8.73

8.67

8.0 Borate + 2.0 HCl

8.96

8.89

8.83

8.77

8.71

8.66

8.59

7.5 Borate + 2.5 HCl

8.84

8.79

8.72

8.67

8.61

8.55

8.50

7.0 Borate + 30 HCl

8.72

8.67

8.61

8.56

8.50

8.45

8.40

6.5 Borate + 3.5 HCl

8.54

8.49

8.44

8.40

8.35

8.30

8.26

6.0 Borate + 4.0 HCl

8.32

8.27

8.23

8.19

8.15

8.11

8.08

5.75 Borate + 4.25 HCl...

8.17

8.13

8.09

8.06

8.02

7.98

7.95

5.5 Borate +4.5 HCl

7.96

7.93

7.89

7.86

7.82

7.79

7.76

5.25 Borate + 4.75 HCl...

7.64

7.61

7.58

7.55

7.52

7.49

7.47

TABLE 39

Sjrensen's citrate— HCl mixtures

Citrate: 21.008g Crystn. Citric Acid + 200 cc. N NaOH per 1.

HCl: 0.1 tf

Temperature 18 °C.

CITRATE

HCl '

CC.

cc.

0.0

10.0

1.038*

1.0

9.0

1.173

2.0

8.0

1.418

3.0

7.0

1.925

3.33

6.67

2.274

4.0

6.0

2.972

4.5

5.5

3.364

4.75

5.25

3.529

5.0

3.692

5.5

4.5

3.948

6.0

4.0

4.158

7.0

3.0

4.447

8.0

2.0

4.652

9.0

1.0

4.830

9.5

0.5

4.887

10.0

0.0

4.958

Note inconsistency with table 35a.

210 THE DETERMINATION OF HYDROGEN IONS

TABLE 40

Sfrensen's glycocoll—HCl mixtures
Glycocoll: 0.1 M Glycocoll + 0.1 M NaCl per 1.
HC1:0.1AT

Temperature 18°C.

GLTCOCOLL

HCl

CC.

0.0

10.0

1.038*

1.0

9.0

1.146

2.0

8.0

1.251

• 3.0

7.0

1.419

4.0

6.0

1.645

5.0

1.932

6.0

4.0

2.279

7.0

3.0

2.607

8.0

2.0

2.922

9.0

1.0

3.341

9.5

0.5

3.679

Note inconsistency with table 35a.

TABLE 41

S$rensen's phosphate mixtures
Secondary: 11.876g Na2 HPO4 • 2 H20 per 1.
Primary: 9.078g KH2P04 per 1.
Temperature 18 °C.

SECONDARY

PRIMARY

CC.

0.25

9.75

5.288

0.5

9.5

5.589

1.0

9.0

5.906

2.0

8.0

6.239

3.0

7.0

6.468

4.0

6.0

6.643

5.0

6.813

6.0

4.0

6.979

7.0

3.0

7.168

8.0

2.0

7.381

9.0

1.0

7.731

9.5

0.5

8.043

WALBUM S DATA

211

Boric acid,

Twenty grams of boric acid should go completely into solution
in 100 cc. of water when warmed on a strongly boiling water bath.
This solution is cooled in ice water and the nitrate from the crys-
tallized boric acid is tested as follows. It should give no tests for
chlorides or sulfates. It should be orange to methyl orange. A
drop of N/10 HC1 added to 5 cc. should make the filtrate red to
methyl orange. Twenty cubic centimeters of the nitrate evap-
orated in platinum, treated with about 10 grams of hydrofluoric
acid and 5 cc. of concentrated sulfuric acid and reevaporated,
ignited and weighed, should yield less than 2 mgm. when corrected
for non-volatile matter in the HF.

Tables 36-42 give the S0rensen mixtures with the corre-
sponding pH values. Mixtures whose pH values are considered
by S0rensen to be too uncertain and which he has indicated by
brackets are omitted from these tables. The third decimal of
S0rensen's tables are given by S0rensen in small type.

TABLE 42

Sfirensen's citrate — NaOH mixtures

(Walbum's values)

Citrate: 21.008g Crystn. Citric Acid + 200 cc. N NaOH per 1.
NaOH: 0.1 AT

Temperature . .

10°

20°

30"

40°

50°

60°

70°

10.0 Citrate

4.93

4.96

5.00

5.04

5.07

5.10

5.14

9.5 Citrate + 0.5 NaOH..

4.99

5.02

5.06

5.10

5.13

5.16

5.20

9.0 Citrate + 1.0 NaOH..

5.08

5.11

5.15

5.19

5.22

5.25

5.29

8.0 Citrate + 2.0 NaOH..

5.27

5.31

5.35

5.39

5.42

5.45

5.49

7.0 Citrate + 3.0 NaOH..

5.53

5.57

5.60

5.64

5.67

5.71

5.75

6.0 Citrate + 4.0 NaOH..

5.94

5.98

6.01

6.04

6.08

6.12

6.15

5.5 Citrate + 4.5 NaOH..

6.30

6.34

6.37

6.41

6.44

6.4*

6.51

5.25 Citrate + 4.75 NaOH

6.65

6.69

6.72

6.76

6.79

6.83

6.86

WALBUM'S DATA

Walbum (1920) has determined the pH values for the S0ren-
sen mixtures at temperatures of 10°, 18°, 28°, 37°, 46°, 62° and
70°C. and has interpolated data for intervening temperatures.
He finds that the alteration of pH with temperature is for the
most part negligible for the phosphate mixtures, the glycocoll-HCl
mixtures and the citrate-HCl mixtures. In his tables will be
found S0rensen's values at 18°. Tables 39, 40 and 41 are taken
from S0rensen's paper of 1912.

212

THE DETERMINATION OF HYDROGEN IONS

S0rensen and Walbum used the Bjerrum extrapolation which
results in making the pH numbers of the more acid solutions less
than they would be had the specifications of Chapter XXIII been
used.

HASTINGS AND SENDROY7S DATA

For the special purposes of urine and blood analysis Hastings
and Sendroy (1924) required smaller increments of pH than are
usually provided in tables of buffer systems. They also desired
standardized values at 20° and 38°. Table 43 contains their data.

TABLE 43

M/15 phosphate mixtures at 20° and 88°

(Hastings and Sendroy (1924))
0.1 N HC1 : pH 1.08 used as standard of reference

M/15

Na2HPO4

M/15

KHzPO4

nH DETERMINED
AT 20°

pH DETERMINED
AT 38°

cc.

49.6

50.4

6.809

6.781

52.5

47.5

6.862

6.829

55.4

44.6

6.909

6.885

58.2

41.8

6.958

6.924

61.1

38.9

7.005

6.979

63.9

36.1

7.057

7.028

66.6

33.4

7.103

7.076

69.2

30.8

7.154

7.128

72.0

28.0

7.212

7.181

74.4

25.6

7.261

7.230

76.8

23.2

7.313

7.288

78.9

21.1

7.364

7.338

80.8

19.2

7.412

7.384

82.5

17.5

7.462

7.439

84.1

15.9

7.504

7.481

85.7

14.3

7.561

7.530

87.0

13.0

7.610

7.576

88.2

11.8

7.655

7.626

89.4

10.6

7.705

7.672

90.5

9.5

7.754

7.726

91.5

8.5

7.806

7.776

92.3

7.7

7.848

7.825

93.2

6.8

7.909

7.877

93.8

6.2

7.948

7.919

94.7

5.3

8.018

7.977

PALITZSCH'S STANDARDS

213

PALITZSCH'S STANDARD BUFFER SOLUTIONS

Palitzsch (1922) designed his standards for the special con-
venience of those investigators whose interests center upon the
determination of the pH values of sea waters.

TABLE 44

pH values of borax-borate mixtures at 18°C. and "salt-effects" for phenol-
phthalein and a-naphtholphthalein

(Palitzsch (1922))

Borax solution: 19.108gramsNa2B4O7.10H2Oinl 1. Boric acid solution:
12.404 grams H3BO3 + 2.925 grams NaCl in 1 1.

STANDARD

TRUE pH VALUES OP SEA WATER CONTAINING S PARTS PER 1000

SOLUTIONS

SALINITY AT COLOR-MATCH \VITH STANDARD

<O
CO

-i<

'!'§

cc.

6.0

4.0

8.69

8.48

8.49

8.50

8.52

8.54

8.57

8.59

8.63

8.66

8.69

8.72

5.5

4.5

8.60

8.39

8.40

8.41

8.43

8.45

8.48

8.50

8.54

8.57

8.60

8.63

5.0

8.51

8.30

8.31

8.32

8.34

8.36

8.39

8.41

8.45

8.48

8.51

8.54

-s 3

4.5

5.5

8.41

8.20

8.21

8.22

8.24

8.26

8.29

8.31

8.35

8.38

8.41

8.44

§£

4.0

6.0

8.31

8.10

8.11

8.12

8.14

8.16

8.19

8.21

8.25

8.28

8.31

8.34

0? i-£3

3.5

6.5

8.20

7.99

8.00

8.01

8.03

8.05

8.08

8.10

8.14

8.17

8.20

8.23

4.5

8.41

8.19

8.20

8.21

8.23

8.25

8.28

8.32

8.37

8.40

8.45

8.48

4.0

6.0

8.31

8.09

8.10

8.11

8.13

8.15

8.18

8.22

8.27

8.30

8.35

8.38

3.5

6.5

8.20

7.98

7.99

8.00

8.02

8.04

8.07

8.11

8.16

8.19

8.24

8.27

3.0

7.0

8.08

7.86

7.87

7.88

7.90

7.92

7.95

7.99

8.04

8.07

8.12

8.15

2.5

7.5

7.94

7.72

7.73

7.74

7.76

7.78

7.81

7.85

7.90

7.93

7.98

8.01

2.3

7.7

7.88

7.66

7.67

7.68

7.70

7.72

7.75

7.79

7.84

7.87

7.92

7.95

2.0

8.0

7.78

7.56

7.57

7.58

7.60

7.62

7.65

7.69

7.74

7.77

7.82

7.85

1.5

8.5

7.60

7.38

7.39

7.40

7.42

7.44

7.47

7.51

7.56

7.59

7.64

7.67

1.0

9.0

7.36

7.14

7.15

7.16

7.18

7.20

7.23

7.27

7.32

7.35

7.40

7.43

0.6

9.4

7.09

6.87

6.88

6.89

6.91

6.93

6.96

7.00

7.05

7.08

7.13

7.16

0.3

9.7

6.77

6.55

6.56

6.57

6.59

6.61

6.64

6.68

6.73

6.76

6.81

6.84

The stock solutions are: an M/20 Borax solution containing
19.108 grams9 Na2B407 10 H2O in 1 liter; and an M/5 Boric acid,
NaCl solution containing 12.404 grams9 H3B03 and 2.925 grams
NaCl in 1 liter.

9 The values given by Palitzsch were calculated upon the basis of 11.0
as the atomic weight of boron. Since this was the value used, the new
value of 10.82 given in the atomic weight table of International Critical

214

THE DETERMINATION OF HYDROGEN IONS

Since the buffer . solutions are used more frequently for the
study of sea water, table 44 includes the values of the salt effects
of sea water on two indicators. For salt effects in general see
Chapters VIII and XXV.

MCILVAINE'S STANDARD BUFFER SOLUTIONS

Mcllvaine (1921) employs a mixture of 0.2 M disodium phos-
phate and 0.1 M citric acid. The citrate system functions as a
buffer in the region of pH between that buffered by the phosphoric

TABLE 45
Mcllvaine' s standards

0.2MNa2HPO4

0.1 M CITRIC ACID

0.2 M Na2HPO4

0.1 M CITRIC ACID

cc.

CC.

cc.

CC.

2.2

0.40

19.60

5.2

10.72

9.28

2.4

1.24

18.76

5.4

11.15

8.85

2.6

2.18

17.82

5.6

11.60

8.40

2.8

3.17

16.83

5.8

12.09

7.91

3.0

4.11

15.89

6.0

12.63

7.37

3.2

4.94

15.06

6.2

13.22

6.78

3.4

5.70

14.30

6.4

13.85

6.15

3.6

6.44

13.56

6.6

14.55

5.45

3.8

7.10

12.90

6.8

15.45

4.55

4.0

7.71

12.29

7.0

16.47

3.53

4.2

8.28

11.72

7.2

17.39

2.61

4.4

8.82

11.18

7.4

18.17

1.83

4.6

9.35

10.65

7.6

18.73

1.27

4.8

9.86

10.14

7.8

19.15

0.85

5.0

10.30

9.70

8.0

19.45

0.55

acid-mono phosphate system and that buffered by the mono
phosphate-diphosphate system. Consequently the range pH
2.2-pH 8.0 is covered by mixtures of but two stock solutions. If
samples of the salt and acid are well characterized this combina-
tion is convenient for many purposes.

Mcllvaine's data are summarized in table 45.

Tables should not be used in calculating the composition of the specific
solutions given by Palitzsch.

STANDARD BUFFERS

215

See also:

Storage Batteries, Vinal (1925). A summary of characteristics operation,
etc., prepared for the use of laboratory technicians. Contains a brief
bibliography.

CHAPTER XVII

HYDROGEN GENERATORS, WIRING, INSULATION, SHIELDING,
TEMPERATURE CONTROL, PURIFICATION OF MERCURY

Don't descend into the well with a rotten rope. — TURKISH PROVERB.
HYDROGEN GENERATORS

When there is no particular reason for attaining equilibrium
rapidly at the electrode a moderate supply of hydrogen will do.
When, however, speed is essential, or when there are used those
immersion electrodes which are not well guarded against access
of atmospheric oxygen an abundant supply of hydrogen is essen-
tial. Indeed it may be said that one of the most frequent faults
of the cruder equipments is the failure to provide an adequate
supply of pure hydrogen or the failure to use generously the
available supply.

Hydrogen generated from zinc and sulfuric acid has been used
in a number of investigations. If this method be employed,
particular care should be taken to eliminate from the generator
those dead spaces which are frequently made the more obvious
evidence of bad design, to have an abundant capacity with which
to sweep out the gas spaces of cumbersome absorption vessels
and to properly purify the hydrogen. To purify hydrogen made
from zinc and sulphuric acid pass it in succession through KOH
solution, HgCl2 solution, P2O5, and platinized asbestos at about
500°C. (See Franzen, Ber., 39, 906) (Heinrich, Ber., 48, 1915,
p. 2006).

A very convenient supply of hydrogen is the commercial, com-
pressed gas in tanks. According to Moser (1920) the industrial
preparation varies but the chief methods are the electrolytic and
the Linde-Caro-Franck processes. Of these the first yields the
better product. Hydrogen by the second process contains, among
other impurities, iron carbonyl which may be detected by the
yellow flame and the deposit of iron oxid formed when the hydro-
gen flame impinges upon cold porcelain. Moser found that it

350

XVII

HYDROGEN GENERATORS

351

was impractical to remove this iron carbonyl and he states that
hydrogen containing it is unfit for laboratory purposes. On the
other hand, electrolytic hydrogen ordinarily contains only traces

FIG. 66. AN ELECTROLYTIC HYDROGEN GENERATOR

of air and C02 and is free from arsenic and CO. To purify it pass
the gas over KOH and then through a tube of hot, platinized
asbestos. If it is desired to dry the hydrogen, use soda lime or

352 THE DETERMINATION OF HYDROGEN IONS

P2O5, but not H2S04. If P2O5 is used it should be free from P203,
i.e., distilled in a current of hot dry air.

In purchasing tank hydrogen it is well to be on guard against
tanks which have been used for other gases.

For controlling the flow of gas from a high pressure tank the
valve on the tank itself is seldom sufficiently delicate. There
should be coupled to it a delicate needle valve. If this cannot
be obtained use a diaphragm valve for the reduction of the pres-
sure. Even then there should be placed between the tank and
the electrode vessel a T tube, one branch of which dips under
mercury and forms a safety valve.

On the whole electrolytic generators are satisfactory if a direct
current is available. In figure 66 is shown a generator the body of
which is an ordinary museum jar. The glass cover may be
perforated by drilling with a brass tube fed with a mixture of
carborundum and glycerine. If this mixture is kept in place by
a ring paraffined in position, and the brass tube is turned on a
drill press with intermittent contact of the drill with the glass,
the perforation may be made within a few minutes. The elec-
trolyte used is 10 per cent sodium hydroxid. The electrodes are
nickel. To remove the spatter of electrolyte and to protect the
material in the heater, the hydrogen passes over a layer of con-
centrated KOH solution, H; and to remove traces of residual
oxygen the hydrogen is passed through a heater. In the design
shown the gas passes through a tungsten filament lamp. Lewis,
Brighton and Sebastian use a heated platinum wire. More com-
monly there is used a gas-heated or electrically heated tube
containing platinized asbestos.1

In the author's design shown in figure 66 the wiring is so ar-
ranged that, when there is no demand for hydrogen, the heater
may be turned off at S2 and a lamp thrown into series with the
generating circuit by switch Si. The generator then continues
to operate on a low current and sufficient hydrogen is liberated
to keep the system free from air. Such a generator can be run
continuously for months at a time. When in use the generator
carries about 4.5 amperes. If this current be taken from a high
voltage lighting system there must be placed in series a proper

1 Biilmann's interesting remarks on this are cited on page 354.

XVII

HYDROGEN GENERATORS

353

resistance which can be either built up by a bank of lamps or
constructed from nichrome wire.

While it is usually considered good practice to eliminate the
residual oxygen from electrolytic hydrogen by the use of some
such device as a tube of heated platinized asbestos (see below),
there may be occasions when a supply of pure hydrogen direct
from the generator is desired. Oxygen may accumulate on the
hydrogen side of the generator by diffusion from the oxygen side.
This has long been recognized. Biilmann and Jensen (1927)
report 0.13 per cent 02. Gaede (1913) introduced a simple means
of prevention. His principle is illustrated in figure 67. A sup-
plementary electrode at C is supplied a small current through
resistance R. From this electrode ascend fine bubbles of hydro-

FIG. 67. ILLUSTRATING THE PRINCIPLE OF THE GAEDE-NIESE HYDROGEN

GENERATOR

gen which, starting with zero partial pressure of oxygen, "clean
up" the residual oxygen diffusing from the oxygen layer above.
Niese (1923) describes a more practical generator embodying
Gaede's principle. He describes the hydrogen thus obtained as
having exceptional purity. Consult citation to Elveden.

Usually investigators have passed the hydrogen through tubes
containing platinum in some form which, when heated to about
400°C. very effectively removes residual oxygen. On comparing
hydrogen that had passed through platinized asbestos with
hydrogen that had passed through platinum gauze Biilmann and
Jensen (1927) found that the potential of the cell

- Pt, H2 1 HC1 (0.1N), quinhydrone | Pt +

354 THE DETERMINATION OF HYDROGEN IONS

was about half a millivolt higher in the first case than in the second.
This they ascribed to a component in the hydrogen from the
platinized asbestos that was more active than the hydrogen.
They believe it to be silicon hydride. See also their references,
and compare with Bach (1925).

Guntelberg (1926) removes residual oxygen from electrolytic
hydrogen (he prefers KOH solution) by passing it over copper at
450°C. The copper is pretreated with several oxidations and
reductions.

For the conduction of hydrogen over long distances, soft-drawn,
seamless, copper tubing is best. That with about 3.2 mm. ex-
ternal diameter is satisfactory. Where this is to be joined to a
metal connection, silver solder2 applied with borax flux is prefera-
ble to tin-lead solder, since the latter type of junction is apt to

HH BRASS SLEEVE ^H GLASS TUBE
Hi COPPER TUBE d] SILVER SOLDER
ODE KHOTINSKY CEMENT

FIG. 68. JUNCTION OF COPPER AND GLASS TUBES

contain "pin-holes." Where the copper tube is to be joined to
glass tubing use a piece of brass like that of figure 68. This is
quickly turned on the lathe. The copper tube is first silver-
soldered to the brass sleeve. The copper tube should not fit too
loosely. If the metal is very hot when the solder flows, silver
solder will run into the junction nicely. To join with the glass
tube, warm both brass tube and glass tube, smear each with hot
deKhotinsky cement and slip the two together. The interior
diameter of the sleeve should be little larger than the glass tube.
Extra cement is then moulded, while warm, about the whole
joint in order to strengthen it mechanically.

2 Silver solder: composed of 6.5 parts copper, 2.0 parts zinc and 11.0
parts silver. This solder is described as fusing at about 983°C. A nickel
wire is useful in spreading the flux and solder. The flux is prefused borax.
The heat of a blast lamp is required. Hardware stores carry the solder.

XVII

WIRING

355

For tne more elaborate trains there may be used standard
"f inch," bronze cocks of the type with ground keys under spring
tension. These are furnished with all sorts of ends for use with
standard "f inch" pipe fittings and with attachments for either
the so-called "compression" or the "soldered connection" with
copper tubing. See for instance the catalogue of the Lunken-
heimer Company, Cincinnati.

WIRING

Whenever a set-up is to be made more than an improvisation
it pays to make a good job of the wiring. A poor connection may

FIG. 69. SWITCHES FOR CONNECTING HALF-CELLS WITH POTENTIOMETER

be a source of endless trouble and unsystematized wiring may
lead to confusion in the comparison of calomel electrodes and the
application of corrections of wrong sign.

Soldered connections or stout binding posts that permit strong
pressure without cutting of the wire are preferable to any other
form of contact. If for any reason mercury contacts are used
they had best be through platinum soldered to the copper lead.
Copper wires led into mercury should not take the form of a
siphon else some months after installation it may be found that
the mercury has been siphoned off.

Thermo-electromotive forces are seldom large enough to affect

356 THE DETEKMINATION OF HYDROGEN IONS

measurements of the order of accuracy with which we are now
concerned if care be taken to make contacts so far as possible
between copper and copper at points subject to fluctuations in
temperature.

A generous use of copper knife switches can be made to con-
tribute to the ease and certainty of check measurements. For
instance if there be a battery of hydrogen electrodes and a set of
calomel electrodes, wires may be led from each to a centre con-
nection of single-pole, double-throw switches as shown in figure 69.
All the upper connections of these switches are connected to the
+ pole of the potentiometer's E. M. F. circuit, and all the lower
connections to the — pole. By observing the rule that no two
switches shall be closed in the same direction, short-circuiting of
combinations is avoided. The position of a switch shows at once
the sign of the metal of the attached half-cell in relation to any
other that may be put into liquid junction. This is a great con-
venience in comparing calomel electrodes where one half-cell may
be positive to another and negative to a third. Such a bank of
single pole switches permits the comparison of any electrode with
any other when liquid junction is established; and, if a leak occur
in the electrical system, the ability to connect one wire at a time
with the potentiometer and galvanometer often helps in the tracing
of the leak.

INSULATION

For wires perhaps the most satisfactory insulation for general
use is pliable rubber. The textiles are unsatisfactory in damp
weather and although paper is used very successfully in telephone
cables where close packing is desired it must be protected ab-
solutely from dampness. Even the terminals of the lead covered
cables must be boxed. Enameled wire, the enamel of which can
be tested for leaks by obvious connections made while the wire
is run through a mercury bath, makes very pretty wiring.

In ordinary potentiometric measurements, but especially in
the operation of an electrometer, the high intrinsic insulating
qualities of materials which are of supreme importance in high
tension work, may become of secondary importance compared
with surface leakages. Cleanliness of supports is therefore a part
of good technique, for accumulation of dirt may enhance the con-

xvii INSULATION; SHIELDING 357

ductivity of surface films of moisture. As far as moisture films
are concerned paraffin, if kept clean, is an excellent preventive
of excess trouble for moisture does not "film out" very well on
its surface. Of the same properties, but preferred for its mechan-
ical strength, is mineral paraffin known as ozokerite. When
such surfaces become dirty they should first be wiped and then
flamed wherever this is practicable.

The insulating material frequently used for the machined parts
of instruments, e.g., the plate of a potentiometer, is hard rubber.
The qualities of such rubber vary widely. While it usually has
a high insulating value this may become impaired and the surface
may become unsightly by the oxidation of its sulfur under the
action of light. I know of no satisfactory remedy. A pre-
ventive is the protection from light.

Bakelite is replacing rubber for many purposes and since the
advent of amateur radio it is readily available in sheets which can
be cut to good purpose in the installation and wiring of a poten-
tiometer equipment.

For some of the extreme measures necessary in the operation
of the glass electrode with an electrometer as null-point instru-
ment, see Kerridge (1926) and Brown (1924).

SHIELDING

Electrical leaks from surrounding high potential circuits are
sometimes strangely absent from the most crude systems and
sometimes persistently disconcerting if there is not efficient
shielding. The principle of shielding is based on the following
considerations. If between two supposedly well-insulated points
on a light or heating circuit, or between one point of such a circuit
and a grounding such as a water or drain pipe, there is a slight
flow of current, the electrical charges will distribute themselves
over the surface films of moisture on wood and glass-ware. At
two points between which there is a difference of potential the
wires of the measured or measuring system may pick up the
difference of potential to the detriment of the measurement. If
however all supports of the measured and measuring systems lie
on a good conductor such as a sheet of metal, the electrical leak-
age from without will distribute itself over an equipotential
surface and no differences of potential can be picked up. To shield

358 THE DETERMINATION OF HYDROGEN IONS

efficiently, then, it is necessary that all parts of the system be
mounted upon metal that can be brought into good conducting
contact. In many instances the complications of hydrogen elec-
trode apparatus and especially the separation of potentiometer
from temperature bath make a simple shielding impracticable.
Care must then be taken that all of the separate parts are well
connected. Tinfoil winding of insulated wire in contact with un-
shielded points can be soldered to stout wires for connection to
other parts by dropping hot solder on the well-cleaned juncture.

Flexible, rubber-covered wire with a spirally wound armor is
especially valuable for shielded connections. It is sold for
automobile connections.

Shielding should not be considered as in any way taking the
place of good insulation of the constituent parts of the measured
or measuring systems.

For further details in regard to shielding see W. P. White
(1914).

TEMPERATURE CONTROL

Baths

Temperature control is a matter where individual preference
holds sway. There are almost as many modifications of various
types of regulators as there are workers. Even in the case of
electrical measurements where orthodoxy interdicts the use of a
water bath it has been said (Fales and Vosburgh and others) that
it can be made to give satisfaction.

Yet there are a few who may actually make use of a few words
of suggestion regarding temperature control for hydrogen electrode
work.

As a rule the water bath is not used because of the difficulty of
preventing electrical leakage. Some special grades of kerosene
are sold to replace the water of an ordinary liquid bath but for
most purposes ordinary kerosene does very well. The free acid
sometimes found in ordinary kerosene may injure fine metallic
instruments. To avoid this, use the grade sold as "acid-free,
medium, government oil."

A liquid bath has the advantage that the relatively high spe-
cific heat of the liquid facilitates heat exchange and within a half
hour or so brings material to the controlled temperature, but

XVII

AIR BATH

359

compared with an air bath it has the disadvantage that stopcocks
must be brought up out of the liquid to prevent the seepage of the
oil. The advantage of the high specific heat of a liquid is falsely
applied when the constancy of a liquid bath is considered to be a
great advantage over the -more inconstant air bath. The lower
the specific heat of the fluid the less effect will variation in the
temperature of that fluid have upon material which has already
been brought to and is to be kept at constant temperature. For

FIG. 70. CROSS-SECTION OF AN AIR BATH

this reason a well-stirred air bath whose temperature may oscillate
about a well-controlled mean may actually maintain a steadier
temperature in the material under observation than does a liquid
bath which itself is more constant. It is the temperature of the
material under observation and not the temperature of the bath
which is of prime interest when the temperature is once attained.
An air bath can be made to give very good temperature control
and since it is more cleanly than an oil bath and permits direct-

360 THE DETERMINATION OF HYDROGEN IONS

ness and simplicity in the design of apparatus a brief description
of one form used by the writer for some years may be of interest.
A schematic longitudinal section illustrating the main features
is shown in figure 70.

The walls of the box are lined with cork board finished off
on the interior with "transite." The front is a hinged door
constructed like the rest of the box but provided with a double
glass window and three 4-inch hand holes through which appara-
tus can be reached. On the interior are mounted the two shelves
A and B extending from the front to the back wall and providing
two flues for the air currents generated by the fan F.

The writer at one time used a no. 0 Sirocco fan manufactured
by the American Blower Company, demounted from its casing
and mounted in the bearing illustrated. He now uses a four-
blade fan taken from a desk-fan and mounted so that it turns
in the hole F of the partition and blows toward E. The baffle
plates at E, made of strips of tin arranged as in an egg-box, and
intended to establish parallel lines of flow when the centrifugal
fan was used, are now eliminated.

In the illustration the oil cup is shown as if it delivers into an
annular space cut out of the Babbit-metal bearing. In reality
this annular space is provided by cutting away a portion of the
steel shaft.

The heating of the air is done electrically with the use of bare,
nichrome wire of no. 30 B. and S. gauge. When using the
centrifugal fan the wire is strung between rings of asbestos board
(the hard variety known as "transite" or "asbestos wood") which
fit over the fan at H. With the blade-fan the partition at F is
made of asbestos board and the wire is strung over the opening.
The air is thus heated at its position of highest velocity. The
electrical current in this heating coil can be adjusted with the
weather so that the time during which the regulator leaves the
heat on is about as long as the time during which the regulator
leaves the heat off. In other words adjustment is made so that
the heating and cooling curves have about the same slope.

When the room temperature is not low enough to provide the
necessary cooling the box I is filled with ice water. Surrounding
this is an air chamber into which air is forced from the high pres-
sure side of the fan. J should be provided with a damper which

XVII REGULATORS 361

can easily be reached and adjusted. A loop of copper tubing
carrying cold water near the heating wires would probably do as
well.

To lessen danger of electrical leakage over damp surfaces the
air is kept dry by a pan of calcium chlorid placed under B.

A double window at W over which is hung an electric light pro-
vides illumination of the interior. A solution of a nickel salt is
placed at this window to absorb the heat from the lamp.

The double window in the door (not shown) should be beveled
toward the interior to widen the range of vision.

Such a box has been held for a period of eight hours with no
change which could be detected by means of a tapped Beckmann
thermometer and with momentary fluctuations of 0.003° as de-
termined with a thermo-element. The average operation is a
temperature control within ±0.03° with occasional unexplained
variations which may reach 0.1°. Because of the slowness with
which air brings material to its temperature, the air bath is con-
tinuously kept in operation, and if a measurement is to be made
quickly the solution is preheated to the desired temperature.

Regulators

Given efficient stirring and a considerate regulation of the
current used in heating, accurate temperature control reduces to
the careful construction of the regulator. The ideal regulator
should respond instantaneously. This implies rapid heat con-
duction. Regulators which provide this by having a metal con-
tainer have been described but glass will ordinarily be used.
At all events there are two simple principles of regulator construc-
tion the neglect of which may cause trouble or decrease sensitivity
and attention to which improves greatly almost any type. The
first is the protection of the mercury contact from the corroding
effect of oxygen. The second is the elimination of platinum
contacts which mercury will soon or later "wet," and the sub-
stitution of an iron, nickel or nichrome wire contact.

After trials of various designs the author has adopted the form
of regulator head shown in figure 71. (See Clark, 1913.)

Pyrex glass is used in its construction. To seal the platinum
lead at P a very fine wire is used and the seal is made mechanically
strong by a sufficient thickness of glass. Although such a seal

362

THE DETERMINATION OF HYDROGEN IONS

will usually not be vacuum-tight it can be made so by having the
mercury in the exterior arm during the evacuation presently to
be mentioned. Preparatory to rilling the bulb the glass side arm
is constricted at D as a preliminary to sealing; beyond this con-
striction it is drawn off to a fine capillary E. The head is then
attached to a pump and the apparatus exhausted. Then the
capillary side arm is broken under a reservoir of carefully purified
mercury. If the exhaustion has been well
done, mercury will fill the vessel with practically
no gas bubbles left. The vessel is then detached
from the pump and a stream of pure hydrogen
is swept through the head entering at E.
There has previously been prepared the contact
wire of "Chromel" alloy. This should be large
enough to fill the capillary at A nearly
completely. However, its tip, to make contact
at B, is etched with aqua regia until it gives
ample space for the mercury column. If it takes
too much space in the capillary at B, mercury
will be squeezed off as drops when it rises with
overheating. With the wire in place, deKhotinsky
cement is melted at K, with care to prevent it
creeping to the bulb below. Meanwhile the hy-
drogen pressure is kept from building up by es-
caping through a trap. The side arm is now
sealed at D. Ample excess mercury has been
left and this is now thrown into the side arm as
(1913). Drawing shown. Rough adjustment is made by throwing
by Courtesy A. mercury m or out of this reservoir. Fine adjust-
ments are made by warming the cement at K and
raising or lowering the wire. When adjusted the
wire is clamped in the chuck C, designed by A. H. Thomas Com-
pany, or simply held by the cement. The capillary at B and the
size of the mercury bulb can be adjusted to requirements.

For discussion of other regulators and principles of thermostat
control see numerous references in Chemical Abstracts and, for
example, Tian (1923).

FIG. 71. A
TEMPERATURE
REGULATOR
(After Clark

H.Thomas Com-
pany)

XVII

HEAT CONTROL

363

HEAT CONTROL

For electrical heating, the control system shown in figure 72 is
simple and effective. The current from the main, M, passes
through a bank of lamps L to the heater by way of H. Lamps
are used since they provide a convenient variety of resistance
adjustable to the current desired. The current is thrown on or
off by the relay, R, controlled by current from the regulator
connected to T. To lower sparking the gap at the relay is shunted
by lamp B. If direct current is available it may be used for the
operation of the relay by drawing a low potential circuit from the
resistance O. In case only alternating current is available a storage
battery is placed in series with the relay and thermoregulater T.
Too strong a current is to be avoided. A sharp, positive action of

FIG. 72. WIRING FOR HEAT-CONTROL BY RELAY

the relay should be provided against the day when the relay
contact may become clogged with dust. To reduce sparking at
the regulator and at the relay contacts, inductive coils in the
wiring should be avoided. Spanning the spark gaps with properly
adjusted condensers made of alternate layers of tin foil and
paraffin paper may eliminate most of the sparking, if the proper
capacity be used.

For relay contacts the tungsten contacts used in gas engines
are very good.

For heaters to be used in water baths electric filament lamps
are frequently used. With oil baths, base "Chromel" alloy may
be used. This should be kept immersed and the leads made
heavy. For good regulation it is essential to adjust the current
until the heating rate is about the same as the cooling rate. This

364 THE DETERMINATION OF HYDROGEN IONS

is easily determined by noting the number of lamps used in series
with the heater when the current is on about the same length of
time it is off.

PURIFICATION OF MERCURY

Pure mercury is essential for many purposes in hydrogen elec-
trode work, — for the calomel and the mercury of calomel elec-
trodes, for Weston cells should these be "home made/' for thermo-
regulators and for the capillary electrometer.

The more commonly practiced methods of purification make
use of the wide difference between mercury and its more trouble-
some impurities in what may be descriptively put as the "electro-
lytic solution tension." Exposed to any solution which tends to
dissolve base metals, the mercury will give up its basic impurities
before it goes into solution itself, provided of course the reaction
is not too violent for the approach to equilibrium conditions.

The most commonly used solvent for this purpose is slightly
diluted nitric acid although a variety of other solutions such as
ferric chloride may be used.

To make such operations efficient it is necessary to expose as
large a surface as possible to the solution. Therefore the mercury
is sometimes sprayed into a long column of solution which is sup-
ported by a narrow U-tube of mercury. The mercury as it col-
lects in this U-tube separates from the solution and runs out into
a receiver. To insure good separation the collecting tube should
be widened where the mercury collects but this widening should
not be so large as to prevent circulation of all the mercury. A
piece of very fine-meshed silk tied over the widened tip of a funnel
makes a fine spray if the silk be kept under the liquid. This sim-
ple device can be made free from dead spaces so that all the mer-
cury will pass through successive treatments. It is more difficult
to eliminate these dead spaces in elaborate apparatus; but such
apparatus, in which use is made of an air lift for circulating the
mercury, makes practicable a large number of treatments. A
combination of the air lift with other processes and a review of
similar methods has been described by Patten and Mains (1917).

Hulett's (1905, 1911) method for the purification of mercury
consists in distilling the mercury under diminished pressure in a
current of air, the air oxidizing the base metals. Any of these

XVII PURIFICATION OF MERCURY 365

oxids which are carried over are filtered from the mercury by pass-
ing it through a series of perforated filter papers or long fine cap-
illaries. A convenient still for the purpose is made as follows.
Fuse to the neck of a Pyrex Kjeldahl flask a tube about 30 cm.
long which raises out of the heat of the furnace the stopper that
carries the capillary air-feed. Into the neck of the flask fuse by
a T-joint seal a 1.5 cm. tube and bend this slightly upward for a
length of 15 cm. so that spattered mercury may run back. To the
end of this 15 cm. length join the condensing tube, which is simply
an air condenser made of a meter length of tubing bent zigzag.
Pass the end of this through the stopper of a suction flask and
attach suction to the side tube of this flask. The mercury in the
Kjeldahl flask may be heated by a gas flame or an electric furnace.
For a 220 volt D. C. circuit 12 meters of no. 26 nichrome (Chromel)
wire wound around a thin asbestos covering of a tin can makes
a good improvised heating unit if well insulated with asbestos or
alundum cement. A little of this cement applied between the
turns of wire after winding will keep the wire in place after the
expansion by the heat.

In the construction of such stills it is best to avoid soft glass
because of the danger of collapse on accidental over-heating.
Hostetter and Sosman describe a quartz still.

Both the air current, that is delivered under the surface of the
mercury by means of a capillary tube, and the heating should be
regulated so that distillation takes place smoothly.

Since it is very difficult to remove the last traces of oxid from
mercury prepared by Hulett's distillation the author always makes
a final distillation in vacuo at low temperature. An old but good
form of vacuum still is easily constructed by dropping from the
ends of an inclined tube two capillary tubes somewhat over baro-
metric length. One of these is turned up to join a mercury res-
ervoir, the other, the condenser and delivery tube, is turned up
about 10 cm. to prevent loss of the mercury column with changes
in external pressure. The apparatus is filled with mercury by suc-
tion while it is inclined to the vertical. Releasing the suction
and bringing the still to the vertical leaves the mercury in the
still chamber supported by a column of mercury resting on atmos-
pheric pressure and protected by the column in the capillary
condenser. The heating unit is wire wound over asbestos. The

366 THE DETERMINATION OF HYDROGEN IONS

heat should be regulated by a rheostat till the mercury distills
very slowly. By having the mercury condense in a capillary the
still becomes self-pumping.

CAUTION

Perhaps few of us who work with mercury have a proper regard
for the real sources of danger to health. The vapor pressure of
mercury at laboratory temperatures is not to be feared, but
emulsification with the dust of the floor may subdivide the mercury
until it can float in the air as a distinct menace. Its handling
with fingers greasy with stop cock lubricant is also to be avoided
on account of possible penetration of the skin but more particu-
larly because of the demonstrated ease with which material on
the hands reaches the mouth.

CHAPTER XVIII
OXIDATION-REDUCTION POTENTIALS

We must remember that we cannot get more out of the mathematical
mill than we put into it, though we may get it in a form infinitely
more useful for our purpose. — JOHN HOPKINSON.

THE RELATION OF HYDROGEN ELECTRODE POTENTIALS TO
REDUCTION POTENTIALS

The hydrogen electrode is constructed of a noble metal laden
with hydrogen, and it may be asked what relation it bears to
those electrodes which consist of the noble metal alone and
which are used to determine the so-called oxidation-reduction
potentials of solutions of mixtures such as ferrous and ferric iron.

If a platinum or gold electrode be placed in an acid solution of
ferrous and ferric chlorides there will almost immediately be
assumed a stable potential which is determined by the ratio of
the ferrous to the ferric ions. The relation which is found to
hold is given by the equation:

RT .

where Eh is the observed potential difference between the elec-
trode and the standard normal hydrogen electrode, E0 is a con-
stant characteristic of this 'particular oxidation-reduction equilib-
rium and equal to Eh when the ratio L, +++ is unity, R, T, n

and F have their customary significances, and [Fe++] and [Fe+++]
represent concentrations of the ferrous and the ferric ions re-
spectively. This equation will be referred to later as Peters'
(1898) equation. Its general form is:

nF [Ox]

where [Red] represents the concentration of the reductant and
[Ox] represents the concentration of the oxidant.

367

Titrations,
Reduced Indiao Sul|>honatcs

at f)H 3.11
= ynono- 3=tri-

2= di-

4=Tetra-

0 20 40 60 80 100

FIG. 73. RELATION OF ELECTRODE POTENTIAL, Eh, TO PERCENTAGE
OXIDATION AT CONSTANT pH

368

XVIII OXIDATION-REDUCTION 369

•

If we plot Eh on one coordinate and the percentage reduction
on the other coordinate, we obtain a set of curves identical in
form for a given value of n. The position of each curve along
the Eh axis is determined by the value of E0' which fixes the
middle point and thereby places the curve of a specific system.

Such curves for four different systems are shown in figure 73.
In these cases the hydrion concentration was held constant for
reasons which will appear later. Each of these particular curves
has the slope characteristic of an oxidation-reduction system in
which the transformation of oxidant to reductant involves at one
and the same step two electrochemical equivalents. That is, n,
in equation (2), has the value 2. With the noteworthy excep-
tion that these titration curves reveal no stepwise oxidation,
they are analogous to the curves for acid-base equilibria described
in Chapter I.

It will be clearly understood that in using the term "oxidation"
or the term "oxidant" we do not imply that oxygen is neces-
sarily concerned. Oxidation is one of those terms established
under an old order of thought and carried into a new order with
its meaning broadened. As COg is a "higher" oxide of carbon
than CO it is natural to regard the process represented by 2CO
-{- O2 — » 2C02 as an oxidation. The reverse process, which leads
to reduction in the degree of oxidation, is naturally called reduc-
tion. At one time it was seen fit to classify certain types of
chemical change in terms of the participation of oxygen. A
schematicized representation of the transformation of ferrous to
ferric iron may be based upon this practice.

<— reduction

oxidation — >
2FeO + 0 ^=± Fe203

solution -f -f solution

4HC1 6HC1

I I

2FeCl2 2FeCl3

ionization | I ionization

2Fe++ ±^2e + 2Fe+++
<— reduction
oxidation — >

370 THE DETERMINATION OF HYDROGEN IONS

•

Neglecting the by-products in the above reactions and con-
centrating attention upon the states of the iron, we see that Fe+++
may be related to the higher oxide and Fe++ may be related to
the lower oxide. Hence Fe+++ may be called the oxidant and
Fe++ the reductant of the system Fe+++: Fe++. Through a
variety of such schemes a number of transformations which are
now conveniently pictured as mere gain or loss of electrons are
described as reductions and oxidations respectively. For some-
what more detail see Clark (1923).

The term ' 'reduction" does not, in itself, imply any relation to
the participation of hydrogen; but it is often assumed that hydro-
gen is concerned in reduction in much the same way that oxygen
was thought to be concerned in every "oxidation."

Before coming to a more generalized presentation we shall
describe the relation between the hydrogen electrode and the
oxidation-reduction electrode in terms of hydrogen and hydrogen
ions.

It is known that certain reducing agents are so active that
they evolve hydrogen from aqueous solutions. In such a solu-
tion an electrode would become charged with hydrogen and
would conduct itself much like a hydrogen electrode. The rela-
tions then obtaining can be extended and, if we wish to represent
the interaction of the reducing agent with the hydrogen ions, we
have:

H+ + reducing agent ^± H + oxidation product
If equilibrium is established for the above reaction

[H+] [Red] _
[H] [Ox]

T, [H] [Red]
^ [H+] " [Ox]

Substituting K =L.Lfor the ratio „ in Peters' equation,
(2), and placing n = 1 for the case at hand we have

, RT [H]

Eh = E0-— Z«K —

XVIII FORMULATION IN TERMS OF HYDROGEN ELECTRODE 371

Since the atomic hydrogen bears a definite relation to the partial
pressure of molecular hydrogen, P, through the equilibrium ex-
pressed by;

[H? = KhP,

we may substitute, collect constants under another constant K',
combine E0' and In K' as E0 and obtain

\/p ,

Eh= E0- Jn

Compare this with the general relation for the hydrogen elec-
trode

(4)

EH in (4) is zero by definition when there is used the "normal
hydrogen electrode" system of reference. When (3) is placed
on the same basis E0 is also zero, since each of the other terms in
(3) is identical with the corresponding term in (4).

In other words we have substituted for the oxidation-reduction
equilibrium the corresponding point of equilibrium between
hydrogen and hydrogen ions, and have considered the potential
difference at the electrode as if it were that of a hydrogen elec-
trode. An inference is that wherever we have an oxidation-
reduction equilibrium the components will have interacted with
hydrogen ions (or water) liberating free hydrogen and building
up at the electrode a definite pressure of hydrogen. Conversely,
if hydrogen is already present at the electrode with a pressure
too high for the oxidation-reduction equilibrium in question,
hydrogen will be withdrawn until its pressure is in harmony
with the oxidation-reduction equilibrium (the position of the
latter having been shifted more or less by reduction). When
a constant pressure of hydrogen is maintained at the electrode,
as it is in the customary use of the hydrogen electrode, no true
equilibrium can be attained until this hydrogen has so far re-
duced all the substances in the solution that they can support
one atmosphere pressure of hydrogen.

Incidentally it may be mentioned that it is a matter of indiffer-

372 THE DETERMINATION OF HYDROGEN IONS

ence whether we regard the re duct ant to interact with the hydro-
gen ions or the oxidant with the hydroxyl ions or each with water.
By use of the equilibrium equations which are involved we reach
the same end-result whatever the path.

Furthermore by the use of certain theoretical relations between
the hydrogen electrode and the oxygen electrode we could define
a potential in terms of that of an oxygen electrode.

This method of relating oxidation-reduction equilibria to elec-
trode potentials is convenient for showing the condition which
must obtain for a true hydrogen electrode potential; but when we
attempt to follow some of the logical consequences of this, the
customary exposition, we not only meet some serious difficulties
but obscure some very important relations.

Let us calculate the hydrogen pressure in equilibrium with an
equimolecular mixture of ferrous and ferric chlorid in a solution
held at pH 1. A platinum electrode in such a solution will have
a potential about 0.75 volt more positive than the "normal hy-
drogen electrode." Let us consider this to be the difference of
potential between a hydrogen electrode at pH 1 and a normal
hydrogen electrode. Let us calculate, then, the hydrogen pressure
at 25°C. from the equation:

0.75 = - 0.059 log — - (5)

We find the hydrogen pressure to be about 10~27 atmospheres.
At one atmosphere pressure a mole of hydrogen occupies about
22 liters and contains about 6 X 1023 molecules. If the pressure
is reduced to 6 X 10~23 atmospheres there would be but one
molecule of hydrogen in 22 liters. If reduced to 10~27 atmos-
pheres there would be but one molecule in about 37,000 liters.
To assume any physical significance in such values is, of course,
ridiculous. It is only by courtesy then that an electrode in a
mixture of ferrous and ferric iron at pH 1 can be considered as a
hydrogen electrode.

FORMULATION BY USE OF ELECTRON TRANSFER

The problem of mechanism suggested above will not be solved
by the following formal treatment; but this treatment may aid
the student to retain an orderly view of important relations, and

XVIII ELECTRON TRANSFER 373

it will provide a basis on which to discuss the interrelations of
electrodes of different type. When this interrelation is under-
stood a more generalized point of view is easier to attain.

It is generally agreed that one of the fundamental parts of an
oxidation-reduction process is an exchange of electrons. Al-
though too great an emphasis on this as a reality may be objec-
tionable, the objection is not relevant to our present purpose,—
the organization of relations.

We shall use the concept as a means of developing several
different equations by a common route. On entirely different
grounds we shall return to the discussion of actuality later.

An example of a process involving electron exchange is:

Ferric ion + electron ^± ferrous ion

+ e ^± Fe++

Since such a reversible reaction is not dependent upon the
presence of an electrode (acting as a catalyst) it is probable that
an exchange of electrons is going on continuously. There must
then be some condition virtually equivalent to a free-electron
pressure. If we desire a mechanistic picture we may imagine a
moment in the exchange during which the electron is balanced
between the forces of each ion. At this moment the electron
may be considered to belong to neither ion and to be a property
of the environment. Undoubtedly the situation is not so simple
as this picture suggests; and, although the presence of free elec-
trons has been demonstrated in liquid ammonia and methylamine
solutions, the experimental evidence is not sufficient to justify
our assuming the presence of free electrons in aqueous solutions
to be a fact. However, it may be said at once that we are not
now concerned with the objective actuality of a "freedom." A
pressure of free electrons may be postulated as the virtual equiva-
lent of a condition not yet clearly formulated; it may be used in
much the same way that Nernst used "solution tension," —
destined from the first to be eliminated from those equations
which are employed to formulate experimental data.

An electron escaping tendency may be postulated without
necessarily implying appreciable numbers of free electrons and
without immediate investigation of the source of the electrons
which are transferred from one system to another when the oxi-

374 THE DETERMINATION OF HYDROGEN IONS

dant and reductant of one system interact with the oxidant and
reductant of another system.

Imagine an aqueous solution of ferrous- and ferric chlorides in
which there is, initially, an exact equivalence between the positive
charges carried by all cations and the negative charges carried by
all anions. If an electron should leave a ferrous ion without
passing over to a ferric ion (thereby creating a new ferrous ion
to take the place of the first) no disturbance of the solution's
electroneutrality would occur. There would still be equivalence
of positive and negative charges. The same would be true if
the ferrous and ferric ions reacted with components of the solu-
tion as

Fe++ + H+ ^ Fe+++ + H
Fe++ + Cl ^± Fe+++ -f Cl~

We are evidently not concerned with ordinary, electrostatic
affairs.

There might be expected some degree of action between the
iron ions and components of the solution in the sense written
above. However, it has already been indicated (page 372) that
the action of ferrous ions on hydrions to form hydrogen and
ferric ions cannot be appreciable. Indeed we shall anticipate a
conclusion to be drawn when the formulation is complete and the
data are at hand. We shall state that no appreciable chlorine
would be formed from the second of the above reactions. In
general none of the oxidation-reduction systems to be considered
in this section acts appreciably on other components of the solu-
tions to be considered.

Therefore, in an acid1 solution of ferric and ferrous chlorides,
we shall consider the oxidation-reduction system to be exclusively
that represented by

electron

*Acid to prevent hydrolysis and the formation of Fe(OH)2 and Fe(OH)3.
The participation of these and other complexes is considered in a separate
section.

XVIII DERIVATION OF EQUATION 375

This we shall call the "iron system." The equilibrium state
we shall describe by

fFo-H-n (^

- - KFe (6)

Where ( ) represents activity and (e) Fe is the electron activity2 in
the iron solution.

Next imagine another oxidation-reduction system described by

; - * H2
hydrion electron hydrogen

This we shall call the hydrogen system.

Knowing that hydrogen by itself acts slowly, we may assume,
in the following discussion, the presence of a catalyst that will
always insure the attainment of the equilibrium states to be con-
sidered. For convenience we shall use hydrogen pressure, P,
(in atmospheres) in defining the equilibrium equation.

For the transfer of F (one faraday) electrons from activity
(c)H to activity (e)Fe

- A*1 = E F = RT In 7% (9)

WFe

Where E is the electromotive force in volts.

Substitute in (9) the equivalents of (e)n and (e)pe from equa-
tions (6) and (7)

Rewrite (10) as (13) where

(11)

2 The electron activity need not be defined. It is a tentative expedient
destined from the first to be eliminated from the final equations. But
see page 376.

RT. 1
' = "F" ln *T

J^-Fe

RT7 \/P

RT (Fe~+)

(12)
(13)

F ln (H+) H

F (Fe++)

376 THE DETERMINATION OF HYDROGEN IONS

and

E = EH + EFe

We shall now make the definition that when P = 1 and when (H+)
= i, (e)H = 1. Then by (7) KH = 1 and by (11) EH = 0. Equa-
tion (13) may then be written

T>rp /TT< U4-N

(14)3

3If the solution containing the iron system and that containing the
hydrogen system were mixed the two systems would react either toward
the right or the left as expressed below.

H + Fe+++^ Fe++ + H +

We can anticipate and say that it would he largely toward the right as
written. That is, hydrogen (represented for brevity as atomic) gives up
electrons to Fe+++. Fe++ and H + are formed. At equilibrium in the
mixture (e)Fe = («)H. Hence by (6) and (7)

CFe") (H+) KH

- — r = — — (fl)

V P KFe

If relative values of KH and Kpe could be found, the state of the equilibrium
would be denned. Such relative values will appear in due course of the
development.

By mixing the two solutions we obtain no external work of definite
magnitude.

Next suppose the solution containing the iron system were separated
from the solution containing the hydrogen system by an intervening solu-
tion of KC1 (saturated). We shall assume that this solution eliminates
liquid junction potential of the kind caused by unequal rates of diffusion
of ions. We have already anticipated the conclusion that the electron
escaping tendency or activity is greater for the electrons in the hydrogen
system than for those in the iron system. Presumably then electrons
could escape into the potassium chloride solution from the side of the
hydrogen system more easily than from the side of the iron system. But
if we permit free diffusion of ions this should cause no potential difference
since the electrons can be accompanied by positive ions, and since we
have postulated for the sake of simplicity that the KCl-solution eliminates
diffusion potentials of the ordinary kind. Indeed there is no occasion to

xvin "FUNDAMENTAL" EQUATION 377

E of (13) is here written Eh to signify reference to the standard
hydrogen system. When (Fe++) = (Fe+++), Eh = EFe.

In general when (e)H is unity and the hydrogen system is con-
nected as specified with any oxidation-reduction system the
electron activity of which is (e), equation (9) may be written
as (15)

(«) (15)

This will be our "fundamental" equation. See footnotes 3 and 4.

believe that there occurs appreciable transfer of free electrons across the
the boundary. Of course, in time, the components of the iron and hydro-
gen systems will diffuse, meet and interact. But we shall assume that this
does not occur within the time of an ordinary experiment. For ordinary
purposes we can assume that the interposed solution of KC1 is itself
"unattacked" and keeps the two oxidation-reduction systems from inter-
acting.

But suppose that the intervening KCl-solution contained some oxida-
tion-reduction system which could be acted upon by the iron system on
the one hand, or by the hydrogen system on the other hand, or by both.
If we permit diffusion of the components of this new system within the
intervening solution, or assume transfer of electrons in the tendency of
the intermediate system to maintain equilibrium between contiguous
layers, it is obvious that the new system will transmit to the iron system
the reducing action of the hydrogen system or that it will transmit to the
hydrogen system the oxidizing action of the iron system. Then, in the iron
solution, the concentration of Fe+++ will be lowered and that of Fe++
raised; while, in the hydrogen system under constant hydrogen pressure,
the concentration of H+ will be raised. To compensate for these effects
negative ions must migrate from the iron side to the hydrogen side and in
quantity equivalent to the virtual flow of electrons in the opposite direc-
tion. Consequently no unidirectional electric current has been produced.
No external work of definite magnitude is produced.

In passing it may be emphasized that we are assuming both free move-
ment of ions and simultaneity of events. In the absence of either of these
conditions interesting phenomena might occur.

Return to the case in which the iron- and the hydrogen systems are
separated by the pure solution of potassium chloride. But now provide
any new path by which electrons unaccompanied by ions can pass from the
side where their escaping tendency is the higher to the side where their
escaping tendency is the lower. Filter the ions, as it were. Continuing
with our anticipation which is to be fulfilled when the formulation is
complete and the data are at hand, we state that the electron escaping
tendency is the greater at the hydrogen side. Therefore, through the path

378 THE DETERMINATION OF HYDROGEN IONS

In general an oxidation-reduction system can be defined by
Ox + ne ^± Redn~

Oxn++ ne = Red

or by any intermediate case. To avoid complexity of symbols
consider the first of the above cases to be the type and write
the equilibrium equation

Substitute the equivalent of (c) by equation (16) in equation (15)
and separate the constant as E0.

This is the type equation for the electromotive force between any
oxidation-reduction system (involving n equivalents in a non-
stepwise oxidation or reduction) and the standard hydrogen
system connected in the manner indicated.

The procedure provides a uniform method of deriving the
electromotive force equation for any oxidation-reduction system
referred to the hydrogen standard.

In the development given above we have not specified the

provided, electrons will pass from the hydrogen side leaving an excess of
H+ on that side. They will enter the iron system and transform Fe+++
to Fe++. Excess chloride ions are left on the iron side. These migrate to
the excess H+ on the hydrogen side. A unidirectional electric current is
generated. Simultaneity of the steps, separated for purposes of descrip-
tion, is, of course, assumed.

Were these processes allowed to take place without restraint there
would be waste of energy by resistance, heating, etc. But now let the
electron path be supplied with any device whereby the pressure of the
electron stream can be exactly counterbalanced. Presumably, if the
whole system is under constant external pressure and constant tempera-
ture, and if the pressure of the electrons is balanced, we have the condi-
tions for the measurement of the free energy change of a reversible process.

"FUNDAMENTAL" EQUATION 379

nature of the path4 whereby electrons without accompanying ions
may pass from one oxidation-reduction system to another.

The path usually provided, although not necessarily the only
path that could be provided, is a metallic path. In providing
such a path we feel fairly sure that appreciable transfer of ions
does not occur and that movement of electrons, or the equivalent
thereof, does occur in that path.

However, if our formulation is to hold there should be no appre-
ciable attack upon the metal immersed in either solution. Were
that to occur there would be a local effect comparable with the
local effect in the case of direct contact between the iron and

4 That the Volta-effect does not enter is indicated as follows: Let dF
be the increase in total free energy of a system when dn equivalents of

electrons are added. Then — - is the partial molar free energy of electrons

in that system.

When an electron is removed from a material system an unmatched
positive charge is left. There is then an electrostatic attraction which

must be overcome. This electrostatic effect is part of — • Therefore,

— - will be considered to be made up of two terms. One of these, F. corre-
dn

sponds to the free energy of neutral molecules. The other is the electro-
static energy, N0€V where V is the electrostatic potential, N0 is the Avo-
gadro number ande the electron charge (negative).

|^ = F - N0eV (a)

Assume two metals indicated in the following equations by subscripts mi
and m2 and two solutions indicated by subscripts Si and s2.

Let metal mi be contiguous to solution si and metal m2 be contiguous
to solution s2. At these contiguous faces interchanges of electrons or
material permit establishment of equilibrium between the contiguous
phases.

Hence

— J = — J = Fm - NoeVmi = p. - N0eV. (b)

dn dn

Also

dn dn

380 THE DETERMINATION OF HYDROGEN IONS

hydrogen systems discussed in footnote 3. To avoid the latter we
separated the two solutions by "unattackable" KCl-solution. To
avoid the similar effect at the electrode we provide an "unattack-
able" metal.

A base metal in contact with a solution of its ions is a very
special and a comparatively rare case, although it is the case
which, until recently, has received the most attention. Certain
aspects of this case can be discussed to better advantage later.
For the moment we may assume that the massive metal maintains
the activity of the metal molecules or atoms in the given solution
at a constant value. Therefore, the equilibrium equation (18)
of the system

Mn+ + ne ^± M

may be written

(19)

In accordance with the scheme discussed above, solutions Si and 83 are
to be separated by an "unattackable" solution to prevent transfers which
will establish a mixing. But for present purposes we can neglect the
intermediate solution and retain the conditions it was supposed to es-
tablish. One of these was elimination of junction potential due to unequal
migration of ions. Another was such an unrestrained migration of ions
as to prevent the production of any excess electric charge of any kind in
either solution. In short, it is supposed that no electrostatic difference
of potential exists between the two solutions. Therefore,

V., - V82 = 0 (d)

By (b) (c) and (d)

dn dn

But it is the difference in free energy per equivalent of electrons which
is measured by the potentiometric method, and it is the difference FS
— FS2 that was used in our formal equations.

For references on the Volta-effect see Rodebush (1927), Langmuir
(1916), Lodge (1885) and Corbino (1927).

XVIII SUMMARY OF EQUATIONS 381

By the usual procedure we substitute the equivalent of (e) by
(19) in the "fundamental equation," (15). We also separate the
constant as usual and obtain:

Eh = Eo + ^- In (M«+) (20)

For convenience we shall now assemble a few equations of part icu-
lar importance to our subject.

The "hydrogen system":

Eh= - ^fc(g| (21)

The " oxygen system":

02 + 2H20 + 4e ^± 40H-
Let (H20) be constant. p0 = pressure of 02.

RT7 (OH-)

Eh = E°-T^VpT (22)

Metal-metal ion system :

Mn+ + ne ^± M
See above

Eh = E0 + - In (M»+) (23)

Any oxidation-reduction system of the type
Ox + ne ^ Red*-

*•*!! **O — - l/*v / s~~ \

nF (Ox)
Special oxidation-reduction system

Ox + 2e ^ Red—

RT ^ (Red~)

(24)

382 THE DETERMINATION OF HYDROGEN IONS

The development given above may not be comprehensive
enough to meet all requirements as to detail but it is general
enough and sufficiently rigid to have some advantage. Its chief
advantages are: first an easily remembered device for the formula-
tion of the orienting equation of any cell, second the emphasis of
the family relationship of cells which all too often are considered
unique. Both of these advantages will be utilized in the dis-
cussion of important matters to follow.

THE PARTICIPATION OP HYDRIONS

Of importance to the subject of this book is the fact that the
reductant appearing in equation (25) is an anion. There are
various cases analogous with this but different in type. For in-
stance, a positive charge in an oxidant's cation may be neutralized
by one electron and an anion may be created by a second electron.

Ox+ + 2e ^± Red-

It will not alter the principle if we continue with the very simple
case described by

Ox + 2C = Red—
The orienting electrode equation is

And now to avoid complexities, the consideration of which
would not seriously alter the conclusions, we shall assume that
activities may be replaced by concentrations. Equation (26)
then becomes:5

Assume that the oxidant has neither acidic nor basic groups and
that its concentration during shifts in hydrion concentration can
always be identified as that of the total oxidant, [SJ. If we wish
to reconstruct (27) to include the total reductant, [SR], as is

6 In this book () signifies activity and [ ] concentration.

XVIII PARTICIPATION OF HYDRIONS 383

necessary when we know nothing about the concentration of the
anion, Red , and are forced to measure the total reductant, it
is necessary to use the equilibrium equations:

[H+] [HRed-] _
[H2Red]

[H+][Red-~] _

[HRed-]
and the summation

[SK] = [Red—] + [H Red-] + [H2Red] (30)

Substitute (28) and (29) in (30) and solve for [Red—]

[SR] Ki K2

Substitute (31) in (27), collect constants under E0 and replace
[Ox] by [SJ.

ra I
Eh = Eo " F ln [sj + W ln [Kl K2 + Kl IH+1 + [H+]2] (32)

If [H+] is kept constant, as by means of a strong buffer solu-
tion, the last term of (32) is constant and (32) may be written :

It was this equation that was used in constructing the curves of
figure 73.

When the acidic or basic nature of the system is changed, the
form of the last term in equation (32) is altered. For the system

Ox + 2e ^± Red-

RT [SR] RT
Eh==E°-W^[sJ + WZn

where Kr is defined by

• [Red-] [H+]
[HRed]

384 THE DETERMINATION OF HYDROGEN IONS

and Ko is defined by

[Oi] Kw

[OxOH] [H+]

Thus it is evident that the peculiarities of a given system are
(with some exceptions) expressed by the last term of such equa-
tions as (32) and (34).

Obviously if [H+] is constant, (34) like (32) may be written as

(33).

To study the last term of (32) set ^1 = -t Then (32) be-

[S0] 1

comes (35)

Eh = Eo + ^- In [KiK* + K! [H+] + [H+]2] (35)

The geometry of (35) is illustrated in figure 74. Vary [H+] but
let [H+] be determined in each instance by the independently
measured pH value of a buffer solution. When [H+] is large in

relation to KI and K2, Eh varies as — In [H+], or, at 30°, -0.06

pH. When [H+] is small in relation to KI and K2 the last term
in (35) is practically constant and the potential is no longer
affected by alteration of pH. Between these extremes the curve
passes through points of inflexion centered at values of pH equal
to pKi and pK2.

In figure 74 the geometry of (33) is illustrated by the curves
for certain fixed values of [H+]. Left of figure.

To obtain the picture representative of the complete equation
(32), a figure in three dimensions is necessary. It will be similar
to that represented by the isometric drawing of figure 75. This
shows a surface descriptive of the system of which 2-6 dibromo
benzenone indophenol is the oxidant. (See Cohen, Gibbs and
Clark (1924).)

In many cases which have proved amenable to measurement,
other than the two acidic groups assumed above for purposes of
simplicity must be taken into consideration. Even a group not
directly concerned in the oxidation-reduction process may have its
dissociation constant altered when the substance is transformed

XVIII

PARTICIPATION OF HYDRIONS

385

from an oxidant to a reductant. The resulting energy-change then
becomes evident; and the equation required to account for the
actual measurements may be more complicated.

The more varied examples of the several effects are to be found
in a series of papers entitled Studies on Oxidation-Reduction by

-*E

I apH

^--

\ P«1

V -AE _ ..

HK^-"

\. \ oK -AE

I H5 ^

=^_

00 5

0 (

> 8 10 214

OXIDATION

FIG. 74. (Le/0 RELATION OF ELECTRODE POTENTIAL TO PERCENTAGE
OXIDATION AT CONSTANT pH AT VARIOUS LEVELS OF pH; (Right)
RELATION OF ELECTRODE POTENTIAL TO pH AT CONSTANT PERCENTAGE
(50 per cent) OXIDATION

SYSTEM: Anthraquinone,2,7-disulfonic acid and its reductant at 25°.
Drawn from data of Conant, Kahn, Fieser and Kurtz (1922).

0.05912 expressed as 0.06.

ApH

Clark, Cohen, Gibbs, Sullivan, Cannan et al. reviewed up to 1925
by Clark in Chemical Reviews, 2, 127, (1925). See also the ref-
erences there given to papers by Biilmann, by LaMer, by Conant
and their coworkers.

386

THE DETERMINATION OF HYDROGEN IONS

Since, in the majority of cases, equation (33) applies when [H+]
is constant, this equation may be considered applicable at any
fixed level of [H+] and attention may be centered upon the rela-

ro I

tion of potential to pH when L-I*I = 1.

[S0J

With this understood a

FIG. 75. ISOMETRIC DRAWING OF THE SURFACE DESCRIPTIVE OF THE SYSTEM
COMPOSED OF 2-6 DIBROMO PHENOL INDOPHENOL AND ITS REDUCTANT
(After Cohen, Gibbs and Clark (1924). See Clark et al. Studies on
Oxidation-Reduction, VI.)

system may be described graphically by the so-called E'0: pH
curve. Figure 76 illustrates a few of the many cases in which

[•Q I

[S0J

has been maintained at a ratio of unity and the potential

measured as pH is varied. On curves 3 and 4 (fig. 76) the points
at pH = 3.91 correspond to the mid-points of the corresponding
curves in figure 73.

+1.2

+ .8
+.6
+ .4
+ .2
0
-.2

-.4

Eh
-.6

-.8

> p
H/0,

- 10°

icr4
10°

FIG. 77
FIG. 76

1. Relation of potential of hydrogen electrode (1 atmosphere^Hz) to pH.
12. Theoretical relation of potential of oxygen electrode (1 atmosphere

O2) to pH.

2-11. Systems at 50 per cent reduction, named below by one component.

2. Anthraquinone-/3-sulfonic acid (oxidant).

3. Indigo disulfonate (oxidant).

4. Indigo tetra sulf onate (oxidant) .

5. Methylene blue (oxidant).

Br S08Na

6. Oxidant: HO

7. Oxidant: HO

- N

= 0.

8. Benzo-quinone (oxidant).

9. K,Fe(CN)6:K4Fe(CN)6.

11. o-Tolidine (reductant).

FIG. 77. THEORETICAL RELATIONS BETWEEN ELECTRODE POTENTIAL, Eh, pH
AND PARTIAL PRESSURES OF HYDROGEN AND OXYGEN

Each decrement of the partial pressure of hydrogen by 10~4 shifts the
potential of a hydrogen electrode at 30° + 0.03 X 4 = 0.12 volt.

Each decrement of the partial pressure of oxygen by 10~4 shifts the theo-
retical potential of an oxygen electrode — 0.015 X 4 = —0.06 volt.

Since the position of any one of the diagonals of figure 77 is determined by log
hydrogen pressure' Clark Pr°P°sed the term "rH" *°r this quantity, believing that it would be
a convenience for the general discussion of,' the general position of an oxidation-reduction sys-
tem. Unfortunately the term rH has been frequently used where potential would be far pref-
erable. Because of this indiscriminant use, further employment of rH is to be discouraged.

387

388 THE DETERMINATION OF HYDROGEN IONS

THE RELATION OF HYDROGEN POTENTIALS TO GENERAL RELATIONS
DESCRIBED GRAPHICALLY

To show graphically the possibilities of interpreting the poten-
tials of one system in terms of the potentials of another consider
figure 77. At pH = 0 a properly prepared electrode under one
atmosphere of hydrogen is given the arbitrary reference poten-
tial of 0. As pH increases, the potential of such an electrode
becomes more negative, and, at the temperature chosen for
purposes of the drawing, it becomes more negative by 0.06 volt
per unit increase of pH. In short the line thus defined, and
readily identified on the chart, is the line of the potential of a
hydrogen electrode under one atmosphere of hydrogen. Above
this line and distant about 1.23 volts at all values of pH is the
line of the hypothetical oxygen electrode under one atmosphere
of oxygen. The region above this line of the oxygen electrode
may be considered for present purposes as the region of oxygen
"overvoltage" and the region below the line of the hydrogen
electrode may be considered the region of hydrogen " over volt age."
In other words they are regions in which the potentials would
be such that, at the given pH value of the solution, hydrogen
or oxygen, as the case might be, would be liberated from water
at an equilibrium pressure of over one atmosphere. Between these
arbitrary limits lie the oxidation-reduction systems which are
stable enough in the presence of water not to decompose this
solvent extensively.

If the hydrogen electrode be under a partial pressure of hydro-
gen less than one atmosphere, but constant, the line will be shifted
upward (calculation by equation (21)). The successive positions
of the shifted lines in the figure are determined by hydrogen
pressures. each of which is 1/10,000 that of the preceding.

In a similar manner there is illustrated the shift in the position
of the line of the oxygen electrode as the oxygen pressure declines
in steps of 1/10,000 the pressure of the preceding case. (Calcula-
tion by equation (22).)

By superimposing figure 76 on figure 77 it is possible to make a
formalistic interpretation of the potentials of the various systems
in terms of the potential of either an oxygen or a hydrogen
electrode.

XVIII INTERRELATIONS 389

It has already been indicated that such an interpretation may
be highly artificial.

Now each curve in figure 76 is for the half-reduced state of the
actual system. If the potential becomes more negative, the per-
centage reduction of a given system increases as shown, for in-
stance, by figure 73. To attain true equilibrium at the hydrogen
electrode the methylene blue system, for instance, would first have
to be "completely" reduced. To attain true equilibrium at a
definite one to one ratio of methylene blue and methylene white
both hydrogen and oxygen would have to be practically elim-
inated.

The reader himself can carry forward the further interrelation-
ships and might profitably consider the interpretation of any
electrode potential in terms of any one of the systems. He might
assume, for instance, the universal presence of iron (E0 = 0.75)
and interpret all potentials in terms of the system Fe+++ + e
^± Fe++.

The practical aspect of the matter is this. We cannot avoid
the possibility of other systems participating when we set up an
experiment on one. Thus with a platinum electrode immersed
in a mixture of ferric and ferrous ions in aqueous solution, we
must, strictly speaking, consider the following oxidation-reduction
systems: Fe+++:Fe++; H+:H2; O2:OH-; and Pt++++:Pt. How-
ever, when we come to know the quantitative values of the
equilibrium potentials for different systems, or even their orders
of magnitude, we come to realize that the ferric-ferrous system
by interaction with water or water constituents or with chloride
ions in a ferrous-ferric chloride mixture cannot liberate appre-
ciable quantities of hydrogen, oxygen or chlorine and that the
potential of the system is incompatible with appreciable amounts
of platinum ions. No appreciable energy flows into the transfor-
mation of these systems and we rest content that we are con-
cerned practically with only the energy changes of the system
Fe++:Fe+++.

In general, characteristic data for one system should be ob-
tained under conditions which preclude interference by another
system.

This is the conclusion we anticipated during the formulation
in the first instance. The quantitative data of accuracy suffi-

390 THE DETERMINATION OF HYDROGEN IONS

cient for the purpose may be found in the compilation by Abegg,
Auerbach and Luther (1911-1915). Cf. Gerke (1925).

USE OF THE GENERAL RELATIONS IN DETERMINING pH VALUES

Suppose the potential of an electrode were stabilized by some
definite oxidation-reduction system which involved the hydrion.
As one instance consider a system to which there applies the
equation

Eh = E0 - ln + j in [KlK2 + Ei [H+] + [H+?] (36)

If there were no interaction of oxidant or reductant with constitu-
ents of the solution, the addition of the oxidant and reductant in
a one to one ratio would leave

Eh - Eo + - In [EiE. + E, [H+] + [H+?] (37)
«v

If KI and K£ were very small in relation to [H+] it would mean
that, while this relation held, the acidic nature of the reductant
would not be brought into play to affect the acid-base equilibrium
of the solution. Also the above equation would then reduce to

Eh = Eo + - In [H+] (38)

If we may assume that E0 has been evaluated by a set of stand-
ardizing measurements with known values of [H+], then in any
other case a determination of Eh yields the value of [H+].

Chapter XIX will be devoted to such cases.

There remains a possibility not yet given the attention it
deserves.

It was specified above that the oxidant or reductant should not
react with other reductants or oxidants in the solution and thus
suffer a change in ratio. This is a severe limitation, which, as
we shall see in a later chapter, appears less prominently in prac-
tice than might be expected because of the slowness of certain
oxidation-reduction processes. If the potential-controlling system
were to suffer oxidation or reduction, there would be a change of

XVIII NEW SYSTEMS FOR pH MEASUREMENT 391

potential independent of a change in pH. In many cases this
means that protection from the oxidizing action of the air would
have to be provided. In all cases it means avoidance of the
presence of any oxidizing or reducing agent sufficiently active
to appreciably attack, within the time of the experiment, either
the reductant or the oxidant employed. This does not mean
that any oxidizing or any reducing agent is an incompatible.
Quite the contrary will reveal the still unutilized possibilities in
determining the dissociation constants of very active oxidants and
reductants.

Assume for instance that the system designated by Oxa:Reda
is to be employed in equimolecular mixture. Suppose that the
potential of this system varies linearly with pH. Now let it be
applied to the measurement of the pH values of solutions con-
taining the reductant of a system designated by Redb:0xb.

Were the characteristic potential of the "b" system negative
to that of the "a" system, there would be extensive interaction
between the "a" and "b" systems. The reductant of the "b"
system would reduce some of the oxidant of the "a" system.
The extent is determined by the relative concentrations and also
by the "spread" between the "characteristic" potentials of the
two systems.

But were the potential of the "b" system positive to that of the
"a" system the reductant of the "b" system could not act ex-
tensively upon the oxidant of the "a" system. Therefore, if the
"b" system were used in an extensively reduced condition (prac-
tically the reductant alone), the ratio of oxidant to reductant in
the "a" system should not be seriously affected.

How seriously remains to be calculated by specific assumptions.

At constant pH the potentials of the systems separately are
defined by

Eha = Ea - 0.03 log (39)

Ehb = E;- 0.03 log (40)

[bObJ

The systems react to a common potential, Eha = Ehb. Hence:

TT' TT' ^ no 1^ [Sra] [Sob] x.v

E. - Eb = 0.03 to (41)

392 THE DETERMINATION OF HYDROGEN IONS

Let Ea = 0.15 volt and Eb = 0.60 volt.

Then

[Sr>] [Sob] ,v

[Soa][Srb]"

Let the initial concentrations of the measuring system be as
low as [Sra] = [SoJ = 10 ~4 while of the measured system let
[Srb] be as high as 1 normal, initially. In changing from the
initial state to that defined by (42) x moles of reductant "b" have
reacted with x moles of oxidant "a" to increase by x moles the
concentration of reductant "a" and form x moles of oxidant "b."6

+ X] [X]

[10~4 - x] [1 - x]

An approximate solution of this yields a value of x very nearly
zero. In other words the measuring system, "a," nas n°t been
appreciably affected.

This principle is tacitly assumed in the application of the
hydrogen: hydrion system to the measurement of pH values in
solution containing a reductant of another oxidation-reduction
system; but the principle should be applicable generally, and not
only to measurements in the presence of reductants, but also to
measurements in the presence of oxidants. In the latter case the
measuring system should be one as positive as can be selected.

It is to be hoped that when a sufficient variety of well defined
systems are available the principle here described will be applied
and will leave no excuse for an ionization constant of any oxidant
or reductant remaining undetermined when its value is of appreci-
able magnitude.

For an example see Cannan and Knight (1928).

On page 375 the electromotive force of a cell is formulated by
use of the postulate that the escaping tendencies or activities of
the electrons are different in two oxidation-reduction systems.
In the cell these two oxidation-reduction systems are placed in

6 For simplicity there are assumed equivalent valences.

XVIII SIGN OF ELECTRODE POTENTIAL 393

liquid junction with an intermediate solution which can be
attacked chemically by neither oxidation-reduction system but
which will permit migration of ions. We assume, for sim-
plicity, equality of ionic migrations and, therefore, no potential
difference at the junction. The metallic circuit provides a path
which permits electrons but not ions to migrate from one system
to the other.

The introduction of a path through which electrons alone pass
from the one system to the other establishes a unidirectional
electric current. If the current is not entirely restrained it will
appear that this path (usually a metal) has the more negative
potential in the section nearest the system of higher electron
escaping tendency.

With this scheme it becomes a convenience to give to the
potential of an electrode the sign of the metal as found in a cell
made up of the given electrode and the standard of reference, the
normal hydrogen electrode.

This is, I am told, in harmony with the convention to be used
in International Critical Tables.

In relating a cell reaction to the signs of the cell terminals it is
convenient to argue as follows.

The system Cl2:Cl~ has a much greater tendency to absorb
electrons (oxidize) than has the system H2:H+ (which is the re-
ducing system par excellence. An indifferent electrode may be
thought of as an indicator of the relative ability of the solution
system to give or take electrons. It is charged positively by an
oxidizing system such as C12 : Gh, relative to the charge produced
by a reducing system such as H2 : H+. The extension of the con-
cept is simple. It must, of course, be combined with some con-
vention regarding the way of writing the cell reaction in cases
which are not obvious.

When a cell description is written in this book, it will be written
not only with the relatively negative metal phase at the left, but,
to avoid any ambiguity, each sign will be given as that of the
exterior lead on open circuit, the open circuit being the ideal
potentiometric balance as if against a condenser. Thus

- Pt, H2 1 HC1, HgCl | Hg +

means that the mercury is positive relative to the platinum as it
would be found to be at potentiometric balance. The reductant

394 THE DETERMINATION OF HYDROGEN IONS

(H2) of the system having the higher electron escaping tendency
releases electrons to the nearest metal. These electrons flow in
the exterior circuit to attack the oxidant and set free the reductant
(Hg) of the system with the lesser electron escaping tendency.

Lewis and Randall in Thermodynamics adopt "the convention
that the electromotive force given shall represent the tendency
of the negative current to pass spontaneously through the cell
from right to left." (Thermodynamics, p. 390.)

They write

H2(g), HC1 (0.1 M), Cl2(g); E = 1.4885
or

Cla(g), HC1 (0.1 M), H2(g): E = -1.4885

When they represent a half-cell such as

Hg | HgCl, KC1 (0.1 N) ||

they state the order electrode | electrolyte. "We then say that
the single potential measures the tendency for negative elec-
tricity to pass from right to left." When they write

"D.E.;E = -0.3351"

they refer the potential of the "decinormal electrode" to the
normal hydrogen electrode by

Hg | HgCl, KC1 (0.1 N) || H+ (activity 1) | H2 (1 atmos.) Pt

and, since the negative current goes from left to right through
the cell as written, the negative sign is given, as above.

As a consequence it is found that the signs given to single
electrode potentials by Lewis and Randall, and by many who
adopt their convention, are opposite to those used in this book.

We could use the system of Lewis and Randall by writing, for
instance,

|| KC1 (0.1 N), HgCl | Hg; E = 0.3351
instead of their

Hg | HgCl, KC1 (0.1 N) || ; E = -0.3351

Although this will frequently be done we here ignore the order
and use the following convention. The sign of an electrode

XVIII FINITE EATIOS 395

potential of a given half-cell shall be the sign of the potential of
its metal relative to that of the metal of the normal hydrogen
half-cell.

For interesting discussions of the sign of electrode potentials
see: Lewis and Randall (1923), Porter (1924) and Transactions
American Electrochemical Society 31, 249; 33, 85; 34, 196.

ON FINITE RATIOS

In any case where a definite potential difference is to be established at
the electrode there must be in the system two species, one of which is the
direct or indirect reduction product of the other, and the ratio of their
concentrations or activities must be of finite magnitude. Neglect of this
principle is not infrequent, and is doubtless due to the emphasis which has
been placed upon the final, working-form of the equation for the differ-
ence of potential between a metal and a solution of its ions. See equation
(20) page 381 . In obtaining the final form of this equation certain assump-
tions have been made and the potential-difference at the electrode is made
to appear as if it were dependent only upon the concentration of one
species, namely the metal ions. Whether this be the explanation or not,
there are not infrequently encountered in the literature attempts to
measure electrode potential differences with a single oxidant or reductant.
It should be plain from a study of figure 73 that, when the oxidant or re-
ductant alone is present, the electrode potential-difference becomes
asymptotic to the Eh axis. Were it possible to eliminate absolutely every
trace of the oxidant, the potential-difference obtained with the reductant
alone would tend to become infinite.

When we meet such a prediction in an equation we should be suspicious.
Perhaps for the potential produced by a pure reductant or by a pure
oxidant there is an inherent limitation of a kind not implied by the equation
which rests upon the assumption of a reversible system. On the other
hand the general treatment implies the following.

The potential could not become infinite for two reasons. In solution an
infinitesimal reaction with the solvent would prevent it. Second the
production of a pure reductant could not be attained in a world which has
suffered extensive interactions of its components unless there were created
de novo another reducing reagent belonging to a system of infinite nega-
tive potential or unless there were created de novo an absolutely pure re-
ducing agent which could be the reductant of a low potential system if it
were employed in infinite mass.

Wherever stable potentials are reported as having been found with re-
ductant alone it is doubtless due to the presence of the oxidant as an
impurity.

While there may be no rigid proof of the statements made above they
are implicit in the equations. Whatever their limitations, they have
several practical implications.

396 THE DETERMINATION OF HYDROGEN IONS

So far as mere formulation is concerned it should be possible to attain
the electrode potential of the system metal-metal ion by means of an un-
attackable metal immersed in a solution of the metal ions, provided the
saturation value of the metal were maintained by a piece of the metal
placed elsewhere. The system metal-metal ion is a special -case of an
oxidation-reduction system which should be measurable in the ordinary
way. The difficulty would be in maintaining between the metal serving
merely as electrode and the metal serving merely as saturator a sufficiently
fast diffusion of the almost insoluble metal molecules to maintain a finite
ratio of oxidant to reductant at the electrode. For this reason the only
practical way is to make the electrode of the metal itself or to have it
present at the electrode in appreciable quantities, as in the case of an
amalgam electrode. Otherwise the inevitable impurities, such as hydrogen
or oxygen, of the "unattackable" electrode would make it behave as a
more or less indefinite hydrogen, oxygen or other kind of electrode.

By the same token a system which does not reversibly maintain a finite
ratio of oxidant and reductant, leaves the electrode functioning in an
almost uninterpretable manner. Irrespective of what can be done under
such circumstances, the recognition of this fact leads to skepticism re-
garding all measurements which cannot satisfy the requirements of the
equations on introduction of known components. There is ample room
and frequent occasion for bold adventure in the use of electrode measure-
ments, especially in the study of so-called irreversible, organic oxidation-
reduction systems; but, unless the equations can be satisfied by the intro-
duction of known components, one should warn his reader that he is ad-
venturing and that he is not citing definitive data.

FREE ENERGY CHANGES

Since the validity of Faraday's law is assumed and measurements of
cells are measurements of electromotive force, it has been convenient to
separate Eh and to place nF on the other side of the equation. However,
nFE is the free-energy change in volt-coulombs. Therefore, all the electro-
motive force equations permit the calculation of the free energy-change,
— AF, from

-AF = nFE (43)

It is unnecessary to repeat all the equations in the new form; but one case
will be instructive. Consider equation (32) page 383 and rewrite it as:

r« -1

- AF = 2FEh = 2FE0 - RT In ^ + RT In [KiK, + Ki [H+] + [H+]2] (44)

|koj

The employment of Eh signifies (by subscript h) reference to the "normal
hydrogen electrode." For simplicity we shall consider this to be a hydro-
gen electrode in a solution of unit hydrion concentration under one atmo-
sphere pressure of H2. Therefore, the processes to be discussed involve
reference to this standard hydrogen system.

XVIII FREE ENERGY CHANGES 397

We shall assume that KI and K2 have such values that [H+] can be made
either large or small with relation to either.

Let it be assumed in all cases that [SR] = [S0] = 1. Then equation (44)
can be written

-AF = 2FE0 + RT In [KiK, + Kj [H+] + [H+]»] (45)

First make [H+] large in relation to KI and K2. Then we have prac-
tically

-A*1! = 2FE0 + 2RT In [H+] (46)

When [H+] = 1 we have

-AF2 = 2 FE0 (47)

There is implied the suppression of the dissociation of the reductant.
Hence (47) gives the free energy of the process

(1 atmos.)
S0 + H2 ;=± SR (hydrogenated)l

(48)
Ox + H2 ^± H2Red J

For any value of [H+] other than 1, equation (46) gives not only the
free energy of the process (48) but the free energy of transport of hydrions
from the standard solution to any value of [H+J. See (49)

-AFi + AF2 = 2RT In [H+] (49)

Second, make [H+] small in relation to KI and K2. Then (45) is prac-
tically

-AF3 = 2FE0 + RT In KiK2 (50)

Subtract (47) from (50)

-AF3 + AF2 = RT In KiK2 (51)

tH+P [Red"]

[H2Red]
Hence

Equation (52) gives the free energy of the process

H2Red -» 2H+ + Red" - (53)

This is the free energy of ionization which, by the use of [H+] = 1 in
the derivation, is the energy which would have to be expended to accom-
plish ionization against a normal concentration of hydrions. Likewise the
free energy of the separate ionizations can be formulated.

398 THE DETERMINATION OF HYDROGEN IONS

When the hydrion concentration is lowered ionization takes place
spontaneously. This condition is met when the free energy of hydrion
transport, between IN and the normality permitting practically complete
ionization, compensates the energy which would have to be expended on
the system to cause ionization at 1 N H+.

In short, our equations contain implicitly the free energies of ioniza-
tion and what may be called rather inexactly the free energy of hydrion
dilution.

SOME REMARKS ON MECHANISM

It was stated early in this chapter that the use of the electron-transfer
concept was to be a formality and a convenience; and, although it may
have been stressed here and there in a manner which betrayed the author's
preference for the concept as a picture of actuality, it remains a formality.
The satisfaction of the resulting equations is no proof of the validity of
the postulate, for it was made clear that there are several other ways in
which the equations could be derived. Also the equations are of thermo-
dynamic origin, and,, although mechanistic ideas were introduced both
to clarify the subject, and to make general equations specific, the fulfill-
ment of a thermodynamic relation cannot per se throw any light on mech-
anism.

It has been repeatedly stated that the strength of thermodynamics is
its independence of mechanistic concept. This is because the energy
change, which a thermodynamic equation may formulate, is independent
of the path. The thermodynamic method per se has nothing to say about
conditions which might make the change take one path rather than another.
Yet in this chapter we have made rather free use of certain mechanistic
concepts. This is because we have to face the following situation. If free
energy change is to be formulated, all that thermodynamics offers is an
equation for a process. The methods of general chemistry must be used
to give some idea of specific components to be used in the practical solution;
otherwise the experimentalist is not equipped to handle the process. The
innumerable methods of formulating cell reactions thermodynamically
have been advanced after the cells have been devised.

In all cases some molecular theory is introduced. So it was that we
found ourselves specifying, for instance, that a reductant can take the
form H2Red, HRed" or Red" ~. Were the theory of electrolytic dissocia-
tion in disrepute this would be considered horribly mechanistic.

In general we find ourselves dealing with relations which take the form
of the thermodynamic equation but in which we have introduced molecular
theory. This introduction carries with it not only the truth of our molecu-
lar theory but its assumptions. When we put the true and the assumed
into the mathematical mill the mill grinds out in new and often startling
form only what is put in. Many of the consequences are very alluring and
it behooves us to be on guard.

XVIII MECHANISM 399

It has been shown above that whether we start with the orienting
reaction

Ox + 2e ^ Red- ~
or Ox + H2 ^ H2Red

we attain the same final working equation which in this case is:
Eh = E0 - H In !jg + g In [K,K2 + K, [Hi + pi*].]

Let us disregard implied electrode mechanism and consider this last equa-
tion as an empirical one which correctly formulates experimental facts.
We then still imply solution processes such as

i H+ + HRed-
and HRed- ;=±H+ + Red- -

In the preceding section it was shown that the equation involves the
free energies of ionization and of hydrion "dilution." It, therefore,
appears that a choice between the orienting reactions

Ox + 2€;=± Red~~
and Ox + 2e + 2H+ ^± H2Red

(the latter being formally equivalent to
Ox + H2 = H2Red

is somewhat like the choice permissible in measuring the height of a ladder.
We may measure from the bottom up or from the top down. We may
measure the total free energy change by counting in the free energy of
ionization from one direction or the other.7

But suppose there is under consideration an oxidation-reduction system
the reductant of which can take either the form HRed or Red". While we
may have properly formulated the free energy change for the formation of
one or the other or both, it might well be that the species Red" is effective
in the electrode phenomena and that the species HRed is not effective or
that HRed is effective and Red" not. Now let the dissociation constant,
Ka, of

[H+][Red-]
[H Red] Ka

7 Dixon (1927) chooses his position at the top of the ladder and leaves
the impression that this has something to do with the argument of Cohen,
Gibbs and Clark (1924), which, of course, it has not. See pages 402,
521 and Studies on oxidation-reduction, V. (Clark et al.).

400 THE DETERMINATION OF HYDROGEN IONS

have the value 10~13. The ratio — — — would be 1 at pH = 13 while at

[Hrveclj

pH = 0 the ratio would be 10~13. A thousandth normal solution would
contain the species Red" at only about 10"16 normality. If we choose to
say that this species is the exclusively active reductant we have to account
for physical effectiveness at 10~16 N. The discussion now joins with the
remarks on page 372 concerning the assumed functioning of the electrode
as a hydrogen electrode in a ferric-ferrous ion solution. We found there
but one of many instances of the physically absurd values encountered
when restricted points of view and restricted methods of expressing relations
are applied to electrode potential differences. One or two other instances
will be given.

Lehfeldt (1899) says of the so-called solution pressures postulated by
Nernst and briefly discussed in Chapter XII:

" we have Zinc 9.9 X 1018

Nickel 1.3 X 10°

Palladium 1.5 X 10~36

The first of them is startlingly large. The third is so small as to involve

the rejection of the entire molecular theory of fluids."

Lehfeldt then shows that, in order to permit at the electrode the pres-
sure indicated above for palladium, the solution would have to be so
dilute as to contain but one or two ions of palladium in a space the size of
the earth. No stable potential could be measured under such a circum-
stance. On the other hand Lehfeldt calculates that to produce the high
pressure indicated for zinc ''1.27 grams of the metal would have to pass
into the ionic form per square centimeter, which is obviously not the case."

Another aspect of the matter was emphasized in a lively discussion be-
tween Haber, Danneel, Bodlander and Abegg in Zeitscrift fur Elektro-
chemie, 1904. Haber points out that, if the well established relation
between a silver electrode and a solution containing silver ions be extra-
polated to include the conditions found in a silver cyanide solution, the
indicated concentration of the silver ion will be so low as to have no phys-
ical significance. Haber mentions the experiment oi Bodlander and Eber-
lein where the potential and the quantity of solution were such that there
was present at any moment less than one discrete silver ion. The greater
part of the discussion centred upon the resolution of the equilibrium
constant into a ratio of rates of reaction, and upon the conclusion that,
if the silver ion in the cyanide solution has a concentration of the order
of magnitude calculated, it must react with movements of a speed greater
than that of light or else that the known reactions of silver in silver cyanide
must take place directly from the position in the complex. Previous ioniza-
tion is then unnecessary. Were the latter assumption not true, how could
the stability of the electrode potential be supported?

A similar question was raised but not answered in a discussion between
Langmuir and Patten printed in Trans. Am. Electrochem. Soc. 29, (1916)

XVIII MECHANISM 401

pp. 293 and 296. It concerned the hydrogen electrode operating in a solu-
tion of hydrion concentration of 10~10 normal. Whatever the validity of
the conclusion that so and so much free energy-change is involved in the
transfer of hydrions from one normal to 10~l° normal, is such a low con-
centration physically effective?

These matters may be somewhat clarified if we return to a consideration
of the oxidation-reduction systems noted above.

Here are systems in the description of which there are included the
free energies of complex formations, i.e., the formation of the undissociated
acids or bases from their ionization products. By analogy, there should
be included in the description of the silver system the free energy of
formation of the silver cyanide complex. By the neglect of this aspect,
the chosen, orienting reaction

Ag+ + e ^ Ag

has been raised to an importance to which it is not entitled. It is because

of emphasis upon this orienting reaction that there has been created the

puzzle mentioned above.

But there still remains a real, mechanistic problem. The only answer

that appears plausible is, as mentioned above, that the silver cyanide

acts directly.

Thus Br0nsted (1926), in discussing a similar situation, remarks:
"Nernst's formula often leads to absurd ion concentrations — for instance

in the case of a copper electrode in a potassium cyanide solution — and it

seems unreasonable to assume

metal ;=± metal ion + electron

In such circumstances, and in general, the potential between electrode
and solution might be denned by means of more direct reactions. For the
copper-copper cyanide system we might have:

Cu + Cn~ ^ CuCn + «
or Cu + 2Cn~ ^± Cu(Cn)2 + 2e."

In the case of the oxidation-reduction systems which we have discussed
there are cases in which the reductant has high dissociation constants
and cases in which it has low dissociation constants. If, in either case,
the effectiveness of the reductant were dependent on but one form, rapidity
in the attainment of electrode potential would not be expected over the
entire range of the enormous variation in hydrion concentration used
experimentally. Thermodynamics has nothing to say on this matter of
rapid attainment of equilibrium. The fact is that no significant variation
from a nearly instantaneous adjustment is observed.

In these same cases, analysis suggests that two equivalents are con-
cerned in the oxidation-reduction process. So far as thermodynamics is
concerned it is ready to provide equations for the transfer of the equiva-

402 THE DETERMINATION OF HYDROGEN IONS

lents either together or separately and step-wise. Experiment (in the
cases under consideration) reveals no trace of step-wise reduction!

Not all oxidation-reduction processes are amenable to study by the
electrode method. So far as thermodynamics is concerned it is able to
provide a formulation of the free energy of reduction in terms of volt-
coulombs or of calories. It is incapable of predicting what systems are
and what systems are not amenable to study by the electrode method.
The fact that in the cases under consideration there can be generated
an electric current and that presumably electrons are sent into the measur-
ing system, must have a significance to mechanism. Cohen, Gibbs and
Clark8 (1924) argued from these non-thermodynamic aspects that the essen-
tial or determinative factor is the pairing of electrons in the molecule and
the impossibility of passing from reductant to oxidant without breaking
the original structure with the transfer of an electron pair (in the specific
cases they discuss).

In emphasizing this aspect they stated that the question of hydrogen-
ation was an incidental matter depending on the hydrion concentration of
the solution and the dissociation constant of the reductant. There might
have been an inference of a division in time between transfer of electrons
and transfer of protons. This and a misunderstanding of the nature of
the argument evidently threw Dixon (1927) completely off the theme and
led to his placing undue emphasis upon one special formulation the particu-
lar nature of which was pointed out in the previous edition of this book
and by Clark (1923). The inference of separate steps divided in time is
not essential to the conclusion which has to do with the determinative
as distinct from the incidental processes convenient to use in formulations.

It will readily be perceived that the non-thermodynamic dimensions of
molecular theory have been used in the argument on mechanism. loniza-
tion, pairing of equivalents, an electrical phenomenon, statistical num-
bers, etc., are the subjects discussed.

The resulting picture is laden with assumptions and some of these are
important to the main subject of this book.

The greater part of the troubles mentioned arise from trying to get
more out of the mathematical mill than we put into it. When we put into
the mill an assumed mechanistic relation (as we eventually must to bring
thermodynamics from its ethereal heights to deal with material problems)
we shall get out so much of the truth and so much of the limitations as are
inherent in the assumption. Since mechanistic concepts are based not
on rigid arguments but are attempts to harmonize a picture drawn with
imperfect knowledge, there should be on the one hand no hesitancy in
artistic efforts toward harmony, and, on the other hand no disposition to
impose the artistry where it serves no good purpose.

We suggest the direct action of undissociated molecules in phenomena
usually attributed to ions only. It should not be forgotten that this does
not place the two kinds of species on a parity. Thermodynamically they

8 Clark et al.

XVIII MECHANISM 403

differ by the energy of formation of the one from the others. There is no
inherent reason for undue emphasis upon the transcendent importance of
ions as participants in chemical reaction. There is every reason for
utilizing the distinction, noted above, in the free energy-changes.

From the foregoing discussions it should be evident that the designation
of a particular electrode-solution system depends so far as convenience is
concerned upon relations which we seek, it being more convenient in some
instances to formulate all data in terms of hydrogen electrode potentials
and in other instances in terms of reduction potentials. So far as the
actual physical maintenance of electrode conditions is concerned the
designation of an electrode as of one or the other type will certainly depend
upon a finite ratio of two products, one of which is the reduction product of
the other; but the discovery of what these species are is often a most diffi-
cult problem for the solution of which the electrode equations by them-
selves and thermodynamics by itself are not sufficient. Here the methods
of general chemistry must be employed. Here also are pitfalls. Never-
theless, in the end, the strength of the accumulating information will
doubtless be found to be not in the purely thermodynamic contributions
alone nor in the purely statistical contributions alone but in harmonious
union.

CHAPTER XIX

THE QUINHYDRONE AND SIMILAR HALF-CELLS

A half-cell which has won favor as a convenient device with
which to determine hydrion activity is the so-called quinhydrone
electrode. Its development has been due largely to the work of
Biilmann and his collaborators. See the re'sume' by Biilmann
(1927).

PH "
FIG. 78. RELATION OF ELECTRODE POTENTIAL, Eh, TO pH

QQ, Quino -quinhydrone electrode; Q, quinhydrone electrode; C, chlor-
anil electrode; HQ, hydro -quinhydrone electrode. Potential of saturated
KC1 calomel electrode shown by S.

Structurally the half -cell is very simple. An "unattackable"
metal, such as gold or platinum, serves as electrode proper. The
solution to be examined is saturated with quinhydrone. To
complete a cell, the quinhydrone half-cell may be put in liquid
junction with a calomel half-cell, with a standard hydrogen half-
cell, or with another quinhydrone half-cell in which the solution
is a standard buffer.

See page 259 and figure 78 for graphs showing the relation of
the potential to pH.

404

XIX

THEORY OF QUINHYDRONE ELECTRODE

405

THEORY

Quinhydrone is a peculiar complex formed of equimolecular
proportions of quinone and hydro quinone.1 The first is the
"oxidation product" of the second. We shall first regard the
quinhydrone as furnishing equimolecular concentrations of an
oxidant and reductant.

Whatever may be the actual mechanism by which the one is
transformed into the other, we may, for present purposes, assume
two, reversible, main steps, of which the second and not the first
is, in turn, stepwise.

O 0-

quinone + 2 electrons

anion of hydroquinone

anion of hydroquinone -f 2 H+ ^± hydroquinone
(stepwise)

The approximate equation for such a system was developed in
Chapter XVIII. Its development need not be repeated; but it
may be noted that in writing the sum of all forms of reductant
and oxidant we should include the dissolved, undissociated
quinhydrone, Q. Then the equation is:

1 Strictly speaking we should speak of benzoquinone and benzohydro-
quinone, since the terms "quinone" and "hydroquinone" have generic
as well as specific meanings.

406 THE DETERMINATION OF HYDROGEN IONS

Here Eh is the observed potential referred to the normal hydrogen
electrode, E0 is the characteristic constant of the system, [SR]
and [S0] are, respectively, the concentrations of total reductant
and total oxidant, [Q] is the concentration of dissolved, undis-
sociated quinhydrone and KI and K2 are the dissociation constants
of the reductant. The first dissociation constant of hydro-
quinone is of the order of 10~10 and the second is somewhat lower.
Consequently at pH 8 the compound is only about 1 per cent
dissociated, at pH 7 about 0.1 per cent dissociated and from then
on through the lower values of pH it can be considered for certain
purposes as completely in the undissociated form. By referring
directly to equation (1) we see that, when [H+] is large (over 10~8
for approximate limit) compared to KI and K2 the sum in the
last term reduces practically to the value of [H+]2. Hence, with
an approximation that the better approaches the truth the higher
the value of [H+], we may write the last term:

Assuming [SR] — [Q] = [S0] — [Q], we have

Eh = Eo + -^ In [H+] (2)

At 25°C., for instance, (2) would be:

Eh = Eo - 0.05912 pH (3)

The above was stated in terms of concentrations for the sake
of deriving the approximate equation and showing why alkaline
solutions should be avoided if (2) is to be applied. The ap-
proximation also serves another purpose. It indicates that
if we are content to operate in acid solutions we may simplify the
development of the more exact equation which is to be in terms
of activities.

For the reaction

Quinone + 2 H+ + 2 e^± Hydroquinone

(quinone) (H+)2 (e)2 _ R
(hydroquinone)

XIX QUINO- AND HYDROQUINHYDRONE ELECTRODE 407

Solve for (e) and introduce in equation 15 of Chapter XVIII.

Eh _ Eo _ ln (hydroquinone) fa

2F (qumone)

[Note: In this book activities are denoted by () while concentra-
tions are denoted by [].]
For the equilibrium in the reaction

quinone + hydroquinone ^± quinhydrone
we may write:

(qumone) (hydroquinone) ,r /rN

—f — . , , -- ^— — = Kq (5;

(quinhydrone)

But, since (quinhydrone) is a constant when the solid phase is
present,

(quinone) (hydroquinone) = Kqa (6)

Now consider the case when there is added to the quinhydrone
in solid phase either quinone or hydroquinone to keep the solu-
tion saturated with two of the three substances. Then, in addi-
tion to constancy in the activity of quinhydrone which establishes
(6), one of the variables in (6) is made constant and hence the
other must be.

We need not know the values of (quinone) or (hydroquinone)
to know that equation (4) will be reduced to :

Eh = EQq + In (H+) (7)

when quinone and quinhydrone are the solid phases. This then
is the equation for the system which Biilmann and Lund (1921)
call the quino-quinhydrone electrode.

Likewise when hydroquinone and quinhydrone are the solid
phases equation (4) reduces to:

Eh = Ehq + In (H+) (8)

This is the equation for the so-called hydro-quinhydrone electrode.
The values of Eqq and Ehq may be established independently

408 THE DETERMINATION OF HYDROGEN IONS

by a procedure similar to that noted in determining the charac-
teristic constant of the quinhydrone electrode.

It is to be particularly noted that the only variable remaining
at the right of equations (7) and (8) is (H+). Therefore, in the
sense that nothing that can effect the activities of the quinone,
hydroquinone or quinhydrone will affect the potential, these
electrodes are said to be " without salt effect." There will be less
chance of misunderstanding if we say that, if these electrodes
and the hydrogen electrode at constant pressure respond only to
changes of (H+) their potentials should run parallel. Within the
limits of experimental error it seems to have been demonstrated
that they do.

When quinhydrone is the only component of the solid phase
the situation is not so easily simplified. We cannot assume
equality of the activities : (hydroquinone) and (quinone) ; but we
may assume equality of the concentrations [S0] and [Sr], the total
oxidant and the total reductant in solution. But, in acid solution,

1 (hydroquinone)
[SJ - [Q] = [hydroquinone] = — —

and

[SJ - [Q] = [quiBone]

where [Q] is the concentration of quinhydrone and 7,. and j0 are

the activity coefficients of the hydroquinone and quinone, re-

spectively.

Using the above relations and

[8J = [S0]
we reach:

(hydroquinone) _ 7,
(quinone) y0

Consequently equation (4) becomes:

iCH+J (9)

Zb 70 *

This equation for the true quinhydrone electrode now contains
the activity coefficients of the hydroquinone and quinone and,

XIX

SALT-EFFECT; QUINHYDRONE ELECTRODE

409

since the ratio does not remain the same while the constitution
of the solution is changed, the electrode exhibits what is called
a "salt-effect," which is a special "salt-effect."

S0rensen, S0rensen and Linderstr0m-Lang (1921) confirmed
equation (9) by determining yT and y0 through solubility measure-
ments with hydroquinone and quinone. They also traced the
details contributing to the conclusions of equations (7) and (8).

Equation (9) in its numerical form for 18°C. may be recast
to the form:

0.05773

0.5 log -
To

(10)

Linderstr0m-Lang replaces —0.5 log — nby Q, the magnitude of

TABLE 54

"Salt correction," Qg, for quinhydrone electrode at 18°

Add value to q to obtain corrected value of pH.

0.0577o

SOLUTION

0 01 N HC1

-0 001

0.5 M (NH4)2SO4

+0 019

0 02 N HC1

-0 002

1 0 M (NH4)2SO4

0 038

0 05 N HC1

-0.003

1.5M (NH4)2SO4

0.057

0 10 N HC1 . . .

-0 005

2 0 M (NH4)2SO4

0 078

0 01 N HC1 + 0 09 N KC1

-0 009

2.5M (NH4)oSO4

0 097

0 04MNaCl

-0.005

3.0M (NH4)2S04

0.116

0 09 M NaCl

-0.008

3.5M (NH4)2S04

0.135

0 49 M NaCl

-0 021

4 0 M (NH4)2SO4 . .

0 156

0 99 M NaCl

-0.045

4 5 M (NH4)2SO4

0.175

1 99 M NaCl

-0 094

5 0 M (NH4)2SO4

0 194

2 99 M NaCl

-0.145

3 99 M NaCl .

-0 200

which must be added to the observed value of

Eq - Eh

to obtain

0.05773

the true value of pH. Since this correction term, Q, will vary
it is feasible to list only a few cases. Linderstr0m-Lang (1924)
gives the values shown in tables 54 and 55. His estimates of
the corrections applicable to milk and blood serum are not in
very good agreement with those of Lester (1924) on the one hand

410

THE DETERMINATION OF HYDROGEN IONS

or of Kolthoff (1925) on the other hand; but his data are the
more carefully rationalized. They may serve to indicate the
order of magnitude of the corrections to be expected and for
approximate purposes may be considered additive for limited
ranges of concentrations. For rough work the salt effect may be
ignored as negligible compared with errors of technique.

PREPARATION OF QUINHYDRONE

Biilmann (1927) after some years experience recommends the
following method of preparing quinhydrone, the method used by
Biilmann and Lund (1921).

TABLE 55

Protein correction Qp for quinhydrone electrode at 18° at indicated pH value

of solution

EGG ALBUMIN

SEBUM
ALBUMIN

0.3Cn*

4.0

+0.003

0.3 Cn*

4.0

+0.048

O.SCn

4.5

-0.017

0.3Cn

4.5

+0.033

0.3Cn

5.0

-0.028

0.3Cn

5.0

+0.028

0.3 Cn

5.5

-0.031

0.3 Cn

5.5

+0.029

8EBDM
ALBUMIN

SERUM
ALBUMIN

0.1 Cn*

4.7

+0.009

0.6Cn*

4.7

0.045

0.2 Cn

4.7

+0.017

0.8 Cn

4.7

0.055

0.4Cn

4.7

0.033

1.0 Cn

4.7

0.064

* Cn = gram equivalents of protein nitrogen.

A solution of one hundred grams of iron alum in 300 cc. of
water at 65°C. is poured into 100 cc. of a warm solution contain-
ing 25 grams commercial hydroquinone. The mixture is cooled,
the quinhydrone is filtered with suction and washed three or four
times with cold water. Dry between filter paper at room tem-
perature and store in dark bottles. Yield: 15 to 16 grams.

This preparation may contain traces of iron which Biilmann
believes to have no appreciable effect on the potential. High
temperature drying should be avoided since quinone may vol-
atilize sufficiently to alter the desired ratio of reductant to oxidant.

XIX QUINHYDRONE ELECTRODES 411

Schreiner (1925) prefers a purer product. He crystallizes
hydroquinone from 50 per cent aqueous acetic acid and quinone
from water acidified with acetic acid. For the preparation of
quinhy drone from these pure products an acetic acid solution of
the hydroquinone is added in excess to an acetic acid solution of
the quinone.

Arnd and Siemers (1926) find that occluded acidic impurities
may appreciably affect the potential in poorly buffered solutions
and therefore they recrystallize the quinhydrone from water at
70°C. Kolthoff (1927) thinks crystallization from water has an
unfavorable effect. He extracts the preparation with water
before use.

It is not improbable that attempts to prepare quinhydrone of
high purity by repeated crystallization have sometimes failed
to yield a reliable product because no attention was given to the
tendency of the product to oxidize, or otherwise change, in neutral
as well as in alkaline solution. While I have had little experience,
I would suggest that recrystallization be done in acid solution.
As the preparation becomes purer the amount of acid necessary
becomes small. Recrystallization in acid solution followed by
washing in the absence of air would seem a priori to be the better
procedure.

ELECTRODES AND ELECTRODE VESSELS

Since the possible effects of atmospheric oxygen in changing the
ratio of oxidant to reductant are usually neglected, the common
forms of electrode vessel make no allowance for the management
of a gas phase as does any well designed vessel for the hydrogen
electrode. This simplifies the design. Indeed there is not very
much to say about the vessel, unless one describes all the unim-
portant details which have been made the occasion for papers
on the subject.2

Biilmann and Lund's vessels are shown by 1 and 2 of figure 79.
Biilmann recommends that at least two electrodes be used.
Among several vessels designed to handle small quantities of solu-
tion may be mentioned that of Cullen and Biilmann (1925),
No. 3. The gold plated wire is moistened and dipped into crystals

2 Apparently we have here a case where multiplicity of design is in
direct proportion to the simplicity permissible.

412 THE DETERMINATION OF HYDROGEN IONS

-Q
-Au

FIG. 79. VESSELS FOR QUINHYDRONE HALF-CELLS

XIX ERRORS WITH QUINHYDRONE ELECTRODE 413

of quinhy drone. These adhere. The electrode is then placed in
the capillary and solution is drawn in. The tip of the vessel is
then placed in the KC1 bridge.

No. 4 is a simple quinhy drone cell, one half -cell of which
contains a standard buffer solution, e.g., "standard acetate."
The junction is made with a bridge of KCl-agar. This was used
by Viebel.

No. 5 represents the vessel of Mozolowski and iParnas (1926).
A small platinum wire is fused to a copper lead. The platinum
wire runs through the bottom of the vessel and makes contact
with a gold film. No. 6 represents one of the vessels of Mis-
lowitzer (1925). One of the compartments carries a reference
solution the other the tested solution. Junction is made with
KC1 solution in the joint. Smolik (1926) uses a similar device.

No. 7 is a micro-electrode vessel designed by Ettisch (1925).

Regarding the electrode itself it may be said that there apply
the precautions discussed in Chapter XIV during the description
of the preparation of the base of the hydrogen electrode. No
"black" is to be deposited but Biilmann emphasizes the necessity
for a good and clean surface. There are those who prefer plati-
num and those who prefer gold surfaces. Biilmann is a bit in-
definite regarding his preference; but Corran and Lewis (1924)
prefer gold while Mislowitzer (1926) and Grossmann (1927) prefer
platinum.

SOURCES OF ERROR

In alkaline solutions two effects must be taken into account.
In the first place the ionization of hydroquinone becomes appreci-
able above about pH 8.5 and renders inapplicable the simplified
equation. If the dissociation constants of hydroquinone were
accurately known this could be corrected for; but it would not
obviate a serious difficulty, — the decomposition and oxidation
which takes place readily in the system when subjected to alkaline
solutions. See, for example, LaMer and Parsons (1923), LaMer
and Rideal (1924), and Conant, Kahn, Fieser and Kurtz (1922).
In a more or less arbitrary way Biilmann (1927) sets pH 8.5 as
the limit of measurements of the accuracy of 0.01 unit pH but it
must be noted that his basis is the effect of dissociation.

A second fundamental consideration is the avoidance of oxidiz-

414 THE DETERMINATION OF HYDROGEN IONS

ing or reducing solutions which can change the ratio of oxidant
to reductant the mainteinance of which is essential. It is by no
means a simple matter to treat this aspect with complete assur-
ance. As indicated on page 371 the complete avoidance of solu-
tions which are potentially capable of exercising a reducing or
oxidizing action would seriously limit the application of any
device for the determination of pH by electrode methods. It
would eliminate the quinhydrone electrode from one of its spheres
of greatest value. For it was shown by Biilmann (1921) in one
of his first papers on the subject that the quinhydrone electrode
may be used to determie the pH values of dilute nitric acid solu-
tions and of solutions of unsaturated organic acids which cannot
be well handled with the aid of the hydrogen electrode. The more
obvious explanation of this success is that the oxidizing or the
reducing agent acts so slowly that the ratio of quinone to hydro-
quinone is not appreciably changed within the time required for
the attainment of the equilibrium in the system quinhydrone-
quinone-hydroquinone-electrode. And here it may be remarked
that the absence of a gas phase, the absence of a complicated
solid phase (platinum black) and the absence of the catalytic
effect of the platinum black probably contribute to the rapidity
of the attainment of equilibrium. Indeed those who are accus-
tomed to the hydrogen electrode and to the necessity of establish-
ing by long waits the fair permanence of potential and the ab-
sence of significant drift of potential will be inclined to use poor
judgment in the application of the quinhydrone electrode. Of
course some time must be allowed for the attainment of equi-
librium. We may reasonably assume that the equilibrum poten-
tial is approached asymptotically; but if we do not seek the utmost
refinement we may rely on the experience (with stable buffer
solutions) that the equilibrium potential is very closely ap-
proached within a very few minutes.3 Subsequent drifts of
potential in complicated and unstable solutions may then be due
to secondary reactions causing a fundamentally true error in the
measurement. A clear separation of the two effects, asymptotic

8 The photographic record of potential change made by Buytendijk
and Brinkman (1926) indicates that, in the absence of carbonate, the
equilibrium potential is reached, or closely approached within a few seconds
after a change is made in a previously equilibrated system.

XIX ERRORS OF QUINHYDRONE ELECTRODE 415

approach to equilibrium potential on the one hand and reaction
of the oxidation-reduction system internally or with constituents
of the solution on the other hand, is probably the greatest puzzle
in the practical application of the quinhydrone electrode or of
any similar system.

Among the problems which have not yet been adequately
solved is that of the conduct of the quinhydrone system in protein
solutions. In the first place there occur in the literature scattered
references to the combination of quinone with protein. See for
example Cooper and Nicholas (1927) and the subject of quinone
tanning dealt with in treatises on tanning. Yet the application
of the system to the study of milk, beer, blood serum etc. has
been fairly successful. A summary with references pertaining to
these applications is given in Biilmann's review, (Biilmann, 1927).

True errors caused by reaction of the system with the con-
stituents of the solution must be carefully distinguished from
apparent error resulting from the attempt to apply to all sorts of
solution the simple equation cast in terms of concentrations or the
data standardized with the aid of simplifying assumptions.

There remain a number of sources of error due to faulty tech-
nique. Quinhydrone is not always easy to wet. Compare Cor-
ran and Lewis (1924). Loss of quinone by drying quinhydrone
at too high temperature, the occlusion of oxidation products etc.,
alter the ratio of oxidant to reductant. In buffer-poor solutions
the occlusion of acid or of impurities having a direct effect on the
acid-base equilibrium of the solution with which the quinhydrone
is mixed have been detected as sources of error. Biilmann (1927)
presents an elaborate discussion of the errors of temperature
fluctuation. Biilmann cautions against the use of electrodes
which have developed minute cracks in the glass seal. It would
seem from his discussion that a good part of the false potentials
thereby attained is due to the mercury. Let it be noted however
that mercury electrodes have been used successfully in similar
cases. In the cases cited by Clark and Cohen (1923) the mercury
was of very high purity. Compare also Butler, Hugh and Hey
(1926).

APPLICATIONS

The quinhydrone and similar self-cells have found many ap-
plications. In some instances they have been applied simply as

416 THE DETERMINATION OF HYDROGEN IONS

substitutes for the hydrogen half -cell. However, they have
unique uses. The absence of a catalytically active metal and of
an intense reducing system has permitted the quinhydrone elec-
trode to be applied to solutions of dilute nitric acid, unsaturated
organic acids and a variety of oxidizing systems which either are
too slow in their action to appreciably disturb the equilibrium of
the electrode or are oxidants of low oxidizing intensity. (See
page 391.) Furthermore there is no gas phase and consequently
no complexity such as is encountered when the hydrogen half-
cell is used with carbonate solutions. This is of particular im-
portance to the study of biological systems.

Because the quinhydrone electrode is much more simple to
operate than the hydrogen electrode and yet can be used with
the potentiometer system and other equipment provided for the
hydrogen electrode, it has been put into practice by very many
of those who are already equipped for hydrogen electrode measure-
ments and by those entering the general field for the first time.
Because of this it is practically impossible without diligent and
detailed examination of the world's literature to assemble a com-
plete list of applications. And yet it is in special applications
that there have appeared special sources of error, better knowledge
of limitations and the occasions for special technique. These
minutiae cannot be covered adequately in a general text. Hence
there are assembled below an incomplete list of references to
applications by subject, — a list which it is hoped will be of use to
those who are in search of the records of applicability in their
several specialties.

Alkaloids, medicinals, etc.: Baggesgaard-Rasmussen and Shou
(1925), Brunius and Karsmark (1927), Wagener and McGill
(1925); Aluminum solutions: Felling (1925); Blood, plasma,
serum, etc.: Corran and Lewis (1924), Cullen and Biilmann
(1925), Cullen and Earle (1928), Grossman (1927), Runge and
Schmidt (1926), Liu (1927), Meeker and Oser (1926), Mis-
lowitzer (1925, 1926), Schaefer (1926), Schaefer and Schmidt
(1925), Vellinger and Roche (1925); Copper solutions: O'Sullivan
(1925); Dairy products: Lester (1924), Knudsen (1925), Linder-
str0m-Lang and Kodama (1925), Watson (1927) ; Feces: Robinson
(1925); Gastric juice: Schaefer and Schmidt (1925), Va"na (1926);
Nickel solutions: Parker and Greer (1926); Plant-juices: Dom-

XIX CHLORANIL ELECTRODE 417

ontvich (1925); Protein solutions: Freundlich and Neukircher
(1926), Linderstr0m-Lang and Kodama (1925); Soils: Arnd and
Siemers (1926), Baver (1926), Biilmann (1924), Biilmann and Tov-
borg-Jensen (1927), Brioux and Pien (1925), Hissink and van
der Spek (1926), Itano, Arakawa and Hosoda (1926-1927), Kappen
and Beling (1925), Olsen and Linderstr0m-Lang (1927), Schmidt
(1925), Snyder (1927); Sugar solutions; Balch (1925), Biilmann
and Katagiri (1927), Paine and Balch (1927); Tanning: Hugonin
(1925) ; Water (natural) : Parker and Baylis (1926) ; Wine: Dietzel
and Rosenbaum (1927); Titrations, measurements of dissociation
constants, theoretical work, non-aqueous solutions, etc.: Auerbach and
Smolczyk (1924), Bodforss (1922), Biilmann and Henriques (1924),
Buytendijk, Brinkman and Mook (1927), Conant et al. (1922-
1927), Cray and Westrip (1925), Daniel (1927), Darmois (1924),
Darmois and Honnelaitre (1924), Ebert (1925), Harris (1923) ,Itano
and Hosoda (1926), Klit (1927), Kolthoff (1923, 1927), KolthofT
and Bosch (1927), LaMer and Baker (1922), LaMer and Parsons
(1923), LaMer and Rideal (1924), Larsson (1922), Pring (1923,
1924), Rabinowitsch and Kargin (1927), Schreiner (1922, 1925),
S0rensen and Linderstr0m-Lang (1924), Wagener and McGill
(1925).

THE CHLORANIL ELECTRODE

Among the several quinone-hydroquinone systems studied by
Conant and Fieser (1923) and by others, that of tetrachloroquinone
and its hydroquinone promises to rival the benzoquinone-benzo-
hydroquinone system in usefulness. With tetrachloroquinone
(Chloranil) and the corresponding hydroquinone

Chloranil Hydroquinone of chloranil

418 THE DETERMINATION OF HYDROGEN IONS

it is possible to saturate solutions simultaneously with both
oxidant and reductant as is not the case with hydroquinone and
quinone.

If then a cell be formed as follows

C6C14O2 (sat.)

Solution A

Bridge

(sat.)

Solution B

C6C14O2H2 (sat.)

and if the bridge can be assumed to eliminate junction potential
the electrode process is

C6C1402 (solid) + 2H+ + 2e ^± C6C1402H2 (solid)

Here the end products are solid phases which at a given tempera-
ture and crystal form may be regarded as having fixed activities.
The free energy change attending the passage of one mole of
hydrion from one solution to the other is given at once by FE
and E is the electromotive force of the cell. Obviously the solu-
tion must be acid enough to permit the retention of the solid phase
of the reductant. The cell potential is then a measure of the
relative activities of the hydrion in the two solutions

RT (H+)A

Accordingly Conant, Small and Taylor (1925), Hall and Conant
(1927) and Conant and Hall (1927) find the chloranil electrode
eminently suited to the comparison of solutions with different
solvents. See Chapter XXIX.

One difficulty arises in the very small solubility of chloranil
and its reductant. Because of this the solution rates become im-
portant to the approach of an equilibrium potential. Hall and
Conant determine by preliminary measurements how much of
each substance is necessary to give a quick crystallization when
heated to 50° and cooled to the working temperature.

SUMMARY OF EQUATIONS

Quinhydrone electrode

•prp

Eh = Eq + — - In (H+) + (a correction term specific for each solution)
F

For values of the correction term see pages 409-410. Omitting

XIX

EQUATIONS, QUINHYDRONE CELL

419

consideration of the correction term we have the numerical
form at 25°C.

Eh = Eq - 0.05912 pH

For the numerical factor at various temperatures see Appendix.
For the cell

- Pt, H2 (1 atmos.) | HC1 (0.1N), quinhydrone | Pt + I

at 18°C. Biilmann and Jensen (1926) obtain 0.70439 d= 0.00004
volt. Since the difference of potential between the hydrogen
and quinhydrone electrodes should be the same at all values of
pH in the acid region under ideal conditions, we may regard
+0.7044 to be the value of Eq at 18°C. Biilmann and Krarup
(1924) obtained the following expression for the temperature
coefficient of cell (I)

Eht = 0.7175 - 0.00074 t

To conform to Biilman and Jensen's value at 18° we shall use
Eht = 0.7177 - 0.00074 t

Accordingly there can be found the values of Eq given in table 56.

Veibel (1923) recommended the quinhydrone half-cell as one
which, if prepared from day to day with a standard solution
could serve in the standardization of hydrogen- or calomel half-
cells.

When, however, the quinhydrone half-cell is put in junction
with saturated KC1 solution, as it is in standardizing the saturated
calomel half-cell, there is introduced an uncertain liquid junction
potential. It then becomes a matter of considerable importance
to distinguish the manner in which the two type cells below are
to be handled.

HgCl, KC1 (sat.)

HC1 (0.1N)

quinhydrone

Phosphate buffer

quinhydrone

III

In cell II the liquid junction potential is doubtless much larger
than in cell III.

420

THE DETERMINATION OF HYDROGEN IONS

The practice is either to neglect the change or to estimate it by
the Bjerrum extrapolation. Partly because of diversity in this
practice, and partly because of the discrepancies in primary
experimental data involving no calculations, we have been unable
reconcile various estimates of numbers used in the practical appli-
cation of the quinhy drone electrode.

Most of the data assembled by Biilmann (1927) proceed from
standardizations with 0.01N HC1 + 0.09N KC1 but with 2.029
as the assumed pH value.

We shall make the following tentative estimates.

Assume 1.078 for the pH number of 0.1N HC1 and calculate
therefrom the'hydrogen potentials at various temperatures. See
table A page 672. From these estimates compile with the aid of
table A the numbers found in table 56 below.

TABLE 56

Tentative values for cells containing the quinhydrone half-cells

Cell A

Half-Cell B

CeU C Hg

CellD

Ft, H2(l atmos.)

KC1

(sat.)

HgCl, KC1 (0.1N)

(H+) = 1
quinhydrone

HC1 (0.1)

quinhydrone

KC1 (sat.)

[HC1 (0.1N)
quinhydrone

HgCl, KC1 (sat.)

HC1 (0.1N)
quinhydrone

CELL OE HALF-CELL

•c.

volts

volts (approx.)

0.7044

0.6423

0.3043

0.391

0.7029

0.6404

0.3025

0.390

0.6992

0.6356

0.2980

0.3898

0.6955

0.6308

0.2937

0.389

0.6918

0.6261

0.2896

0.388

0.6896

0.6232

0.2871

0.387

0.6881

,0.6213

0.2855

0.387

XIX

EQUATIONS

421

See pages 259 and 404 for the position of the line of the quin-
hydrone electrode on the E:pH diagram.

Quino-quinhydrone electrode

or at 25'

For the cell

- Pt, H2(l atmos,)

Eh = Eqq - 0.05912 pH

quinone (s)

HC1 (0.1N)

quinhydrone (s)

Biilman and Lund (1921) found at 18° 0.7564. Schreiner'
(1925) data give

Eh = 0.7759 - 0.000842 t
for the range 5° to 18°. We then have

EQQ

Eqq

°c.

•c.

0.7716

0.7664

0.7674

0.7548

0.7632

0.7505

0.7590

Conant and Fieser (1923) find 0.7488 at 25° and 0.7699 at Oc
Hydro-quinhy drone electrode
Eh = Ehq + — In (H+)

or at 25°

Eh = Ehq - 0.05912 pH.

For the cell

- Pt, H2(l atmos.;

HC1 (0.1N)

quinhydrone (s)
hydroquinone (s)

422

THE DETERMINATION OF HYDROGEN IONS

Biilmann and Lund (1921) found at 18° 0.6177. Schreiner (1925)
finds a temperature coefficient of —0.000651 volt per degree
between 12° and 22° and -0.000641 volt per degree between 22°
and 32°. Hence we have:

_Ehq

Ehq

•c.

°C7.

0.6294

0.6164

0.6242

0.6132

0.6197

0.6100

0.6177

Conant and Fieser (1923) find 0.6126 at 25° and 0.6272 at 0°.

Chloranil electrode
Eh = Ee + ^ In (H+)

Conant and Fieser (1923) found that when chloranil and hydro-
chloranil are present in the solid phase Ec = 0.664 at 25° C. and
0.683 at 0°C.

Note that this not the potential of a homogeneous system
(solution) at 50 per cent reduction.

SUMMARY
See Appendix, table A for a table of standardized values.

CHAPTER XX

METAL OXIDE ELECTRODES; THE GLASS ELECTRODE; THE
OXYGEN ELECTRODE

METAL OXIDE ELECTRODES

Equations

The reversible exchange of electrons between a metal and its
ions may be regarded as an oxidation-reduction process. For the
system :

Mn+ + ne ^± M,

we may write the electrode potential equation (1) directly from
equation (15) of Chapter XVIII (page 377).

Were the metal-metal ion system the only one present, the
saturation of the solution with respect to the metal should be
accomplished by the presence of a mass of the metal in a solid
phase other than that of the electrode itself. E should then be
determinable by an unattackable electrode. Of course this is
quite impracticable because M, specified formally as a com-
ponent of the solution, has an activity (M) of such an insig-
nificant magnitude that the slightest disturbance of the electrode
itself, by the presence of the slightest trace of another oxidation-
reduction system, would vitiate the measurement. Consequently
in the study of the metal-metal ion system the electrode itself is
made of the metal in question in order that this metal may
dominate the situation in the immediate interface between elec-
trode and solution.

We develop this point of view in order that we may avoid the
confusion arising from the consideration of the electrode as highly
specialized. We shall regard it as fundamentally an oxidation-
reduction electrode the potential of which may be determined by
the system Mn+:M or by the system Ma+:Mb+.

423

424 THE DETERMINATION OF HYDROGEN IONS

In the first case we assume the activity of the metal in solution
to be constant and equation (1) reduces to

E = Eo + = In (M»+) (2)

nJb

Now suppose the alkalinity of the solution is sufficient to form
the metal hydroxide. For the reaction

M*+ + n OH- ^± M OHn
write the equilibrium equation

(M»+) (OH-)*
(MOHn)

Let the activity of the metal hydroxide in solution be constant
by reason of the presence of the solid phase. Then

(Mn+) (OH-)n = KB (3)

Hence by (2) and (3)

B-Ei+5£zn(H+) (5)

If, in place of the hydroxide, there is present the oxide it is
necessary for purposes of formal treatment to assume that the
oxide will attain equilibrium with its hydrate d product namely
the hydroxide in question, and that this in turn will attain con-
stancy of activity in the solution by reason of the presence of the
solid phase. Hence equation (5) should still hold, if the condi-
tions are met.

The above theoretical discussion assumed but one oxide. In
the presence of two oxides there could be only a pseudo-equilib-
rium; but that the main result should not be affected were there
two oxides in the presence of the metal, is revealed by the follow-
ing. Consider a metal in two states of oxidation, Ma+ and Mb+.

Ma+ + ne ^ Mb+

XX THEORY OF OXIDE ELECTRODES 425

By equation (15) page 377

Using the two solubility products

(Mb+) = Kb (H+)b

(Ma+) = Ka (H+>
we have

RT (H+)» ,

E° + lH

But b — a = n. Hence:

T?T

E = E; + ^-MH+) (8)

Equation (8) is equation (5) again. The reason the same equa-
tion is reached may be put in general terms as follows. In addi-
tion to those energy changes associated with electron exchange
and which are not directly associated with the hydrogen ions or
hydroxyl ions, there are involved the energies of ionization of the
metal hydroxides and the energy of hydrion dilution. We have
assumed that one determinant of the ionization is fixed by the
constant activity of the hydroxide or hydroxides. There remains
the effect of varying hydroxyl or hydrion concentration. This
effect takes the form, in the energy equation, of the free energy of
dilution of the hydrions, or hydroxyl ions, according to the choice
in formulation. Separating from the free energy cnange the po-
tential, or intensity factor, we have a relation parallel to the
case of the hydrogen electrode. Compare equation (5) or (8)
with equation (38) page 390.

The situation would be very different were the hydroxide, or
one of two or more hydroxides which might be involved in a
pseudo-equilibrium to not saturate the solution. Any one of such
instances would then become a very special case and no common
equation would be applicable.

There will be detected in this development several aspects,
expressed or implied, which impose difficult experimental restric-

426 THE DETERMINATION OF HYDROGEN IONS

tions. In addition to the difficulty of attaining complete equilib-
rium with materials so susceptible to acquiring different forms
(see for example Maddison, 1926) or degrees of dispersion as are
the metal hydroxides and oxides, there is implied the difficulty
of controlling the activity of any one form by control of the con-
stitution of the solution. Furthermore it would appear that the
water activity must be involved for the ionic product entered the
equation in step (4)~(5). This is probably of secondary con-
sequence in most instances.

With the exception of one or two of the simpler cases which
have been worked upon, for example the mercury-mercury oxide
system, little of a systematic nature has been done to illuminate
those "oxide electrodes."

THE MERCURY-MERCURIC OXIDE ELECTRODE

Br0nsted (1909) finds that the cell

- Pt, H2 1 KOH, HgO | Hg +

gives the same electromotive force when the concentration of
KOH is changed. There are small differences due to the chang-
ing activity of the water. On the assumption of complete disso-
ciation of KOH these findings satisfy equation (5) and the tacit
implication spoken of above.

A few references. Br0nsted (1909), Donnan and Allmand
(1911), Fried (1926), Kolthoff (1916), Lamb and Larson (1920),
Chow (1920), Knobel (1923), Fricke and Rohmann (1924), Aten
and Van Dalfsen (1926).

THE "ANTIMONY ELECTRODE"

Uhl and Kestranek (1923) used the combination antimony-
antimony oxide with promising results. Although they believed
that ordinary commercial antimony contains enough oxide to
fulfill the requirements, Kolthoff and Hartong (1925) recommend
the addition of the oxide. This they prepare by treating antimony
with nitric acid, evaporating to dryness and igniting.

In studying the potentials of their electrodes in buffer solutions
of known pH-values Kolthoff and Hartong did not obtain the
coefficient 0.057 demanded by equation (5) and the temperature

XX ANTIMONY ELECTRODE 427

of operation. They found it to be about 0.0485 between pH 1
and pH 5 and approximately 0.0536 above pH 9. Between 5 and
9 their results were erratic.

Buytendijk and Woerdeman (1927) have used this electrode in
micro form.

Vies and Vies and Vellinger (1927) in a study of the antimony
electrode find that the empirical equation

pH == 0.0175 E + a

holds at 24° over a considerable range of pH. In this equation a
is a constant which must be determined for each particular
electrode by measurements with buffer solutions. E is ex-
pressed in millivolts. Consequently if E is expressed in volts
we have

E = 0.05714 pH - 0.05714 a

At 24° the coefficient should be 0.05892.

Dr. Fenwick1 kindly permits me to quote as follows from the
manuscript of a paper entitled The antimony-antimony trioxide
electrode and its use as a measure of acidity by E. J. Roberts and F.
Fenwick. ". . . The potential of the antimony-antimony
trioxide electrode attains its maximum accuracy only provided
that the presence of any unstable solid phase in the system,
notably orthorhombic antimony trioxide, is carefully avoided,
dissolved oxygen is eliminated from the solution, and the equi-
librium is approached from the alkaline side. Under these condi-
tions the potential of the electrode is a linear function of the
logarithm of the activity of hydrogen ion, with the theoretical
slope, from pH 1 to 10." Their paper when published should
be consulted as the best treatment available. See also Schuhmann
(1924).

THE MANGANESE DIOXIDE ELECTRODE

Gesell and Hertzman (1926) prepare the manganese dioxide
electrode as follows. A platinum wire about 0.5 mm. diameter
is sealed into the end of a glass tube leaving a 1 mm. length pro-
truding. This is rounded with a fine stone "to avoid point
effects," plated with platinum black, and fired in an alcohol

1 Personal communication from Dr. Fenwick.

428 THE DETERMINATION OF HYDKOGEN IONS

flame. It is then coated during 1.5 minutes by connecting it to
the positive lead of a 6 volt battery while it is immersed in a
solution of manganese sulfate ("0.4 N")> acidified with sulfuric
acid. The negative electrode was placed 2 cm. from the positive
and 650 ohms were placed in the external circuit. According to
these authors the above procedure accomplished a compromise
between the production of an electrode which adjusts rapidly but
which has a coating too thin and too easily dissolved and an elec-
trode which is substantial but sluggish.

That the potential tends to be a linear function of the pH- value
of the solution is roughly confirmed; but Gesell, for instance,
found with different solutions at pH 7.4 that the potential might
vary as much as 0.22 volts corresponding to 3 units pH by the
formula deduced above and to 2.3 units pH by GeselFs formula.

Gesell's interest in the manganese dioxide electrode is chiefly as
a convenient means of following changes for instance in the
circulating blood or in the expired air.

Parker (1927) has used the manganese dioxide electrode in
control of industrial processes.

References. Tower (1895), Smith (1896), Roaf (1914), Gesell
and Hertzman (1926), Gesell andMcGinty (1926), Parker (1927).

OTHER OXIDE ELECTRODES

Several other oxide electrodes including those with Pb02,
Ag203, and T1203 were studied by Tower (1895) and occasionally
one has been subjected to further study. See for example Kolt-
hoff (1921) and especially Fried (1926). Baylis (1923) found,
empirically, promising results with the tungsten filament of an
electric light bulb. While the response to pH-changes might be
ascribed to a tungsten oxide electrode the relation of pH to poten-
tial does not follow that formulated above. Parker and Baylis
(1926) made some further studies of its empirical use.

THE OXYGEN ELECTRODE

Theoretically an unattackable electrode under a definite partial
pressure of oxygen should give a potential which is a linear func-
tion of the pH value of the solution. See equation 22 page 381.

XX OXYGEN AND GLASS ELECTRODES 429

Practically the calculated potential (see figure 77, page 387) is
not attained with platinum, gold and other "unattackable"
metals, nor is the linear relation always found. Empirically this
electrode has been put to use occasionally.

See: Arthur and Keeler (1922), Furman (1922-1923), Goard and
Rideal (1924), Malaprade (1926), Montillon and Cassel (1924),
Naray-Syabo (1927), Popoff and McHenry (1925), Smith and Giesy
(1923), Tilley and Ralston (1923), Van der Meulen and Wilcoxon
(1923).

Numerous combinations of electrode metals differing in po-
larization ability have been put to use in end-point titration. See
references in Kolthoff and Furman Potentiometric Titrations (1926).

THE
Imagine a cell of the following type.

Potentials at A and A' balance one another. Assume that
potentials at B and B' balance one another. Instead of an
ordinary, liquid junction at C imagine some material which permits
the passage of a particular kind of ion between solutions 1 and 2.
If this ion, i, were alone able to pass, it would tend to go from the
solution in which its chemical potential were the higher to the
solution in which its chemical potential were the lower and would
carry nF per mole. At potentiometric balance the potential of
the cell would be

"-¥"8;

Suppose solutions 1 and 2 were solutions of silver nitrate with
silver ion activities (Ag+)i and (Ag+)2, and suppose the partition
at C were metallic silver. Instead of formulating the equation
by means of single electrode potentials, we may consider the
metallic silver partition to be one permeable only to silver ions.
Then by equation (10) we have

430 THE DETERMINATION OF HYDROGEN IONS

Now Haber and Klemenziewicz (1909) found that, with such an
arrangement as that stated by schema I, the electromotive force
of the cell conformed to the equation

when a very thin partition of glass was placed at C.

They regarded the glass as a phase containing water and
hydrions and hydroxyl ions at constant concentration. If water
penetrates and not the other electrolytes of solution 1 and 2,
equation (12) should apply. Michaelis2 pointed out the analogy
between this case and the silver cell mentioned above.

However, Horovitz (1923) showed that equation (12) would
express experimental results only under particular conditions and
that the nature of the glass and the kind of ions in solution are of
great importance. Accordingly he formulated in terms of ionic
exchange between glass and solution, thereby taking into con-
sideration the specific properties of the glass. Another method of
approach is suggested by Michaelis' study of membrane per-
meabilities. See Michaelis (1926). Should it happen that the
ionic mobility of the hydrion in a particular membrane is much
larger than that of any other ion there would be a virtual approach
to the condition leading to equation (12).

See Hurd, Engel and Vernon (1927) on ion replacement in glass.

Horovitz presented a paper on the theoretical aspects at the
Richmond Meeting of the American Chemical Society in April,
1927, but I have not noted its publication.

In all events the matter reduces very largely to a selection of
glass which will give the desired effect. Considerable information
on this aspect was furnished by Horovitz (1923), Horovitz, Horn,
Zimmermann and Schneider (1925) and Horovitz and Zimmer-
mann (1925) who showed that certain glasses could function ap-
parently as "sodium electrodes," "potassium electrodes," "zinc
electrodes," "silver electrodes," etc., according to their compo-
sition and the solutions in contact. In a solution containing
sodium ions the well known thermometer glass 59 III and glass
397 III (a soda glass) behaved as "sodium electrodes." Gerate-

2 See Perlzweig's translation (1926).

XX GLASS ELECTRODES 431

glas 16 III and glass 1447 III, which contain zinc, behaved as
"zinc electrodes." A number of glasses were also found to func-
tion as "silver electrodes" in solutions of silver nitrate. Mis-
cellaneous lead glasses functioned fairly well as "hydrogen elec-
trodes."

For the purposes of ordinary measurements with buffer solu-
tions it is difficult to judge the conduct of particular glasses from
Horovitz's papers. He employed none of the common buffer
solutions and the hydrogen electrode function was judged by acid-
alkali cells.

Kerridge (1925) obtained poor results with "Durosil" glass and
fused silica and reported glasses which acted as mixed "sodium-"
and "hydrogen electrodes" in sodium phosphate buffers and as
"hydrogen electrodes" in potassium phosphate buffers. Among
the glasses acting as mixed electrodes were borosilicate glasses.
She reports success with "an ordinary soft soda laboratory

Hughes (1928) concludes that a glass should be as free as
possible from potash, alumina and borates. He suggests a glass
made of 72 per cent Si02, 8 per cent CaO and 20 per cent Na2O.
The bulb should be blown as rapidly as possible to avoid
devitrification.

APPARATUS

Wolf (1927) gives references to some earlier uses of glass
membranes.

Helmholtz (1881) in his picture of what was one of the first
"glass electrodes," used a bulb as did Haber and Klemensiewicz.
Others have continued the use of a bulb of extremely thin glass
blown from the end of a piece of relatively thick glass tube.
Korridge (1925) introduced more convenient and more rugged
designs one of which is shown in figure 80. The chief feature is
to give to the glass membrane the form of a deep spoon which is
"0.025 to 0.030 mm. thick in its thinnest part." This is filled
with the unknown. On the other side of the membrane is placed
a buffer solution of known pH- value.

Kerridge states that newly blown vessels require careful clean-
ing with hydrochloric acid, steaming for two hours and soaking

432

THE DETERMINATION OF HYDROGEN IONS

with distilled water for 24 hours before use. The cell used is
according to the following scheme.

Hg | HgCl, KC1 (sat.) | Solution 1 | JJ Solution 2 | KC1 (sat.), HgCl [ Hg

glass
membrane

In the figure the vessel is shown mounted with two calomel
half-cells.

Insulator

'SA — 7" Insulator

FIG. 80. THE CELL

The "insulator" indicated in the figure is "amberite" or "orca."
Blocks of such material support the calomel half-cells from the
stand through rack-and-pinion adjusters. For further details of
insulation, etc., see Brown (1924) and for description of quadrant
electrometer see page 338.

"Diffusion of potassium chloride into the solution in the glass

XX GLASS ELECTRODES 433

electrode is prevented by small ground caps fitted over the tips
of the calomel electrodes and the two taps, ungreased in the middle
race, are turned off while the measurements are being made."
The caps are rinsed and wiped before immersion.

If, for instance, a;cid potassium phthalate is used as the buffer
within the vessel and its pH value be regarded as 3.97, the formula
should be according the Kerridge (1926) :

where Es is the potential found with the phthalate and Ex is
that found with the solution under test.

Kerridge (1926) claims an accuracy characterized by a probable
error of 0.01 pH unit. This requires of the quadrant electrometer
alone a sensitivity capable of detecting ±0.6 millivolt.

Reliability of results are suggested by the following comparisons:

Blood by glass electrode method ......... .................. 7 . 75

Blood by Dale-Evans method .............................. 7.73

Phosphate solution by glass electrode method ............... 7.37

Phosphate solution by H-electrode method ................. 7. 39

Sycamore leaves, extract, by glass electrode method ........ 4.88

Sycamore leaves, extract, by H-electrode method ........... 4.91

For further details of theory and practice see: Bayliss, Ker-
ridge and Verney (1926), Borelius (1914), Brown (1924), Cremer
(1906), Freundlich (1921), Freundlich and Ettisch (1925),
Freundlich and Rona (1920), Gross and Halpern (1925), Haber
and Klemensiewicz (1909), Hoet and Marks (1926), Hoet and
Kerridge (1926), Horovitz (1923) (1925), Horovitz and Zimmer-
man (1925), Horovitz, Horn, Zimmerman and Schneider (1925),
Hughes (1926-1928), Katz, Kerridge and Long (1925), Kerridge
(1925), Kerridge (1926), Schiller (1924), and v. Steiger (1924).

CHAPTER XXI

SOURCES OF ERROR IN POTENTIOMETRIC MEASUREMENTS OF pH

The way to be safe is never to feel secure. — BURKE.
ERRORS OF TECHNIQUE

Sources of error are legion. Some of them are specific to the
hydrogen electrode; some of them are specific to the quinhydrone
electrode; some of them may arise in the use of any cell; occa-
sionally one evinces the stupidity of the operator.

During a series of measurements it became necessary to empty
and refill a horizontal tube having a stopcock. Potentials became
erratic. This was traced to a bubble of gas which had clung to
the bore of the stopcock key. To avoid this the "horizontal"
had been given a pitch but the flow had not been adequate that
time. One day after a year or so of smooth operation potentials
became erratic. Tne drain tube from the electrode vessel emptied
through a six inch air gap to the laboratory drain. The tube was
hidden for aesthetic reasons, and it had not been observed that a
stalagmite and a stalactite of KC1 were forming. On the day in
question they met! Not only was faith in the shielding shattered
and the shielding redone; but the hiding of the drain tube and
even remote connection with the piping became taboo.

These little incidents from the writer's experience are cited
merely to suggest the constant watchfulness both in the design
of apparatus and in its operation which is necessary. How often
has it been suggested that the high tension charging line and the
delivery line of the potentiometer's storage battery be placed on a
double throw, double pole switch! This neat scheme pleases till
some damp day at the end of which a day is counted lost.

The reader, if he counts himself an experimenter, knows full
well the impossibility of attempting to caution on every point of
technique. Something must be left to common sense and if this
is not possessed, how hopeless is the task of going over in absentia

434

XXI ERRORS 435

the details of a measurement in an attempt to trace a suspected
fault. The hoarding of solutions which should be used to wash
away the buffer action of solutions previously occupying the
electrode vessel, miserly supplies of hydrogen, contamination of
standard half-cells by the solutions of liquid junctions, electric
leakage, poor reproduction of liquid junctions, dirty electrodes,
forgetfulness of hysteresis in cells subjected to temperature
changes, neglect of corrections for particular half-cells, barometer
changes etc., plain carelessness and ordinary stupidity all usually
disappear at the hands of anyone who understands the ele-
mentary theory of his device and sets about it to meet the require-
ments of that theory. Then day after day as the eye is taken
from the galvanometer at balance the readings of the poten-
tiometer dial are found to hit the mark within ±0.1 millivolt for
the same solution and confidence that something definite is being
measured becomes conviction. And at last, when cells and condi-
tions are changed and small, distinct discrepancies appear, the
experimenter learns to his sorrow that he has yet to master many
a detail of technique.

ERRORS ARISING FROM THE INHERENT LIMITATIONS OF THE
HYDROGEN ELECTRODE

Presence of oxidizable material

We have already discussed in Chapter XVIII the relation be-
tween the hydrogen electrode and the "reduction electrode," and
have shown that no true hydrogen electrode potential can be
attained until the solution is so far reduced that it can support one
atmosphere of hydrogen. It is thus made perfectly obvious that
a measurement of pH must be preceded by a very thorough reduc-
tion of the solution.1

The hydrogen electrode if properly treated gives such a pre-
cisely defined potential in well buffered solution, reaches this
potential so rapidly, returns when polarized, and adjusts itself to
temperature and pressure changes so well that there is little doubt

1 In some instances it is important to remember that reduction of the
constituents of a solution may so change the acidic or basic properties of
these constituents that serious shifts in pH may occur.

436 THE DETERMINATION OF HYDROGEN IONS

of its being a reversible, accommodating, fairly quick-acting elec-
trode. It is perhaps because of this that it shows a hydrogen
electrode potential in solutions which could be slowly reduced
by hydrogen. For instance there are many organic and inor-
ganic substances which theoretically may be reduced by any
system having the reduction potential of the hydrogen elec-
trode, but which, nevertheless, give stable and reproducible
potentials as of the acid-base equilibria of their solutions and
without being appreciably reduced. It is simply that advan-
tage is taken of the rapidity in the adjustment of the acid-
base equilibria and the comparatively great slowness in the
adjustment of the oxidation-reduction equilibria. One is almost
afraid to estimate the limitations which would be placed upon
the hydrogen electrode were this not so. Not only would
there be left hardly a biological solution suitable for the measure-
ment but many an inorganic solution which the physical chemist
has studied with the utmost care and with supreme confidence in
the measurements would be thrown out of court.

In a sense we face a paradox. We prepare the electrode to
catalyze reduction and yet must avoid that "thorough" reduction
which almost inadvertently was specified in one of the paragraphs
above.

It is impracticable to list all the systems which are incompatible
with a hydrogen electrode potential. The practical way to deal
with the problem is to assume that a rapid attainment of electrode
equilibrium and its maintenance after attainment is evidence
that the small amounts of oxidants such as oxygen, ferric iron
etc. which are frequently present, have been reduced and that no
important constituent of the solution is "depolarizing" the
electrode. : . •£;.§ '•$$'$

Evans (1921) has maintained that in the electrometric measure-
ment of carbonate solutions the carbonate is reduced to formate
and that for this reason previous measurements of the pH of
blood have been in error. There are various reasons for doubting
the validity of Evans' last conclusion; but, since the question is
one of fact, Cullen and Hastings (1922) have investigated the
matter and have failed to confirm Evans. Martin and Lepper
(1926) concur with others in believing that Evans criticism has

XXI ERRORS 437

little significance in measurements of bicarbonate solutions of
ordinary strength but they believe they have detected the forma-
tion of formic acid in solutions of bicarbonate so dilute (0.0002 M)
that the minute amount of the stronger acid formed makes an
appreciable difference in pH. Since these investigators employed
phenol red and neutral red to show the pH-change and did not
recognize, or at least did not discuss, the changes which may take
place in these indicators on reduction, their observations must be
repeated and their conclusion regarded with caution. See also
comments on Evans' objection by Conway-Verney and Bayliss
(1923).

Oakes and Salisbury (1922) threw doubt on the reliability of
the phthalate solution which Clark and Lubs (1916) recommended
as a convenient working standard for checking hydrogen elec-
trode measurements. Clark (1922) repeated some experiments
which might haVe revealed the instability of the phthalate solu-
tion at the hydrogen electrode but found no sign of electrode
drift. See also Wood and Murdick (1922). Draves and Tartar
(1925) believed they had shown the nature of the discrepancy
when they found that, under ordinary conditions, the phthalate
solution is stable but that with heavy coatings of platinum black
appreciable reduction of phthalate occurs. Yet Blackadder
(1925) refers to his preference for very heavy coatings of platinum
black on his electrodes and at another part of his paper remarks
that his measurements "have invariably checked with the pub-
lished pH figures of an M/20 potassium acid phthalate solution,
namely 3.97" (Clark and Lubs' value). Evidently the last word
on this subject has not been said. However, Clark and his co-
workers continue to use phthalate as a working standard, having
never observed discrepancies with highly purified preparations.

The depolarizing action of such solutions as those of ferric
iron is rapid. However, it is interesting to note that the hydrogen-
hydrogen ion equilibrium also adjusts rapidly, and that, if it be
given its opportunity, it can compete fairly well. I once had
occasion to attempt the measurement of the pH value of a ferric
chlorid solution with the hydrogen electrode! A reasonable
magnitude was obtained by use of initial potentials as the elec-
trode in a shaking vessel descended into the solution. Of course

438 THE DETERMINATION OF HYDROGEN IONS

the values were quite unreliable and are not to be compared with
initial potentials taken with the much more rapidly adjusting
oxidation-reduction electrode such as the quinhydrone electrode.
I would never have had the courage to mention these very crude
experiments had Browne (1923) not had reasonable success with
ferric oxide hydrosols containing small quantities of ferric chloride.
He presaturates the electrode with hydrogen and thrusts it into
the liquid, taking the first potentiometric reading, which he says
remained fairly constant for a few seconds. He used three or
four electrodes to fix the approximate value for the setting of the
potentiometer and then operated with several other electrodes.
The effect of an intense and active oxidizing agent will be at
once recognized. At the other extreme are the cases where no
drift of the E.M.F. in the direction of an oxidizing action at the
hydrogen electrode will be detected. Between these extremes lie
the subtle uncertainties which make it advisable to check electro-
metric measurements with indicator measurements and to apply
tests of reproducibility, of the effect of polarization, of the effect
of time on drift of potential and all other means available to
establish the reliability of an electrometric measurement in every
doubtful case.

POISONS

There are effects of unknown cause which are included under
the term "poisoned electrodes." An electrode may be "poisoned"
by a well defined cause such as one of those to be mentioned
presently; but occasionally an electrode will begin to fail for
reasons which cannot be traced. There is hardly any way of
putting an observer on his guard against this except to call his
attention to the fact that if he is familiar with his galvanometer
he will notice a peculiar drift when balancing E.M.F.'s.

Adsorption of material by the platinum black (with such avidity
sometimes that redeposition of the black is necessary), the deposit
of films of protein, have been detected as definite causes of elec-
trode "poisoning." Kubelka and Wagner (1926) call attention
to the coating of the electrode by deposits of colloidal material
in the solutions they studied. For rough measurements they
believe it permissible to avoid the effects of such coatings by
pushing the wire of the Hildebrand type electrode deeper into the

XXI ELECTRODE POISONS 439

solution to expose new surface. In measuring a series of protein
solutions or other solutions from which gummy precipitates may
form, it is good practice to make the measurements in the order of
increasing solubility. This will tend to protect the electrode from
becoming clogged.

Michaelis (1914) places free ammonia and hydrogen sulfid
among the poisons. However, there is no special difficulty in
obtaining hydrogen electrode potentials agreeing with colorimetric
measurements in bacterial cultures containing distinct traces of
ammonia or hydrogen sulfid. My recollection is that S0rensen
has not expressed worry over the reliability of measurements with
protein solutions containing ammonium salts. (See, for instance,
S0rensen, Linderstr0m-Lang and Lund (1926.)) Aten and Van
Ginneken (1925) record consistent values for the basic dissocia-
tion constant of ammonia as measured with solutions 0.2 M with
respect to ammonia in ammonium chloride solutions. Yet
Prideaux and Gilbert (1927) quote Bottger as saying that the
hydrogen electrode is untrustworthy with ammonia and some
amines.

Alkaloids have been listed as electrode "poisons." (Isgarischev
and Koldaewa (1924).) Yet alkaloids have been titrated fre-
quently with the hydrogen electrode as end point indicator and
their dissociation constants have been measured by hydrogen
electrode equilibrium studies by Prideaux and Gilbert (1927).

Britton (1925) finds the electrode to function poorly in the
presence of sulfur and sulphites.

The mercury ions which may diffuse into the hydrogen electrode
vessel from the calomel electrode have been the cause of a caution
by Earned (1926) and by Bovie and Hughes (1923). The latter
used a rather drastic means of prevention. They introduced a
very thin glass partition between the calomel electrode vessel and
the bridge of pure KC1 solution. They could still get current
enough for they used the quadrant electrometer as null-point
instrument. With proper design of the flushing arrangements,
this drastic precaution seems quite unnecessary.

Koehler (1920) uses several cocks and flushing side-tubes for
protection.

Aten, Bruin and Lange (1927) have studied the poisoning action
of As2O3. They distinguish two phases, acute and permanent,

440 THE DETERMINATION OF HYDROGEN IONS

and say that although there may be complete or partial recovery
from the first the permanent effect may increase. They also say
that HgCl2 behaves like As20a, that H2S and KCN have but
slight poisoning effects and that the hydrolysis of KCN in solu-
tion may be studied with the hydrogen electrode.

Of the antiseptics used in biological solutions Michaelis (1914)
states that neither chloroform nor toluol interfere if dissolved.
Chloroform may hydrolyze to hydrochloric acid. Drops of toluol,
however, affect the electrode. Phenol is permissible but of
course in alkaline solutions participates in the acid-base equilibria.
While he gives no details Schmidt (1916) apparently finds the
presence of octyl alcohol permissible. This he uses to prevent
frothing of protein solutions. Without study of details I have
used octyl alcohol for the same purpose and find no reason to
doubt Schmidt's conclusion.

There is an extensive literature upon the so-called "poisons"
which interfere with the catalytic activity of the finely divided
noble metals used on the hydrogen electrode. This literature is
most suggestive, but there is still need for more direct studies of
the conditions surrounding the catalytic activity of the hydrogen
electrode.

Simply for the sake of clearness we may distinguish two func-
tions of the electrode. The electrode is first of all a convenient
third body by which there is established electrical connection with
the system, hydrogen-hydrogen ions. That the equilibrium of
this system should not be disturbed by the presence of a sub-
stance "poisoning" the catalytic activity of the platinum black
has been tacitly assumed in the derivation of the thermodynamic
equation for electrode potentials. If the reduction of the solu-
tion could be accomplished without dependence upon the catalytic
activity of the electrode, it should be theoretically possible to
attain a true hydrogen electrode potential even in the presence of
a substance acting as a poison of catalysis.

Aten, Bruin and Lange (1927) say: "In order to test whether a
hydrogen electrode is poisoned, a small quantity of oxygen, for
example 0.05 per cent, may be added to the hydrogen and the
effect of stopping the hydrogen current may be observed. If there
is no rise of potential in the first case, and no decrease in the
second, one can be fairly sure that there is no poisoning effect.

XXI EFFECT OF OXYGEN 441

If there is a rjoisoning substance present, the best way of working
is to use an electrode of large area, covered with finely divided
platinum black, to have the hydrogen as free of oxygen as possible
and to stop the hydrogen current before taking a reading."

Hammett (1923) has made an interesting study of the poten-
tials of hydrogen electrodes when oxygen in definite proportions
is added to the hydrogen. He finds that the change of potential
for any given percentage of oxygen varies with the condition of
the platinum, a fact which may be attributed to variation of the
catalytic activity. On long exposure to hydrogen the electrode
becomes so sensitive to oxygen "that no reasonable precautions
can give correct results." For instance in a phosphate buffer
after an hour or so the addition of 0.009 per cent 02 gave only
0.02 millivolt change and 0.43 per cent O2 4.0 millivolts change.
But twenty hours later 0.048 per cent O2 caused 8 millivolts
change. The sensitiveness becomes greater in alkaline solution.
Thus the addition of 0.046 per cent 02 to the hydrogen gave:

with 0.1 M HC1 0.00 mv. change

with phosphate buffer 0.38 mv. change
with 0.1 N KOH 20 .00 mv. change

This is doubtless one of the chief reasons for the difficulty in
making precise measurements of alkaline solutions.

It is, therefore, appropriate to note the following relative rates
of diffusion of gases through rubber

GAS

KATE

Nitrogen

1 00

Air

1 15

Oxygen

2 56

Hydrogen

5 50

Carbon dioxide

13 57

In refined measurements the use of rubber tubing is avoided
whenever possible. Regarding the effects of oxygen which diffuses
through rubber see Biilmann and Jensen (1927). With an
electrode in 0.1 N HC1 50 cm. of rubber tubing made a difference
of 0.13 millivolt. But see above for alkaline solutions.

That the catalytic action of the "black" need not be present

442 THE DETERMINATION OF HYDROGEN IONS

at the electrode itself has been shown by Biilmann and Klit
(1927). They obtain good hydrogen potentials with blank
platinum when colloidial palladium is used in the solution.

In ordinary practice an electrode is used not only as an
electrode per se but also as a hydrogenation catalyst. As such it
is very sensitive to "poisons." "Poisons" are then to be regarded
as the cause of sluggish electrodes. Among these we find all
degrees. Hydrogenation to a point compatible with a true hydro-
gen electrode potential may be delayed but slightly and we may
say that the electrode is a bit slow in attaining a stable potential
without our ever suspecting a "poison," or the "black" may be
so seriously injured that it becomes entirely impractical to await
equilibrium.

And just as "poisons" may render an electrode useless for prac-
tical measurements, so the employment of accelerators of catalysis
may promote efficiency. With the exception of a brief, unpub-
lished note by Bovie little work has been done in this direction.

The attempt by Centnerszwer and Straumanis (1925) to affect
the potential of a hydrogen electrode by radium emanation gave
negative results.

UNBUFFERED SOLUTIONS

Not infrequently the attempt is made to measure potentio-
metrically the pH value of an unbuffered solution such as that of
KC1. It is not entirely the fault of the method but rather of the
nature of the solution that this is a task requiring the very highest
refinements known to experimental art. If for the sake of the
argument we assume that the solution under examination is that
of a perfectly neutral salt having under ideal conditions a hydro-
gen ion concentration of 0.000,000,1 N, a simple calculation will
show what an enormous displacement in pH will be caused by
the admittance of the slightest trace of C02 from the atmosphere,
of alkali from a glass container, of impurities occluded in the
electrode or of impurities carried into the solution with the sol-
vent or solute. Conversely, even if the measurement were such
as to give the true value under ideal conditions it would have
little practical significance because of the difficulty in holding the
conditions ideal.

By the same reasoning it appears probable that it would be

XXI EFFECT OF C02 443

difficult to obtain true electrode potentials even with a potentio-
metric system drawing no current during its adjustment. When
no buffer is present there is a negligible reserve of hydrogen ions.
But the introduction of the electrode with its enormous surface
must displace the equilibrium. How much the displacement
will be depends both on relative proportions of electrode and
solution and on the technique used.

The writer can see little practical use in attempting electrode
measurements with unbuffered solutions and would prefer in-
direction in the treatment of certain theoretical matters which
might be illuminated were reliable measurements available.

There are however instances in which it is very desirable to
obtain measurements of slightly buffered solutions. Various ex-
tracts and washings reveal the condition of their source if care-
fully measured. If the retention of the acid of the electrolyzing
bath by the black of the electrode can be avoided and if the ab-
sorptive nature of the black can be reduced, there seems to be
inherent in the electrode method greater delicacy than in the use
of very dilute indicator solutions which are often the preferred
means of studying slightly buffered solutions. Beans and Ham-
mett (1925) seem to have accomplished this by preparing catalyti-
cally active, smooth deposits of platinum. They obtain such
deposits by using pure chloroplatinic acid.

PARTICIPATION OF C02

From what has already been said, the effect of the presence of
oxygen is obvious. Indifferent gases such as nitrogen may be
considered merely as diluents of the hydrogen and as such must
be taken into consideration in accurate estimations of the partial
pressure of hydrogen. Gases like carbon dioxid on the other hand
act not only as diluents but also become components of any acid-
base equilibrium established in their presence.

In very many instances biological fluids contain carbonate and
the double effect of the carbon dioxid upon the partial pressure
of the hydrogen and upon the hydrogen ion equilibria render
accurate measurements difficult unless both effects are taken into
consideration and put under control.

At high acidities in the neighborhood of pH 5 carbon dioxide
will have relatively little effect upon a solution buffered by other

444 THE DETERMINATION OF HYDROGEN IONS

than carbonates.2 As the pH of solutions increases, the participa-
tion of CO2 in the acid-base equilibria becomes of more and more
importance. The C02 partial pressure in equilibrium with the
carbonates of a solution is a function of both the pH and the
total carbonate. If, however, we consider for the sake of the
argument that the total carbonate remains fairly low and constant,
the C02 partial pressure becomes less with increase in pH while
its effect upon the hydrogen ion equilibria increases with increase
in pH. Therefore it may be said that it is of more importance
under ordinary conditions to maintain the original C02 content
of the solution than it is to be concerned about the effect of CO2
upon the partial pressure of the hydrogen. Furthermore the effect
of diminishing the partial pressure of the hydrogen is of relatively
small importance.

For these reasons the bubbling of hydrogen through the solu-
tion is to be avoided unless one cares to determine the partial
pressure of C02 which must be introduced into the hydrogen to
maintain the carbonate equilibria and then provides the proper
mixture (Hober 1903). Cf . Schaede, Neukirch and Halpert (1921).
The method usually employed is to use a vessel such as that of
Hasselbalch, of McClendon or of Clark in which a preliminary
sample of the solution can be shaken to provide the solution's
own partial pressure of CO2, and in which there is provision for
the introduction of a fresh sample with its full C02 pressure.
The hydrogen supply is then kept at atmospheric pressure and
the partial pressure of hydrogen in the electrode vessel is either
considered to be unaffected by the C02 pressure or corrected from
the known CO2 pressure of the solution under examination.

Another method is to employ such a ratio of solution volume
to gas volume that the loss of C02 from the solution into the gas
space is insignificant. [Compare Michaelis (1914), Swyngedauw
(1927), Etienne, Verain and Bourgeaud (1925).]

Of course, in cases where the total carbonate in solution rises to
considerable concentrations, the partial CO2 pressure may become

2 Like so many problems of this kind it can be adequately solved only
by use of quantitative data. No definite limit, such as pH = 5, can be
given. The relative effectiveness of a given partial pressure of CO2 de-
pends upon the total carbonate and the pH region. See page 561. By
"carbonate" is meant either carbonate or bicarbonate.

XXI CRITERIA OF RELIABILITY 445

of very significant magnitude and its effect in lowering the hydro-
gen pressure must be carefully considered.

With the demand for ever higher accuracy in the study of solu-
tions containing carbonates a return is being made to Hober's
(1903) practice of supplying in the hydrogen stream or atmos-
phere the desired partial pressure of C02. See for instance War-
burg (1922) and Walker, Bray and Johnston (1927).

CRITERIA OF RELIABILITY

The criteria of reliability of hydrogen electrode measurements
are difficult to place upon a rigid basis but certain practical tests
are easy to apply. Reproducibility of an E. M. F. with different
electrodes and different vessels is the foremost test of reliability,
but not a final test. Second is the stability of this E. M. F. when
attained. In case flowing hydrogen is used the potential should
be the same with different rates of flow. It is not always prac-
ticable to distinguish between a drift due to alteration in the
difference of potential at liquid junctions and a drift at the elec-
trode but in most cases the drift at the liquid junction is less rapid
and less extensive than a drift at the electrode when the latter
is due to a failure to establish a true hydrogen-hydrogen ion
equilibrium. A test which is sometimes applied is to polarize
the hydrogen electrode slightly and then see if the original
E. M. F. is reestablished. This may be done sufficiently well by
displacing the E. M. F. balance in the potentiometer system.
Where salt and protein errors do not interfere, the gross reliability
of a hydrogen electrode measurement may be tested colorimetri-
cally. This checking of one system with the other is of inestimable
value in some instances as it has proved to be in the study of soil
extracts. There the possibilities of various factors interfering
with any accurate measurement of hydrogen ion concentration
dimmed the courage of investigators until Gillespie (1916)
demonstrated substantial agreement between the two methods.
Subsequent correlation of various phenomena with soil acidity so
determined has now established the usefulness of the methods.

In addition to the tests so far mentioned there remains the test
of orderly series. Certain of the general relations of electrolytes
are so well established that, if a solution be titrated with acid or
alkali and the resulting pH values measured, it will be known

4:46 THE DETERMINATION OF HYDROGEN IONS

from the position and the shape of the "titration curve" whether
the pH measurements are reasonable or not. This of course is a
poor satisfaction if there is any reason to doubt the measurements
in the first place but it is a procedure not to be scorned.

TEMPERATURE VARIATIONS

The effect of temperature variations upon the accuracy of
electrometric measurements is a question upon which it is difficult
to pass judgment. Of course, if measurements are not intended
to be refined, one may assume the temperature of the room to be
the temperature of the system at the moment of the electrical
measurement. It is then a simple matter to select from tables
the values and factors applicable at the selected temperature.
Since such a procedure introduces errors which are not serious
for many purposes, insistence upon temperature regulation may
be open to criticism as an unnecessary luxury. Those who take
this position are doubtless able to escape the psychological effects
of uncertainty, but they can hardly escape the inconvenience of
having to deal with new values and new factors with every shift
in temperature. Temperature control so simplifies rough measure-
ments that much time is saved, and for this reason is recommended
even when it is unnecessary. But before the practice of neglecting
temperature control can have scientific standing it needs more
experimental investigation than it has been accorded. Calcula-
tions are quite insufficient for we have little data upon the hys-
teresis in the adaptation of different systems to temperature
variation. Thus Hammett (1922) notes that although the cell

Hg | HgCl, KC1 (sat.) | HC1 (0.1 M) | Pt, H2

has a comparatively small temperature coefficient, it is very
sensitive to sudden changes of temperature.

Cullen (1922), finding that the temperature in an electrode
vessel is seldom that of the surrounding air in a room subject to
temperature variation, has devised a modification of the Clark
electrode vessel whereby the temperature of the solution can be
measured. The same modification can easily be made in a calomel
electrode vessel.

Of course no data for which accuracy is claimed should ever be

XXI TEMPERATURE EFFECTS 447

reported without there having been temperature control of appro-
priate accuracy. In view of the hysteresis that may occur a mere
record of the temperature at a given moment is of no use, nor
is it worth while to attempt calculations of ''temperature
corrections."

ERRORS WITH THE QUINHYDRONE ELECTRODE

See Chapter XIX, page 414.

CHAPTER XXII
TEMPERATURE COEFFICIENTS

An isolated system obviously cannot be said to have reached equilib-
rium until the temperature is the same in all its parts. — EASTMAN.

In deriving the type equation

(H+) (A)
(HA)

we assumed constancy of temperature as one of the fundamental
conditions. If this equation can be satisfied at one fixed tem-
perature, it is to be presumed that it can be satisfied at another
fixed temperature; but it is also to be presumed that each change
in the temperature to some new value will result in a new value
for Ka. Therefore it would be necessary to determine the values
of Ka for a series of fixed temperatures if the temperature coeffi-
cient of Ka is to be determined. At each temperature the value
of Ka would be determined by the specific properties of the com-
ponents of the system at that temperature and the temperature
coefficients of Ka would not be predicted from any universal rule
of conduct with an accuracy sufficient for our purposes.

The same would be true of the activities of the hydrions in a
solution of some specific, completely ionized acid.

Most of the data of our subject rest ultimately upon measure-
ments of hydrogen cells. In the treatment of these cells it is
agreed that the standard of reference shall be the so-called normal
hydrogen electrode, and that the potential of this electrode shall
be called zero.1 Since this is our ultimate standard and since it

1 The Gibbs-Helmholtz equation is

T dE E + AH
TdT= HS

where E, T, n and F have their customary meanings and AH is the increase
in heat content (see page 238). If, instead of applying this to the whole

448

XXII TEMPERATURE COEFFICIENTS 449

is not permitted to employ any of the ordinary equations except
at constant temperature, we must add the specification that the
potential of this electrode is to be zero at all temperatures.
However, we must operate with some material system the
hydrion activities of which are known at different temperatures
or are assumed to be the same within moderate variation of tem-
perature.

It will be made plain in Chapter XXIII that it is a very difficult
matter to determine the hydrion activity of any actual solution
which is to be used as an original standard. Nevertheless, this
must be done if there is to be maintained a consistent use of the
equation

RT7

- Eh = — - In

F (H+)

Imagine, for the sake of the argument, that tenth molar hydro-
chloric acid solution is to be the original standard and that
(H+)25 is determined for one temperature, 25°C. Strictly (H+)30,
the hydrion activity of this particular solution at 30°C. might be
different. Then it would be necessary to repeat at 30° the method
used in reaching the value at 20°.

However, there are three justifications for regarding the hydrion
activity in a dilute hydrochloric acid solution to be fairly con-
stant within moderate ranges of temperature. The Debye-
Hiickel theory indicates that at high dilution the activity coeffi-
cient should not change greatly with change of temperature.
(See page 500.) • Experimental values of the heat of dilution are
very small up to 0.1 M. Various measurements of the colligative
properties indicate that the change is small. For these reasons
the assumption of constant hydrion activity of a dilute hydro-
chloric acid solution has entered estimates of various tempera-
ture coefficients, notably that of the potential of the tenth normal
calomel half-cell.

Before discussing specific cases it may be emphasized that we
are not at all concerned with the absolute temperature coefficient

cell, we write it for the normal hydrogen half-cell and define E = 0 and —

= 0, it follows that AH = 0. That is, the change in heat content of the
normal hydrogen half-cell is zero by definition.

450 THE DETERMINATION OF HYDROGEN IONS

of any single electrode potential. Since there is no way of measur-
ing a single electrode potential, it has been convenient to introduce
the definition that the standard selected shall be zero. Since
none of the ordinary equations applies to systems which are not
in thermal equilibrium we have no fundamental interest in
measuring the difference of potential between two half-cells of
the same composition, each at a different temperature. There-
fore, there is added the specification that the standard potential
shall be zero at all temperatures. There is a still more pertinent
reason for lack of interest in this latter type of experiment. We
have difficulties enough with liquid junctions without introducing
the large potentials at liquid junctions in a temperature gradient.

The confusion in the subject should be apparent if we now state that
measurements with cells not at thermal equilibrium frequently have been
introduced in discussions of temperature coefficients of quantities apply-
ing to our subject. Furthermore, in several of these discussions the
"normal hydrogen electrode" itself has been given a temperature coeffi-
cient. Thus S0rensen and Linderstr0m-Lang (1924) say .... the
hydrogen electrode, with an electrode liquid 1 N with regard to hydrogen
ions, has a temperature coefficient of almost the same magnitude as the
0.1 normal calomel electrode . . . . " also they say " .... it seems to
us hardly practical, in the definition of TTO (potential of normal hydrogen
electrode) to introduce as Clark2 has done the supposition that the poten-
tial between hydrogen platinum electrode and the IN hydrogen ion solu-
tion should be taken as nil at all temperatures, since the whole tempera-
ture coefficient of the cell3 would thus fall upon the calomel electrode, the
true temperature coefficient of which is as mentioned above, quite differ-
ent from that of the cell."

Also Kolthoff and Tekelenburg (1926) say " . . : . the potential of
the N hydrogen electrode increases with the temperature." Compare
also Kolthoff and Furman (1926) and Mislowitzer (1928).

Since the problem necessitates the definition of some standard of refer-
ence, there seems to be no fundamental reason why various schemes can-
not be devised for dealing with the temperature coefficients of cells. How-
ever, I have failed to find, either in the treatment by S0rensen (1912),
S0rensen and Linderstr0m-Lang (1924) or in the treatment by Kolthoff and
Tekelenburg (1927), a precise definition of the problem. I shall, there-
fore, refrain from joining them in this matter and shall use Lewis' (1914)
definition. This is, I believe, the custom in the treatment of cells not

2 It was Lewis (1914) who specified that the "normal hydrogen electrode"
shall be considered as having zero potential at all temperatures.

3 Referring to the cell Ft, H2 j H+ (1M) j KC1, HgCl | Hg.

XXII

CALOMEL HALF-CELL

451

concerned in pH measurements. Furthermore, I must confess inability
to trace the manner in which either S0rensen and Linderstr0m-Lang or
Kolthoff and Tekelenburg have utilized their measurements of cells not
in thermal equilibrium. It appears to me that in the end the determinative
measurements they made were of cells in thermal equilibrium and that
the hydrion activity of some definitive material solution was either calcu-
lated or assumed to be the same at different temperatures. The poten-
tial of a hydrogen electrode in any material solution other than that
which maintains unit activity will of course have a temperature coefficient
within the meaning of the definition adopted.

TEMPERATURE COEFFICIENT FOR THE CALOMEL HALF-CELL

Lewis and Randall (1914) give the following method of deter-
mining the temperature coefficient for the tenth-normal KC1
calomel half-cell.

FIG. 81. ELECTKOMOTIVE FORCES, E, AT TEMPERATURES t°C. FOR THE CELL
-Pt, H2 (1 atmos.) | HC1 (0.1 M), HgCl | Hg+

Figure 81 depicts the change of potential of the celt

-Pt, H2 1 HC1 (0.1 M), HgCl | Hg+ I

when, in each case at constant temperature, the potentials of the
cell are measured at different temperatures.

The data led Lewis and Randall (1914) to the empirical equation

Ej = 0.0964 + 0.001881 T - 0.000,002,90 T2 (1)

Differentiation of (1) gives

= 0.001,881 - 0.000,005,80 T

(2)

452 THE DETERMINATION OF HYDROGEN IONS

As was stated before, the temperature coefficient of the poten-
tial of the half-cell

Pt, H2 1 HC1 (0.1 M)

should, in strictness, be determined experimentally (by some
procedure such as is outlined in Chapter XXIII) . However, in the
absence of adequate data, Lewis and Randall assume that for
moderate changes of temperature the hydrion activity in 0.1 M
HC1 will remain a constant, C. The potential of this half-cell
is given by

Eh = 0.000,198,322 T log C (3)

Lewis and Randall used for Eh the value —0.0684 at 25°. In-
troduce Eh = -0.0684 and T - 273.1 + 25 into (3) and solve
for log C. This gives: log C = -1.15696. Introduce this
value in (3) and differentiate to obtain :

AEh

~^-= ~ 0.000229 (4)

This is the temperature coefficient of the potential at the plati-
num electrode of cell I, the over-all temperature coefficient of
which is given by equation (2). Consequently 0.000229 must
be subtracted from the right of equation (2) to yield in (5) the
temperature coefficient of the calomel half -cell with 0.1 M HCL
We shall round off the numbers and use :

— = 0.00165 - 0.000,005,80 T (5)

Lewis and Randall assume that (2) will apply also to the cell
- Pt, H2 1 HC1 (0.1 M) || KC1 (0.1 M), HgCl Hg+ III

Consequently (5) gives the temperature coefficient of the half-
cell

||KC1 (0.1 M), HgCl|Hg IV

Equation (5) is the differential of (6)

Ec = Eoc + 0.00165 T - 0.000,002,90 T2 (6)

XXII

CALOMEL HALF-CELL

453

Eoc can be found by taking either S0rensen's value Ec = 0.3380
for 18°C. or the value 0.3353 at 25° from table 61 (see page 472).
Then the values of Ec at different temperatures may be calcu-
lated.

In Chapter XXIII are presented arguments leading to the use
of a standardized value for the standard half-cell :-

|| KC1 (sat.) | KC1 (0.1 N), HgCl | Hg V

Assuming that the temperature coefficient of half-cell IV applies
to the standard half-cell V and adopting S0rensen's value for

TABLE 57

Values of calomel half-cells at different temperatures
Half-cell IV || KC1 (0.1 M), HgCl | Hg
Half-cell V || KC1 (sat.) | KC1 (0.1 N), HgCl | Hg
Half-cell VI || KC1 (0.1 N) | KC1 (1.0 N), HgCl J Hg

HALF-CELL IV
USING 0.3353
AT 25°

HALF-CELL V
(S0RENSEN)
CALCULATED

HALF-CELL V

(S0RENSEN)
FOUND

HALF-CELL VI

(S0REN8EN BASIS)

0.3357

0.3380

0.2865

0.3356

0.3379

0.3378

0.2860

0.3353

0.3376

0.2848

0.3348

0.3371

0.3370

0.2835

0.3365

0.3361

0.3335

0.3358

0.3359

(0.3315)

(0.3338)

0.3344

18° as a point of reference, we obtain the values for the standard
half-cell V shown in table 57.
For the cell

- Hg | HgCl, KC1 (l.ON) | KC1 (0.1N), HgCl | Hg +

the author finds at 20° 0.0519, and at 30° 0.0536. Interpolation
between these values on the assumption that the E. M. F. is a
linear function of the temperature gives an E. M. F. at 25°
which is within 0.15 millivolts of that found by Lewis, Brighton
and Sebastian for a similar cell with molal and 0.1 molal KC1
and a linear temperature coefficient of 0.000,17. Sauer's value

454 THE DETERMINATION OF HYDROGEN IONS

at 18° is 0.0514 and that of Fales and Vosburgh at 25° is 0.0524.
Neither of these values falls in with those mentioned above but
when taken by themselves and with the 15° value, 0.0509, given
in the footnote of the paper by Fales and Vosburgh (1918) they
furnish a temperature coefficient of the same order.

With these data we can calculate the value of the half -cell

|| KC1 (0.1 N) | KC1 (1.0 N), HgCl | Hg VI

from the standardized value of the " tenth normal" calomel
half-cell.

For the potential of the saturated KC1 calomel half-cell Michaelis
(1914) gives values at different temperatures which are not quite
a linear function of temperature. Vellinger (1926) finds a linear
relation. Neither author gives all the details of the method of
reference. Fales and Mudge (1920) report potentials at different
temperatures for the cell

•- Pt, H2 1 HC1 (0.1 M) | KC1 (sat.), HgCl | Hg +

The temperature coefficient of this cell was almost linear. If, as
was done in calculating the temperature coefficient for the
0.1 N KC1 calomel half -cell, we assume that the potential of the
hydrogen electrode in 0.1 M HC1 becomes more negative by
0.00023 volts per degree increase of temperature we calculate
from the data of Fales and Mudge the following approximate
temperature coefficients.

- = -0.000,788 between 25° and 40°
dt

— = -0.000,695 between 40° and 60°
dt

— = -0.000,75 between 25° and 60° by best curve
dt

A best straight line through Michaelis' data gives —0.000,761.
Vellinger gives -0.000,66.

Fales and Mudge (1920) give only their value at 25° as re-
liable4 for the potential between the 0.1M calomel half-cell and

4 They did not adequately protect their half-cells from interdiffusion.

XXII

SATURATED CALOMEL HALF-CELL

455

the saturated calomel half-cell. They report as the average of
36 cells 0.0918±0.0002. If we use 0.3376 for the half-cell

|| KC1 (sat.) | KC1 (0.1 N), HgCl | Hg
we obtain 0.2458 =t 0.0002 for the half-cell1
||KCl(sat.),HgCl|Hg

This is practically the same as the value 0.2457 for 25° re-
ported by Vellinger, 0.2458 (0.2460 corrected to our value for
the tenth normal) reported by Michaelis and 0.2454 Scatchard
(see page 470). We shall use 0.2458 at 25° as an orienting value.

The several temperature coefficients are not in adequate agree-
ment for the satisfactory calculation of values for other tempera-

tures. If, however, we use -

-0.000,76 (the average of

Michaelis' and Fales and Mudge's values for the lower tempera-
tures) we obtain the values of the following table.

TABLE 58

Tentative values for the cell
IIKC1 (sat.), HgCl ! Hg

0.2511

0.2420

0.2496

0.2382

0.2458

0.2359

0.2344

At 38° the value in the table is 0.0013 volt lower than that of
Vellinger and 0.0009 volt higher than that of Michaelis.

Tentatively it will be wise to use the above values as approxi-
mations and to standardize each saturated half-cell as used.

It is interesting to note that the saturated calomel half-cell
has a large temperature coefficient and, by reason of its nature,
is especially subject to hysteresis. Temperature fluctuations
therefore jeopardize accurate measurements. On the other hand
the potential of a cell composed of a hydrogen or quinhydrone
half-cell and a saturated KC1 calomel half-cell has a small tem-
perature coefficient so that, if constant temperature prevail, the

456 THE DETERMINATION OF HYDROGEN IONS

temperature value may be in considerable error without causing
great error in the potential. The error then incident to the
mistaken temperature lies in the use of the wrong temperature
factor.

TEMPERATURE COEFFICIENTS FOR BUFFER SOLUTIONS

In the standardization of buffer solutions, cells of the type
given below were used directly or indirectly by S0rensen (1909),
Clark and Lubs (1916), Walbum (1920) and others.

- Pt, H2 (1 atmos.)

Buffer
Solution

KC1

(sat.)

KC1
(0.1 N)

,HgCl

B C D

If, at a given temperature, the electromotive force of the cell
is measured, the potential at A is readily calculated when the
potential of the half-cell

|| KC1 (sat.) | KC1 (0.1 N), HgCl | Hg

at the given temperature is known and the potential of B is zero.

In Chapter XXIII it will be recommended that variation of the
potential at B be neglected and that the algebraic sum of the
potentials at B, C and D be regarded as the potential of the so-
called tenth normal calomel electrode as it has been applied in
these instances. The previous section gives the standardized
values of this half-cell at various temperatures.

This procedure standardizes an arbitrary method of computing
the potential at A.

The so-called pH-values of buffer solutions are calculated from
the relation

— potential at A

pH =

0.000,198,322 T

This gives a definite methodical meaning to pH values. The
pH values of any given buffer solution at stated' temperatures
must then be determined experimentally by the standardized
procedure. Such essentially is the procedure followed by Wal-
bum. His values are found in Chapter IX.

Kolthoff and Tekelenburg (1927) have stated an extensive

XXII

BUFFERS

457

TABLE 59

Kolthoff and Tekelenburg's data for pH values of buffers at different

temperatures

BUFFER

TEMPERATURE

(HYDROGEN ELECTRODE
SERIES)

•c.

0. 1 M acetic acid

4.60

0.1 M sodium acetate

4.61

4.63

Mono sodium citrate 0.1 M

3.66

3.65

3.66

3.65

Di sodium citrate 0.1 M

4.96*

4.96

4.97

Acid potassium phthalate 0.05 M

3.92

3.93

3.94

Sprensen's "citrate 4.45"

4.45

4.43

4.41

4.40

S0rensen's "Glycine— HC1 2.28"

2.26

2.25

0.15M Na2HPO4

11.29

0.1 MNaOH

11.08

* Compare Walbum. See page 211,

458 THE DETERMINATION OF HYDROGEN IONS

series of pH values for various buffer mixtures at different tem-
peratures. They state that they "have made a thorough in-
vestigation" of the temperature coefficients of "the hydro gen-
and quinhydrone electrodes" but the details are contained in
Tekelenburg's dissertation (1926) and have not been available
to me. It appears that although they give an extensive dis-
cussion of the absolute temperature coefficients of various half-
cells, measured without thermal equilibrium of the cell as a
whole, Kolthoff and Tekelenburg assumed pH 2.038 as the value
of 0.01 N HC1 + 0.09 N KC1 at all temperatures (?).

As already indicated a similar assumption of the constancy of
the hydrion activity of a hydrochloric acid solution entered
Lewis' derivation. It is, therefore, not improbable that the data
of Kolthoff and Tekelenburg finally are in terms of the system
here recommended so far as temperature coefficients are con-
cerned.

Representative data from their paper are given in table 59.

By reason of a departure from usual methods of standardization
Kolthoff and Tekelenburg's pH values are somewhat lower than
usual. This should not affect the temperature coefficients.

Hastings and Sendroy (1924) have obtained the data for
phosphate solutions at 20° and 38° which are tabulated on
page 212.

TEMPERATURE COEFFICIENTS OF INDICATOR CONSTANTS

• In the older literature very little was said of the effect of tem-
perature variation.

Kolthoff (1921) has extended the theory of Schoorl in which
account is taken of the acidic or basic nature of an indicator,
but there often remains some question as to how a given indicator
is to be classified. Kolthoff, using the values of Kohlrausch and
Heydweiller for the dissociation constant of water at various
temperatures, has reduced his observations to the following
table. In this table the displacement of —0.4 for the thymol
blue means that if thymol blue in a solution at 70° C. shows the
same color as the same concentration of this indicator in a buffer
of pH 9.4 at ordinary temperature then the pH of the solution
at 70°C. is 9.0. Corrections for temperatures between room

XXII

INDICATORS

459

temperature and 70°C. may be interpolated from the data in the
table.

In determining their temperature coefficients for indicator
constants Michaelis and Gyemant (1920) (see page 129) assumed
constancy in the pH of acetate buffers used with p-nitrophenol
In the study of m-nitrophenol they used phosphate buffers to the
pH values of which they ascribed a temperature coefficient based
on the work of Michaelis and Garmendia. They also used a

TABLE 60
Displacement of indicator exponent between 18°C. and 70°C. after Kolthoff

INDICATOR

DISPLACEMENT

pOH

DISPLACEMENT

KATIO OF
DISSOCIATION
CONSTANT AT
70°C. TO THAT
AT ORDINARY
TEMPERATURE

Nitramine

— 1 45

0 0

1 0

Phenol phthalein

-0 9 to 0 4

—0 55tol 05

About 5

Thymol blue, alkaline range . . .
a-naphthol phthalein

-0.4
-0 4

-1.05
-1 05

2.5

2 5

Curcumine

-0.4

-1.05

2 5

Phenol red

—0 3

— 1 15

2 0

Neutral red

-0 7

-0 75

Brom cresol purple

0 0

-1 45

1 0

Azolitmin

0 0

— 1 45

1 0

Methyl red

—0 2

-1 25

Lacmoid

—0 4

— 1 05

2 5

p-nitro phenol

-0 5

—0 95

3 2

Methyl orange . .

-0 3

— 1 15

14 0

Butter yellow

-0.18

-1 17

15 0

Bromphenol blue

0 0

— 1 45

1 0

Tropaeolin OO

-0 45

-1 0

10 0

Thymol blue, acid range

0.0

-1.45

1.0

temperature coefficient for borate buffers in determining, for
instance, the temperature coefficients for salicyl yellow. The
original articles must be consulted for the somewhat involved
detail.

Hastings and Sendroy (1924) and Hastings, Sendroy and Rob-
son (1925) have systematized the Gillespie method as applied by
Cullen (1922), see also Austin, Stadie and Robinson (1925).
They determined anew the pH values of phosphate buffers (see

460

THE DETERMINATION OF HYDROGEN IONS

page 212) at 20° and 38° and of acetate buffers at 20°. In the
latter case they assumed no change of pH with change of tem-
perature to 38°C. In these standardizations 0.1 N HC1 with
assigned value of pH 1.08 was employed. They obtain the
pK' values of the following table:

Indicator exponents at different temperatures

INDICATOR

Phenol red.

7 78

7 65

Brorn cresol purple

6 19

6 09

Chlor phenol red

6 02

5 93

Brom cresol green

4.72

Compare these with values of table 11, page 94. See figure
18, page 103.

TEMPERATURE COEFFICIENTS OF OTHER EQUILIBRIUM CONSTANTS

In the older literature are to be found numerous measurements
of the temperature coefficients of acid and base dissociation con-
stants. These were based upon conductivity, for the most part.
Extensive data are assembled by Scudder (1914) and in Landolt-
Bornstein's Tabellen (1923).

See page 45 for estimates of Kw at different temperatures.

TEMPERATURE COEFFICIENTS OF QUINHYDRONE ELECTRODE

POTENTIALS

See page 419.

CONCLUSION

At the present time the lack of sufficiently extensive systematic
data has made necessary various and divers assumptions by
different authors who have dealt with the temperature coeffi-
cients of the quantities briefly treated in this chapter. By reason
of the variety of these assumptions and, in many cases, the lack
of sufficiently specific detail, it is impracticable to systematize the
existing data. The operator must choose his system and should
state in detail the assumptions he makes.

CHAPTER XXIII

STANDARDIZATION OF pH MEASUREMENTS

// there is a service which philosophy can render with more advan-
tage to science than any other, it is probably to keep reminding
men of science never to forget to criticise their categories before
employing them. — VISCOUNT HALDANE.

In the development of the theory of electrolytic dissociation
the hydrogen electrode came upon the scene comparatively late
and after many of the quantitative relations had been outlined
by conductance data. It was, therefore, natural that these data
should have been accepted in the standardization of poten-
tiometric measurements. It now appears that the interpretation
of conductance data is more complicated than at first supposed
and that certain of the values that have been used in the stand-
ardization of potentiometric measurements are in doubt. Also,
it is now recognized that the hydrogen cell does not directly give
information upon relative hydrion concentrations. The result-
ing confusion demands careful consideration.

Let us review briefly the way in which conductance data entered
the standardization of potentiometric measurements.

Assume, first, the validity of the ideal gas laws. Then the
following equation relates the electromotive force of a hydrogen
cell to the concentrations of hydrions in solutions 1 and 2, pro-
vided the hydrogen partial pressure is the same at each electrode.

By use of this relation one can determine in the first instance only
the ratio of two hydrogen ion concentrations. If the value of
either [H+]i or [H+]2 is to be found, the value of the other must
be known. Conductance data have been relied upon to furnish
one known.

Likewise, when there is used a cell composed of a calomel half-
cell and a hydrogen half-cell, the value assigned to the calomel

461

462 THE DETERMINATION OF HYDROGEN IONS

half-cell is such that, when it is subtracted from the total E.M.F.
of the cell, the resulting E.M.F. is as if between a normal hydro-
gen electrode and the hydrogen electrode under measurement.
This implies the experimental determination of the difference of
potential between a normal hydrogen electrode and the calomel
electrode or else between the calomel electrode and a hydrogen
electrode in some solution of known hydrogen ion concentration.
To determine this known hydrogen ion concentration conduct-
ance data upon hydrochloric acid solutions have been relied
upon.

Only when some standard of reference is agreed upon, can [H+]i,
of equation (1), be set at unity and the equation written:

E. M. F. X F _J_

2.3026 RT °g [H+j

E. M. F.

= pH (2a)

0.000,198,322 T

The principle which was assumed in the use of the conductivity
method may be described briefly as follows.

With a given potential gradient between two fixed electrodes,
the current carried by the ions in the solution should be a direct
function of the number of equivalents of ions and of the speeds of
their ionic migrations. If, independent of the dilution, each of
the several kinds of ions has its fixed migratory speed under the
given potential gradient, the current becomes a measure of the
number of equivalents of carrying ions. Suppose then that the
solution has been diluted until its solute, an ionogen acid, has
attained complete dissociation. Further dilution does not in-
crease the proportion of ions to total acid and the current, per
equivalent of acid, per unit volume, under the given conditions,
becomes constant. While complete dissociation was not sup-
posed to occur until infinite dilution was reached, we shall assume
that the means of extrapolating to this condition were adequate.
Then for a simple acid, of type HA, the ratio of equivalent
conductance at a given concentration, to the equivalent conduct-
ance at infinite dilution should give a, the degree of dissociation.

XXIII STANDARDIZATION 463

It is then a simple matter to calculate the hydrogen ion concen-
tration.

We have already noted that attempts to apply this idea of
progressive ionization to strong acids in solution rested upon a
misconception of the nature of strong acids. But in addition
there is the view, outlined in Chapter XXV, that, although ions
in solution may be regarded as free and separate entities in the
sense that they have departed from fixed combinations in their
ionogens, they are still subject to an interionic force. On dilu-
tion the effect of this becomes less. Under the stress of an elec-
tric field the ion groups become distorted and the fields between
them and the solvent molecules change from point to point of the
migration. The energy involved varies with the density of the
ion atmosphere (i.e., with dilution) and enters the formulation
of conductance in a complicated manner. It appears as if the
ions of a given kind have migratory speeds which vary with the
composition (e.g., dilution) of the solution. Therefore, one of
the important postulates of the classical theory fails. Jahn
(1900) and Lewis (1912) long ago noted the discrepancies and ex-
pressed them as the failure of the postulate of constant migratory
speed. For a discussion of the matter in terms of Debye's
treatment see Debye (1927) and Onsager (1927) (see references
under Faraday Society).

The remodeling of the theory of conduction in solution has left
open to serious doubt the older values for hydrogen ion concen-
trations in specific solutions.

But let us suppose that adequate methods are available for
determining the hydrogen ion concentration of some solution to
be used as a standard for hydrogen electrode comparisons. Is
the problem solved? It is not. It will be recalled that the
potentiometric method, employed in the use of the hydrogen
electrode, measures the free energy of transport of hydrogen ions
between two solutions. There is no simple, general relation be-
tween this free energy change and the corresponding change in
concentration. As explained in Chapter XI, solutions of differ-
ent composition have different constraints upon the ease with
which hydrogen ions may be removed. This necessitates the
inclusion of a correction term specific for each member of a pair
of solutions when the energy equation for a "concentration" cell
is formulated in the classical manner.

464 THE DETERMINATION OF HYDROGEN IONS

The more extensive and accurate data which bear upon our
subject are those obtained with solutions of hydrochloric acid.
But both experiment and the Debye-Hiickel equation show that
the correction cannot be eliminated in the range of concentration
of hydrochloric acid solutions within which it is practicable to op-
erate. In other words it is impossible in the first instance to
calculate a definite electrode potential by reference alone to a
unit concentration of HCL We have to console ourselves with
the remembrance that the correction disappears only at infinite
dilution. The problem then is to establish a substantial basic
datum with that somewhat unsubstantial hydrochloric acid solu-
tion of zero concentration ! Obviously the only way this can be
done is to extrapolate some function to the condition of zero
concentration. How this is done and what function is used will
appear presently.

By way of illustration one of many routes will now be followed
to specifications which could serve in the standardization of pH
measurements.

Consider the cell:

- Pt, H2 1 HC1, AgCl | Ag +,

namely a hydrogen electrode and a silver-silver chloride electrode
both in contact with the same solution of hydrochloric acid. Since
no appreciable liquid-junction potential is concerned and since
the silver-silver chloride electrode is probably better than the
calomel electrode for use with the hydrogen electrode in acid
solution, there is a distinct advantage in considering this cell first.
At the hydrogen electrode the single potential difference may be
formulated by equation (3) where a constant, E'H, is included
because no standard of potential-difference has yet been defined.

VH (3)

VH is a variable correction introduced to allow for the failure of
the classical equation.

At the silver electrode the potential difference may be formu-
lated in its lowest terms by:

•'

Cl-l-VA. (4)

XXIII STANDARDIZATION 465

Here again a variable correction, VAg, is introduced to allow for
the failure of the classical equation which is based on the ideal
gas laws.

At unit hydrogen pressure, when P = 1, we have for the cell
as a whole (silver positive to platinum):

EA. - EH = Ei, - EH - ~ In [H+] [C1-] - VAe - VH (5)

In accord with a rather widely accepted conclusion we shall
now assume that hydrochloric acid is completely dissociated
within the range of concentration to be considered. Then

[H+] [C1-] - [HClp

where [HC1] represents simply the analytical concentration of
hydrochloric acid without specification of its state.

Introducing this assumption and using the numerical form of
the equation for 25°C., we have

EAg - EH = E'AS - E'H - 0.11824 log [HC1] - VAe - VH (6)
or
- EH = E'Ag - E'H - 0.05912 log [H+] - 0.05912 log [Cl] - VAg - VH (6a)

In figure 82 experimental values for EAg — EH, as assembled by
Scatchard (1925), are charted as the curve labeled A. To
harmonize with a subsequent figure, the abscissa is made the
square root of the molality of the hydrochloric acid solution.

If the classical equations were followed VAg and VH of equation
(6a) would each be zero. Then, if complete dissociation of hydro-
chloric acid were assumed, the values of [H+] and [Cl~] could be
calculated from the known molality of the hydrochloric acid
solution. Then, since EAg — EH has been determined in each
instance, the equation can be solved for E'Ag — E'H. This con-
stant value should determine the level of a line such as that shown
in figure 82 at 0.2226 volts. Line B. It is evident that E'Ag - E'H,
when so calculated ^y neglect of VAg and VH, furnishes data which
do not conform to this reference line at 0.2226.

Since the corrections disappear at infinite dilution, a curve
drawn through the blackened cycles should meet the desired

466

THE DETERMINATION OF HYDROGEN IONS

base line at M = 0. The problem is thus resolved into the diffi-
cult task of extrapolating this to M = 0 or V£ = 0.

To this problem we shall revert presently. For the moment
assume that the extrapolation has been carried out correctly and
that the intersection has been found to be at 0.2226 volt. This is
value of E'AE — E'H in equation (6). Now introduce the defini-

.2226
.2

1COT .1

FIG. 82. CURVE A: ELECTROMOTIVE FORCE E AT VARIOUS VALUES OF

VM FOR THE CELL

Ft, H2 (1 atmos.) | HC1 (X), AgCJ | Ag
V/* = Vmolality of HC1. Curve B: EAS' - EH'.

tion of the normal hydrogen electrode given on page 257; but,
for the convenience of the present purpose, recast the definition
to the following. The normal hydrogen electrode shall have a
single potential difference of zero when the hydrogen pressure is
one atmosphere and the concentration of hydrogen ions is such
that

In [H+] + VH = 0

XXIII

STANDARDIZATION

467

As a result of this definition it will be seen from equation (3)
that E'H is zero by definition. Consequently the value of E'Ag
— E'H in (6) is the value of E'Ag, namely the constant of the silver-
silver chloride electrode, referred to the defined hydrogen stand-
ard of potential.

Now let us return to the extrapolation of the curve through the
points shown in figure 82 by blackened circles. For this purpose
the curve will have to be made on larger scale. See figure 83.
Extrapolations to M = 0 have been made with the aid of em-
pirical curve-fitting or empirical equations. Thus Linhart (1917),

.236

.234

£32

.228
.226

.22il^

j ^
v/r

FIG. 83. CORRECTIONS AT VARIOUS VALUES OF Vi« FOR THE CONSTANT OF

THE CELL

-Ft, H2 (1 atmos) | HC1, AgCl \ Ag+

whose admirable data are those falling closest to M = 0, ex-
trapolated to 0.2234. Scatchard (1925), however, gives to Lin-
hart's last point more weight than Linhart allows. He also uses
as guides to his own extrapolation the Debye-Hiickel equa-
tion1 both in its simplest reduced form to give the tangent shown,
and, in a more extended form, to pick up the departure from this
tangent at the points for the higher concentrations. By these

Chapter XXV.

468 THE DETERMINATION OF HYDROGEN IONS

means Scatchard finds the intersection with the ordinate M = 0,
to be at 0.2226 volt.2

For present purposes we shall use Scatchard's -value 0.2226
volt for the electromotive force of the cell :

Pt, H2 1 HC1, AgCl | Ag

which would obtain were [HC1] = 1 and were there no correction
terms. In other words it is the electromotive force when the
activity is unity, i.e., (HC1) = I.3

Returning now to the experimental data for the real cell with
0.1 M HC1, we might assume that the correction, ( — VAK — VH) =
0.0114 (see fig. 83) could be equally divided between VAK and VH.
This would be equivalent to assuming the activity coefficients of
the hydrion and chloride ion to be equal to one another. On this
basis we obtain

0.2226 + 0.05912 + 0.00570 = -f 0.2874
for the silver chloride half-cell with 0.1 M HC1 and
0 - 0.05912 - 0.00570 = -0.06484

for the hydrogen half-cell with 0.1M HC1. Although the above
assumption will later be rejected, we might use the value —0.0648
for the hydrogen half-cell with 0.1 M HC1 and consider this our
standard. However, if we were to join this half-cell with other
miscellaneous half-cells, we would encounter the difficulty of
varying liquid junction potential. As explained in Chapter XIII
the magnitude of the liquid junction potential is greatly reduced
when one side is a saturated solution of potassium chloride. For
this reason it is usual, in miscellaneous measurements, to form a
cell in which saturated KC1 solution forms a bridge. Were the

2 LaMer (1927) has criticized Scatchard's employment of the Debye-
Hiickel equation in this extrapolation. However, it will presently be-
come clear that there is no occasion for our attempting here to resolve this
difference of opinion or to enter a detailed discussion of the comparison
between Scatchard's data and those of Nonhebel and of Randall and
Vanselow to which LaMer refers. There has just come to hand Randall
and Young's paper in which the value is lowered to 0.2221.

3 The reader is again reminded that () is used to indicate activity while
[] is used to indicate concentration.

4 This corresponds to pH = 1.096.

XXIII STANDARDIZATION 469

calomel half-cell with saturated KC1 considered by all to be a
safe, permanent standard of reproducible qualities, we might
consider alone* the comparisons of this half-cell with the hydrogen
half-cell discussed above. It is preferable to seek the value of the
more reproducible "tenth normal" calomel half-cell. Scatchard
proceeds as follows.
He used the arrangement

Hg | HgCl, KC1 (sat.) $HC1 (X), AgCl | Ag
A

and varied X. A flowing junction was used at A. The equation
may be written:

Eoba = E'0 - E'Ag - 0.05912 log [Q-] - VAg - VL. (7)

where E'c is the constant potential at the mercury, E'Ag is the
constant, 0.2226 volt (see above), characteristic of the silver-
silver chloride electrode discussed previously, VAg is the correc-
tion for the silver-silver chloride electrode and VL is the variable
potential at junction A.

The data can be treated graphically in a manner quite com-
parable with that used in the former case. Scatchard made the
extrapolation with the aid of the simplified Debye-Htickel equa-
tion. However, in the present instance there is a rather delicate
point to watch. If the extrapolation were made purely em-
pirically there might be obtained the value of E'c — E'Ag + VL.
Here VL is included since the loci of the points are certainly deter-
mined by VL in part and its value might well be changing. In-
herent in such an extrapolation would be the conclusion that the
part contributed to the value of E'c — E'Ag + VL by VL at
the limit would then be the potential of the junction saturated
KC1 \ Water. However, if, within the range of the last points
nearest the tangent drawn by means of the Debye-Hiickel relation,
the liquid-junction potential does not vary much, the fact that the
Debye-Hiickel relation was used and that this has nothing to do
with liquid junctions, would lead to the conclusion that the con-
tribution of VL is as if it were of the liquid junction potential of
saturated KCl^HCl in the lower experimental ranges of [HC1].
Apparently this is Scatchard's interpretation. He finds E'0 —
E'Ag = 0.0228 volt. E'Ag, as noted, is 0.2226. Hence E'c + VL

470

THE DETERMINATION OF HYDROGEN IONS

= 0.2454 volt. This is the potential at Scatchard's saturated
KC1 calomel electrode including a liquid junction potential as if
against 0.1 (or less) M HC1 and made with flowing junction.

Instead of attempting to go to the decinormal calomel half-cell
by direct comparison, Scatchard takes a route summarized as
follows with the aid of figure 84.

We have already discussed the cell composed of the half-cells
(3) and (8) of figure 84 (potential x). We have noted how a
study of cells of this type may be made to yield the value of

.3373--.- HdlHdCf.KO (O.IMH (I)

.. !.. -. ....

Pt, H,| H+Mctiwty/) (0)

1___L_L pttHt | HCI (0.1 M)

(8)

FIG. 84

Note: First steps do not require activity of Cl- but of HCI

half-cell (7) with potential (a) standardized with reference to
half-cell (0) the potential at which is defined as zero. In a
comparable way the cell composed of half-cells (2) and (8)
(potential y) and of variations of this cell with different con-
centrations of HCI are made to yield the value of half-cell (5)
(potential b). For this purpose Scatchard uses the data of others
for4"cell (2)-(8) and applies his own value for the correction term
that yields the value of (5).

XXIII STANDARDIZATION 471

Next cell (6)-(8) with potential z, was treated as outlined above
to reach the standardized value of (6), potential c. Experi-
mental cell (6)-(8) possesses a junction potential, namely that of
KC1 (sat.)jHCl (0.1 M), which will be called VLI. In reach-
ing a value for half-cell (4) by observation of potential d this
junction potential, VLI, is carried along in the standardization.
Also the potential of the new junction KC1 (sat.)fKCl (0.1 M)
is introduced experimentally.

The difference between b and a, that is the difference of poten-
tential between the calomel and the silver chloride electrodes in a
solution of the same chloride ion activity, is e. This same dif-
ference should apply to the cell (l)-(4). Thus the value 0.3373
for the calomel electrode with 0.1 molal KC1 is reached. A
correction for change from 0.1 molal to 0.1 normal brings the
value to 0.3372 for the decinormal calomel electrode. There
has been carried along, in the standardization, the potential of
the customary junction KC1 (sat.)jKCl (0.1 N), which should
be included for practical purposes, and also a junction potential
as of KC1 (sat.)iHCl (0.1 M, or less).

If the value for the tenth normal calomel half-cell is to be ob-
tained without those liquid-junction potentials which were car-
ried along in the above calculations, we may take a new start
with half-cell 5 (fig. 84). Introduce the estimated activity of
chloride ions in 0.1 M KCl-solution. Scatchard uses 0.0762 for
this activity. Whence 0.3353 is the estimated potential of the
decinormal cell without liquid-junction.

In summary we have :

HC1 \ KC1 (sat.), HgCl | Hg ; Eh = +0.2454 at 25°

|| KC1 (0.1 M), HgCl | Hg ; Eh = +0.3353 at 25°

HCljKCl (sat.) | KC1 (0.1 N),HgCl | Hg ;Eh = +0.3372 at 25°

Now let us return to the problem mentioned on page 468 namely
the partition of the correction between the silver chloride and
hydrogen half-cells. It is a bold assumption, and one which is
not in good repute, to make the even partition there used. Scat-
chard employs his measurements with the cell

Hg | HgCl, KC1 (sat.) $HC1, AgCl | Ag
A

472

THE DETERMINATION OF HYDROGEN IONS

He employs the aforementioned assumptions regarding liquid
junction potentials and the Debye-Hiickel equation for extra-
polation to zero concentration of HCL Thereby he is able to
calculate the corrections for the chloride half-cell at the several
concentrations of hydrochloric acid. Having already obtained
the sum of th§ corrections for the chloride and hydrogen half-cell,
he obtains the corrections for the hydrogen half-cell.

Using activity coefficients in place of potential corrections and
the relation

THCI =

X TCI"

Scatchard finds, for instance in the case of 0.1 M HC1:
7ci =0.762; TH+ = 0.841 and V7H~ x 7cT = THCI = 0.801.

We have rounded off the value of 7H+ to 0.84 and employ this
to calculate the pH values of HC1:KC1 solutions given on page 201.
We also employ it to obtain those calculated potentials of the
hydrogen half-cell with 0.1 N HC1 which are given in table A,
page 672.

TABLE 61

Some values assigned to calomel half-cells at %5°C.

Parenthesized values are calculated from unparenthesized values.
Bracketed values are calculated from measurements at other tempera-
tures.

HALF

-CELL

AUTHORITY

|| KC1 (0.1M),

HgCl | Hg

II KC1 (0.1M) 1
KC1 (l.OM), HgCl|
Hg

Beattie (1920)

(0 3353)

0 2826

Lewis and Randall (1921)

0 3351

(0 2822)

S0rensen and Linderstr0m-Lang (1924) . . .
Scatchard (1925)

[0.3354]
0.3353

(0.2825)
(0.2826)

Average. . . .

0 3353*

* There has just come to hand Randall and Young's paper in which they
give 0.3341 for the potential of the half-cell in vacuum but state that the
value of the half-cell in air will be about 0.3354 by reason of an error of
one to three millivolts caused by the presence of air.

It seems hardly necessary to outline other routes. That men-
tioned shows not only the nature of the argument but two aspects

XXIII STANDARDIZATION 473

of special interest to the purpose of this chapter. In the first
place it is evident that methods of reaching standard values are
becoming more rationalized. In the second place there remain a
number of small discrepancies and fundamental difficulties
(especially with liquid-junction potentials) sufficient to cause
appreciable variation in the values used by different authors in
arriving at the value of any specified half-cell. The latter fact is
obscured by the uncritical comparison in table 61. The apparent
agreement obtains because of a remarkable cancellation of small
differences. But even if it be granted that the average in table
61 is final, its acceptance settles only part of our problem. Con-
sider the cell :

Pt, H2 (1 atmos.) | solution X | KC1 (sat.) | KC1 (0.1 N), HgCl | Hg
ABC D

As solution X is changed there is not only a change of potential
difference at A, but there is also a change of liquid junction poten-
tial at B. Knowledge of the potential of C + D and a measure-
ment of the whole cell is, therefore, not sufficient to give the
potential at A. Strictly, each change of solution X will produce
a change of potential at B. Since there is no universal rule by
which the potential at B can be calculated in each and every
case, it is necessary in practice to introduce an assumption. Two
assumptions have been the more customary. One is that the
junction potential at B shall be neglected. The other is that it
shall be estimated by the Bjerrum extrapolation (see page 277),
using 3.5 M and 1.75 M KC1 in place of saturated KC1 solution
as bridge.

The latter assumption was used by S0rensen (1909) in deriving
the value of the "tenth normal calomel electrode" from measure-
ments of the cell

3.5N
Pt, H2 (1 atmos.)! HC1 (0.1N) | KC1 or | KC1 (0.1N), HgCl | Hg

1.75N

It has usually been assumed that because S0rensen used con-
ductivity data to obtain the hydrion concentration of 0.1 N HC1
and thence calculated 0.3380 (18°) for the potential of the "tenth
normal calomel half-cell" that this value must necessarily be

474 THE DETERMINATION OF HYDROGEN IONS

erroneous. As a matter of fact the Bjerrum extrapolation5
which he used was large (74 mv.) and it appears that, by chance,
he obtained a value which can still be justified. If we compare
the S0rensen value at 25° (see page 453) with Scatchard's es-
timate for the half-cell,

HC1 $ KC1 (sat.)

KC1 (0.1 N), HgCl

B C D

we have:

0.3376 (S0rensen)
0.3372 (Scatchard)

According to Scatchard's estimate the potential at C is 0.0027
volt with the orientation shown above and, at B, 0.0047 with
the orientation shown when the solution in the hydrogen half-
cell is 0.1 M HC1. (Earned (1926) calculated 0.0016.)

Since the S0rensen value, for the so called "0.1 N calomel electrode" is
now frequently used as if of the above half-cell and happens to be so near
to a significant value under particular circumstances, it may be con-
sidered. It is especially important to consider the Sprensen value because
it has been used extensively in the standardization of buffer solutions,
ionization constants and a host of miscellaneous data. The value was in
substantial agreement with that recommended by Auerbach (1912) and
adopted by the "Potential Commission," whence arose substantial agree-
ment with other types of investigation. It would be quite impracticable
to cite all of even the types of data that conform substantially to the basis
established by S0rensen. Much of it is data of high accuracy and com-
plexity. See, for example, the researches on blood and the involved car-
bonate equilibria.

6 S0rensen's average value for the cell

Pt, H2 | HC1 (0.1 N) | KC1 (3.5 N) | KC1 (0.1 N), HgCl [ Hg

was 0.4025 volt. His use of the Bjerrum extrapolation reduced this to
0.3975 volt. If we neglect the extrapolation and use 0.3380 volt for the
potential of the tenth normal calomel half-cell, we obtain

0 4025 0 3380

- = 1.12, as the pH number of 0.1 N HC1 at 18°C. in

place of S0rensen's assumed value 1.04; but this calculation is made with
the use of a potential obtained with 3.5 N KC1 solution, instead of
saturated KCl_solution, as bridge.

XXIII STANDARDIZATION 475

For purposes of discussion we shall use the S0rensen value 0.3376 (25°)
for the half-cell

HC1 | KC1 (sat.) | KC1 (0.1 N), HgCl | Hg
and 0.3353 (25°) for the half-cell

||KC1 (0.1 N), HgCl | Hg

Since there are only a few who retain confidence in the Bjerrum extra-
polation we shall neglect it and shall continue with the assumption that
saturated KC1 solution is to be used. In discussing the cell

Ft, H2 (1 atmos.) | solution X | KC1 (sat.) | KC1 (0.1 M), HgCl | Hg

B C

the junction potential at B is to be neglected in calculations.

Undoubtedly when solution X is a phosphate solution this junction
potential is much less than when solution X is a dilute hydrochloric acid
solution. How much less, there is no certain way of telling. As an ex-
treme we can consider it to compensate that at G. If so the value
0.3353 should be used for the "calomel half-cell" instead of the customary
0.3376. But if, on the dangerous assumption made above, we adopted
0.3353 for universal use, we would certainly be in error when operating with
very acid solutions.

Attempts to proceed with the adoption of any fixed single value for a
half -cell involving a liquid junction, the potential of which is susceptible
to appreciable change as the solution under study is changed, is, of course,
not strictly logical; but we are now considering arbitrary assumptions
necessary to ordinary operation. In the study of phosphate buffers will
the use of 0.3376 in place of 0.3353 be serious? So far as pH numbers are
concerned

0.3376 - 0.3353

= 0.0389^0.04

0.05912

gives the correction that should be added to a pH number at 25° were
0.3353 used in place of 0.3376.

But such an error is of no practical consequence in the comparison of
acid-salt systems in which the acid is very weak. When [H+] is of the
order of 10~5 or less it may be neglected in calculating the undissociated
residue from [HA] — [H+] = [A], except at impracticably high dilutions.
As discussed in Chapter XXVII any standard of reference will do and our
chief concern is then with agreement upon the standard selected.

A more or less uncertain but reasonable compromise may be made by
allowing the error for the extreme case of the phosphate buffer where the
error is of no practical importance and adopting 0.3376 which leads to
substantially reasonable values in very acid solutions where [H+] is of
importance not only as an index but of itself.

476 THE DETERMINATION OF HYDROGEN IONS

Possibly a sliding scale of values could be devised but in the present
state of affairs this would be dangerous.

The adoption of a fixed value, which is roughly adapted to the more
acid solutions and which allows an error for the extreme case where the
error is of no practical importance, will doubtless lead to appreciable error
in the study of intermediate cases.

Cohn, Heyroth and Menkin (1928) believe they detect this in their treat-
ment of acid, acetate solutions, a discrepancy in the drift of — log 7 being
removed by the employment of 0.3357 instead of 0.3380 for measurements
at 18°. They also note that, if electromotive force measurements are to
be brought into harmony with recent corrected conductivity measurements
of the dissociation constant of acetic acid, the value of the half-cell

|| KC1 (sat.) | KC1 (0.1 N), HgCl | Hg

with neglect of liquid junction potential "should be between 0.3364 and
0.3370."

To what extent such adjustments will have to be made as the case is
changed is a question on which I shall not even venture an opinion; but
that, strictly, each individual case is a new case, in which allowance for a
different junction potential must be made, can hardly be gainsaid, es-
pecially when the cases are those in which [H+] is high.

The use of a stated pH value for 0.1 N HC1 and the use of the cell

Pt, H2 (1 atmos.)

HC1
0.1 N

KC1 (sat.), HgCl

in standardizing the saturated calomel half-cell has the appearance of
being direct, simple and clear. However, it is not always certain that
liquid junctions are established in a uniform manner by different workers
and, as emphasized by Clark and Lubs (1916), the variability of potential
at the junction HC1 | KC1 (sat.) with different methods of forming the
junction makes the use of HC1 dangerous for routine standardization
purposes.

To illustrate the variation of present practice there may be cited a few
of many bases of standardization.

Cullen, Keeler and Robinson (1925), Hastings and Sendroy (1924) and a
group of American students of blood equilibria have been using pH 1.08
for 0.1 N HC1 as a standardizing value with which to establish the value of
a "working," saturated calomel half -cell. Neglecting liquid junction
potentials, they obtain, for M/15 phosphate buffers, pH values about 0.01
unit pH greater than S0rensen's values. Hence pH 1.09, as used by Simms
(1926), would leave another 0.02 pH unit to be added were the 0.04
correction mentioned above to be followed. Levene, Simms and Bass
(1926) use 1.075 for 0.1 M HC1.

S0rensen and Linderstr0m-Lang (1924) in no. 10 of their recommenda-

XXIII

STANDARDIZATION

477

tions advocate the use of 0.4556 volts as the extrapolated (Bjerrum) value
of the following cell (presumably at 18°) :

Pt, H2 (1 atmos.)

0.01 N HC1

0.09 N KC1

3.5 N KC1

and
1.5 N KC1

KC1 (0.1 N), HgCl | Hg

If we tentatively assume that this is also the potential of the cell

Pt, H2 (1 atmos. )

0.01 N HC1
0.09 N KC1

KC1 (sat.) | KC1 (0.1 N) HgCl | Hg

and assume 0.3380 for the half-cell

KC1 (sat.) | KC1 (0.1 N), HgCl | Hg

we obtain pH = 2.037. This is substantially the number, 2.04 suggested
by Cullen, Keeler and Robinson (1925) for use with sat. KC1 and neglect
of liquid junction, and 2.038 by Kolthoff and Tekelenburg (1927) for use
with the Bjerrum extrapolation. Biilmann (1927) accepts 2.029 on the basis
of a personal communication from Bjerrum, and uses it with the Bjerrum
extrapolation in his discussion of the quinhy drone electrode.

Other values for 0.01 N HC1 + 0.09 N KC1 are included in the following
list of contrasts.

2.029 Biilmann (1927)

2.038 Kolthoff and Tekelenberg (1927)

2.063 Gjaldbaek (1925)

2.078 Table 35a, page 201

2.093 Larsson (1922)

S0rensen and Linderstr0m-Lang (1927) have recently abandoned the
0.3380 value for the "tenth normal" calomel half -cell and are using 0.3357
(18°) as a basis, with intervening solution of saturated KC1 and neglect
of liquid junction. Their former (1924) general recommendations permit
the Bjerrum extrapolation and their specification no. 10 provides for it
in "specially accurate measurements."

Many other cases could be cited to show appreciable differences in
standards.

American practice has tended toward the use of saturated potassium
chloride solution as a bridge or the use of the saturated KCl-calomel half-
cell as a working standard and the stated tentative assumption that the
liquid junction potential shall be neglected. Many European workers
still operate with the old method of extrapolation introduced by Bjerrum
and with the 3.5 N KC1 calomel half-cell. Although S0rensen and Linder-
str0m-Lang state that the two methods give practically the same result in
ordinary buffers, it is by no means certain that the two methods will lead
to the same set of values when hydrochloric acid solutions of one kind or
another are used as ultimate standards. Direct comparison of the results

478 THE DETERMINATION OF HYDROGEN IONS

of the two kinds of practice is beset with danger when the practical stand-
ard of reference is a hydrochloric acid solution.

In the absence of any thoroughly developed fundamental basis we may
well expect in the near future as many slight but distinct differences in
methods of standardization as have appeared in the recent past. Indeed
it may be questioned whether any recommendation is worth while. A
decision would not permit a recalculation of all important data, because
these data in very many instances have been published without the detail
necessary to that purpose. A decision might have no weight unless it
either formulate custom or presage the value of the final standard. Custom
is now less easily formulated than when the second edition was written
and, insofar as we may judge by past experience in this matter, the accept-
ance of the " latest value" is a dangerous procedure. However, it is quite
impracticable to review all the various standards in detail and some
decision must be made for the purposes of this book. I dislike to be
merely conservative but am constrained to adhere to the principle stated
in the second edition, where it was said: " .... it will be wise during
the present period of transition to adopt a provisional standard and in
lieu of agreement reached in convention to let that standard be in har-
mony with that tacitly implied in the greater body of data." In one
respect the future can be safely predicted. The Bjerrum extrapolation
will be abandoned as contributing nothing definite. If so the saturated
KC1 calomel half-cell will doubtless become the "working standard" and
the 3.5 N KC1 calomel half -cell will -become an "extra" in the scheme.
However, while there remains doubt concerning the reproducibility of the
saturated KC1 calomel half-cell (a doubt which may not be well founded)
either the redefined tenth normal calomel half-cell, oi the hydrogen half-
cell with 0.1 N HC1, will be preferred as the ultimate, practical standard.
Of these two half-cells the last has a dangerously high liquid junction
potential at the junction HC1 | KC1 (sat.). Undoubtedly the individual
operator will be able to reproduce his data; but the practice has shown
such a variety in the manner of forming the liquid junction that the
specification of this half-cell would have to involve very careful specifica-
tion of the manner of forming the liquid junction. Therefore the first
half-cell is, for the present, to be preferred.

As already noted, it is impracticable to attempt correction of all6 im-
portant data to strict conformity with the specifications to follow and
a certain speciousness results if it be thought that these specifications
lead to strict harmony between measurements made accordingly and the

6 The data for the buffer mixtures of Clark and Lubs (1916) [see page 200]
were obtained with the use of a saturated KCl-calomel half-cell which was
standardized against a group of tenth normal KC1 calomel half-cells.
There were also used Bjerrum extrapolations which were very large in
the case of the HC1-KC1 mixtures. To conform to the specifications of
this chapter the original data have been used in recalculations which are
embodied in table 35, page 200.

XXIII STANDARDIZATION 479

measurements of the past which were "based on the S0rensen value for
the tenth normal calomel half-cell." Nevertheless the agreement should
be substantial. That is the best that can be made of the situation.

That a considerable part of the discrepancies appearing in the literature
is due to disagreement of primary experimental data rather than to the
selection of different bases of reference appears in the footnote to table A,
page 672. In that footnote are a few data which, for the most part, rep-
resent direct measurements. They are compared with the numbers
derived from the table. In some instances, such as Walpole's use of a
seasoned, saturated, calomel half-cell, and the author's measurement of
cell III: VI, the experiments cited are of intermediate measurements and
as such are not fundamental. In other instances a careful scrutiny of
conditions might reveal reasons for rejecting one or another of the numbers
given. However, a comparison of numerous other data, which are less
easily compared and tabulated, supports the impression made by this set
of comparisons. The problem appears to be quite as much one of technique
as of formulation. For this reason recurring shifts of standard and the
absence of data revealing the reproducibility of measurements, both of
which characterize a considerable part of the modern literature, have made
the second decimal of pH numbers as uncertain as they were in a less so-
phisticated period.

The following specifications are substantially those recom-
mended in the second edition, accepted by S0rensen and Linder-
str0m-Lang and then, by a curious fate,7 abandoned by the latter.

7 Originally pH was denned by pH = log Actually, the numerical

values called pH have been determined by dividing the potential of a

O QftO f\ ~R T

hydrogen cell by J .. In the comparison of one solution with a

standard solution of hydrion activity of unity, the rigid relation may be
written

1 -EF

°g (H+) " 2.3026 RT

where (H+) represents the hydrogen ion activity of the solution under
investigation. Consequently the measured values called pH are log

and not, as defined, log p^~pj*

Recognizing this Sprensen and Linderstr0m-Lang (1924) proposed that
pH retain its original defined meaning and that a new symbol pafl be

used for log •— •

480 THE DETERMINATION OF HYDROGEN IONS

1. The following half-cell shall be used as a standard of reference

KC1 (saturated) | KC1 (0.1 N), HgCl(s) | Hg

2. It shall be assumed, arbitrarily, that in the cell

Pt, H2 (1 atmos.) | H+ (activity, X) | KC1 (sat.) | KC1 (0.1N), HgCl(s) 1
ABC D

the potential difference at B remains constant as X varies and
that the sum of the potential differences at B, C and D is as
follows "at each indicated temperature.

Temper-
ature,
°C 18° 20° 25° 30° 35° 38° 40°

Potential
Differ-
ence... 0 . 3380 0 . 3379 0 . 3376 0 . 3371 0 . 3365 0 . 3361 0 . 3358

3. The standard experimental meaning of pH shall be the
potential of the above cell considered as of positive numerical

This proposal is in itself quite consistent and elegant. It provides con-
sistent symbols to be used whenever there is occasion to abbreviate log

— — and log — — in the writing of equations.

But Sprensen and Linderstr0m-Lang went beyond questions of defini-
tion and coupled their symbols with two proposed values of the 0.1 N
calomel half-cell. One, e.g., 0.3380 at 18°, was to be used in estimating
values of pH, and the other, 0.3357, was to be used in calculating values
of paH. Such coupling of the proposals is a source of confusion. Spren-
sen and Linderstrpm-Lang should have warned their readers that there is
no constant difference between hydrogen ion concentration and hydrogen
ion activity as implied on page 37 of their article. They appeared to be in
agreement with the proposals of the second edition of this book but ig-
nored its proposal of an experimental meaning for a pH number.

In their later articles (see, for instance, Sprensen and Linderstr0m-Lang
(1927)) they use 0.3357 instead of the older value, 0.3380, for the "0.1 N
calomel half-cell."

In this book pan is not used. It must be assumed that the reader appre-
ciates the qualifications stated or implied in the use of the laws of an
ideal solution. These idealized relations are useful within limits to outline
the subject. Then "pH" can retain its original meaning. With regard
to meticulous uses the following may be said. Any numerical value
given to (H+) implies customary usage. Unless liquid junction potentials
are accurately estimated when the potential of the customary cell is used

XXIII STANDARDIZATION 481

value, less the above value for the calomel half-cell pertaining to
the temperature used, the difference being divided by the nu-
merical quantity 0.000,198,322 T, where T is the absolute tem-
perature.

4. When a value of pH is modified by attempts to correct for
the potentials at B and C, or by the use of some estimated value
of the potential at D alone, or by any other modification of the
above procedure, a statement of all essential modifications shall
be made.

5. If there be used any secondary standard, such as the poten-

to calculate log , it is not strictly proper to name the calculated

value log , or pan- However, it is legitimate to proceed with the

recognition that the measurement is of an energy relation which if it
could be carefully analyzed would give a measure of activity, and to
assume for purposes of approximation that numbers called "pH" can be

used where log would occur in the energy equation. That the ideal

equation in terms of concentrations could not be applied strictly has long
been recognized, although not emphasized in the past. The modern
developments have served to make the emphasis strong but have created
no essentially new situation. Since almost all of the values entering our
subject are based on the conduct of hydrogen cells they might be renamed
pag, were the uncertainties of liquid junction potentials adequately
taken care of. But, in the absence of %iality both in regard to liquid
junction potentials and the hydrion activity of any given standard solution,
it seems preferable to give an arbitrary but definite meaning to numbers
called pH.

That the introduction of pan may accomplish no good purpose appears
in such comparisons as the following. Hastings, Murray and Sendroy
(1927), in using pan, with stated assumptions in regard to the calculation
of numerical values, find occasion to note that their values differ from
similarly named values given by Sprensen and Linderstrpm-Lang. The
latter authors in the same year were using 0.3357 for the calomel half-
cell while Hastings, Murray and Sendroy were using as a basis of reference
pan = 1.08 for 0.1 N HC1. Both were neglecting the liquid junction
between saturated KC1 solution and the several solutions placed on the
other side of the junction. In the absence of finality in regard to several
of the questions concerned it is probable that each set of workers could
establish a reasonable justification for the usage they adopted. In that
case, and others of like nature, we have different meanings for paH so
far as its quantitative aspect is concerned.

482 THE DETERMINATION OF HYDROGEN IONS

tial, of a hydrogen electrode or of a quinhydrone electrode in a
standard buffer solution, the attempt shall be made to use this
standard in accordance with the specifications made above.

It may be emphasized that section 5 provides for the use of
any secondary standard if there is no desire to actually use the
tenth normal calomel half-cell; but that, if the other specifications
are adopted, the secondary standard should not be evaluated
de novo.

In case the above system is not accepted, it is recommended that
every assumption and every detail of the system adopted be
carefully stated. In particular it may be said that a statement
regarding the potential of a half-cell without statement of as-
sumptions regarding the liquid junctions used in actual cells is
misleading.

In the next chapter there will be stated secondary standards
which conform more or less closely to the above specifications.
Lest the values there stated appear too neglectful of values given
elsewhere in the literature let it be said here that the matter has
now come to such a pass that it would be impracticable to review
and reconcile all the schemes in use.

Experimental and theoretical difficulties with liquid junction
potentials are largely responsible for discrepancies in primary ex-
perimental data and for diversity of treatment. The cells with
which we are chiefly concerned are distinctly different from cells
without liquid junction. While the treatment of the latter has
been acquiring elegance, demands upon the practical application
of the former have left several matters undecided. Indeed it ap-
pears as if progress with cells having no liquid junction has
created the erroneous impression that our main problem is near-
ing complete solution. Yet, for the purpose at hand, there is
neither adequate knowledge of liquid junction potentials nor ade-
quate information upon the reproducibility and the temperature
coefficients of standard half-cells. Therefore that otherwise de-
testable practice of arbitrary standardization seems necessary for
the purposes of routine reports.

CHAPTER XXIV

STANDARD SOLUTIONS FOR THE ROUTINE CHECKING OF HYDROGEN
ELECTRODE MEASUREMENTS

Thou shall not have in thy bag divers weights, a great and a small.
Thou shalt not have in thy house divers measures, a great and a

small.
But thou shalt have a perfect and just weight, a perfect and just

measure shalt thou have. — Deuteronomy, XXV: 13-15.

In the routine measurement of hydrogen ion concentrations it
is desirable to frequently check the system. To do so in detail
is a matter of considerable trouble ; but if a measurement be taken
upon some solution of well defined pH, and it is found that the
potential of the cell agrees with that which someone has deter-
mined by careful and detailed measurements upon all parts, it
is reasonably certain that the several souices of E.M.F. are
correct.

Any one of the buffer mixtures whose pH value has been es-
tablished may be used for this purpose, but there are sometimes
good reasons for making a particular choice.

In view of the fact that different authors have recently been
selecting several reference values which do not agree, there is
need that each author state definitely the value selected and the
mode of its application. The following discussion concerns values
in substantial harmony with the recommendations of the pre-
vious chapter, — a restriction made necessary by the fact that
discussion of all standards would be impracticable.

STANDARD ACETATE

Michaelis (1914) recommends what has come to be known as
"standard acetate." This is a solution tenth molecular with
respect to both sodium acetate and acetic acid. Its preparation
and hydrogen electrode potential at 18°C. have been carefully

483

484 THE DETERMINATION OF HYDROGEN IONS

studied by Walpole (1914). Walpole proposes two methods for
its preparation:

(1) From N-sodium hydroxid solution free from carbon dioxid and
N-acetic acid adjusted by suitable titration (using phenolphthalein), so as
to be exactly equivalent to it.

(2) From N-sodium acetate and N-acetic acid adjusted by titration of
a baryta solution, the strength of which is known exactly in terms of the
N-hydrochloric acid solution used to standardize electrometrically the
normal solution of sodium acetate.

Walpole defines N-sodium acetate as a "solution of pure sodium
acetate of such concentration that when 20 cc. are taken, mixed
with 20 cc. of N-hydrochloric acid, and diluted to 100 cc., the
potential of a hydrogen electrode in equilibrium with it is the
same as that of a hydrogen electrode in equilibrium with a solu-
tion 0.2 normal with respect to both acetic acid and sodium
chloride." By mixing the N-acetate with the N-HC1 in accord-
ance with this definition and then determining the potential of a
hydrogen electrode in equilibrium with it, Walpole shows that the
N-sodium acetate solution may be accurately standardized. In
table 62 are given Walpole 's values showing the relation of the
E.M.F. of the chain:

- Pt, H2 1 Acetate | KC1 (sat.) | KC1 (0.1 M) Hg2Cl2 1 Hg +

at 18°, to the cubic centimeters of N-HC1 added to 20 cc. N-
sodium acetate and diluted to 100 cc. If, for instance, the poten-

x- i f j • n xo™ M ^ j.- Concentration of HC1 .

tial found is 0.4800 volts, the ratio is

Concentration of NaAc

20 2

— '— Hence the sodium acetate is 0.9901N.

20.0

TABLE 62

CUBIC CENTIMETERS OF N/l HC1 TO 20 CUBIC
CENTIMETERS N/l NaAc DILUTED
TO 100 CUBIC CENTIMETERS

E. M. F.

19.00

0.5270

19.40

0.5155

19.50

0.5125

19.90

0.4945

20.00

0.4898

20.39

0.4712

20.89

0.4549

21.00

0.4525

XXIV CHECK SOLUTIONS 485

These values are more convenient to use if plotted as Walpole
has done.

Walpole found the above cell with "standard acetate" at 18°C.
to be 0.6046. The contact potential still to be eliminated was
estimated by the Bjerrum extrapolation to be 0.0001 volt. This
is negligible.

The value 0.6046 seems to be the value of the chain corrected
to one atmosphere hydrogen plus vapor pressure.
M

ACID POTASSIUM PHTHALATE

It will be noted that both S0rensen's standard glycocoll (see
page 486) and the standard acetate solutions must be constructed
by adjustment of the ratio of the components. While there is
no great difficulty in this there remain the labor and the chance of
error that are involved. Clark and Lubs (1916) have shown
that acid potassium phthalate possesses a unique combination
of qualities desirable for the standard under discussion. The first
and second dissociation constants of phthalic acid are so close to
one another that the second hydrogen comes into play before the
first is completely neutralized (see fig. 5 page 28). As a con-
sequence the half-neutralized phthalic acid (KH Phthalate)
exhibits a good buffer action. The salt of this composition crystal-
lizes beautifully without water of crystallization, and, as was
shown by Dodge (1915) and confirmed by Hendrixson (1915) it
is an excellent substance for the standardization of alkali solutions.
As such it is used to standardize the alkali entering into the buffer
mixtures of Clark and Lubs (see page 197). The outstanding
feature is that the ratio of acid to base is fixed by the composi-
tion of the crystals and not by adjustment as in other standards.
The salt may be dried at 105CC. and a solution of accurate con-
centration constructed.

The original data of Clark and Lubs (1916) for the cell •

Pt, H2 (1 atmos.) | KH Phthalate (0.05 Molar) | KC1 (sat.)

B
| KC1 (0.1 N), HgCl | Hg

was 0.5689 volts at 20°C. Using 0.3379 for the half-cell to the
right of B and neglecting liquid junction potential at B, we ob-
tain pH = 3.974.

486

THE DETERMINATION OF HYDROGEN IONS

If we assume inappreciable change in this value between 18°
and 40° [see Kolthoff and Tekelenburg (1927)] we obtain the
following tentative values.

Half Cell I: Pt, H2 (1 atmos.)

KC1 (sat.)

Cell II:
Cell III:

Half cell I
Half cell I

KH Phthalate

0.05 M

KC1 (sat.) | KC1 (0.1 N), HgCl
KC1 (sat.), HgCl | Hg

TABLE 63

POTENTIAL IN VOLTS OF CELL OR HALF-CELL

TEMPERATURE

III

°c.

volts

volts (approx.)

-0.2292

0.5672

0.480

-0.2310

0.5689

0.481

-0.2347

0.5723

0.481

-0.2386

0.5757

0.481

-0.2426

0.5791

0.481

-0.2449

0.5810

0.481

-0.2465

0.5823

0.481

There have been objections to the use of phthalate solutions
as standards, based upon the reduction of phthalate at the hydro-
gen electrode. A discussion of this is found on page 437. See
also Kolthoff and Tekelenburg (1927).

OTHER STANDARD BUFFERS

Any one of the buffer mixtures having a well defined pH-value
may be used. There then is implied the acceptance of the
standard conditions under which the pH value was determined
in the first instance. S0rensen (1909), having established his
basis by the method indicated in the previous chapter, used that
mixture of eight volumes of his standard glycocoll to two volumes
of his standard hydrochloric acid which is described in Chapter IX.

HYDROCHLORIC ACID SOLUTIONS

S0rensen and Linderstr0m-Lang (1924), Cullen, Keeler and
Robinson (1925), Michaelis, Kolthoff and others advocate

xxrv

CHECK SOLUTIONS

487

0.01 N HC1 + 0.09 N KC1, or other mixtures of low acid con-
centration. See Michaelis and Kakinuma (1923), Michaelis and
Fujita (1923) and Michaelis and Mizutani (1924), Biilmann
(1927) and page 472. Michaelis and Kruger (1921) use 0.0025 N
HC1 + 0.0975 N KC1. Because of the difficulty of calculating
(H+) in such mixtures 0.1 N HC1 is preferred by some.

In the use of 0.1 M HC1 solution as a working standard
the inclination has been to make it the ultimate standard. How-
ever, attention has been called to the fact that the liquid junction
potential is a difficult matter to handle both experimentally and
theoretically. It is doubtful whether these standards are well
adapted to routine standardization.

With this caution we may call attention to the pH values
stated in table 35a, page 201, and to the corresponding hydrogen
electrode potentials given in table A, page 672.

For convenience we shall repeat here the arbitrarily assigned
values of the practical half -cell

| KC1 (sat.) | KC1 (0.1 N) HgCl | Hg
This is not the half-cell

||KCl(0.1N),HgCl|Hg

which is the true tenth normal calomel half-cell without liquid
junction.

TABLE 64
Arbitrary values of practical tenth normal calomel half-cell

POTENTIAL

0.3380

0.3365

0.3379

0.3361

0.3376

0.3358

0.3371

488 THE DETERMINATION OF HYDROGEN IONS

SATURATED KC1 CALOMEL HALF-CELL

As stated in Chapter XXII the temperature coefficient is un-
certain. The values given in Chapter XXII are as shown in
table 65.

TABLE 65

POTENTIAL

0.251

0.238

0.250

0.236

0.2458

0.234

0.242

QUINHYDRONE HALF-CELLS

See Chapter XIX.

CAUTION

The investigator who has been following a particular system
of standardization may find in table A, page 672, one or another
value which he is prepared to dispute. The author's own data
for the "saturated calomel half-cell" at 30°C. is appreciably
higher than that given in the table. Attention has been called
to the unsatisfactory temperature coefficient in this case. See
page 455. At several points in this book attention is being called
to several matters which need investigation. Emphasis of this
aspect seems wiser than partiality in the selection of values. The
emphasis seems particularly important at the present time be-
cause in some instances the elegancies of formulation have ob-
scured discrepancies in experimental data.

In addition the assumption on which table A is based introduces
a source of discrepancy.

CHAPTER XXV

THE THEORY OF DEBYE AND HUCKEL

I am not satisfied with the view so often expressed that the sole aim
of scientific theory is "economy of thought" I cannot reject
the hope that theory is by slow stages leading us nearer to the truth
of things. — A. S. EDDINGTON.

INTRODUCTION

The chemist who is untrained in the methods of mathematical
physics will regard the papers of Debye and Huckel as of "f rightful
mien;" but he is becoming familiar with the simple, final equations
as they occur with ever increasing frequency in current journal
articles, and as they are applied to a wide variety of important
problems. The theory attains its momentum at the time our
respected and beloved Arrhenius passes from the world. It will
doubtless come to be regarded as the greatest of the justifications
of Arrhenius' brilliant theory. This is not alone because it deals
vigorously with those anomalies which have constituted the weak
point in the theory of electrolytes; it is largely because Debye
and Huckel, going in the direction indicated by Milner, have es-
tablished connection between the more purely thermodynamic
trend of the recent period and statistical mechanics. This
achievement, and the fact that it is stimulating new types of in-
vestigation, mark the beginning of a new period in the develop-
ment of Arrhenius' theory. The achievement is injured but little
by the several stated and implied limitations imposed by the
introduction of simplifying assumptions in the first struggle with
the difficulties.

Because of the difficult mathematical argument used by Debye
and Huckel, I cannot discuss the details. Only the outline will
be given. No doubt this will not be considered satisfactory by
those who are well acquainted with the subject. However, the
importance of the theory is my justification for an attempt to
sketch the argument. If a reader will not make the mistake of
using such an outline when he should consult the original papers

489

490 THE DETERMINATION OF HYDROGEN IONS

he may find it to be of some aid to his understanding of what the
simple final equations are about.

The central idea in the theory of Debye and Hiickel (1923) is
this : Although ions in solution may not obey strictly the ideal gas
laws because of the same sort of interferences which obtain in the
case of neutral molecules, there is, in the case of ions, the added
interference of the mutual interaction of the electrically charged
particles. Account of this must be taken when there is formu-
lated the free energy of transfer of a particular kind of ion from
one concentration to another, because the free energies of separa-
tion at two different ion concentrations differ. Dilution of a
solution increases the dispersion with consequent closer approach
of the conduct of the ions to the laws of the ideal gas. Were this
interionic action alone responsible for deviations from the gas laws,
its effect should fully account for those correction terms which we
have previously described as the activity coefficients. (See Chap-
ter XI, page 236.) Debye and Hiickel show that on this basis
the correction terms for very dilute solutions can be calculated.

One of the most important of the main results is the following
simple equation, applicable to very dilute aqueous solutions at
25°C.

- log 7, = 0.5 zj

where 71 is the activity coefficient of an ion of the ith kind with
valence zi? and where /* is the "ionic strength" of the solution.
The ionic strength of the solution is obtained by multiplying the
concentration of each ion by the square of that ion's valence
number, summing all these products and dividing the result
by two.

The equation written above is a limiting equation applicable
only at very high dilution. For moderately dilute solutions the
average diameter of the ions is taken into account and the equa-
tion then is

0.5 z?
- log 71

1+3.3X
where a is the average ionic diameter.

XXV DEBYE-HUCKEL THEORY 491

DERIVATIONS

Fix attention upon a positive ion (see figure 85). Let it have
an effective radius a, by which will be understood a limit within
which other ions cannot penetrate. This radius, a, will enter the
argument later. Concentric with the ion considered, imagine
there to be shell of radius r, in which we find an element of space
of infinitesimal thickness dr and infinitesimal volume dv, situated
as shown in figure 85.

The first problem is to find some expression for the relative
numbers of positive and negative ions which will enter dv, which
is in the electric field of the central ion.

For this purpose there is used the Boltzmann principle. We
shall employ it somewhat loosely.

FIG. 85

When a positive ion enters dv it gains potential energy of posi-
tion by reason of its approach to the repelling central ion. Like-
wise when a negative ion enters dv it loses potential energy. When
an ion enters dv let AF be the gain in energy per mole of a
positive ion of valence za. Let N0 represent the Avagadro
number. Let [a]! be the concentration of positive ions of the ath
kind expressed in moles per cubic centimeter.1 Let e be the
elementary electric charge and \j/ the potential.

(I)2
Were there no interionic force, the positive ions of the ath

1 This space relationship will later be translated to moles per liter.

2 N0[ali dv gives the number of particles and N0[a]i dv zae the number of
charges. The number of unit charges multiplied by the potential at the
place found is the energy required to bring the ions from a place of zero
potential.

492 THE DETERMINATION OF HYDROGEN IONS

kind would be evenly distributed and their concentration would
be, stoichiometrically, [a]2. Except for the work included in AF
we will assume that the ions behave as an ideal solute. Then
the free energy of transfer between an imagined homogenous
solution in which the concentration is [a]2 and the place where the
concentration is [a]i is given by (2).

- AF = RT In [^~ (2)

LaJ2

Apply (2) to account for the energy-change locally between the
condensed state and that of complete dispersion. A combina-
tion of equations (1) and (2) gives (3)3 where e is the base of
Naperian logarithms.

r i r i ( No za e $\ (

[aji-[a]tle— RT 1

This is a special application of the Boltzmann principle.4 Equa-
tion (3) states that the concentration of the ions in dv, namely
[a]i is a function first of the concentration, [a]2, which would be
found there were there no interionic force and second an ex-
ponential function of the ratio of the potential energy to the
thermal energy. The parenthesized term of (3) can be expanded
by the formula

•\r -y-2 V-3

«-1 + ii + fi + fi etc-

(See Mellor, Higher Mathematics.) An approximation5 is here

- i —

8 x = y In w may be written w = ey. Hence 7-7- = eRT.

[a] 2

4 See p. 1025 of article by Dushman in Taylor's Treatise on Physical
Chemistry.

6 Instead of the approximation being presented in this way, it is some-
times found that the equations are kept in exponential form till the equa-
tion for the density 5, appearing in our equation (6), is in exponential form.
Then there appears the term

which is —2 sin hyp jr™. Here "sin hyp," sometimes written "sinh,"
signifies hyperbolic sine (see Mellor-Higher Mathematics). It is at this

point that the approximation is introduced since —2 sin hyp -j^-p is ap-

fj,
proximately —2;.

XXV DEBYE-HUCKEL THEORY 493

considered permissible and all terms after the second are ignored.
Then (3) becomes:

r i r i r -, No za e i/' , N

[a]i = [a]2 - [a]2 — - (4)

Likewise for a negative ion of the bth kind and valence Zbi

<5>

Confine attention for the moment to a solution which contains
only ions of the kinds a and b. The density of electrostatic
charge in any element of volume dv is determined by the dif-
ference between the numbers of positive and negative charges
brought there by these ions. If this density be denoted by 5,

5 = No [a]i za e - N0 [b]i zb fe (6)

Combination of (4), (5) and (6) yields (7).

5 = (N0 [a], za e - No [b], zb €) - ^ [[a], z* + [b], zj] (7)

Since the subscripts "2" refer the concentrations to the
stoichiometrical, the rule of electroneutrality of the solution as a
whole demands that the first parenthesized two terms to the right
of (7) reduce to zero. Were more than two kinds of ions con-
cerned, there would appear a similar but more extended set of
these terms, but the differences between them would be zero. To
express the more general equation the bracketed part of the last
term in (7) may be replaced by 2 (cz2) which indicates that the
concentration per cubic centimeter of each ion is to be multiplied
by the square of that ion's valence and all such products added
together. Equation (7) may then be written in the more general
form of (8)

(8)

There is now to be found a relation between the density of
electrostatic charge, 6, the potential ^ and the radial distance, r,

494 THE DETERMINATION OF HYDROGEN IONS

of the element of volume dv from the central, positive ion. Here
there is applied Poisson's6 equation, which is :

dr D

Here D is the dielectric constant of the medium and TT has its
ordinary mathematical significance.
Substitute (8) in (9) to obtain (10).

DRT

On examination of the coefficient of \J/ in (10), it is found to have
the dimensions7 of the square of a reciprocal length. Designate

this length by -. Then

1 47rN*62:S(cz2)

= K --

6 It has been said that the introduction of the Poisson equation in the
treatment of this subject was a stroke of genius. By its use Debye and
Hiickel avoided the chief difficulty encountered by Milner (1912-13) who
had mastered the principles of the subject but who failed to develop equa-
tions which da not require elaborate trial calculations.

This equation of Poisson (Simeon Denis Poisson, 1781-1840) is

- 47r5
v"V = — =— Vector Analysis

5V dV 5V 4?rS

-- 1 --- 1 -- = -- Rectangular coordinates

dx2 dy2 Oz2 D

dr dr> sin 6 50 50 sin2 6

= -- Polar (spherical) coordinates

The last equation becomes (9) on the assumption of spherical symmetry.
In the equation written in the terms of Vector analysis VV represents the
operation of the next equation. V is called "nabla," "alted" or "del."

For the development of Poisson's equation see Gibbs and Wilson (1925),
Vector Analysis, pp. 206 and 230.

7 For brief discussions of dimensions see Smithsonian Physical Tables
or International Critical Tables.

[N3 [e2] fc] _ [m-2] U2] [ml-3] _ 1

[D] [R] [T] = [e2 f-1 I-2] [flm-1 T-1] IT] = F2

XXV DEBYE-HUCKEL THEORY 495

On examining the equations leading to (11) Debye and Hiickel
find that the length - is (approximately) that radial distance at
which the density of the ion-atmosphere about the central ion

declines an - th part.8 As shown by (11) this length is determined
e

by the concentrations of the ions, the ion valencies, the dielectric
constant of the medium and the temperature. If, for instance,
the temperature T increases, the length increases, — an expression
of the tendency of increased thermal agitation to make the ion-
distribution more nearly uniform. If z, any ion valence, increases,
the length decreases, — an expression of the local clustering effect
of ions with high valence.

Now substitute (11) in (10) and obtain (12), or (12a) (the latter
by the notation of footnote 6).

;r) = *2 * (12)

ar/

V2 \f/ = «2 \l/ (12a)

Equation (12), or (12a), is a linear differential equation of the
second order when all terms involving powers of ^ greater than
one are suppressed in accordance with the first approximation
noted on page 492. Then the solution of (12) becomes:

(13)9

8 The conception involved is of importance to the treatment of the so-
called Helmholtz double-layer. Consider a particle or an electrode sur-
face which, for any reason, has a potential different from the solution with
which it is in contact. There will be near the interface a greater density
of positive or negative ions according to the sign of the relative potential

of the particle or electrode. The distance — represents the distance at

which the potential difference has declined to - th of its value at the inter-

face considered as a mathematical surface.

For a discussion of the applicability of this concept to the study of the
precipitation of colloids by neutral salts see Burton (1926) and forth-
coming article by Mueller.

9 The general solution of (12) has been given by Gronwall (1927). A
more complete treatment is to appear in Physik. Zeit. in a joint paper
with LaMer and Sandred. — Personal correspondence with Dr. V. K. LaMer.

496 THE DETERMINATION OF HYDROGEN IONS

In equation (13) A and A' are integration constants. Of these
A' must be zero; otherwise \l/ would approach infinity instead of
zero as r approaches infinity. Hence

I = A (14)

The linear approximation can be obtained as follows. Perform the
indicated operations to obtain the identities:

1 d ( dA _ dty 2 <ty _

I j.2 \ = _l_ =

r2 dr \ drj ~ <fr* r <fr

Hence by (e), (f) and (d)

(12)

Multiply by r and transpose to obtain:

d2<f/ d\f/

dr2 dr

— — K2 (rtfO = 0 (b)

dr2

We now have r ^ as variable instead of \f/.
Let

r^ = y (c)

Then

-*>y=0 (d)

Now try the solution

Then

Xr f ^

y = e (e)

X' eXr - *2 e^ = 0 = eXr (X2 - /c2)
or

X = ± K (g)

Now combine (g) and (e)

y = e* " (h)

Substitute (h) in (c)

iV = e±lcr
or in general

where A and A' are integration constants.

Equation (i) is identical with (13) of the text. The result may be
verified by performing the operations indicated by the operator V2^ of
equation (12a). See footnote 6.

XXV DEBYE-HUCKEL THEORY 497

The potential \f/i at any point in the interior of the central ion
(see figure 85) of valence Zi is:

where — is the part contributed by the ionic charge of the central
Dr

ion and B is the part contributed by the surrounding ion-atmos-
phere. In the description of figure 85 it was specified that a
is the limit of approach of other ions to the central ion. At this
limit the potential of the surrounding ion-atmosphere, given by
(14), must equal \f/i given by (15). Also at this limit r = a.
Then

Ae-n=^ + B (16)

a Da

Furthermore the field strengths — must become equal. Hence

da.

differentiate (14) and (15) and equate by — = — letting r = a.

dr dr

Solve for A, substitute in (16) and find B.

_ ZiC* /.ox

These steps have not only yielded the integration constant, A,
of (14) but have led directly to B, the desired quantity, which is
the potential of the central ion due to the surrounding ion-
atmosphere, assuming that there is a definite limit, a, to the
approach of the ion-atmosphere. If the central ion, instead of
being the positive ion considered so far, has a valence ±zj, the
work of removal will be:

,M(=FB) = . 4*'*
2 r 2 D(l + « a)

10 This may be derived from Poisson's equation by making 5 = 0.

498 THE DETERMINATION OF HYDROGEN IONS

For No ions the work, w, of removal will be:

No z? c2 K
W = 2D(l+Ka)

(20)

In (20) w is the free energy11 involved in the removal of one
mole of ions of the i th kind from the electrical field of their ion-
atmospheres to an infinitely dilute solution of the same medium
at the same temperature.

If two solutions of these ions of concentrations Ci and Co were
ideal, the free-energy of transfer would be

- A F = RT In *£ (21)

If the solution of concentration Ci were not ideal but that of
the infinitely dilute solution of concentration C0 were ideal, the
observed free energy increase would be

- A F = RT In *£ + RT In Tl (22)

where 71 is the activity coefficient described on page 236. On the
assumption that the interionic electrostatic forces are alone
responsible for deviation from the ideal (or limiting) law of solu-
tions it is obvious that the term RT In 71 of (22) is — w of (20),
and that, when solutions are being described by the ideal laws,
this term must be applied as a correction. Hence

No zf e2 K

The equivalent of K by equation (11) will now be recalled; but
instead of retaining c, moles per cubic centimeter, we shall use C,
moles per 1000 cubic centimeters (approximately moles per
liter). Then equation (11) becomes (24).

-/:

1000 DRT

(24)

11 "Free energy" (Lewis) by reason of the nature of the method of
measurement of the electrical quantities involved. See Debye (1925),
Bjerrum (1926), Br0nsted (1927) and particularly E. Q. Adams (1926).

XXV DEBYE-HUCKEL THEORY 499

In combining equations (23) and (24) we may segregate the
universal constants, N0, e, R, and IT and may substitute their
numerical values.

No = 6.061 X 1023; 5 = 4.774 X 1Q-10;
R = 8.315 X 107; TT = 3.1416.

Equation (23) will also be transformed to the use of logarithms
to the base 10. 12 There will then remain two quantities D, the
dielectric constant, and T, the absolute temperature, which may
be given numerical values only under special conditions. To
note how variations of D and T affect the calculated numerical
form of the equation it will be convenient to write the combined
equations (23) and (24) as follows:

-log 7,-- •=£ (25)

1 + li a Vs (Cz')

where

1.2833 X 106
(DT)1-5

and

(26)

3.557 X 10' , ,

(DD»

In place of S (Cz2), used in the above, there is usually employed
Lewis' p., which is called the ionic strength and defined by:

fj. = - (miZi + m2Z2 + msZg +, etc.) (28)

Here mi, m2, m3 etc., are the molalities (moles per 1000 grams
of solvent) of the ions. Since the Debye-Hiickel theory was
derived with the aid of space relations, concentrations should be
expressed in moles per 1000 cc. However, assuming the dis-
tinction between moles per 1000 cc., moles per liter and moles
per 1000 grams water to be negligible, we may write

2M = 2 (Cz2)
12 By use of: Inx = log ex = 2.3026 logio x = 2.3026 log x.

500

THE DETERMINATION OF HYDROGEN IONS

Then equation (25) becomes:
- log 71 =

V2 z2 VI

For values of 8, &V2, P and PV2 see table 66.

TABLE 66

Coefficients for the Debye-Huckel equation
1.2833 X 106 ™ 3.557 X 109

(29)

(DT)

0-6

t° (CENTI-
GRADE)

8V2

WV2

273.1

88.0

0.344

2.29 X 107

0.487

3.24 X 107

288.1

82.5

0.350

2.31 X 107

0.495

3.26 X 107

291.1

81.0

0.354

2.32 X 107

0.501

3.28 X 107

293.1

80.5

0.354

2.32 X 107

0.501

3.28 X 107

298.1

78.8

0.356

2.32 X 107

0.504

3.28 X 107

303.1

77.0

0.360

2.33 X 107

0.509

3.29 X 107

* The values for the dielectric constant of water as given in the litera-
ture vary to an extent important to the present purpose. Since this situa-
tion is stimulating reinvestigation of the subject, the reader will look for
new values in the literature subsequent to the publication of this book
and will realize that the values given above are purposely rounded.

Table 66 shows that temperature has little effect upon the
magnitude of the coefficients. Therefore the final equation (29)
may be simplified to :

- log 71 =

0.5 zf VM

1 +3.3 X ]07 a VM

(29a)

The constant, a, was specified to be the radial distance within
which other ions could not approach the central ion of figure 85;
but, in the course of the development of the final equations, a
should be reinterpreted as the average effective diameter of all
the ions. In the absence of experimental, specific values for this
average effective diameter of the possibly hydrated ions, the
constant, a, becomes more or less an arbitrary constant. To a
ascribe the value 1 X 10~8, which is merely the order of magni-
tude of ion diameters. It is then readily calculated, by equation

XXV

DEBYE-HUCKEL THEOKY

501

(28) and the values of JB-v/2 in table 66, that, when VM is less
than the order of magnitude 0.1, equation (29a) reduces^prac-
tically to:

- log 71 = 0.5 zf VM (29b)

There are several experimental verifications of this last simple
equation (29b) at the high dilution called for by the above condi-
tion that VM < 0.1. Furthermore the introduction of an average
diameter, a, of a reasonable order of magnitude tends to extend
the verification of the Debye-Hiickel theory by making (29a)
appear applicable to somewhat more concentrated solutions.

The above equations relate to the activity coefficient of an
ion of the ith kind. If a salt dissociate so that each molecule
furnishes za ions of the bth kind and zb ions of the a,th kind, za
being the valence of the "a" ion and zb the valence of the "b"
ion, the mean activity coefficient of the ions, 7B, may be de-
fined by

Zb log 7a + za log 7b

log 7s =

Application of (29b) then yields (31)

— log 78 = 0.5 zazb V/i

(30)

(31)

If a salt like MgS(>4 dissociate to two ions of the same valence
number, equation (31) is obtained again for this case.

For salts of different valence-type the coefficient 0.5 zaZb for
25°C. has the values shown below.

EXAMPLE

VALENCE-TYPE

COEFFICIENT

KC1

1-1

0 5

K2S04

1-2

1.0

A1(N03)3

3-1

1 5

MgS04

2-2

2 0

Ca3(P04)2

2-3

3.0

(Co(NH3)6(Co(CN)6)

3-3

4 5

DISCUSSION

There have been numerous experiments designed to test th*e
simple equation applicable at high dilution where the average

502 THE DETERMINATION OF HYDROGEN IONS

ionic diameter is negligible and also to test the equation contain-
ing a, the average ionic diameter. These experiments cover
variation of dielectric constant by the use of solvents of various
dielectric constant; they cover variation of the ionic strength in
which the ionic strength is obtained with salts of very different
valence-type; they cover measurements of the activity coeffi-
cients of solutes of very different valence-types.

See Noyes et al. on various tests of the Debye-Hiickel equation.

Substantially, the theory in the quantitative form given by the
equations is confirmed as a limiting law; but obviously the theory
makes no pretense to deal with effects other than the electro-
static and there are two approximations introduced. One is the
use of the dielectric constant of the solvent in place of the di-
electric constant of the solution. Htickel (1925) attempts to
correct for this. He introduces a reasonably deduced additional
term. The other approximation is in the mathematical develop-
ment. It is in the step taken to reach equation (4). After
expanding the series term only the first two terms of the ex-
pansion were considered. LaMer (1927) claims that a considera-
tion of the higher terms is sufficient to account for the major por-
tion of those discrepancies between theory and experiment which
have been particularly noticeable with salts of high valence, since

a factor — enters at successively higher powers for each succes-
a

sive approximation in the solution of equation (12). When -

is greater than 0.5 (i.e. when a is less than two Angstrom units
for a uni-univalent salt, or less than eight Angstrom units for a bi-
bivalent salt) a consideration of the Debye approximation alone
gives distorted calculated results and quite misleading values of

"a" according to LaMer. When — approaches unity, the in-

fluence of the higher terms is sufficient to make it appear as if
the limiting slope were larger than its value of 0.5 at concentra-
tions as low as those corresponding to O.OOlju. For further details
of this aspect see a forthcoming paper by LaMer, Gronwall and
Sandred.13

is private correspondence with Dr. LaMer.

XXV DISCUSSION 503

There has also been considered the inherent difficulty resulting
from the assumption that the ions have spherical fields. This
is to neglect, not only the spatial configurations demanded es-
pecially of organic molecules, but also the polarities of large ions.

Pending the highly refined investigations, experimental and
theoretical, which are expected to throw light upon the manner
in which these and other details of the theory are to be handled,
we may consider the Debye-Hiickel theory from the following
two points of view.

In the first place the theory has been so well substantiated in
its main outline that we may have considerable confidence in
using the reduced equation to calculate corrections of the first
order for very dilute solutions (e.g. v> < 0-1)- For solutions of
slightly higher ionic strength it will be recalled that the apparent
ionic diameter enters as of numerical significance. That the use
of values of a reasonable order of magnitude leads to corrections
in the right direction is of general theoretical interest.

In the second place it will be well to remember that there are
some conflicting views regarding several aspects of the theory.
Mention was made of LaMer's objection to the approximation in
the expansion of the series (see page 492). Others believe this
objection to be not serious. By adjusting the value of a in
equation (29) there is extended the range of concentrations within
which experimental data conform to the calculated curves. Such
adjustment will be considered empirical curve-fitting by some.
Others will regard it as entirely justified by the demands of the
theory.

It is not the function of this outline to discuss these and several
other matters which are now under discussion. The point to be
emphasized is this. In the immediate future we may expect an
orderly presentation of correction terms stated by means of the
equations given above.

In addition to the terms stated there is frequently employed an
additional term KP/i placed as follows

0.5 z?

K8/x has been called the "salting out term" and is supposed to
operate at high salt concentration.

504

THE DETERMINATION OF HYDROGEN IONS

SOME APPLICATIONS

A few examples of the application of the theory follow.

Consider a salt which will not react chemically with the solvent
or with other salts present in the solution. Let the salt chosen
have a very low solubility and let it be present in the solid phase
so that its activity in solution will be maintained constant while
the ionic strength of the solution is changed.

(salt) in solution = (salt) 8Olid phase

[salt]i7i = [salt]2T2 = [salt]373 etc.

.08
.07
.06
.05
.04
.03
.02
.0 I

.00

oNaCI

K2SO4

.01 .02 .03 .04 .05 .06 .07 .08 .09 JO Jl

V7T

FIG. 86

Here subscripts indicate solutions 1, 2, 3 etc., brackets indicate
concentration and parentheses indicate activity. Hence by
introduction of equation (31)

i [salt]i

[salt! = loS ^2 - log 71 = zazb 0 .5

(32)

If a pure, aqueous solution of the salt alone is used, only its ions
(and those of water) contribute to M; but /* may be varied by

XXV

APPLICATIONS

505

adding extraneous salts in various concentrations and various
valence-types. These should have effect on the ratio of solu-
bilities ^ only as. they affect p.. On the other hand a change

[salt]2

in the valence-type of the salt under study, while still affecting /*,
will make itself felt chiefly through new values of zazb. For a
salt of fixed valence-type the logarithm of the ratio of two solu-
bilities is in linear relation to the increment in the square root
of the ionic strength of the solution. At infinite dilution, /* = 0
(neglecting the ions of water) and, since there is no correction to
the gas law, log 7 = 0. Hence the data on solubilities should
give a straight line when charted as in figure 86, and this line,
extrapolated, should pass through the origin.

In figure 86, reproduced from LaMer's (1927) paper, the curves
are for the valence-types tabulated below.

CURVE

SALT

VALENCE-
TYPE

SOLUBILITY IN
WATER

[Co(NH3)4(N02) (CNS)]'
[Co(NH3)2(N02)2(C204)]'

1-1

0. 000335 M

[Co(NH,)4(C,04)]'i [S206]"

1-2
or 2-1

0.00015 M

III

[Co(NH3)6]^[Co(NH,)2(N02)J(C204)]/3

3-1
or 1-3

0.0000504 M

fCo(NH3)6'" [Fe(CN.)]"'

3-3

0.000030 M

In the figure the salts used to produce variation of /x are indicated.

The extrapolation should lead to the origin VM — 0 and — log 7
= 0, i.e., to no correction to the gas laws at infinite dilution.

Thes^e data verify the theory. At high dilutions the slope of a
curve is that predicted from the numerical form of the equation
which takes account of the electrical environment. The valence
factor (zazb) is correct, since the slopes of the several curves have
the corresponding ratios 1:2:3:9.

While such results are eminently satisfactory, difficulties begin
with salts of higher solubilities for the reasons mentioned in the
foregoing text. It will be found that a large number of the charts

506

THE DETERMINATION OF HYDROGEN IONS

in the literature take the form of one of the curves of figure 87.
The linear relation of the reduced equation (31) is seen as a
limiting relation obtaining when the ionic diameter approaches
zero. The introduction of an assumed ionic diameter (un-
doubtedly of the right order of magnitude) will give a curve of
the form shown in figure 88.

We may now pass to some examples of particular importance
to our main subject matter.

Cohn (1927) has gone over the subject of phosphate buffer
solutions with the aid of previous data and new data of his own

MOLAR

O .3
O

1.0

a=OA

.4 .6 .8

V7T

FIG. 87

1.0 1.2 \A

and has attempted to account for deviations from the simple
equilibrium equations by means of the Debye-Hiickel equation.
Let us write the relation:

(33)

Here activities are indicated by use of parentheses. Equation
(33) can be rewritten as

(34)

XXV

APPLICATIONS

507

Here brackets represent concentrations.

72 is the activity coefficient of the ion HP04~~ ~
71 is the activity coefficient of the ion H2P04~

pH is used in (34) in its physical meaning of log — — , since its

values are obtained by the method of the hydrogen electrode.

Assume complete dissociation of salts and therefore that
[HPO4 — ] and [H2PO4~] are determined from the known concen-

4.71
4.72
4.73

6.56
6.66 K
6.76 |

6.96 CL
7.06
Tl«

°s

& A .6 .8 1.0 1.2 1.4 1.6

FIG. 88. CORRECTION CURVES FOR pK2' OF PHOSPHATE (o) AND pK' OF

ACETATE (•)

trations of the alkali salts. Now let
duce equation (29a) in numerical form.

pK = PH - °'5

[HPO,

[H2P04-]

1 + 3.3 X 107 a

= 1, and intro-

(35)

Where za is the valence of the ion H2P04~, namely 1 ; and ZB is
the valence of the ion HP04~ ", namely 2. Then (35) is

pK = PH +

1.5

1 + 3.3 X 107 a

(36)

If a in (36) were very small the equation would reduce prac-
tically to

pK = pH-h 1.5V/I (37)

508 THE DETERMINATION OF HYDROGEN IONS

In Chapter I it was shown that under ideal conditions pK = pH

when the ratio of concentrations

— 1

= 1. The term 1.5 V/x

[H2P04-

' 1.

of the approximate equation (37), or the term —

1 + 3.3 X 107aVM

of (36) is then a correction term for the interaction of all the ions
present. If the observed values of pH are plotted against the
square root of the ionic strength there should be obtained with
equation (37) a straight line; and with (36) a set of curves any one
of which is dependent on the value of a. In figure 88 the linear
relation is shown and also a curve which passes very nicely through
or near the observed values. The latter curve is drawn with
(36) and Cohn's assumption that the mean ionic diameter, a,
has the value 5 X 10 ~8 cm. Although this is a reasonable assump-
tion in so far as it is a possible order of magnitude, it remains
an assumption. Yet its use, which in (36) yields (38),

pK = pH + L5 ^ r (38)

1 + 1.65 VM

gives a mathematical formulation of the observed values which is
satisfactory. Another way of showing this is to use (38) as is
done in table 67 to calculate pK. It is seen that, whereas the pH
values (which should be the constant pK according to the simpli-
fied theory of Chapter I) differ in the extreme by 0.568 unit, the
corrected values differ in the extreme by only 0.040 unit.

Of course when the ratio of primary to secondary phosphate
changes, as it does in ordinary buffer solutions, the value of the
ionic strength, /z, changes.

Cohn has also made use of the extended equation:

1+3.3X 107a\/M

where K8ju is the so-called "salting-out term." K8 varies with
the composition of the [mixture and is determined empirically.
Cohn regards the above] formula as an "empirical interpolation
formula." With its aid he has prepared a series of charts and
tables with which to ''facilitate the preparation of buffer solutions

XXV

BUFFERS

509

of the same ionic strength and varying pH or the same pH
and varying ionic strength." See page 216.

Cohn, Heyroth and Menkin (1928) have applied the same
principles to acetate systems. This is of particular interest in
connection with the discussion of Chapter I where, with due
warning of the consequences, we found that the application of
the more extended classical equations failed to yield a constant

TABLE 67

Corrected constants for phosphate system (after Cohn, 1927}

EXPERIMENTERS

a.
M

•*

w
A

0.00133

0.00267

0.052

7.088

0.071

7.159

0.00266

0.00532

0.073

7.068

0.098

7.166

Michaelis and Kriiger <

0.00334

0.00667

0.082

7.069

0.108

7.177

0.01333

0.02667

0.163

6.990

0.193

7.183

Clark and Lubs

0.03334
0.05000
0.06667
0.06667
0.06667

0.06667
0.10000
0.13333
0.13333
0.13333

0.258
0.316
0.365
0.365
0.365

6.904
6.843
6.813
6.813
6.817

0.272
0.312
0.342
0.342
0.342

7.176
7.155
7.155
7.155
7.160

Michaelis and Kriiger . .

S0rensen

0.12000

0.2400

0.490

6.737

0.406

7.143

0.16667

0.3333

0.577

6.721

0.433

7.154

Cohn <

0.33334
0.50000
0.60000

0.6668
1.0000
1.2000

0.817

i.ooo

1.095

6.638
6.599
6.570

0.522
0.566
0.585

7.160
7.165
7.155

0.66667

1.33333

1.154

6.573

0.596

7.169

1.20000

2.4000

1.549

6.520

0.653

7.173

Average

7.163

pK = pH +

1.5

1 + 1.65

which is satisfactory for other than purposes of approximate
treatment. Cohn, Heyroth and Menkin find that in this case
an apparent error is introduced by use of the value 0.3380 for
the tenth normal calomel half-cell at 18°C. This is because [H+]
enters equation (19) of Chapter I in a sum and the higher the
value of the calomel half-cell the higher the apparent value of
[H+]. By reducing [H+] by use of a smaller value (0.3355) for

510

THE DETERMINATION OF HYDROGEN IONS

the calomel half-cell they find a good correspondence between
calculated and observed corrections. They then find that the
acetate system can be described by

- log

[CH3 COO-]

0.5

= pK

The graphically interpolated values for the correction term are
given on page 219. Figure 88 shows the correction for various
dilutions of an equimolecular mixture of acetic acid and sodium
acetate.

C2J 030 035 040 045 050

005 010 015

02i
1?

030 035 040 045 050

FIG. 89. APPARENT DISSOCIATION EXPONENTS, pK/ AND pK2r, OF CARBONIC

ACIDS AT DIFFERENT IONIC STRENGTHS

Left: Points marked o and ® determined by Hastings and Sendroy;
points marked El calculated from Warburg's data. Line determined by
pKV = 6.33 - 0.5 V?. Right: pK2' = 10.22 - 1.1 VM. (After Hastings
Sendroy (1925).)

With the phosphate and acetate systems so described it is now
possible to prepare buffer solutions of known ionic strength be-
tween pH 3.6 and 7.6.

Figure 89 shows the effect of ionic strength (plotted as square
root) upon the apparent dissociation constants (in terms of pK7)
of carbonic acid as determined by Hastings and Sendroy (1925).

We owe to Br0nsted (1921) a first sketch of a possible syste-
matic description of the "salt effects" found in the use of indi-
cators in solutions of different salts. He emphasized the necessity
of introducing the more rigid equations and of considering the
"salt effect" as an expression of the alteration of activity under

XXV

INDICATORS

511

specific changes of condition, v. Halban and Ebert (1924) give
an extensive treatment of picric acid which will repay careful
study. In this they make use of the Debye-Hiickel equation.

I am indebted to Dr. A. B. Hastings and Dr. Julius Sendroy,
Jr., for their permission to publish figure 90 in which they show
the apparent variation of the pK values of indicators as the ionic
strength of the buffer solution is changed by means of different

•».0

4.6
4.7
4.8
4.9

CL 6.3
6.4

7.7
7.8
7.9
8.0

B.C.G.

^^°

— ^"

— *

^. ._
r-^^

0 MgCI2
A NaCI

acp.

x'',

,^-

*- '

. — »-

— •£

x-''

rr^

.-^0—

*-^

A NaCI
O MgSO4

RR.

. — *

. >•

^*-

. — <"

,-^<*^

^*-

U MgCS04

.1 .2 .3 .4 .£

V/7

FIG. 90. "SALT EFFECT" WITH INDICATORS

B.C.G. = brom cresol green; B.C. P. = brom cresol purple; P.R. =
phenol red. (Courtesy of Hastings and Sendroy.)

buffers and added salts of various types. Although the limiting
equation is inapplicable these investigators have systematized the
experimental data in a way which is of far greater value than
the loosely constructed tables of the past, and by use of the
coordinates - - log 7 and VM- There remains distinct evidence
of "specific salt errors." This shows that, in the use of indicators
with specific solutions, experimental calibration must still be used
whenever precise values are to be stated.

512 THE DETERMINATION OF HYDROGEN IONS

REVIEWS

The Theory of Strong Electrolytes. A general discussion held by The

Faraday Society, Trans. Faraday Soc., April, 1927.
LaMer. Recent Advances in the lonization Theory as Applied to Strong

Electrolytes. Trans. Am. Electrochem. Soc., April, 1927.
Scatchard. The Interaction of Electrolytes with Non-electrolytes.

Chem. Rev., 3, 383 (1927).
Annual Reports on the Progress of Chemistry issued by The Chemical

Society (London) 1926 and 1927.
Also Hiickel (1924) and Noyes (1924).

CHAPTER XXVI

SUPPLEMENTARY METHODS
But yet I'll make assurance double-sure. — MACBETH, IV: 1

When the control of any process has been found to be indexed by the
activity or concentration of the hydrogen or hydroxyl ions, when the
quantitative relations have been established and contributory factors are
controllable, there is established a possible means of estimating the activity
or concentration of the hydroxyl or hydrogen ions. Many such instances
are known. From among them a few may be chosen for their convenience.
They are spoken of here as supplementary methods because they are super-
seded in general practice by indicators, the hydrogen electrode and the
quinhydrone electrode. Several have historical value because they were
used in establishing the laws of electrolytic dissociation. Others have
intrinsic value because they are available either for checking the customary
procedures or for determinations in cases where there is reason to doubt
the reliability of the usual methods. Those which are kinetic methods
will in the end make their distinctive contributions by showing what they
can of the correlation of certain kinetic affairs with equilibrium states.
Generally they are rather useful to "make assurance double sure."

An instance of the last procedure is the following. Clibbens and Francis
(1912) found that the decomposition of nitrosotriacetonamine (see Heintz,
1877) into nitrogen and phorone is a function of the catalytic activity of
hydroxyl ions. Francis and Geake (1913) then applied the relation to the
determination of hydroxyl ion concentrations, Francis, Geake and Roche
(1915) improved the technique, and then McBain and Bolam (1918) used
the method to check their electrometric measurements of the hydrolysis
of soap solutions.

It is just in such checking that the value of these so called supple-
mentary methods will be appreciated. But, since they will find only occa-
sional use and under circumstances which will require a detailed considera-
tion of their particular applicability, there seems to be no reason to do
more than indicate a few of the methods in brief outline.

Among the reactions which have historical interest there are, besides
the most frequently studied inversion of cane sugar, the following.

Bredig and Fraenkel (1905) used diazoacetic ester

N2CH-CO2 C2H5 + H2O = N2 + (OH)CH2CO2C2H5

The nitrogen evolved from time to time was measured and the values

k
used in the equation for a monomolecular reaction. At 25°C., —- = 32.5.

513

514 THE DETEKMINATION OF HYDROGEN IONS

The method was applied with only partial success by Hober (1900) to
blood. Van Dam (1908) used it in the examination of rennet coagulation
of milk.

The decomposition of nitrosotriacetonamine is represented in outline
by the following equation:

/CH2 • C(CH3)2\ /CH : C(CH3)2

C0<; >N - NO -> C0<( + N2 + H20

XCH2 - C(CH3)/ NCH : C(CH3)2

The original quantity of nitrosotriacetonamine is known and the extent
of the decomposition at the end of measured intervals of time is measured
by the volume of nitrogen evolved.

Francis, Geake and Roche (I.e.) found the relation between the velocity

constant and [OH~] to be - "— ; = 1.92 at 30°. See Colvin (1926).
(OH J

Br0nsted (1926) finds that the rate of ad,dition of water to nitratoaquo-
tetramine cobalt ion is very sensitive to the hydrion activity of the solu-
tion and suggests the use of the rate in determining hydrion activities.

Numerous other methods are mentioned in the texts of physical chem-
istry and, now that interest in the theory is reviving, are detailed in current
journal articles.

For the most part these supplementary methods are catalytic and
involve what are called pseudo-unimolecular reactions. Consider the
reaction

A + H+-^ H+ + products

If [H+j is maintained constant, as by a buffer solution, the decline of [A]
with increase of time may be described by

- d[A] = k' [A] [H+]

- d(A]
[A]

= k7 [H+] dt

Treat [H+] as constant and integrate between [A]i at time ti and [A]2
at time t2

_ in j^ji = k' [H+] (ti - t2)
If 2.303 k' = k

log ^ = k [H+] (t, - ti) = tk [H+]

XXVI INVEKSTON OF SUGAR 515

Many methods have been used to follow reaction velocities. Among
these may be mentioned measurement of the gas evolved, as, for instance,
i» the decomposition of nitrosotriacetoneamine and the change in optical
rotation during the hydrolysis of cane sugar to invert sugar.

Brpnsted and King (1925) describe an apparatus suitable for following
either the decomposition of nitrosotriacetonamine or any reaction of a
similar nature wherein nitrogen is evolved. Their paper should be con-
sulted for a discussion of the manner in which the salt concentration of a
buffer solution affects the velocity constant.

The polarimetric method is described as follows by Lamble and Lewis
(1915) (see Rice in Taylor's Treatise}.

Polarimeter tubes 4-dcm. in length were used, surrounded by jackets,
through which water at 25° ± 0.1 was circulated. 25 cc. of standard hydro-
chloric acid solution was added to 25 cc. of a 20 per cent solution of sucrose,
both solutions being at 25°C., and immediately the mixture was placed in
the observation tube; the rotation at is noted at convenient time intervals
and the final rotation ««, is measured after at least 48 hours from the start
of the reaction. We can assume that the velocity of the reaction will be
proportional to the concentration of the cane sugar and to the concentration
of the hydrochloric acid, if the reaction takes place in dilute solution.
The velocity equation will be, therefore,

[H+] kt = log jgl

[A] 2

where [H+] is the initial concentration of the hydrochloric acid which re-
mains constant during the experiment, [A]i is the initial concentration of
the cane sugar and [A]2 is its concentration after time t. The ratio is
independent of the particular unit of concentration used so that if the

rotations are additive we can replace -r~ by — ~» where a0is the initial

IA]2 at — « oo

rotation and aro is the final rotation. Rosanoff, Clarke and Sibley showed
that the specific rotation of the solution is an additive function of its com-
position and also gave a method for calculating a0; a slight error in the
value of «0 will be greatly magnified in the value of k calculated for the
earlier stages of the reaction, so instead of trying to obtain a0 by direct
observation they extrapolated to t = 0 the straight line obtained by
plotting values of t against corresponding values of log (at — «<») ; this gives
far more reliable values of log («0 — «„) than can be obtained by direct
measurement.

For other methods consult texts of physical chemistry, for example the
article by Rice in A Treatise on Physical Chemistry, edited by Taylor.

A large proportion of reactions proceeding in homogeneous solutions
are catalyzed by hydrion or hydro xyl ions. For this reason emphasis was
first placed upon these ions. However, it was soon found that neutral
salts when added to solutions of strong acids markedly increase the rates

516 THE DETEKMINATION OF HYDROGEN IONS

of such reactions as the inversion of cane sugar. Several theories have
been advanced to account for this. Considerable systematic advance has
been made by the use of activities in place of concentrations in the equa-
tions for reaction kinetics and by the use of the hypothesis that, in the
formation of an unstable critical complex between reacting molecules and
ions, the charged complex is subject to those interionic forces which
markedly affect the activity coefficients. Also catalytic functions are now
admitted for ions other than hydrogen and hydroxyl.

In many instances these catalytic methods of determining hydrogen or
hydroxyl ion concentrations may be applied with neglect of the salt-
effect if only the order of magnitude be desired; but if they are applied for
accurate data the current literature should be consulted for important
treatments of what is often called the salt effect. See especially Br0nsted
(1923-1927), Dawson (1926-1927), Scatchard (1926), Kilpatrick (1926),
Pedersen (1927) and references to other modern work in Annual Reports
on the Progress of Chemistry for 1927, London Chemical Society (1928),
pp. 33 and 331.

CONDUCTIVITY

The conductivity of a solution is dependent upon the concentrations ot
all the ions and upon the mobilities of each. It is therefore obvious that
a somewhat detailed knowledge of the constituents of a solution and of
the properties of the constituents is necessary before conductivity measure-
ments can reveal any accurate information of the hydrogen or hydroxyl
ion concentration. Even when the constituents are known it is a matter
of considerable difficulty to resolve the part played by the hydrogen
ions if the solution is complex. However, the mobilities of the hydrogen
and hydroxyl ions are so much greater than those of other ions (see page
279) that methods of approximation may be based thereon. If, for in-
stance, a solution can be neutralized without too great a change in its
composition it may happen that with the disappearance of the greater
part of the hydrogen ions there will appear a great lowering in conductance.
Then, with the appearance of greater hydroxyl ion concentration, the
conductance will rise. The minimum or a kink in the curve is a rough
indication of neutrality. Thus the conductivity method is sometimes
useful in titrations. See Kolthoff for details and references on titration
by the conductivity method.

The elementary principles of conductivity measurements will be found
in any standard text of physical chemistry but the more refined theoretical
and instrumental aspects are only to be found by following the more
recent journal literature. See Jones and Josephs (1928).

Of course, the major field of usefulness of the conductivity method has
been in the determination of dissociation constants of weak acids.

As mentioned in Chapter XXV, change in the ionic strength of a solu-
tion changes the inter-ionic forces which affect the mobilities of ions.
Therefore, the original basis for calculating the degree of ionization from
the ratio of conductance at one concentration to the conductance at in-

XXVI MISCELLANEOUS METHODS 517

finite dilution must be altered. However, Maclnnes (1926) proposes
dividing the equivalent conductance of an acid at a given concentration by
the equivalent conductance of completely dissociated acid at the same ion
concentration. He thereby obtains for acetic acid, for instance, Ka =
1.743 X 10~5 to 1.784 X 10~6. (A discrepancy of only 0.01 pH unit in the
range of concentration 0.07 to 0.002.)

MISCELLANEOUS METHODS

Were it worth while there could be detailed under this heading a wide
variety of phenomena which have actually been used to determine approxi-
mately the hydrogen ion concentration of a solution. We may instance
the precipitation of casein from milk by the acid fermentation of bacteria.
This has not been clearly distinguished in all cases from coagulation
produced by rennet-like enzymes; but, when it has been, the precipitation
or non-precipitation of casein from milk cultures has served a useful
purpose in the rough classification of different degrees of acid fermentation.
In like manner the precipitation of uric acid or of xanthine has been used
(Wood, 1903). See also pages 575 and 582.

Many of the physical methods are of considerable interest. For in-
stance the determination of distribution ratios of a given substance be-
tween different solvents enters very frequently into the determination of
activities and into the determination of hydrion activities. The fact that
water completely extracts certain salts from benzene solution has been
used as an argument for complete dissociation in the aqueous phase (see
for example Hill ('21)). Distribution between liquid and liquid is only
a special case of heterogeneous equilibria and if we attempted to discuss
even the main principles a chapter of considerable magnitude would soon
develop. An exposition of the matter is given in such treatises as that of
A. E. Hill in Taylors Treatise on Physical Chemistry page 343. Of peculiar
interest to biochemistry is the manner in which the distribution of carbon
dioxide between the gaseous and the liquid phases enters an equilibrium
equation whereby, with the measurement of CO2 partial pressure and one
other quantity such as "total carbonate," the pH value of a bicarbonate
solution may be determined. See Chapter XXX under "Blood." Thus
the bicarbonate system is made an indicator as truly as phenol red is an
indicator.

An interesting application of equilibria involving a gas phase is the
"electric nose" developed by Hickman and Hyndman (1928). A small
amount of ammonium salt is placed in the acid solution which is to be mixed
with an alkaline solution. On admixture, ammonia is set free at a partial
pressure depending largely upon the pH value of the mixture. This
ammonja can be aspirated to a separate aqueous solution the conductivity
or reaction of which now becomes a function of the adjustment in the main
mixture. A device operating upon the response of this "nose" controls
the main mixing.

See also Osterhout (1918) on the use of partial pressures of CO2 for
following respiration.

518 THE DETERMINATION OF HYDROGEN IONS

In the literature are found many and divers interesting, suggestive or
obviously cumbersome physical methods. The heat of neutralization of
acids and bases and the cessation of heat evolution when, in a titration,
neutralization is complete has been put to use by Dutoit and Grobet
(1921). Cornec (1913) attempted to estimate the end-point in titrations
by changes in refractive indices. His following of the changes in freezing
points yielded some interesting curves, for instance that of chromate-
bichromate. Windisch and Dietrich (1919-1921) put alteration of surface
tensions to use. In this connection we may remark that Harkins and
Clark (1925) find that the surface tensions of solutions of sodium nonylate
are especially sensitive to changes in pH.

Correlation between changes in optical rotation and pH are discussed
briefly in Chapter XXX. In Chapter VII fluorimetry is mentioned.

Taste has its very restricted place.

CHAPTER XXVII

AN ALTERNATE METHOD OF FORMULATING ACID-BASE EQUILIBRIA

A particular statistical law can have various origins. — GUYE

"// there's no meaning in it," said the King, "that saves a world
of trouble, you know, as we needn't try to find any." — LEWIS
CARROLL, in Alice in Wonderland.

The usual formulation of acid-base equilibria starts with the con-
sideration of the ionization of the acid or the base. If there is used Br0n-
sted's generalization, namely

Acid ^± Base + H +

e.g. HA ?± A- + H+

or NHt ^ NH3 + H+,

and the equilibrium equation

(Base) (H+) =
(Acid) '

the hydrion appears of importance coordinate with the acid and the base,
the acid and the anion or the base and the cation.

Likewise the usual formulation of the equilibrium established at the
hydrogen electrode involves the assumption that hydrogen ionizes in the
sense of

and that equilibrium between the free hydrions in the electrode and those
in the solution is of primary importance. Accordingly the activity of
free hydrions appears to be of paramount importance to the operation of
a hydrogen electrode, even in alkaline solution. But the activity of
hydrions may be as low as 10~~14, or less, in alkaline solutions and the
concentration of hydrions, calculated in the usual manner, l is of that order
of magnitude. The opinion has been expressed that the support of stable
potentials by hydrions acting at concentrations less than 10~~10 is not to
be expected on grounds of kinetic theory. (See Chapter XVIII.)

Now that No, the number of molecules of solute present per liter in a
molar solution, is accurately known, it is certain that in a solution having

1 The discussion is not seriously altered by maintaining a meticulous
distinction between "activity" and concentration.

519

520 THE DETEKMINATION OF HYDROGEN IONS

a hydrogen ion normality as low as 10~13 there are about 1010 hydrogen ions
per liter. This estimate, when taken in conjunction with the electrical
charge associated with each ion, may indicate how it is that a normality
of ID"13 H+ may be detected.

But there still remains the fact that this normality is very low in com-
parison with the other material present even in distilled water. In solu-
tions heavily buffered at pH 13 we find the hydrogen electrode or an acid
indicator rigidly stabilized in its conduct and it is questioned whether this
can be brought about by such extreme relative dilutions of the hydrogen
ions alone. Keller (1921) has expressed doubt of another sort. He calls
attention to the diminutive size of the hydrogen ion (allowing for hydra-
tion) compared with a giant protein molecule, and, picturesquely pro-
portioning the one to the other as a bacterium to a Mont Blanc, he
questions the influence upon the protein which is attributed to the
hydrogen ion.

All these are "sharp-hooked questions" which, were they "baited with
more skill, needs must catch the answer." In many of the answers given
there lies an easily detected fallacy. It is that our present convenient
modes of formulating relations are regarded as complete pictures of the
physical facts and as such are followed to the bitter end with disastrous
results. In a previous chapter we have attempted to broaden the outlook
just a little, and have suggested that in many cases a more complete
formulation of relations would show that as the physical effectiveness of
one ion fades out at extreme dilution other components of the solution
maintain the continuity. From this point of view even the more extreme
"calculation values" retain a definite significance.

We shall show that an extremely low hydrogen ion concentration is sig-
nificant as an index of the state of an equilibrium in which the hydrogen
ion itself has little actual physical significance. Its introduction as a
component of the equilibrium is a convenient and at the same time a
stoichiometrically true and mathematically correct mode of expression
containing no implications regarding the actual physical effectiveness of a
low hydrogen ion concentration as an individual quantity separable from
the other components of a solution. At higher concentrations there can
be little doubt of the physical effectiveness of the hydrogen ions whatever
their size, or energy relative to other bodies. The energy placed on the
grid of an electron tube may be small, but the potential of the grid may
determine a large flow of energy between filament and plate. The hydro-
gen ions in a solution may be small in relative size or relative numbers, but
they may control the mobilization of a large reserve.

These remarks need not be left in the above form. They may be stated
mathematically.

To emphasize one important aspect we shall deal first with acids any
one of which is so "weak" that the hydrions which it liberates, when
the salt is present in solution, are too few for their concentration to ap-
proach the order of magnitude of the concentration of either the acid or
of the salt of that acid. Indeed we shall assume that the hydrion con-

XXVII ALTERNATE FORMULATION 521

centration is so low in comparison with that of any of the chief components
of the solution that it may be entirely neglected in approximate equations.
We shall then proceed to develop the ordinary equilibrium equations, and
shall deal later with the hydrogen electrode, — in each case dispensing with
the use of concentrations of free hydrions.

Experiment makes us familiar with the fact that a weak acid may be
displaced partially or completely from its salt by certain other weak acids.
For instance, consider the reversible reaction between sodium phenolate
and acetic acid. Assuming complete dissociation of the salts, we may write
the reversible reaction

P- + HAc ^± HP + Ac-
phenolate acetic acid phenol acetate

and the equilibrium equation

- K (1)

" K

[HP] [Ac-] ~

Evaluation of the constant KAB of equation (1) would be of great value
in calculating both the direction and the extent of the interaction be-
tween the system acetate -acetic acid and the system phenolate-phenol. To
make the matter simple assume first that the acetate-acetic acid system

is to be used with the initial ratio *• j at unity and in such relatively
large concentrations that the addition of small quantities of phenol or
phenolate will not appreciably change the ratio *• ^ . Were KAB greater

than unity, it would signify that the acetate-acetic acid system would
convert phenol to phenolate. We know that the conversion is in the
opposite direction. KAB is less than unity, indicating the tendency for
the conversion of phenolate to phenol. Furthermore, KAB is much less
than unity, indicating the tendency toward extensive conversion. Now

consider the converse case in which the phenolate-phenol system is pre-

rp-i
dominant and the ratio J is unity. The fact that KAB is not only

[HP]

less than unity but much less, indicates that the phenolate-phenol sys-
tem will convert the acetate-acetic acid system extensively in the direc-
tion of acetate and not in the direction of acetic acid.

In general the extent of conversion at the attainment of an equilibrium
state may be calculated as follows. Introduce the initial values in place
of [HAc], [Ac-], [HP] and [P~]. Use the value* 1(T«-4 for KAB and solve
the following equation for x, the change between initial and final con-
centration.

([P-] - x) ([HAc] - x)

([HP] + x) ([Ac-] + x) W

2 Approximate value.

522 THE DETERMINATION OF HYDROGEN IONS

In the special case where, initially, [P~] = [HAc] = [HP] = [Ac~], equation
(2) reduces practically to x = [P~] = [HAc]. Whence the conversion to
phenol and acetate is practically complete.

Obviously it would be a great advantage to have a constant comparable
with KAB for each system composed of one weak acid and its salt in ad-
mixture with another weak acid and its salt. Of course we have data for
these; but derived in a way different from that to be discussed. A system-
atic study of this problem could have been made as follows.

Let us choose as a standard of reference any system of a weak acid and
its salt. To be specific let us choose as the standard a solution made with
0.1 mole acetic acid and 0.1 mole sodium acetate per liter of solution.

Add to this standard solution so small a quantity of brom cresol green
that it may be assumed not to change appreciably the ratio of acetic acid
to acetate. Experiment shows that this indicator is partially transformed
by the mixture; while in a solution of sodium acetate it is "blue" and in
a solution of acetic acid it is "yellow." Assume that the "yellow" is
proportional to the concentration of the acid, HI, and the "blue" is pro-
portional to the concentration of the anion, I~. Write the equilibrium
equation

IHAc] H-]

KAI

It will be convenient to rewrite (3) in the following logarithmic form:

When we have the selected standard condition, namely -

[HAc]

III
[HI]

log KAI = log r^ (5)

Now the ratio }~-. can be determined colorimetrically by the Gillespie
[HI]

method (See Chapter VI). This experimental datum being determined,
KAI is made known.

[Ac~]

Next proceed to vary the ratio and in each instance to determine

[HAcJ

colorimetrically the ratio ~^- . With the aid of (4) chart the results as
[HI]

[Ac~]

shown in figure 91. There the ordinates are log rLTT . . and the abscissas

[HAc]

are percentage salt formation — in this first instance that of brom cresol
green.

Next proceed with brom cresol purple in the acetic acid-acetate mix-
tures. In this instance we encounter some experimental difficulty be-
cause it is impossible to produce a high percentage of salt formation with

XXVII

ALTERNATE FORMULATION

523

brom cresol purple without using such high values of the ratio

that

[HAc]

exact knowledge of the values of this ratio are subject to considerable
uncertainty because of experimental errors. Nevertheless a considerable
portion of the complete data may be obtained experimentally and written
into the equation

log

[Ac~]
[HAc]

log

+ log

AI'

[r-1

[HI']

(6)

-3

-4

B.CG.

PHENOL

50 75 100

PERCENT NEUTRALIZATION

I
OL

FIG. 91. APPROXIMATE DESCRIPTION OF ACID-BASE EQUILIBRIA BY
REFERENCE TO 0.1 M ACETIC ACID + 0.1 M SODIUM ACETATE AS

STANDARD OF REFERENCE
Subsequent alignment with usual pH scale

Here HI' and I~~' refer to brom cresol purple and its anion respectively,
and KAI' is the equilibrium constant for the reaction

HAc + I7" 5=± HF + Ac~

The results are charted in figure 91.

Although there was difficulty in using the acetic acid-acetate mixtures
to produce a wide range of transformation in brom cresol purple, it is found

524 THE DETERMINATION OF HYDEOGEN IONS

experimentally that no such difficulty arises when mixtures of KH2PO4 and
Na2HPO4 are used. We shall then have the equilibrium equation

[I'-l
log L— T = log KPT, + log l— (7)

Combine equations (6) and (7)

When kP°^ = 1, we have:

log 7777-; = loS 77— + log 77— = log 77- 0)

lllAcJ -^AI' ^PI' ^AP

In (9) the constant KAP has been substituted for the product KAI' Kpi'.
The significance is made clear in figure 91.

It is unnecessary to proceed further with the detail of such a develop-
ment. What has been given briefly is sufficient. By selecting some
solution of a weak acid and its salt as a standard of reference, and by
comparing other systems of weak acids and their salts with this standard
(either directly or indirectly) it is possible to systematize equilibria in
terms of the standard of reference.

We find in figure 91 that the system phenol-phenolate is charted with

ordinate log * • There should be no difficulty in appreciating how,

[Jri A.CJ

by the use of intermediate systems, the placement of this system could
be found and there should be no doubt of the real value of such data.

Yet someone might note the very large value of log •' when phenol is

90 per cent neutralized and might object that such a value can have no
physical significance. Such an objection would be quite comparable with
one objection to the use of large values of pH. But, should the occasion
arise, the objector would not hesitate to use the equilibrium constants
indicated in figure 91 to calculate the extent of a change in a given phenol-
phenolate system produced by the addition of a given mixture of primary
and secondary phosphates.

However, the objection to employing these "calculation values," ex-
pressed in terms of a particular system, can be removed. Our present
interest is only in the relation of one system of a weak acid and its salt to
another system of a weak acid and its salt. The relative position of each of
the systems shown in the figure (or of any other system we may wish to
include) is our only concern. This relative position will not be changed
if we preserve the same numerical scale for the ordinate but change the

XXVII ALTERNATE FORMULATION 525

origin. One might add the constant 777 and call the ordinate the axis of
pQ. A distance between the centre points of any two curves would remain
the same and would be the negative logarithm of the equilibrium constant
for the reaction between the two systems described by those curves.

By considering the brom cresol green system to be the temporary
working standard we would be able to work out the curve for the acetic
acid-acetate system. To avoid confusion this has not been included in

the figure, the ordinate of which is log f- *•

[rlAcj

If, for purposes of illustration, we continue to use approximate equa-
tions, we can easily introduce into this scheme of presentation the case
of any acid which directly furnishes appreciable concentrations of hydrogen
ions.

Consider the equilibrium between hydrochloric acid and the acetate-
acetic acid system.

The equilibrium for the reaction

Na+ + Ac- + H+ + Cl- ^ Na+ + 01 - + HAc

is expressed by

[Ac-] [H+]

[HAc]
or

iog-o ao)

[Ac"]

When we choose the standard state, namely r - - = 1, we find

[HAc]

los it (11)

We need not pause to outline direct, or intermediate, means whereby
equation (10) can be experimentally studied, or how the value 4.63 for
—log KAC is reached. Assuming that this relation is determined, apply
(10) to the case of 0.1 N hydrochloric acid during titration with sodium
hydroxide. Assume that at each stage of this titration the concentration
of residual hydrochloric acid equals [H+]. The "titration curve" is
plotted in figure 91 with the aid of (10). For example, at half-neutraliza-
tion [H+] = 0.05 or

With any given value of [H+] established, it is now possible to recon-
struct the scale of the ordinate in terms of pH. See this scale at the
right of figure 91.

526 THE DETERMINATION OF HYDROGEN IONS

The development given above is so obvious in its outline that perhaps
some of the detail was unnecessary. From the main theme we may draw
these conclusions. No physical effectiveness of extremely small hydrion
concentrations need be sought and no particular virtue need be attached
to a standard of reference so long as we are concerned only with the ap-
proximate equations expressing equilibria in mixtures of weak acids and
their salts.

When exact formulation is undertaken there apply to the equations
given above the same type of correction for departure from the laws of the
ideal gas that have been discussed in previous chapters; but in some in-
stances different standards of reference would be used.

There remains a matter of some physical significance. The scheme out-
lined in this chapter implies that ionization of a weak acid is not a neces-
sary preliminary to reaction but that a reaction can proceed in the sense: —

HA + R- ^ HR + A-

i.e., by direct transfer of a hydrion from the molecule of one species to the
anion of another species. There is no reason to suppose that this is the
exclusive process any more than there is reason to believe that preliminary
ionization is necessary. There is reason to believe free hydrions to be
present in solutions of acids as "weak" as acetic. Historically such cases
became prototypes the conduct of which has been extrapolated to cases
in which there is no direct evidence of free hydrions. So far as the author
knows there is no way to call forth the characteristic "acid" properties
of extremely weak acids except to attack them with bases. Then the
formulation can legitimately follow that outlined, not necessarily in ex-
perimental procedure, but rather in the interpretation which does away
with the necessity of thinking in terms of hydrion concentrations.

However the customary formulation with the use of pH values is by
far the more convenient.

Now consider the hydrogen electrode, which is usually regarded as a
means of measuring the activities of free hydrions.

As usual, assume that at the electrode hydrogen ionizes to protons and
electrons. In a solution of a strong acid containing only the ions of the
acid and no undissociated acid molecules, we very naturally assume that
the equilibrium potential is determined by the distribution of hydrions
between solution and electrode. The assumed scheme is successfully
extrapolated to apply to the conduct of an electrode in a solution contain-
ing a weak acid and its salt, the calculated hydrion activity being in
some cases as low as 10~n, or less.

We may equally well assume that the electrons arising from the ioniza-
tion of the hydrogen attack the peripheral protons of the weak acid directly.
Idealizing the reaction as

2HA + 2e ^ H2 + 2 A-,

XXVII ALTERNATE FORMULATION 527

and proceeding to the formulation of the potential at a single electrode by
the method of Chapter XVIII we have equation (12)

In (12) P is the pressure of hydrogen in atmospheres. Hereafter we shall
maintain this pressure at one atmosphere and so eliminate P from the
equations.

If one hydrogen electrode is immersed in a solution of acetic acid and
sodium acetate and another hydrogen electrode is immersed in a solution
of primary and secondary alkali phosphates, if the solutions are joined and
liquid junction potential is supposed to be eliminated, we have:

RT (HAc) (HP04
F ' (Ac-) (H2P07)

E.M.F. = EA - Ep + — In „._: V/TT_V (13)

Now choose the solution which is 0.1 M with respect to acetic acid and
0.1 M with respect to sodium acetate as a standard of reference. Also
assign to EA (which is the single potential for the equimolecular mixture)
the arbitrary value 0. Also when the potential of the cell under considera-
tion, or any other cell, is referred to this standard let the reference be
shown by the subscript "a" in Ea, the electromotive force of the cell.

Then equation (13) becomes:

When = '• we have

Without being shown the detail, the reader will at once perceive that
by constructing cells one half of which contains the standard acetate solu-
tion and the other half of which contains in succession mixtures of weak
acids and their respective salts we can construct a systematic chart of
equilibrium relations comparable with figure 91.

It is also evident that any standard of reference can be chosen, for in-
stance the calomel half-cell. Such changes of reference are similar to the
addition of a constant quantity to each value on the ordinate of figure 91
discussed previously.

But of more importance is it to note that we need not specify the elec-
trode process. We may simply specify that we are dealing with some
process by which the weak acid is converted to its anion. Consider any
half-cell as the standard of potential reference. The process at this half-

528 THE DETEEMINATION OF HYDROGEN IONS

cell need not be known. Use the subscript "a" to show reference to this
standard. It was suggested above that the reference can have any value.
We shall then still have the relation

E8 F = E F - RT In - (15)

This formulates the free energy change in the transformation of a mole
of an acid to a mole of the corresponding anion by some process, standard,
but of unknown nature. Evaluations have a most obvious use for they
enable one to calculate the direction and extent of the conversion of one
acid into its salt by another system of an acid and its salt.

We have already stated that a hydrogen electrode in a solution of hydro-
chloric acid can be considered most reasonably as functioning in response
to free hydrions. If such a solution of hydrion activity of unity is made
the standard of reference and if the process at the other electrode is con-
sidered to be

2HA + 2€ ^ H2 + 2A-

we can formulate the potential of the cell, as mentioned previously, by the
method of Chapter XVIII and so obtain (when the hydrogen pressure
on both sides is unity):

or in numerical form for 25°C.

Eh E

' los

It will now be remembered that a value of pH as actually determined is

E E

none other than — ~*V . The constant — "would, by any other name be
0.059 0.059

a constant still. Call it pK. Then equation (17) may be written as (18)
pH = PK + log - (18)

This is, of course, the familiar Henderson-Hasselbalch equation in
terms of activity. It was derived by using the customary standard of
reference which implies the participation of free hydrions in that half
of the cell which is the standard half-cell; but it is now implied that in
that half-cell which is of particular interest no appreciable quantities of
free hydrions need be present.

The above outline should not be interpreted as meaning that no hydrions
are present in solutions buffered by very weak acids and their salts. In-

XXVII ALTERNATE FORMULATION 529

deed the complete equations would take into consideration both hydrions
and hydroxyl ions. These components would then be of particular im-
portance in very acid or very alkaline solutions, of relatively negligible
importance in "neutral" solutions and in the intermediate zones they
would rise or fall in their importance according to the concentrations and
states of equilibria of the components of a solution. Here we are probably
dealing with a class of cases in which the physical effectiveness of one or
another species dwindles gradually as conditions change and while the
dwindling occurs other species take up and maintain the continuity of
effects.

The above outline has no advantage over the usual presentation. In-
deed it is clumsy because no advantage has been taken of the common
component of acid-base equilibria, namely the hydrion. Use of the hydrion
concentration or activity makes the ordinary presentation direct and
elegant. The purpose of the alternate presentation is to convince the
elementary student that the extremely small "calculation" values he is
asked to use are truly indices of positions of equilibria among relatively
large quantities of material. It then appears that he is dealing with a
problem in the organization of his experimental facts. Furthermore the
alternate method, in spite of its formality, may help to dispel illusions
which some writers have introduced into a comparatively simple set of
formulations. For instance Dixon (1927) uses, as the keynote of an argu-
ment on mechanism, the assumption that the hydrogen electrode actually
functions in the way ordinarily described. He does not tell his reader
that the ordinary description, although an invaluable convenience, is not
necessary even to the formulation of acid-base equilibria.

One suggestion of possible value comes from the use of the alternate
formulation. Suppose an event involving kinetics is apparently under the
control of the hydrion concentration as ordinarily described. If the ap-
parent critical range is say 5-6 on the pH scale, may it not obscure insight
to say that the event "is controlled by the hydrogen ion concentration?"

CHAPTER XXVIII

ELEMENTARY THEORY OF TITRA.TION

In figure 92 are shown titration curves of hydrochloric acid at
two concentrations and titration curves of acetic and boric acids.
In each case the curve has been extended to reveal its course when
excess alkali is added. The abscissa of the figure is made per-
centage neutralization for a purpose which will appear presently.
In the construction of the curves volume changes are neglected
for purposes of simplicity.

Neglect for the moment the curve for the more dilute solution
of hydrochloric acid. Consider the nature of the end-points in
the other three cases.

When all but a very small part of the hydrochloric acid has been
neutralized there comes an approach to what appears, in prac-
ticable operations, to be a sharp "break" in the titration curve.
On the addition of the last trace of base required for complete
neutralization the pH value of the solution plunges to the alkaline
region. Much the same sort of phenomenon occurs in the titra-
tion of acetic acid; but it is important to note that the range of pH
values, compatible with a negligible error in the estimation of the
true end-point, is now much narrower. As shown by the figure
no significant error would be made were the hydrochloric acid
solution which is under consideration to be titrated to pH = 6.0;
while a very considerable error would be made were the acetic
acid solution to be titrated to this value. In the case of boric
acid there is no precipitous change of pH at the end-point. Con-
sequently a high, and almost impracticable, accuracy would be
required in titrating to an exactly determined pH value.

In the titration of the more dilute solution of hydrochloric acid
the latitude allowable has constricted and again a very high
accuracy in the attainment of an end-point pH-value is required.

Theoretically any method which reveals the pH value of the
correct end-point and which does not seriously interfere with the
equilibria involved can be adapted to the purposes of titration.

530

XXVIII

THEORY OF TITRATION

531

However the hydrogen electrode and indicator methods are most
widely used. Of these the indicator method is best adapted to
the ordinary work of the analytical laboratory.

It is obvious that, having selected the stoichiometric per-
centage neutralization as the abscissa of figure 92, we may place in
this figure the independent titration curve for a very dilute solu-
tion of an indicator just as we placed in the same figure the

53fe^

20 40/ 6.0 60
Bsrcent. Neutralization

100 120 140 160 180 200

FIG. 92. TITRATION CURVES

titration curve for a very dilute solution of hydrochloric acid.
Moreover such a curve for the high dilutions usually employed is
practically the same as the curve relating the percentage apparent
dissociation (and consequently percentage color transformation)
to pH. Furthermore no large error is made if it be assumed that
the indicator when present in a solution of the acid being titrated
does not displace the titration curve of that acid. Then the

532 THE DETERMINATION OF HYDROGEN IONS

buffer system (titrated acid + salt of the acid), by determining
the value of pH, determines the degree of color developed in the
indicator. (See Chapters I and V).

As shown by figure 92, either brorn cresol green or phenol-
phthalein could be used as end-point indicator in the titration of
tenth normal hydrochloric acid, because at, or extremely close
to, the completion of neutralization the value of pH sweeps through
the whole range of brom cresol green and well into the range of
phenolphthalein. On the other hand the dissociation constant
of acetic acid is so low that the flat portion of the curve for acetic
acid lies in the region of partial color-transformation of brom
cresol green and only gradual color transformation is observed
with no satisfactory large change at the end-point. The use of
phenolphthalein is indicated in this case.

As already noted the requirement in the case of boric acid is
so strict that boric acid is considered to be an untitratable acid
until by a curious combination with glycerine it is made a stronger
acid. It is not so generally realized that at high dilutions a
similar restriction is placed on the titration of an acid even so
strong as hydrochloric.

The principles thus briefly outlined • apply to the titration of
bases with strong acids, but, of course, with the direction of pH
change reversed and with the end-points tending to lie on the
acid side of pH 7.0. A hydrogen ion concentration of 10~7 N or
pH 7.0 is called the neutral point because it is the concentration
of both the hydrogen and the hydroxyl ions in pure water; but
evidently it is seldom the practical or the theoretical point of
neutrality for titrations.

The problem of titration with weak acids or bases as reagents
is complicated and by reason of the ever shifting end-points re-
quired in passing from case to case and the very narrow limits,
the practice is to be avoided.

With this brief outline in mind the reader will do well to .study
the classic paper of A. A. Noyes, Quantitative Application of the
Theory of Indicators to Volumetric Analysis (J. Am. Chem. Soc.
32, p. 815, 1910) and the monograph by Niels Bjerrum, Die
Theorie der alkalimetrischen und azidimetrischen Titrierungen
(Sammlung chem. chem.-tech. Vortrdge, 31, p. 1, 1914). Much
less elegant than the treatments there found, but more condensed,
is the following.

XXVIII THEORY OF TITRATION 533

In Chapter I there was developed an equation relating all the
components of a solution containing a univalent acid and a uni-
valent strong base. That equation is

[Sa] - [B+] - [H+] + £

This was derived by means of the classic equations which do
not hold accurately. Tentatively we shall neglect this aspect
and shall return to it later.

It will be in accord with modern tendencies to consider [s],
the concentration of undissociated 'salt, negligible under most
but not all circumstances.

Consider first the situation obtaining under ideal conditions
when at the true end-point of a titration exactly equivalent
amounts of acid [Sa] and total base (equal to [B+]) are present.
Then the equation reduces to

[H+P + [Sa] [H+]2 - Kw [H+] _

Kw - [H+p

Although it is impracticable to solve this equation for [H+],
it is practicable to proceed by either of two methods. In the
first, there are introduced assumed values of [Sa] and [H+] and
the equation is solved for Ka. With a sufficient number of such
numerical solutions of the equation there can be drawn up a
table (or chart) showing the ideal values of [H+] (or pH) for
various values of [Sa] and Ka. By the second procedure use is
made of the fact that in numerical solutions of the equation with
values ordinarily encountered the terms [H+]3 and Kw [H+]
usually can be neglected without serious error. As a consequence
there may be used within proper limitations the expression;

pH (of ideal end-point) = J [log ([SJ + K.) - log KaKw]

Either procedure leads to data for figure 93.

Figure 93 may be used in the following manner. Given the
value of Ka of the acid to be titrated, note the corresponding
diagonal in the figure and follow it to its intersection with the

534 THE DETERMINATION OF HYDROGEN IONS

line indicating the concentration of the salt at the final volume.
Then read upon the abscissa the ideal value of pH for the end-
point.

In the figure the diagonals have been continued only to the
heavy, interrupted line signifying the limit for 0.1 per cent error
of excess base. The position of this line is roughly determined
as follows.

Suppose a solution normal with respect to the final concentra-
tion of the salt formed is over-titrated so that there is present
0.1 per cent excess base. Assume that this excess base produces a
solution of the same pH value as that of a pure water solution
containing this same amount of completely dissociated base alone.
Obviously the solution then will be 1 X 10 ~3 normal with respect
to hydroxyl ions or, if pKw = 14, the pH value will be 11.0.
Repeat this calculation with other cases. There is thus deter-
mined the position of the line in question.

For instance, assume that there is to be titrated a solution of
an acid with Ka value 1 X 10 ~4 and that the concentration of
the salt at the end- volume is to be 0.1 normal. The ideal value
of pH at the end-point is shown by the chart to be 8.5 but if an
error of 0.1 per cent excess base is to be allowed the pH value
can be 10. Likewise for a final solution of 0.01 normal salt an
acid of Ka = 1 X 10~5 should be titrated ideally to pH = 8.5
with a limit at pH = 9.0.

The figure does not show directly the limiting values of pELfor
errors due to insufficient base. However, as suggested by figure 92
the full curve is so nearly symmetrical with respect to the end-
point that the "acid limit" is about as far displaced in one direc-
tion from the true end-point as the excess base limit is displaced
in the other direction.

For example if Ka = 10~4 and [S] = 0.01 N the ideal end-
point is pH = 8.0 and the limits for 0.1 per cent error excess base
or insufficient base are respectively pH = 9.0 and pH = 7.0.

The error of the approximate treatment increases with the
dilution of the solution and the pKa value of the acid being ti-
trated. It becomes obvious in the extreme cases where the op-
timal end-point is shown as identical with the limit for 0.1 per
cent error. However, the chart can still be interpreted to mean
that in these extreme cases an impracticable accuracy would be
required, for instance with 0.01 N and Ka = 10~6 or with O.I N
and Ka = 10~7.

1.0 Nj 1

j»

-r-

J—

T* —

/
/

1 /

o.owM

1 /

/ :

\ — A

at
.an
(d
(o

Chart tor Selecting

Ideal value of pHkbcissa)
e-rvd-poiivt irv the titration of

• /

1 /

—

•

, acid of given Ka-value
agon-al) when normality
rdinate) of resulting salt
tlv strorvg base is given.
zLimit for 0.1% excess foas

1 /

—

nnnnsjL-l

FIG. 93

O.OlN

Chart for Selecting

Ideal value of
at end- point in the titration of a
base of given Kf value (diagonal)
wXen normality (ordinate) of
resulting salt with strong
acid is give-TV.

— 'Limit of 0.1V. excess acid.

0.001N =

0.0001N

536 THE DETERMINATION OF HYDROGEN IONS

In an analogous manner there can be developed the chart show-
ing the ideal end-points for the titration of bases of various values
of Kb, and showing the limits for 0.1 per cent excess acid. This
chart is shown in figure 94.

In the titration of multi-acidic acids it usually occurs that the
first and secohd dissociatiofo. constants are sufficiently different
in magnitude to make the end-point at the completion of the
last stage of the titration that which it would be were there being
titrated a univalent acid having the dissociation constant of the
last step in the titration of the multivalent acid- Consequently
the principles already developed can be extended and extended
not only to the complete titration of multivalent acids but also
to the titration of multivalent bases. However, it is well to bear
in mind an item often overlooked. In searching tables of disso-
ciation constants one will frequently find that the constants for
the distinctively strong groups of a given acid or base are the
only constants given. It may be that nothing is said about the
weaker groups; yet it may well be that one or another of these
weak groups begin to function at the higher alkalinities to which
it is often necessary to titrate the stronger groups.

Since the error in the titration of small amounts of acid or base
becomes larger the higher the dilution, Rehberg (1925) advises the
use of low dilutions. The resulting small volume will then throw
the error upon the volumetric apparatus and to meet this Rehberg
advocates micro volumetric methods. This is a deduction from
the theory which is of great practical importance.

Modification of the theory must be introduced if account is
to be taken of the effects of neutral salts. In the first place
the presence of neutral salts will shift the equilibria in such a way
that the stoichiometric end-point is at a value of [H+] or at a
value of the hydrion activity somewhat different than that calcu-
lated by means of the classic equations. In the second place the
color of an indicator used to detect a given end-point will be
somewhat different than that calculated by means of the classic
equations with the aid of constants determined for one environ-
ment (e.g., standard buffer solutions). However, we have al-
ready noted the considerable latitude usually allowed and we
have seen that this latitude becomes narrow only for extremely
weak acids and bases or for very dilute solutions. Therefore, if

XXVIII THEORY OF TITRATION 537

the tendency of the operator is to keep his end-points near the
ideal values he need worry little about the effects of neutral
salts except in the extreme cases or for the very highest precision.
When he does meet the cases requiring exceptional care he is pre-
sented with a situation which may be one of such a variable class
that a general formulation is hardly practicable. Indeed it
would not be permissible to use dissociation constants determined
for only one set of conditions.

There is one set of cases where the matter becomes of some
importance to common practice. Frequently the occasion arises
in which it is desired to titrate a multivalent acid to some inter-
mediate salt, for instance phosphoric acid to NaH2P04. It could
be assumed with very good approximation that the classical
equations apply. Then there is easily calculated the desired pH
value when pKi and pK2 are known. But for high accuracy the
complete equations are necessary.

With this very brief outline of the main features we may turn
again to the selection of indicators. In a more elegant presenta-
tion of the theory of titration, consideration should be given to
such matters as the more favorable degree of transformation of
an indicator which is to be used as end-point indicator. However,
it seems to me to be adequate for most purposes to let the ideal
and limiting end-points graphically exhibited in figures 93 and
94 be the guides and in specific applications to select the proper
indicator either by the aid of the color chart (page 65), or, under
more exacting conditions, to set up a standard color to which to
titrate by means of the selected indicator and standard buffer
solutions.

From the general form of a titration curve it is evident that
the difference of potential between similar electrodes in solutions
which differ always by a fixed amount in the degree of neutraliza-
tion varies with the degree of neutralization and attains a maxi-
mum at the end-point. Cox (1925) put this principle to instru-
mental use in the following way. He divided the solution to be
titrated, placed one aliquot in one beaker and another in a second
beaker, connected the two solutions with a wet filter paper and
proceeded to titrate with two burettes keeping the interval of the
amounts added from each burette 0.2 cc. At the end-point the
difference of potential between the two electrodes reaches a

538

THE DETERMINATION OF HYDROGEN IONS

maximum. Maclnnes and Jones (1926, 1927) simplified the pro-
cedure by an ingenious device so that only one burette is necessary.
They shelter one electrode of figure 95. It will not immediately
attain the potential of the other as reagent is added. At the
end-point the difference of potential between the two will rise

0.6 0.6 1.0

RATIO: BASC / ACID

FIG. 95. MAC!NNES AND JONES' SHELTERED ELECTRODE FOR TITRATION

AND TYPICAL COURSE OF THE CHANGE OF POTENTIAL BETWEEN THE

SHELTERED AND UNSHELTERED ELECTRODES DURING A TITRATION

to a sharp maximum. Maclnnes analyzes the theoretical error
due to this arrangement and concludes that, with the dimen-
sions of the shelter he employs, "the method is capable of high
accuracy and is applicable in every case in which a potentiometer
technique is possible."

For discussion of potentiometric methods applied to titration
in general see: M tiller (1926), Kolthoff and Furman (1926),
Popoff (1927).

CHAPTER XXIX
NON-AQUEOUS SOLUTIONS

Indeed water is not our sole reliance; hundreds of solvents stand us in
good stead to effect electrolysis, and among these are solvents which
bring about the ionization of salts as extensively as water — or even
more extensively. — FREE TRANSLATION OF P. WALDEN.

The main principles discussed in the preceding chapters should
apply to non-aqueous solutions, except in so far as quantities
peculiar to water, for example, Kw, and numerical values applic-
able to water solutions are concerned. On the other hand we
do not have the extensive data which permit so comprehensive
a treatment as that accorded aqueous solutions.

From one point of view each solvent is worthy of a separate
treatment comparable with that accorded water solutions. If
so, individual standardization of activities might be undertaken
without reference to intercomparisons. As one of several exam-
ples of such independent studies there may be cited Banner's
(1922) investigation of the cell:

Pt, H2 1 HC1, HgCl | Hg

with ethanol as solvent, and Scatchard's (1925) treatment of
this and other studies.

However, when we pass from consideration of the solvent,
water, which has attracted most attention, to a consideration of
"miscellaneous" solvents, intercomparison becomes the more
interesting. If the point of view of intercomparison is taken, a
most important caution needs statement at the very beginning.
Let us put it in the following manner.

We have seen that the greater part of our data for aqueous
systems rests upon use of "concentration cells" which, granting
certain assumptions in regard to liquid junctions, determines the
free energy of transport of hydrions between two solutions. As
a reference there is used a theoretical standard of activity or,
practically, a solution of hydrochloric acid which for simplicity
we shall now say has a hydrion activity of unity. But it was more

539

540 THE DETERMINATION OF HYDROGEN IONS

or less immaterial to the purposes of the preceding chapters to
specify the state of the hydrion. It was even said that we would
agree to ignore the hydration. It is highly probably that in
aqueous solutions there are few anhydrous hydrions, H+,and
that the hydrions are largely hydrated,1 e.g., H3+0 (see Br0nsted,
1927 and Schreiner, 1922-1924). If then we have a cell of the
following type

Pt,H2

Aqueous solution II Non-aqueous solution
hydrion activity = 1 || of an acid

Pt,H2

the transport of ' 'hydrions" might well involve a large quantity
of free energy in the exchange of the solvents of solvation.

We can avoid this mechanistic conception and can still choose
the aqueous system as a standard and say that the activity of
the hydrion is unity in the non-aqueous solution when the poten-
tial of the above cell is zero.

Nevertheless, in practice, we still have the liquid junction poten-
tial which was eliminated from consideration in the above dis-
cussion. Suppose two solvents are in junction. Suppose these
solvents are miscible to only a slight extent so that two contiguous
phases may be established in equilibrium. It is convenient to
regard the ions in solution to have individual distribution coeffi-
cients and in general to be distributed between the two solvents
in such proportions that there will be a potential difference at
the interface. This potential difference is now a constraint which
has its part in determining the escaping tendencies of the ions.
When the potential of the above cell (with actual liquid junction)
is zero, it does not mean that the two electrode potentials are the
same. Hence the application of the above definition of unit
activity for the non-aqueous phase would imply some means of
eliminating the phase boundary potential.

The so-called phase boundary potential at equilibrium is not
to be confused with the potential arising from unequal rates of
migration of ions between contiguous but miscible solvents as
discussed in Chapter XIII. Phase boundary potentials may be
very large.2

As set forth in Chapter XXVII, the approximate equations of

1 An extensive review of the literature on ion hydration up to 1922 is
given by Fricke (1922).

2 For discussion see Michaelis and Perlzweig (1926).

XXIX NON-AQUEOUS SOLUTIONS 541

acid-base equilibria are valid when there is chosen any arbitrary
reference and for many purposes the study of non-aqueous solu-
tions by the potentiometric method may well proceed with the
use of any standard of potential. One further caution is then
necessary. As D, the dielectric constant of the solution, de-
creases, the correction term or, — log 71, increases as shown by
inspection of equation 25, Chapter XXV.* Consequently the
apparent dissociation constants of acids in non-aqueous solution
should change more rapidly than in aqueous solutions with
change in the ionic strength of the solution. With few excep-
tions the dielectric constants of non-aqueous solvents are much
smaller than that of water. The following values are approximate.

SOLVENT (LIQUIDS)

DIELECTRIC
CONSTANT

HCN

Water

Glycerol.

Ethanol

Acetone

Ammonia

21 (-34°)

Glacial acetic acid

Benzene

Hexane

1.9

(Air)

1 0006

(Vacuum). . . .

1 0

Before proceeding it will be well to mention the advantage, in
this field, of a formulation of acid-base equilibria developed by
Adams (1916), Michaelis (1914), Bjerrum and particularly
Br0nsted (1923).

Let there be a substance S which can liberate a hydrion

S ^± B + H+ (A)

Examples are

CH3COOH ^± CH3COO- + H+
acetic acid acetate

NH4+ ^ NH3 +H+
ammonium ammonia

COOHCOO- ^± COO-COO- + H+
1st oxalate anion 2nd oxalate anion

NH2C6H4C6H4NH3+ ;=± NH2C6H4-C6H4NH2 + H+
1st benzidine cation benzidine

*For an extreme see Schreiner and Frivold (1926).

542 THE DETERMINATION OF HYDROGEN IONS

By this scheme one avoids the formal inclusion of the solvent as,
for instance, in the formulation of ammonium: ammonia equi-
libria. See page 48. One may then write in general for a
reaction of type A, above :

(BHH+)

(S)
or

(S)

(B) (H+) "

where Ka is called the dissociation constant of an acid and Kb
the association constant of a base.

It is confusing to name cations, anions and undissociated
molecules in the way Br0nsted does below.

NH+ ^± NH3 + H+
acid base

CHsCOOH ^ CH3COO- + H+

acid base

The formal scheme he proposes is convenient and illuminating
and can be used without the new names.

While thermodynamic methods are not concerned with mech-
anism, it is profitable to reconsider the formulation of acid-base
equilibria with regard to the solvent concerned.

In formulating the equilibrium state for the ionization of an
acid

HA ^ H+ + A-
we wrote

(H+) (A-)

(HA)
We could have assumed interaction with water

HA + H2O ^± HjO + A-
and could have written

(HfO) (A-)

(HA) (H20)

= K

XXIX NON-AQUEOUS SOLUTIONS 543

or if (H20) is considered constant
(HJ-Q) (A-)

(HA)

tinguish this hydrion from H+, the proton. Likewise for an
acid in any solvent, the activity of which is considered constant,
we may write:

(HA)

Here Hsol represents the solvated proton.
Now suppose a base B to be added to the acid solution and to
react according to

B + Hsol ^ BH+ + Sol.
Considering (Sol) a constant we have
(B) (Hs+ol)

,
Kbs

(BH+)

Combination of (1) and (2) gives

(BH+) (A-) « ,

(B) (HA) * Kb.

which is the equilibrium equation for

B + H A ^ BH+ + A-

At equilibrium the extent to which this reaction will have pro-
ceeded from left to right, as written, may now be described by

K TC

the ratio -=r*> That is, the magnitude of ^ determines whether

J^bs Kb3

or not a given acid and a given base will react extensively in the
given solvent to furnish a stable salt without what corresponds
to hydrolysis in aqueous solution.

Kas is a measure of the extent to which the solvent tends to
appropriate the proton of HA; while Kbs is a measure of the ex-
tent to which the solvent tends to appropriate the proton of
BH+. If Kas is much larger than Kbs, the cation,feH+ can form.

544

THE DETERMINATION OF HYDROGEN IONS

Thus Hall and Conant (1928) (see figure 96) show that urea
and other bases, which are too "weak" to form stable salts in
water solution, can be titrated and form stable salts with sulfuric
acid or perchloric acid in glacial acetic acid solution.

HAc

FIG. 96/TiTRATioN OF 0.05 N BASES IN GLACIAL ACETIC ACID WITH X

EQUIVALENTS OP PERCHLORIC ACID
(Advance data furnished by courtesy of Dr. Norris F. Hall)

In liquid ammonia we have a solvent with a great "affinity"
for hydrions. In this case the solvated hydrion is the ammonium
ion NH4+. Franklin (1924) shows that phenolphthalein in liquid
ammonia is colorless but on addition of potassium amid the red
color develops.

KNH2 + HP ~+ KNH3+

colored anion

XXJX

NON-AQUEOUS SOLUTIONS

545

On "back-titration" with the acid, (NC)2NH, we may regard
this acid to furnish hydrions which are solvated to NH4+. H+
+ NH3 = NH4+. This ammonium ion, solvated proton, reacts
as follows

NH4+ + P- = NH3 + HP

Thus the discharge of color in a liquid ammonia solution of
phenolphthalein salt may be attributed to the acidifying effect
of the ammonium ion!

In their study of glacial acetic acid solutions Hall and Conant
(1927) and Conant and Hall (1927) use the cell

C6C1402 (sat.)
C6C1402H2 (sat.)

HX in glacial
acetic acid

Bridge

.KC1, (sat.)
HgCl

aqueous

For a note on the chloranil electrode see page 417.

The bridge was a supersaturated solution of lithium chloride
in acetic acid, crystallization being inhibited by a small amount
of gelatin. This solution was enclosed in a glass-stoppered U-
tube. Because of the high resistance of the cell, a quadrant
electrometer was used as null-point instrument.

Figure 96 shows the results with several bases titrated with
perchloric acid in glacial acetic acid. The ordinates are: on the
left the potentials of the cell and on the right the "pH numbers"3
calculated with an arbitrary reference point which is defined by

0.566 - E
0.0591

at 25'

3 It will be noted that the description of the data shown in figure 96
can be accomplished by use of the potentials without the so-called pH
values. In either case an assumption regarding the phase-boundary
potential has been used. According to the temperament of the reader
he will be pleased or offended by the use of "pH" in this instance. No
fundamental objection can be raised since Conant and Hall state their
assumptions and use pH in the activity sense. However, their values are
such as to make correction factors several thousand times the quantity
corrected if the connotation of a "corrected concentration" be retained
for "the activity." If this connotation be retained, the use of "pH" in
these cases is inartistic. Conant and Hall speak of super-acid solutions
in these cases. Compare page 38.

546

THE DETERMINATION OF HYDROGEN IONS

S O5

•e ^

,g T3

*C^ £^

co o3

fe -4-3

^ i

^ §

1 0

02 03 02 ^ 02 ^ ^ ^

® ™ ™ oa t> ,2 ,2 J2 t*

o 1 o*|1 ^ ®|«l«]l:§

'O 'o 'O e8 'o V 03 "^ 03 "° 03 "^ «

£ 2 s

a
1

02 02 03 fe 02 j>
02 02 02 g 02 g

' *J " tj " £_,' i—* j_, .-s *"^ o o ^

t>»

o3 "^f

o o o(i>^'o •— - ^^ ^

Q> f-Z &

"3 *o *o *3 "o ^ ^ "^ ^ ^

§ 8 «ft§ ^P,^^^

^ O K

-2

CQ 02 02 ^ »2 ^ 0)

0) O> O> O03 1>°fe *> feflfe

lO "^

o o o^^o ^1^-5 fl ,2^^

O O O^ O *H ® *-i ® ®

P C

.£

02 t/2 02 |> 02

02 02 02 > m

•<J

C3C3C3OOOC3 03^.

lO "*"

f-if-if-irrJSHZrjH3 ^Q
0 ° £ -2 £,2 § § T3 § ^

"£ S ^ S

•

„.. o e

(

t^f

o3 r "^"

N -2 ^ \

a a o S

sssa^s^ss^

Q^ M ^? ^-

n ^ Si

(

^-2^o d « ^

i O •*"

•S 12 ** 8

'f Fo1>>^:Q3 *§ ^ ^ 'S 2®?

g 3 d e

o p.3^02 £ £ £^2 >>

02 fe C3

J | * g a §P*

^ O

I§

SftS^olSgS^^

>> O

•2 * & §» -1 ^ dd5^

£H

-x ^ O o C ^*^ ,-M ^ S _S

U^^^o o 1 L'a-D0^

rH W

"o •

. li i . i

I i 14 * I ! • 1 i

1 1 li 1 lill!

1 1 15 | ! I.I I 1

rtft-^a .^ftoS^fl

Q3 .^ MH ." 03 rt «iH *«J fl)

« H s?< s ^ e ? s s

uffer number. . .

uffer compositi<

<IlPQOflWfeOWi^-i(~3

XXIX NON-AQUEOUS SOLUTIONS 547

On this scale the zero for pH is the value of a urea solution 44
per cent neutralized.

In table 68 are shown buffer solutions in glacial acetic acid
prepared from sulfuric acid (nos. 1 and 2) from acetanilid and
sulfuric acid (no. 3) from benzamid and sulfuric acid (no. 4),
from acetanilid and sulfuric acid (no. 5) and from urea and
sulfuric acid (nos. 6, 7 and 8). The potentials of the above cell
are shown in the upper row of the table and the "pH" value in
the lowest row. The color changes of several indicators in these
buffer solutions are indicated in the table.

Bishop, Kittredge and Hildebrand (1922) used the following
cell for titrations in ethanol.

H2 (1 atmos.), Pt

Solution in
Ethanol

NaBr (0.1 N)
Ethanol ' HgBr

They titrated various acids with a solution of sodium ethylate
and various bases with anhydrous HC1 dissolved in ethanol.

Bishop, Kittredge and Hildebrand determined roughly the
positions of color-change of various indicators on an arbitrary
scale.

Michaelis and Mizutani (1925) report upon the changes of
apparent dissociation constants (expressed as pK') of several
acids, of ammonia and of several ampholytes as the solvent is
gradually changed from aqueous to alcoholic through inter-
mediate mixtures. While a rough parallelism is to be noticed in
the changes of pK for certain acids, there remain notable ex-
ceptions. Michaelis and Mizutani (1924) give the changes in
apparent pK' of nitrophenol indicators and phenolphthalein
with change in the alcohol content of the solution. See also
Kolthoff (1923), Thiel, Wulfken and Dassler (1924).

Cray and Westrip (1925) have calibrated a series of buffer
solutions and worked out the "pH-ranges" of various indicators
for acetone containing 10 volumes of water in 100 volumes of
acetone-water.

Linderstr0m-Lang (1927) discusses the advantages of titrating
amino acids in acetone solution.

For an example of a study of equilibria in two phase systems
see Murray (1923).

548 THE DETERMINATION OF HYDROGEN IONS

The quinhydrone electrode has been used in the study of non-
aqueous solutions by Schreiner (1924), Larrson (1924), Ebert
(1925), Millet (1927), Pring (1925), Cray and Westrip (1925),
Lund (1926).

A review of the electrochemistry of non-aqueous solutions is
given by Walden (1924) and Miiller (1924). See also Germann
(1925).

CHAPTER XXX

APPLICATIONS

Finally, acidity and alkalinity surpass all other conditions, even
temperature and concentration of reacting substances, in the in-
fluence which they exert upon many chemical processes. — L. J.
HENDERSON.

GENERAL REMARKS

It is because of the great variety of applications in research,
routine and industry that the theories and devices outlined in the
previous chapters have been developed. The physical chemist
sees in them the instruments of approximation or of precision
with which there have been discovered orderly relations of ines-
timable service to the chemist and with which there have been
established quantitative values for free energy changes. The bio-
chemist might almost claim some of these methods as his own, not
only because necessity has driven him to take a leading part in
their development, but also because their application has become
part of his daily routine in very many instances.

As a comprehensive generalization it may be said that the
hydrogen ion concentration of a solution influences in some
degree every substance with acidic or basic properties. When we
have said this we have said that the hydrogen ion concentration
influences the great majority of compounds, especially those of
biochemical interest. Such a generalization, however, would be
misleading if not tempered by a proper appreciation of propor-
tion. Rarely is it necessary to consider the ionization of the
sugars since their dissociation constants are of the order of 10~18
and their ionization may usually be neglected in the pH region
encountered in physiological studies. Likewise there are zones of
pH within which any given acidic or basic group will be found in
dilute solution to be in a practically undissociated or fully dis-
sociated state. Perhaps there is no more vivid way of illustrat-
ing this than by a contemplation of the conduct of indicators.
Above a certain zone of hydrogen ion concentration phenol-

549

550 THE DETERMINATION OF HYDROGEN IONS

phthalein solutions are colorless. Below this zone (until intense
alkalinity is reached) only the colored form exists. Within the
zone the color of a phenolphthalein solution is intimately related
to the hydrogen ion concentration. The conduct of phenol-
phthalein, which happens to be visible because of tautomeric
changes which accompany dissociation, is a prototype of the con-
duct of all acids. Just as we may suppress the dissociation of
phenolphthalein by raising the hydrogen ion concentration of the
solution so may we suppress the dissociation of any acid if we can
find a more intensely ionizing acid with which to increase the
hydrogen ion concentration of the solution. Similar relations
hold for bases, and, if we regard methyl red as a base, we may
illustrate with it the conduct of a base as we illustrated the con-
duct of an acid by means of phenolphthalein.

Such illustrations may serve to emphasize the reason underly-
ing the following conclusion. Whenever, in the study of a physi-
ological process, of a step in analysis requiring pH adjustments or
of any case involving equilibria comparable with those mentioned
above, there is sought the effect of the pH of the solution, it may
be expected that no particularly profound effect will be observed
beyond a certain zone of pH. Within or at the borders of such a
zone the larger effects will be observed. From this we may con-
clude that the methods of determining hydrogen ion concentra-
tions should meet two classes of requirements. In the first
place, when the phenomenon under investigation or control in-
volves an equilibrium which is seriously affected by the pH of
the solution, the method of determining pH values should be the
most accurate available. In the second place, when the equi-
librium is held practically constant over a wide range of pH, an
approximate determination of pH is sufficient and refinement
may be only a waste of time.

Neglecting certain considerations which often have to enter
into a choice of methods it may be said that the electrometric
method had best be applied in the first case and the indicator
method in the second. When the nature of the process is not
known, and it therefore becomes impossible to tell a priori which
method is to be chosen, the colorimetric method becomes a means
of exploration and the electrometric method a means of con-
firmation.

XXX GENERAL REMARKS 551

Exception will be taken to this statement as comprehensive
for there are cases where one or another method has to be dis-
carded because of the nature of the solution under examination.
Nevertheless, in general, the utility of the colorimetric method
lies in its availability where approximations are needed and
exact determinations are useless and also in its value for recon-
naissance; while the value of the electrometric method lies in its
relative precision.

In some instances the qualitative and quantitative relations of
a phenomenon to pH should be carefully distinguished. Note, for
instance, the significance of an optimum or characterizing point.
Consider the conduct of phenol red and of cresol red. These two
indicators appear to a casual observer to be very much alike
in color and each exhibits a similar color in buffer solutions of pH
7.6, 7.8, etc. Careful study, however, shows that each point on
the dissociation curve of phenol red lies at a lower pH than the
corresponding point on the dissociation curve of cresol red. If
the half transformation point be taken as characteristic it may be
used to identify these two indicators. Likewise it is the dissocia-
tion constant of an acid or a base, the isoelectric point of a protein,
the optimum pH for acid agglutination of bacteria, or an optimum
for a process such as enzyme activity that furnishes characteristic
data.

When there is observed a correlation between pH and some
effect, the mere determination of pH alone will of course throw
but little light upon the real nature of the phenomenon except
in rare instances. Determination of the hydrogen ion concentra-
tion will not even distinguish whether a given effect is influenced
by the hydrogen or the hydroxyl ions, nor will it always reveal
whether the influence observed is direct or indirect. The so-
called hydrion concentration or pH number of a solution may be
only an index of the position of an equilibrium state in which the
hydrion is an entity of no great importance from a physical point
of view. See Chapter XXVII. However, if only as an index,
its importance remains. Therefore advantage should be taken
of the comparative ease with which the concentration of hydrogen
ions may be determined or controlled and its influence known or
made a constant during the study of any other factor which may
influence a process. From this point of view methods of deter-

552 THE DETERMINATION OF HYDROGEN IONS

mining hydrogen ion concentration take their place beside ther-
mometers, buffer mixtures beside thermostats and automatic
control devices beside thermoregulators.

Indeed it may be said that the failure to take advantage of
these devices is still a prolific source of error in the experimental
work of every branch of science having to do with solutions. In
one case the neglect may be gross; in another case it may be a
perfectly excusable mis judgment. A complete understanding of
the effects of the hydrogen or hydroxyl ion, or of the effects of
those equilibrium states of which pH is an index, is very far from
attainment and those who faithfully control their solutions are
often rewarded by the most surprising results. To emphasize
this aspect we may call attention to the fact that while the disso-
ciation of glucose is negligible in the region of pH 7 so far as any
great effect upon the displacement of other acid-base equilibria
is concerned, a converse effect, which does not belong to the
category of equilibria, is decidedly not negligible. A shift in pH
from 7.0 to 7.4 has a very marked influence upon the conduct of
glucose in heated solutions as every one who has made culture
media knows.

Nor is it adequately realized that the formulations of the
measurements we make are so fundamentally thermo dynamic
that they may ignore intermediate stages in chemical trans-
formations or may lead to false impressions regarding the entities
which convenience forces us to symbolize in some particular way.
Reference was made on page 540 to the fact that for the purposes
of a limited thermodynamic treatment it is a matter of indif-
ference whether we regard the hydrion in aqueous solution to be
hydrated or not. Yet this item may leap into importance when
we attempt to compare events in different solvents. So, also, the
ignoring of groups which, as measured by ordinary methods,
appear to have in aqueous solution little tendency to dissociate,
may obscure their parts in kinetic events.

Our methods of formulation tend to emphasize either one
particular function or some refinement of this function that re-
quires a new symbolism. We may then fall victim to that
restraint upon outlook which led Comte to remark: "every
attempt to employ mathematical methods in the study of chem-
ical questions must be considered profoundly irrational and con-

XXX ON THE BIBLIOGRAPHY 553

trary to the spirit of chemistry " Mellor, who gives this

translation of Comte, believes that the key to these remarks is
Comte's statement that "our feeble minds can no longer trace
the logical consequences of the laws of natural phenomena when-
ever we attempt to simultaneously include more than two or
three essential factors." Nevertheless the requirements of bio-
chemistry impose the task of simultaneously including many
factors. If this task is to be met, the physical chemist must
develop methods of formulation of such fundamental directness,
simplicity and generality that the biochemist will not mistake
the formalities of convenience which lead to "vanishing par-
ticulars" for those other and still necessarily artificial devices of
the intellect which lead to a comprehension of togetherness.

ON THE BIBLIOGRAPHY

As mentioned in the first edition of this book, the applications
had, by 1920, become so numerous, and in many instances so
detailed, that the time had come for a redispersion among the
several sciences of the material that had from time to time been
assembled by authors who were intent upon emphasizing the
importance of hydrion concentration. The crude statistics noted
in the preface to this, the third edition, indicate the appalling
task that awaits any one who attempts to assemble a complete
bibliography. Even the limited comprehensiveness of the bib-
liography of the second edition is no longer practicable. Con-
sequently, while this chapter retains its old form, there has had
to enter the element of selection. This has been distressing to
the author, ostensibly because of the injustices that may be done
to subject matter and to leading authors, but probably because
selection reveals the ignorance of the selector. However, for
those students who desire "leads" in their first attack upon the
literature there may remain some value in the following sketches.

These sketches and various assemblies of references in the text
serve as crude indices to the bibliography. In this are to be
found only some six hundred of the references in the second edition.
Consequently the older edition should be consulted for many of
the earlier references. The following selection of over 1600 refer-
ences is not to be considered in any other way than as an
introduction to a vast literature.

554 THE DETERMINATION OF HYDROGEN IONS
GENERAL TREATISES

What may be called the fundamental classic is the paper pub-
lished by S. Arrhenius in 1887. The subsequent evolution of the
theory of electrolytic dissociation to 1914 is reviewed by Arrhenius
(1914) and in Faraday Society Symposium (1927).

Among several papers of historical interest is that of Bugarzsky
and Liebermann (1898) who first applied the hydrogen electrode
to a biochemical problem, and Bottger's paper on titration.

Two classics of biochemistry are S0rensen's (19C9) Etudes
enzymatiques II in which are organized the subjects of buffer
solutions and indicators and Henderson's (1909) Das Gleichge-
wicht zwischen Basen and Sauren im tierischen Organismus in
which is outlined the acid-base equilibria of the blood.

The papers of Noyes (1910) and of Bjerrum (1914) on the
theory of titration have needed but slight elaboration since their
publication.

No one has contributed so widely to the applications of indi-
cator and electrode methods as has Michaelis. Indeed an ex-
cellent cross-sectional view of the variety of these applications
can be obtained by reading Michaelis' numerous papers. These
are "easily traced in abstract journals and will not be cited in
detail. The first edition (1914) of Michaelis' Die Wasserstoffio-
nenkonz'entration contained brief reviews of applications. The
second edition (1922), now in an English translation by Perlz-
weig (1926), elaborated the theoretical sections of the first.

As the subject has gained prominence in special fields the
journals and compilations covering these fields have published
reviews. These reviews are too numerous to mention. Books
by the following authors may be cited:

Kolthoff (1923). Der Gebrauch von Farbenindicatoren. Springer, Berlin.
French edition translated by Vellinger, 1927. English edition trans-
lated by Furman (1926). John Wiley.

Kopacewski (1926) . Les ions d'hydrogene. Signification, mesure, appli-
cations, donnees numeriques. Gauthier-Villars, Paris.

Michaelis (1914-1923). Die Wasserstoffionenkonzentration. Springer, Ber-
lin. The second edition (1923) enlarged upon only the theoretical
part of the first. Second edition translated into English by Perlz-
weig, 1926. Williams and Wilkins, Baltimore.

Mislowitzer (1928). Die Bestimmung der Wasserstoffionenkonzentration
von Fliissigkeiten. Springer, Berlin.

f * * . •

XXX SPECIAL APPLICATIONS, A-B 555

Mizutani (1925). The determination of hydrogen ions. (In Japanese)

Tokyo.

Prideaux (1917). The theory and use of indicators. Van Nostrand, N. Y.
Vincent (1924). La concentration en ions hydrogene et sa mesure par la

methode electrometrique. Hermann, Paris.
See also Rona (1926).

SPECIAL APPLICATIONS

Analyses. Hydrion methods have manifold applications through the
theory of titration. See Chapter XXVIII. Intimately related are
methods of oxidation-reduction titration, one aspect of which was discussed
in Chapter XVIII. For particulars in regard to potentiometric Nitrations
in analysis see Miiller (1926), Kolthoff and Furman (1926) and Popoff
(1927). The empiricism that characterized the older developments in
analytical chemistry often left specifications for the use of mixtures of
acids and their salts. These we now know control the ratios of the con-
centrations of ions and undissociated molecules, and a useful index to such
a ratio is the proper combination of the pH number of the solution and the
pKa or pKb number of a given system. The older specifications also
left directions for delicate proportionment of reagents which often can
be conveniently expressed in terms of pH. These conveniences are coming
into wide use without that systematic record which permits adequate
references. As examples in the field of inorganic analysis there may be
cited the papers by Blum (1913, 1914 and 1916), Fales and Ware (1919),
Hildebrand and cowofkers (1913-1916), Robinson (1923). Among several
methods of biochemistry there may be mentioned the benzidine sulfate
method for the determination of sulfate (see any text). General princi-
ples of the application are to be found in modern texts of inorganic anal-
ysis, e.g., Kolthoff and Menzel's Massanalyse (1928), Fales (1925), and the
older text of Stieglitz (1917). Separations of proteins, amino acids etc.
involve constant attention to pH. See, for example, Abel et al. (1927),
Vickery and Leavenworth (1927), Foster and Schmidt (1923).

Bacteriology. The applications in bacteriology up to 1917 are reviewed
by Clark and Lubs (1917). For a bibliography on the role of ions in
general in bacterial physiology see I. S. Falk (1923). For various modern
applications see Jordan and Falk (1928), Buchanan and Fulmer (1928).

Acid agglutination of bacteria, first definitely recognized by Michaelis
(1911) in its relation to hydrion concentration has been found to be of
some diagnostic use. For example, Gillespie (1914). Eisenberg gives an
extensive bibliography up to 1919. See especially Northrop and DeKruif
(1922) and De Kruif (1922).

Adjustment of the reaction of media by the old titrimetric procedure was
criticized by Clark (1915), and, on the introduction of suitable indicators
and the evidence for the advantage of adjusting on the pH basis, the
titrimetric method has been abandoned for more significant and easier
modern methods. Studies on growth optima (which see below) have shown

556 THE DETERMINATION OF HYDROGEN IONS

that for the cultivation of most saprophytes approximate indicator control
is sufficient. For particular purposes and especially for the study of
certain important pathogens, it is well to adjust with the precision at-
tained with standards. Seldom is electrometric control necessary. Data
for special media and special organisms now usually accompany all de-
scriptions. See, for example, Standard Methods of Water Analysis, H. N.
Cohn (1919), Medical Research Committee (1919).

Antigenic action. For example see Falk and Powdermaker (1925).
See Immunology.

Bacterial products, purification. For example, see Michaelis and
Davidsohn (1924).

Bacteriophage. For examples see, Davison (1922), Arloing and Chavanne
(1925), and Todd (1927).

Bacteriostatic action of dyes. For examples see, Churchman (1922),
Smith (1922), and Stearn and Stearn (1924, 1926).

Disinfectant action of acids and bases is certainly in large measure a
function of hydrogen and hydroxyl ion activity; but specific effects of
certain acids and bases which were suspected before, have now been more
clearly demonstrated by the use of hydrogen ion methods. By the con-
ductivity method, Winslow and Lochridge (1906) were able to show the
effect of the hydrogen ion in simple solutions and predicted relations
which more powerful methods have extended to complex media. Cohen
(1922) has reviewed certain of the fundamental relations between pH and
viability of bacteria under sublethal conditions. The more direct action
of hydrion concentration upon cells must be distinguished from its control
upon the effective state of a toxic compound. Knowledge of pH effects is
therefore essential to the assay of disinfectants and to the advancement
of chemotherapy.

See review by Bonacorsi (1923), and references by Jarisch (1926). Ex-
amples: Michaelis and Dernby (1922), Dernby and Davide (1922), Eggerth
(1926), Fleischer and Amster (1923), Kuroda (1926), Levine, Toulouse and
Buchanan (1928).

Electrophoresis . Winslow, Falk and Caulfield (1923), and papers by
Falk in Journal of Infectious Diseases, 1925-1927.

Gram reaction. See "Staining."

Influence of pH on bacterial metabolism. The reaction of the medium,
even within the zone of optimal bacterial growth, is found to influence
either the absolute rate, or the relative rate of specific types of metab-
olism. Not only the activity but also the production of enzymes is
influenced; and the production of special products such as toxins is par-
tially controlled by the pH of the medium.

Examples: Virtanen and Barlund (1926), Arzberger, Peterson and Fred
(1920), Clark (1920), Avery and Cullen (1920), Merrill and Clark (1928).

Morphology. Example: Reed and Orr (1923).

Motility. Example: Reed and MacLeod (1924).

Optimal Zones and the limits of growth and general metabolism have
naturally been the chief interest in the first surveys of the influence of hy-

XXX

BACTERIOLOGY

557

TABLE 69

Optimum and limiting reactions for the activities of microorganisms
(After Waksman, 1927)

ORGANISMS

ACID
MAXI-
MUM

OPTIMUM

ALKALI

MAXIMUM

AUTHOR

Nitrosomonas

3 9

7 7-7 9

9 7

Gaarder and Hagen

Nitrobacter . . .

3 9

6 8-7 3

13 0

IVIeek and Lipman

Nitrification in soils

3 5

65-75

11 9

Gerretsen Waksman

Thiobacillus denitrificans
Th thiooxidans

5.0
1 0

7.0-9.0
2 0-4 0

10.75

6 or?)

Trautwein
Waksman and Starkey

Bac pycnoticus

5 2

6 8-8 7

Q 2

Ruhland

Bac. amylobacter .

5 7

69-73

Dorner

Azotobacter ....

5 6-6 0

6 5-7 8

8 8-9 2

Gainey Johnson and

Bad. radicicola of:
Medicago and Melilo-
tus

5 O]

Lipman, Yamagato
Itano, Stapp

Pisum and Vicia

4 8

Trifolium and Phase-
olus

4 3[

11.0

Fred and Davenport,
Fred and Loomis,

Soja

3 4

Bryan

Lupinus

3 2

Bact coli

4 4

6 5

7 3

Dernby

Bact. vulgare

4 4

6 5

8 4

Dernby

Bact. pyocyaneum
Bact stutzeri

5.6
6 1

6.8

7 0-8 2

8.0
9 6-9 8

Dernby
Zacharowa

Bac subtilis

4 2

75-85

9 4

Itano

Bac. putrificus

5 8

8 5

Dernby

Act scabies

4 8-5 0

6 5-7 5

8 7

Gillespie ^Waksman

Mucor glomerula

32-34

87-92

Asp terricola

1 6-1 8

90-93

Pen. italicum

16-18

91-93

Johnson

Fus. oxysporum.

1 8-2 0

9 2-11 1

Asp niger

1 2

1 7-7 7

Terroine and Wurmser

Gibberella saubinetii
Spore germination of
fungi

3.0

1 5-2 5

4.8-9.4
3 0-4 0

11.7

Maclnnes
Webb

For other data on the culture of microorganisms other than bacteria
see Sakamura (1924), A. Saunders (1924), Sartory, Sartory and Meyer (1927),
Scott (1924), Waksman (1927), Webb and Fellows (1926).

558 THE DETERMINATION OF HYDROGEN IONS

drion concentration upon bacterial activity. It is now clear that more
exact studies will have to differentiate between optimal pH to initiate
growth, optimal zones of growth, optimal zones for general or special
metabolism, optimal zones for preservation, etc. The self-limitation first
clearly defined by Michaelis and Marcora (1912) has been applied to cer-
tain practical tests, for example see Clark (1915), Avery and Cullen (1919).
pH limits for special organisms of commercial significance are exemplified
by control of "rope" in bread (Cohn, Wolbach, Henderson and Cathcart,
1918) and potato scab (Gillespie and Hurst, 1918). Growth optima and
limits usually accompany modern descriptions and are best sought in the
special literature. As illustrations there may be quoted table 69.
Several of the pH numbers are first approximations.

Sporulation. Example : Itano and Neill (1919) .

Testing fermentation. See, for examples: Chesney (1922), Clark and
Lubs (1917), Nichols and Wood (1922).

Toxin production. Examples: Abt and Loiseau (1922), Davide and
Dernby (1921), Dernby and Allander (1921), Dernby and Walbum (1923),
Jonesco-Mihaesti and Popesco (1922), Walbum (1922-1923), Cook et al.
(1921). See also Immunology.

Vaccine virus. Defries and McKinnon (1926) .

Virulence. Felton and Dougherty (1924), Defries and McKinnon (1926) .

Viscosity of bacterial suspensions. Falk and Harrison (1926).

Blood. The hydrion concentration, or the ratio between acid residues
and their anions, is, with the exception of temporary fluctuations (exercise,
etc.), regulated with remarkable constancy in the blood of any normal
individual. It- very seldom varies far from pH 7.4. Van Slyke (1921)
places the normal variation between 7.3 and 7.5 and the limits usually
compatible with life at about 7.0 and 7.8, although he takes these as data
convenient to a general description.

The bicarbonate-carbonic acid equilibrium is important because one of
the chief functions of the blood is to carry C02. The bicarbonate system
is also used as an indicator.

See carbonate equilibria for the derivation of

[HCOj]

PH - PK^ 10g [fr^ck]
and

[free CO2] = K0P

Inspection of relations involving the carbonate ion, CO3~~ (see page 561),
will show that, at pH 7.4, [CO3~~] may be neglected and that the fixed
carbon dioxide may be regarded for present purposes as almost entirely in
the form of bicarbonate. Therefore the above equations suffice. They
can be combined to

[HCOj]
PH = pK; + log -r-

XXX

BLOOD

559

If equations in terms of activities are to be used, it is convenient to know
that Van Slyke, Hastings, Murray and Sendroy (1925) have estimated the
ionic strength of blood to be n = 0.16.

In using the ideal equation with whole blood, serum or solutions such
as hemoglobin, the constants must be evaluated for the specific conditions.
Van Slyke, Cullen and Hastings (1922) use the values shown below

SOLUTION

WHEN FOR-
MULA 18 USED
FOR MILLIMOLS

WHEN FOR-
MULA IS USED
FOR VOLUME —
PER CENT

Water

0 0326

0.0730

Serum or plasma

0 0318

0 0712

6 14

Whole blood

0 0300

0 0672

6 18

12 per cent Hemoglobin in 30 mM
NaHCO3

0.0312

0.0699

6.18

Since [HCO3-J = [Total CO2] - [free CO2], the above equation mav be
used in the form

PH = pKj + log

[Total C02] - KpP
K0P

This shows that, for the definition of the equilibrium state, two measure-
ments are necessary: pH and [Total CO2]; pH and P; or [Total CO2] and P.

Fifty volumes per cent total CO2 and pH 7.4 may be regarded as an
orienting norm.

Investigative methods utilize pairs of these quantities in determining,
among other constituents of the blood, ratios of acid residues to anions,

on the principle that, at a common pH value, the determination of

[tree C/L^J

measures all such ratios of any anion concentration to the concentration
of the dissociation residue.

A tentative hypothesis which is useful for a gross description of the
manner in which these ratios is kept constant is that the "respiratory
center" is sensitive to changes of pH, stimulating lung- ventilation as pH
decreases, and checking lung- ventilation as pH increases. This hy-
pothesis is disputed. (See for example Y. Henderson, 1922.) It remains
a hint the value of which is lost when it is forgotten that hydrion concen-
tration of itself, when unrelated to definite equilibria, means little
chemically.

When "combustion" in the tissues is incomplete and acid products of
combustion replace the CO2 which the lungs can eliminate, and when these
non-volatile or "fixed" acids cannot be eliminated by the kidneys as fast
as produced, the fixed acid anions will replace bicarbonate ions. Hence
[Total CO2] in the last equation has a significance of its own.

560 THE DETERMINATION OF HYDROGEN IONS

While the bicarbonate system is important in itself, it is not the chief
buffer system of the blood. The protein systems are the more powerful
buffers and of these the systems involving hemoglobin and oxyhemoglobin
are the most important. Here are met two distinct aspects. In the first
place oxyhemoglobin behaves in a way conveniently described as if it were
a stronger acid than hemoglobin. Consequently oxidation in the lungs
results in the virtual transfer of base from bicarbonate to oxyhemoglobin
tending to displacement of C02. In the tissues the reverse effect, attend-
ing reduction of the blood pigment, provides base to combine isohydrically
with CO2. In addition, both hemoglobin oxyhemoglobin, and the other
proteins exercise ordinary buffer action. In these two senses the blood
pigment is the most important carrier of C02 as well as the chief carrier
of oxygen.

The buffers of the blood are distributed between the cells and plasma.
Not all the constituents of the buffer systems diffuse freely between the
cells and plasma. Of those constituents of the cell, which are of chief
importance and which do not diffuse out, are the several forms of hemo-
globin and oxyhemoglobin and the base K+. Likewise the plasma pro-
teins and Na+ do not diffuse inward. There is established a complex
Donnan equilibrium (see page 568) in the maintenance of which, during
CO 2 exchanges, the anions HC03~ and Cl~~ migrate in and out to adjust
electroneutrality, and water migrates in and out to maintain osmotic
equilibrium.

Intimately connected with the regulation of the hydrogen ion concen-
tration of the blood are the functions of the kidneys. [See Cushny (1926),
and Marshall (1926).] By their action there are eliminated the non-
volatile products of metabolism, several of which are of great importance
for the acid-base equilibria of the blood. The colorimetric determination
of the pH of the urine is a comparatively simple procedure which furnishes
valuable data when properly connected with other data. (See for in-
stance Blatherwick, and the works of Henderson, of Palmer, of Van Slyke,
of Cullen, of Hastings, of Austin, etc.)

While the greatest interest has centered in the subjects briefly men-
tioned above, there remain innumerable other problems of importance.
Of these there may be mentioned the relation of the pH of the blood to
the calcium-carrying power, to the activity of various enzymes, to the
permeabilities of tissue membranes, to the activity of leucocytes, and to
various reactions used in the serum diagnosis of disease.

There have been numerous studies of the blood of lower animals. See
for example, Bodine (1926), Duval (1924), Glazer (1925), Gellhorn (1927),
Hawkins (1924), and references in Porter (1927).

Gasometric, colorimetric and potentiometric methods of determining
pH numbers of blood, serum etc. are so highly specialized that the special
literature of the technique and of the principles of the equilibria con-
cerned should be consulted.

The following references are selected from a huge literature as being
especially helpful.

XXX CARBONATES 561

Historical. Henderson (1908-1909).

Reviews and theoretical discussions. Austin and Cullen (1926), Hen-
derson (1926), Murray and Hastings (1925), Van Slyke and Van Slyke
et al. (1921-1927), Warburg (1922).

Methods. Austin, Stadie and Robinson (1925), Cullen (1922), Cullen
and Hastings (1922), Cullen, Keeler and Robinson (1925), Dale and Evans
(1920), Eisenman (1927), Hastings and Sendroy (1924r-1925).

Physiological data. Cullen and Robinson (1923), Drury, Beattie and
Rous (1927), Gamble (1922).

Respiration. Haldane (1922), Barcroft (1925).

Carbonate equilibria. Because of their general importance to bio-
chemistry and general chemistry, equilibria in carbonate and bicarbonate
solutions deserve special mention. The following treatment is necessarily
brief.

When carbon dioxide dissolves in water it presumably is present both
as anhydrous C02 and as the hydrate H2C03, carbonic acid. For a dis-
cussion of the rate of hydration and proportions of the forms, see experi-
ments and references by Buytendijk, Brinkman and Mook (1927).* Ana-
lytical methods do not ordinarily distinguish the two forms, and, since the
sum of the two is generally the more important quantity, we may write the
equilibrium equation for the relation between a partial pressure, P (atmos-
pheres) of gaseous carbon dioxid and the dissolved carbon dioxid as follows :

[CO,] + [H2C03] = [free CO2] = Ko'P (a)

In the presence of bases we still have the above relation holding between
the partial pressure and that portion of the total CO2 which remains un-
combined. However, variation in the composition of the solution will
vary the magnitude of KQ. Dissolved CO2 reacts with water and since
[H2O] may be regarded as constant we have the equilibrium equation

[OCM =^+l (b)

[H2C03] [H2C03]

The H2CO3 dissociates in steps and for the first step the equilibrium
condition is:

[HC031

Combining equations (b) and (c) and collecting constants we have

[COJ + [H2C03]

or using the convention mentioned above

[H+] [HC031
[free CO j ~

(d)

Cf. Faurholt (1924).

562 THE DETERMINATION OF HYDROGEN IONS

The constant K/ is sometimes called the first dissociation constant of
carbonic acid. It is not strictly so but is rather of the nature of an "ap-
parent dissociation constant." Ki' is more useful than the true dissocia-
tion constant but is probably much smaller.

For the second stage of dissociation the equilibrium condition is:

For simplicity the above equations were stated in terms of concentra-
tions, as is permissible for ideal conditions, for a limited range of con-
ditions or for limiting equations. Equations (a), (d) and (e) may now be
restated with correction terms or with activities.

[free C02]To = (free C02) = K0P (f)

(H+) [HCO^] 71 (H+) (HCOp

Ki (g)

K2 (h)

(free C02) (free CO2)

(H+) [C03— ] 72 _ (H+) 'CO,"")
(HC03) (HCO~)

The relation

[free CO2] = — P

may be assumed to be subject to use with solutions containing no free
base which would form appreciable amounts of bicarbonate and carbonate

T£-

ions. Values of — -for solutions of sodium chloride are given by Johnston

(1915) from the data of Bohr.
Concentration of

NaCl, molar... 0.0 0.1 0.2 0.3 0.5 1.0
jr

— at25° 0.0338 0.0329 0.0321 0.0314 0.0300 0.0270

See also Walker, Bray and Johnston (1927).

Randall' and Failey (1927) tabulate values of y0 at 15° and 25° for
various ionic strengths, using, however, molality as the basis of calcula-
tion. Their equation is

Molality of CO2 = —
7

XXX

CAKBONATES

563

In water the solubility of C02 is 0.0478 molal at 15° and 0.0370 molal at
25°. Representative values of 7 at 25° are:

SALT

KC1 1

0.508

1.072

HC1 1

1.031
0.505

1.143
1.015

2.080

0.998

See also section on "Blood," and papers by Van Slyke and Neill (1924)
and Van Slyke and Sendroy (1927) for details of manometric measurement
of CO 2 extracted from solutions.

TABLE 70

Values of log <f> interpolated at a series of ionic strengths
(After Walker, Bray and Johnston, 1927)

A«

25°

BASE

37°

BASE

<p25/<p37

0.00

2.491

2.296

2.292

2.296

1.57

0.01

2.403

2.400

2.396

2.205

2.204

2.200

1.57

0.02

2.376

2.371

2.362

2.177

2.174

2.165

1.58

0.04

2.342

2.334

2.318

2.142

2.135

2.118

1.59

0.06

2.319

2.308

2.286

2.118

2.106

2.084

1.59

0.08

2.300

2.286

2.260

2.096

2.082

2.055

1.60

0.10

2.286

2.267

2.238

2.079

2.060

2.031

1.61

0.20

2.236

2.194

2.160

2.015

1.980

1.952

1.64

0.40

2.186

2.100

1.871

0.60

2.158

2.034

1.828

0.80

2.139

1.982

1.0

2.122

1.939

1.5

2.098

1.860

2.0

2.085

1.802

2.5

2.074

1.753

Combination of equations (f) and (g) gives

pH - log [HC03-] + log KoP = pKi + log 71 (i)

The quantities on the left are determinable if [HCO3~] is regarded equal,
for instance, to [NaHCO3].

Hastings and Sendroy (1925) find that pK, at 38° is 6.33 and log 71 =
Hence, if we let pKi' = pKi + log 71

6.33 -

564

THE DETERMINATION OF HYDROGEN IONS

Likewise they find at 38 °C.

pKY = pK2 + log 72 = 10.22 - 1.1 V~

By combining several activity coefficients and the first and second dis-
sociation constants, Walker, Bray and Johnston (1927) derive:

[C03-]P

They tabulate the values of log <p at a series of ionic strengths and at 25°
and 37°C. See table 70.

"This table enables one to calculate the concentration of bicarbonate
and of carbonate in any solution in equilibrium with the partial pressure
P (atm.) of carbon dioxide, provided the total alkali associated with both
carbonate and bicarbonate is known; or conversely, to compute the equi-
librium pressure."

FIG. 97. RELATION OF PAKTIAL PRESSURE OF CO2 IN (ATMOSPHERES) TO
PER CENT Na2CO3 IN CARBONATE-BICARBONATE MIXTURE

As an illustration there are given in figure 97 the pressures of CO2 over
a solution in one case 0.1 molal with respect to [Na2CO3] + [NaHCO3],
and in the other case 0.01 molal with respect to the same sum, when the
per cent of [Na2CO3] is changed. The CO2 partial pressure of our atmos-
phere is about 0.0003 atmosphere. The figure shows that the 0.01 M
solution will absorb CO2 when [Na2C03l is over 10 per cent while the 0.1 M
solution will absorb CO2 when [Na2C03] is over 50 per cent.

Equations (f), (g) and (h) give

Kg P

(H+)«

The equilibrium for the dissociation of calcium carbonate is :

(CO") (Ca++)
(CaC03)

XXX SPECIAL APPLICATIONS, C 565

If (CaCO3) is maintained constant by the presence of the solid phase

(CO,-) (Ca++) = K.
where K8 is the solubility product, or

K8 (H+)2

= •

-T7- T7" -rr T)

JtVo IVl -IA.2 -t

Thus the activity (or concentration) of calcium in a solution in contact
with CaCO3 is a function of the hydrion activity and CO2 partial pressure.
This relation is of importance in geology as well as in biochemistry. See
Hastings et al. (1927), and an application by Atkins (1922).

An interesting discussion of the importance of carbonate equilibria to
life is given by Henderson in The Fitness of the Environment.

Catalysis. See Chapter XXVI.

Colloid chemistry. S0rensen, in the introduction to his 1917 paper,
Studies on Proteins, discusses the significance to colloid chemistry of
careful studies of acid-base equilibria in protein solutions. Michaelis, in
The Effects of Ions in Colloid Systems, discusses several aspects, especially
adsorption. Rideal (1926) gives brief treatments of many of the funda-
mental principles concerned.

There exists, in one school, a rather strange prejudice against attempts
to make the methods of acid-base equilibrium studies yield what they are
capable of yielding. This has doubtless been due in some measure to the
disposition of another school to push the signal triumphs beyond clear
accomplishment. The resulting confusion makes it impossible to give a
fair statement even of the chief topics. The student will do well to culti-
vate ability to detect extremes of statement. He should know that in-
numerable investigators are proceeding, oblivious to controversies, to
make the methods of hydrion control and measurement yield results of
immediate practical and theoretical interest.

Reference to the role of hydrion concentration will be found in such
general texts as those of: Freundlich (1922-1927), Bogue (1924), Colloid
Symposium Monographs (1922-date).

Crystallization. In the crystallization of ampholytes, acids and bases,
it is common practice to adjust the hydrion concentration of the solution
to the point of incipient precipitation. See for instance the crystalliza-
tion of egg albumin (S0rensen (1917) and of insulin (Abel, et al. (1927)).

Dr. Edgar T. Wherry calls my attention to the fact that it has long been
known that the acidity of a solution may have some bearing on the habit
of the crystals separating from it. Alum crystals are octahedral when
deposited from strongly acid solutions, cubic when the acidity is reduced ;
sodium chloride is reported to show the reverse. (See Tertsch, 1926.)
Thus far, however, only qualitative information is available, and the pH
values at which habit-changes become significant remain to be determined.
This may have technical bearings. See Saylor (1928).

566 THE DETERMINATION OF HYDKOGEN IONS

Digestive system. The digestive tract is primarily the channel for the
intense activity of hydrolytic enzymes and as such is provided with mech-
anisms for the establishment of hydrogen ion concentrations favorable to
these enzymes. Hydrogen electrode methods have correlated the regional
activity of particular enzymes with the reactions there found, have clarified
some of the differences between the digestive processes of infancy and
adult life, aided in attempts to explain the formation of acid and alkali
and have been of service in the improvement of clinical methods for the
assay of pepsin activity and the diagnosis of abnormal secretion of hydro-
chloric acid in the stomach. The control of specific physiological func-
tions such as secretion of conditioning agents, permeabilities, and activities
of the varied musculature, as well as investigations upon the condition in
the digestive tract of substances such as calcium and phosphate are sub-
jects which have been discussed. Shohl and King (1920) and Kahn and
Stokes (1926) have reviewed and improved methods of studying gastric
acidity. Some of the problems of gastric acidity have been reviewed by
Michaelis (1927). Schwarz et al. (1924) and McClendon et al. have re-
viewed several aspects of digestion. For references on saliva see G.
Clark and Carter (1927). As two of many examples of studies on lower
animals see Yonge (1925), Redman et al. (1927).

Distribution coefficients. Imagine two phases in contact, e.g., water
and benzene, and neglect the complexities due to the solubility of the
substance of one phase in the other. Dissolve in either phase a substance
A, and let it distribute itself between the two phases. Actually, or in
imagination, let the substance A enter a vapor phase and assume Henry's
law for the distribution between each of the solvents and the vapor phase
where the partial pressure of A is P.

[A]w = kzP (a)

[A]b = k2P (b)

By (a) and (b)

[AIw k:

FTP = r- = -K-d (c)

[A]b k2

The ratio r—r^ should then be constant and independent of that concentra-

tion in either phase which is proportional to P. Kd is the so-called distri-
bution coefficient.

Now let A be an acid, HA, and assume

1) lonization in the water-phase

HA ^ H+ + A

2) The equilibrium

[H+]w [A]w

XXX SPECIAL APPLICATIONS, D 567

3) The summation for the aqueous phase

[S]w = [AJW + [HAJW (e)

4) The distribution of molecules.

[HA1W
[lA]T Kd

Equations (d), (e) and (f) yield (g)

[S]w [H+]w
[HA]b = (g)

If Ka be so small as to be negligible in the sum (Ka + [H+]w), we have (h)

[HAJb = ^ (h)

If [H+]w = Ka we have (i)

[HAJb = ~ (0

If [H+]w be so small as to be negligible in the sum (Ka + [H+]w), we
have (j)

rcn rcr+i

(J)

When[H+]w is very small relative to KdKa, [HA]b is very small relative
to [Slw.

These approximate relations formulate one of the most common of
laboratory practices; namely, the extraction of organic acids from water
solutions by means of organic solvents. Acidification of the aqueous
phase to form the undissociated molecules from the salts may bring about
an enormous increase in the concentration of the substance in the non-
aqueous phase. Change of [H+] from [H+] = Ka to practically complete
suppression of ionization doubles the relative concentration.

In case the dissociation constants of two acids are of very different
orders of magnitude, a fractional separation can be accomplished by
adjusting the hydrion concentration to a value between those of the two
dissociation constants.

The strict application of the principle briefly outlined is frequently
complicated by association of molecules in one phase, by considerable
departures from Henry's law, etc. See further detail by Hill, p. 343
Taylor's Treatise on Physical Chemistry, and Murray (1923).

Donnan equilibria. An elementary example only will be given to il-
lustrate a principle implicit in Gibbs' treatment of equilibria but brought

568

THE DETERMINATION OF HYDROGEN IONS

into prominence by the important work of Donnan (1911) and Donnan
and Harris (1911).

Imagine a membrane, M, on one side of which there is an aqueous solu-
tion of hydrochloric acid and on the other side of which there is not only
hydrochloric acid but an acid HR neither the undissociated molecule nor
the anion of which can penetrate the membrane.

inside"

[H+]

[C1-]

[HR]
[R-]

"outside"
[H+]0

The presence of R~~ upon one side only will tend to produce asym-
metry of electric charge on opposite sides of the membrane, and there will
be a tendency toward the compensation of this both by redistribution of
the diffusible ions and readjustment of the ionization of the HR: R~
system. Also the presence of HR and R~~ upon one side only tends to
diminish the partial molal free energy of the solvent. This will tend to
be compensated by a movement of water which may occur until, at equilib-
brium, the counter hydrostatic pressure has contributed its part to the
balancing.

To simplify the elementary discussion, assume that the species HR
and R~ have so little effect on "osmotic pressure" that their contribution
to this effect may be neglected. Also assume that the solutions are suffi-
ciently near "ideal" to permit the use of concentrations rather than
activities.1

Imagine in each solution a hydrogen electrode under one atmosphere
pressure of hydrogen. The E. M. F. of this gas-cell will be determined in
part by the ratio of the hydrion concentrations on the two sides and in
part by the potential difference EM across the membrane.

We may also imagine two chloride electrodes.

•prp r/->n_i

Kl , IL/1 Jo .

For this cell

1 An entanglement might occur in the use of activities were the electro-
static constraint neglected in applying the definition that the activities
of a substance in two phases are the same when the substance will not of
itself pass from one phase to the other.

XXX

BONN AN EQUILIBRIA

569

But if the system as a whole has attained equilibrium, no work can be
obtained by transfer of either hydrions or chloride ions and E. M. F. =0
in each case. Then, since EM is the same,

[H+h [Cl-]o

[H+]o [Cl-]i

In general the ratio of the concentration of an anion in the "outside"
solution to the concentration of that anion in the "inside" solution is the
same as the ratio of the concentrations of any other anion "outside" and
"inside" and is inversely proportional to the ratio of "outside" and
"inside" concentrations of any cation.

Although asymmetry in the distribution of ions was supposed to be
the origin of the membrane potential-difference, a considerable potential
difference may be caused by such a small inequality of material that we
may still assume the ordinary rule of electroneutrality in each solution.
Then on one side (inside)

Also outside

= [H+Ji

[Cl-]o

(b)

(c)

Substitute the equivalents of [Cl Ji and [Cl J0 from (b) and (c) in equation
(a) and obtain

1H+]2 - [H+]i [R-Ji = [H+]J (d)

If, then, the "outside" and "inside" solutions before the attainment
of equilibrium were of the same hydrion concentration, hydrions would
diffuse inward for the hydrion concentration of the inside solution will be
greater than that of the outside solution at equilibrium. (A quantity
must be subtracted from [H+]? in (d) to equal [H*]2.)

If the non-diffusible substance were an ampholyte, forming R+ on the
acid side of the isoelectric point, the above relations regarding [H+]j and
[H+]0 would be reversed on the acid side of the isoelectric point.

To indicate the magnitude of migrations with no chloride inside initially,
assume that the membrane is placed so that the two solutions are of equal
volume. Between the initial and final states of the system chloride ions
have diffused from right to left (see scheme below) till the concentration
[C1-], is x.

Initial state

Equilibrium state [HR]3
[R-]3
[H+]3

[C1-],
[H+]2

570

Then

THE DETERMINATION OF HYDROGEN IONS

[H+]8 = [H+]i + x and [H+]4 = [H+]2 - x
or, since at equilibrium

[H+]3 = [Cl-]4

[H+]4 [01-],'

[H+h + x = [H+]2 - x
[H+]2 - x " x

Whence

x =

21H-

The following table will give an idea of the magnitude of the effects due
to the conditions assumed.

As we have already indicated, the difference of potential between two
hydrogen electrodes placed on opposite sides of the membrane must, at
the equilibrium state of the system, be equal and opposite to the potential
difference at the membrane. Hence the membrane potential difference
may be expressed in terms of a hydrogen electrode gas chain :

RT. |H+la

F in[H+i;

By using this relation we calculate the membrane potential difference
given in millivolts in the last column of the following table.

«.„,,

INITIAL RATIO

PER CENT HC1
DIFFUSED TO
ESTABLISH
EQUILIBRIUM

EQUILIBRIUM
DISTRIBUTION

RATIO | — ^|*

MEMBRANE
POTENTIAL IN
MILLIVOLTS

0.01

1.0

0.01

49.8

1.01

- 0.3

1.0

33.3

2.0

- 18.0

1.0

0.01

100.0

0.98

101.0

-120.0

Of course the conditions assumed for purposes of illustration are ex-
tremely simple but they suffice to indicate the nature of relations of very
great importance in the physiology of the living cell.

The equations should be used with activities if strictly applied.

For one of many illustrations of the application, see Van Slyke (1926).

Ecology. Cells living in intimate contact with an aqueous solution are
found to be dependent in various degree and various manner upon the
hydrion concentration of the solution. See the manifold aspects il-
lustrated by the texts of references under Bacteriology.

XXX ELECTROPHORESIS 571

Likewise organisms drawing sustenance from the soil are found to be
dependent upon the "soil reaction" as determined by measurements of
aqueous extracts. See Soils. The more complex multicellular organisms
may in some instances respond directly to the hydrion concentration of
the environment but more often they are indirectly affected through the
effects upon organized and unorganized foodstuffs. Through this complex
chain, the distribution of the higher forms of life exhibits a considerable
degree of correlation with the pH values of the natural waters or soils
with which they are associated.

The literature on reaction as an ecological factor has now reached con-
siderable bulk, and only a few typical articles can be noted here: Fungi,
Waksman (1924); Marine Algae, Legendre (1925); Fresh Water Algae,
Wehrle (1927) ; Liverworts, Dop and Chalaud (1926) ; Ferns, Wherry (1920-
1921); Coniferous trees, Hesselman (1926); Higher plants, O. Arrhenius
(1920), Atkins (1922), Wherry (1920), Olsen (1923), Chodat (1924), Christo-
phersen (1925); Earthworms, O, Arrhenius (1921); Snails, Atkins and
Lebour (1923) ; and Fish, Coker (1925) . See especially the book by Mevius
(1927).

Electrophoresis (cataphoresis) and electro-osmosis. An electrically
charged body placed between an anode and a cathode will tend to move
toward the pole having a charge opposite in sign to the charge on the
body. If the body is a simple ion, the movement is called ionic migration.
If the body is a particle suspended in a medium such as water, the move-
ment is called electrophoresis. More generally it is known as cataphoresis.
The distinction between ionic migration and electrophoresis is not always
clear in the case of material in the colloidal state.

We shall not discuss the various theories advanced to account for the
experimental facts but shall treat briefly only that point of view which
it will be profitable to investigate further with the aid of methods for
determining pH.

Since acidic or basic ionization may determine the sign of the charge
upon a body of amphoteric nature the sign may be a function of the pH
of the medium. The direction of electrophoresis is then a function of pH.
At the isoelectric point electrophoresis is a minimum. The method of
electrophoresis is useful in determining isoelectric points.

There can be no movement such as that noted above without a recip-
rocal interaction between suspended or dissolved material and the dis-
persing medium. If then the charged particles are fixed in position, as
in the form of a porous diaphragm, are placed in water and the whole
subjected to a potential gradient, the water will tend to move (electro-
osmosis). The same relative relations indicated above then hold. If the
diaphragm is of an amphoteric nature the direction of water flow will
depend upon the acidic and basic properties of the diaphragm and upon
pH of the aqueous phase.

In either one of the two cases (particles fixed or free to move) the same
end result will be obtained if the particles adsorb hydrogen and hydroxyl
ions according to their adsorption isotherms. Equality of adsorption

572

THE DETERMINATION OF HYDROGEN IONS

TABLE 71

Optimal reactions for the activity of various enzymes
(After Waksman and Davison, 1926)

ENZYME

SOURCE

OPTIMAL pH

Amylase (diastase) — <
Arginase

Asp. niger
Duodenal contents
(infants)
Malt
Pancreas
Potato juice
Saliva

Liver

3.5-5.5
6.0-8.0 (viscosity)

4.4-4.5
7.0
6.0-7.0
5.6 (acetate buffer)
6.6 (phosphate buffer)
10 0

Carboxylase

Yeast

53-62

Catalase <
Emulsin

Blood
Liver

Vegetables

7.5 (10 minutes)
7.0
7.0-10.0
4 4

Erepsin \

Intestine (pig)
Intestine (pig)

7.9 (glycyl-glycin)
8.6 (conductivity
method)

Invertase. .

Intestine (dog)
Ox spleen
Yeast
Asp. niger
Potato juice
Yeast

7.7 (albumose)
7.5-8.5
7.8
2.5-3.5
4.0-5.0
4 4-4 6 (52 1°C )

Lipase \

Yeast
Fresh yeast cells
Blood
Duodenal juice
Duodenal juice

4.2 (22.3°C.)
4.2-5.2

7.8-8.6
5.0
8.5

Maltase

Gastric juice
Gastric juice of dog
Serum
Asp. oryzae

4.0-5.0
4.9 (2.5 to 8.0)
7.0-8.6
3.0 (35.5°C.)-7.2 (47°C.)
4 0

Oxidase

Beer yeast
Vegetables

6.6
7 0-10 0

Pancreatin (trypsin-
erepsin)

Ox pancreas
Ox pancreas

9.7 (gelatin liquef.
37°C.)
7 7_g o (peptone de-

Pectase

Fruit

comp.)
4 3

XXX

ENZYMES

573

TABLE 71- Concluded

ENZYME

SOURCE

OPTIMAL pH

Pepsin J
Peroxidase

Animal tissues
Stomach
Stomach
Yeast
Vegetables

3.0-3.5 (gelatin)
1.2-1.6 (acid albumin)
1.4 (edestin)
4.0-4.5
7 0-10 0

Protease <

Asp. oryzae
Autolyzing animal
tissue

5.1
4.5

6n 7 n

Rennet (lab) /

Malt
Malignant human
and rat tumors
Papain
Stomach

. u— / . u
3.7-4.2
7.0

5.0-7.0
5.0

Trypsin <

Stomach
Animal tissues
Pancreas
Pancreas

6.0-6.4
7.8 (peptone)
9.5
8.3 (casein)

Urease

Pancreas
Yeast
Yeast
Soy bean

7.5-8.3 (fibrin)
7.0 (peptone)
8.0
About 7 0

Zymase J

Living yeast

4.5-5.5 (28°C., no nitro-
gen)

Living yeast

4.5-6.5 (28°C., plus
yeast water)

and consequently equality of electrical charge is attained at a definite
pH value. The position of such an "isoelectric" point is a function of
the properties of the material and may lie anywhere along the pH scale
(according to the nature of the material) with a narrow or broad isoelectric
zone .

See, for examples, Gyemant (1921), Michaelis and Perlzweig (1926),
Northrop and De Kruif (1921-1922), Winslow, and Falk, and Caulfield
(1923), Porter (1921).

Enzymes. The influence of hydrogen ion concentration, or activity,
upon the properties of enzymes has been the subject of an enormous num-
ber of investigations since the classic paper of S0rensen (1909). Data
pertaining to specific enzymes may be traced through the comprehensive
treatise, Die Fermente edited by Oppenheimer. This is now (1928) appear-
ing in sections. A discussion of enzymes as electrolytes and as colloids
is found in Chemie der Enzyme I, 3 aufl. by v. Euler (1925) see also Fodor

574 THE DETERMINATION OF HYDROGEN IONS

(1926), Rona (1926), and in Waksman and Davison's Enzymes (1926).
See also K. G. Falk (1924). Table 71 is part of that compiled by
Waksman and Davison, whose book should be consulted for references.

Foods. Considerable variation in pH values of food extracts, juices,
etc., is of importance to canning (see Canning),2 to thermal destruction of
vitamines [See LaMer (1921), Sherman and Burton (1926) and Zilva (1923)]
and to numerous industrial treatments of food-stuffs.

pH -values of various foods are given by Bigelow and Cathcart (1921),
E. H. Harvey (1924).

The relative quantities of inorganic anions and cations and of acids
or bases which can be "burned" to products which can be eliminated by
the lungs or must be eliminated by the kidney are important to the study
of acid-base metabolism and "neutrality "-regulation. See Blatherwick
(1914).

Filtration. Hydrogen ion concentration, through its influence upon the
dispersion of certain colloids and upon the conditioning of filter material,
may control the filterability of a substance. Holderer's thesis from
Perrin's laboratory presents in admirable form many of the theoretical
aspects of the subject. The subject is not only of considerable theoretical
interest but also of great practical importance. Buffer control with indi-
cator tests may in many instances facilitate nitrations upon an industrial
as well as a laboratory scale. See Electrophoresis.

Glass, effect of, on reaction of solutions. Many glasses contain so
much "free-alkali" that they can seriously affect the pH value of poorly
buffered solutions, especially when used as containers during heating.
See, as examples, Esty and Cathcart (1921), Fabian (1921), fiwe (19?0).

Hydrolysis of salts. Inspection of several titration curves discussed
in previous chapters will show that, when equivalents of a univalent acid
and a univalent base are mixed, the solution has a pH -value which is seldom
that of "neutrality" and varies with the salt. Instead of estimating such
values in the manner described in Chapter XXVIII, it is now desired to
treat the subject from the following point of view. The preformed salt
is used to construct the solution. Now the reaction between an acid and
a base is reversible

HA + BOH ^± BA + H20

Consequently, if the preformed salt, BA, be used, it will react with water
to some extent and will form some acid, HA, and base, BOH. The conse-
quent splitting of water is the occasion for speaking of a hydrolysis.

The resulting acid, HA, and base, BOH, ionize. The ionization of the
acid tends to increase the hydrogen ion concentration, and the ionization
of the base tends to increase the hydroxyl ion concentration. If these
tendencies are equal, the pH value of the original water will not be altered
except through the effect of the salt upon Kw (see page 46). If the acid
is "stronger" than the base, pH will be lessened and if the base is "stronger"

2 See page 576.

XXX

SPECIAL APPLICATIONS, F~H

575

than the acid, pH will be increased. For detail return to the method oi
Chapter XXVIII.

Hydroxides of the metals, precipitation of. See solubility product and
precipitations. Were the precipitates formed from solutions of metal salts
by the addition of strong alkalies, true hydroxides of the type M(OH)n,
the treatment would be simple and could be illustrated in outline by
graphs such as that of figure 100, page 582. There would then be a fairly
narrow zone of pH within which a metal hydroxide having a characteristic
solubility product would be precipitated. Undoubtedly the simple rela-

0 10 20 30 40 50 60 70 80 90 100 110
CCs N/IO-NaOH.

FIG. 98. BRITTON'S CURVES SHOWING ZONES OF PRECIPITATION OF METAL

HYDROXIDES

tions then obtaining may be used to outline one of the chief aspects of the
problem. However, many of the precipitates carry down the anion, are
not true hydroxides and must be regarded either as solid solutions or
treated by the methods of colloid chemistry. In a few instances only
are there evidences of a definite chemical compound of constant composi-
tion within the zone of precipitation and before the true hydroxide is
formed. Hence much of the literature regarding definite "basic salts"
must be revised. Britton (1925) has assembled highly interesting pre-
liminary data on the zones of pH within which the precipitates are formed.
While it is impossible to tabulate extensive data here, there may be repro-

576 THE DETERMINATION OF HYDROGEN IONS

duced Britton's set of curves (fig. 98) showing the approximate location of
zones of precipitation. Trace the more specialized literature through
Britton's references and texts of analytical methods.

Immunity. Since substances concerned in immunological reactions are
the protein antigens, are protein-like or are found in solutions containing
proteins on which they are believed to be adsorbed or with which they
are believed to be in combination, pH control and measurement find fre-
quent application But the literature is vast and the references therein
to our subject are too frequent for review A few references will be cited
by way of illustration: Brooks (1920), Coulter (1920-1922), Defries and
McKinnon (1926), DeKruif and Northrop (1922), A. Evans (1922), Falk and
Caulfield (1923), Falk and Powdermaker (1925), Felton and Dougherty
(1924), Hirsch (1922-1924), Homer (1917), Mason (1922), Michaelis and
Davidsohn (1912), Mond (1927), Shaffer (1924), Sobotka and Friedlander
(1928), Watson and Wallace (1924). See also Wells (1925).

Industrial uses. The most direct applications are in the manufacture
of salts such as KH2PO4, titration of acids or bases for yields, extractions
as of alkaloids (see distribution coefficients) and the control of reaction
rates and equilibria. Processes in which complex equilibria are involved
are exemplified by the treatment of boiler water, see Greer and Parker
(1926) and the coagulation processes of water purification, see Buswell
(1927). Pickling solutions are frequently put under automatic control.

The leather industry furnishes an example of the application of the
physical chemistry of proteins, in the development of which pH -measure-
ments have had a leading part. See book by Wilson (1928). In the bread
industry pH -control has played an important part. Glutin is conditioned
and the activity of yeast and the evolution of CO2 from baking powders
are conditioned by the hydrion concentration of the dough. Adequate
pH control may hold in check the "rope" organism (Henderson, 1918)
and Cohn et al. See review by S0rensen (1924). Cf., for examples, Green
and Bailey (1927) and mill control by Weaver (1925) .

As originally outlined in older terms by Pasteur, the "reaction" of
wort and of must have much to do with the brewing of beer and wine
fermentation. The control of "diseases" of beer and wine and the con-
ditioning of the proteins held in solution are controllable by pH methods.
See innumerable journal articles on brewing, for example, Emslander (1915
-1919), Hulton (1924), R. H. Hopkins (1925), N. Parsons (1924), Wind-
ish, Dietrich and Kolbach (1922), and Ventre's (1925) book on wine.

The gelation optimum of pectin is pH 3.0 and the optimum of pectase
is 4.3. For these reasons pH control is important in the manufacture of
jellies. See for examples Tarr (1923) and Luers and Lochmuller (1927).

Heat-penetration, temperature, holding-time and the hydrion concen-
tration of the food have been so correlated with the death-rates of various
bacteria that economy and certainty in commercial canning of foods can
be assured. See Bigelow et al., Rogers, Deysher and Evans (1921).

The fermentation industries have continuous use for pH measurements.
See "Bacteriology" and "Enzymes."

XXX SPECIAL APPLICATIONS, I~M 577

In the sizing of paper and other processes of the paper industry pH
measurements are used. See Shaw (1925), Atsuki and Nakamura (1927).

Some processes incidental to the textile industry in which pH measure-
ments are useful have been cited by Trotman (1926), Sacks (1927) and
Strachan (1926), King (1927).

Wilson, Copeland and Heisig (1923) and Cobrum (1927) give examples
of application in sewage treatment. See Buswell (1927).

Lyon, Fron and Fournier (1927) describe pH measurements as a means
of judging wood.

A very active field of application is in the sugar industry where pH con-
trol of several steps has become an established practice. Among in-
numerable papers see Paine and Balch (1927), Perkins (1923), Aten, van-
Ginneken and Engelhard (1926), Blowski and Holven (1925) . The methods
have been extended to uses of sugar such as candy manufacture, Sjostrom
(1922).

The potential at which hydrogen is deposited freely upon an electrode
is a function of the hydrogen ion concentration of the solution. Therefore,
pH is important in controlling gassy deposits in electroplating. In addi-
tion it is found that buffer solutions, maintaining the pH within definite
limits, aid in the production of desirable qualities of deposits, especially
of nickel. See Thompson (1922), book by Blum and Hogaboom (1924),
Montillon and Cassel (1924) and Britton's sketch (1927).

On dry cells see Holler and Ritchie (1920).

In corrosion the activity of hydrions plays an important part. See
review by Bancroft (1924) and Corrosion Symposium (1925).

To a greater or lesser degree pH methods have been employed in the
study of cements (Lerch and Bogue (1927); exchange silicates, see Jenny
(1927) and Sweeney and Riley (1926) ; commercial carbons, see Hauge and
Willaman (1927), Miller (1928); the catalytic decomposition of explosives,
Farmer (1920), Angeli and Errani (1920); rubber latex, Freundlich and
Hausen (1925), Bishop (1927); clay, Fessler and Kraner (1927), Randolph
and Donnenwirth (1926) and Oakley (1927) and innumerable other subjects.

Additional references on several of the subjects mentioned above are to
be found in W. A. taylor's (1928) brochure. Parker (1927) has noted
several instances where potentiometric control is used.

In innumerable cases the methods are applied to very incidental steps
of important processes. In other cases acid-base equilibria are funda-
mental to a process. So varied are the examples of each type that the
above sketch has little value other than to call attention to an enormous
field.

Milk. A case exhibiting the tendency of physiological fluids to maintain
constant ratio of dissociated to undissociated forms of acids and bases.
Cow's milk is usually near pH = 6.5. Its variation is used as an index to
diseased condition of udder, or, in market milk, to indicate spoilage.
Complete description of acid-base equilibria of milk is lacking; cf. Clark
(1927). For review of manifold applications of hydrion-methods in dairy
science, see Rogers (1928).

578

THE DETERMINATION OF HYDROGEN IONS

Inorganic chemistry. Studies of inorganic equilibria involving hydrions
are too numerous to mention.

Optical rotation. The specific rotation of an optically active acid,
base or ampholyte may be distinct from that of its salt. Consequently
the apparent specific rotation will vary as the solution passes through a
zone of pH centered at the pK value. See figure 99. As examples of many
studies which have been made, see Liquier (1925), Vies et al. (1926), Levine
et al. (1927).

Mutarotation, especially of sugar solutions, has long been known to be
a function of the hydrion concentration of the solution. See treatment
in modern terms by Br0nsted and Guggenheim (1927), Lowry (1927), Kuhn
and Jacob (1924).

I
0-4

5
6

O^JV

0.2 Q3 0.4- 0.5 0.6 Q7

ROTATION. DEGREES PER CM.

PER MOLE

FIG. 99. ROTATION OF POLARIZED LIGHT BY TARTARIC ACID-TARTARATE
SOLUTIONS AS A FUNCTION OF pH

(After Vies and Vellinger (1925))

Organic chemistry. One of the common practices of organic chemistry
is to modify the properties of a compound by substituting groups of acidic
or basic nature and of different strength or by modifying the strength of
such acidic or basic groups by the introduction of other groups wlr'ch
themselves are not acidic or basic. And yet one can search hundreds of
articles or their abstracts before coming upon mention of the quantitative
aspect which is susceptible to elaboration by the methods here described.
Much of the material is assembled in texts on physical chemistry. The
methods of measurement and control are frequently practiced uncon-
sciously and as often practiced so much as a matter of course as to seem
unworthy of special mention.

XXX SPECIAL APPLICATIONS, I~P 579

Permeability of membranes. In some instances the material of a mem-
brane may be conditioned by the hydrion concentration of the solution
with which it is in contact. Thereby its permeability in general may be
altered. The question whether the ionized form or the undissociated resi-
due of a particular substance is the form penetrating a given membrane is
now receiving considerable attention. See, for example, Osterhout
(1922). The participation of electrostatic forces in the distribution of
ions between solution phase and membrane phase is discussed in a review
by Michaelis (1926). Weber (1926) gives a bibliography 1922-1926. See
also book by Stiles (1924).

Pharmacology, pharmaceutics, etc. Innumerable applications. Exam-
ples :

1. The active form of a drug may be the unionized form. See Michaelis
and Dernby (1922), Dernby and Davide (1922), Trevan and Boock (1927).

2. The stability in solution may be a function of pH. See Levy and
Cullen (1920), Stasiak (1926), Tainter (1926), Macht and Shohl (1920),
Plant Research Lab. (1925).

3. The hydrolysis in situ may be a function of pH. See Shohl and
Deming (1920).

4. The extraction from crudes may depend upon the partition coeffi-
cient of the ionized and non-ionized forms. See "Distribution Coeffi-
cients" and Fabre and Parinaud (1925),Evers (1922).

5. The preparation of a drug for injection may depend upon proper
titration. See Elvove and Clark (1924).

6. The control of an organ used for test is dependent on the pH of the
fluid. See "Physiology" and, for example, Gruber (1926).

See review by Jarisch (1926) and Brunius and Karsmark (1927).

Photographic processes. The most general material for. suspending the
silver halides is gelatine. In the manufacture of gelatine, pH control is
advantageous. In the preparation of the emulsion, in determining the
grain-growth of the suspended silver halide, in affecting that decompo-
sition of thiourea derivatives which has to do with sensitizing, and in
preventing hydrolysis of gelatine and reduction of silver salts, pH control
is used. Swelling of gelatine is controlled by neutral salts as well as
bypH.

Many of the dyes used as optical sensitizers are typical indicators and
only the colored forms are effective. Control of pH on the one hand and
adjustment of dissociation constants on the other hand have obvious uses.

The usual organic developers operate in alkaline solution. The re-
duction potentials of the systems are functions of [H+j. Reaction velocity
and "fog" are, in part, controlled by preventing excess alkalinity.

If the fixing bath of "hypo" (sodium thiosulfate) has a pH value less
than about 4.0, the thiosulfate will decompose with liberation of sulfur.
If the pH value is greater than 6.0, stains may result from fixation of iron
compounds and reduction of silver by traces of developer. The fixing
bath is, therefore, buffered in various ways.

"Temporary" hardening is controlled by salts and the acidity of the

580 THE DETERMINATION OF HYDROGEN IONS

solution. ''Permanent" hardening by alums is similar to certain processes
of tanning. The hardening effect of alum is a function of pH.

Indicators for photographic processes must in many cases show a useful
color change in red or yellow light.

pH control is used in "after processes," e.g., intensification and reduc-
tion by increasing or diminishing the density of the deposit, in the bleach-
ing of the reversal process, in toning and dyeing, and in transfer processes.
References: Rawlings (1926), Sheppard (1925-1926), Sheppard and
Elliott (1923), Sheppard, Elliott and Sweet (1923), Wightman, Trivelli
and Sheppard (1923).

Physiology, general. The classic examples of applications in this field
are the description of the acid-base equilibria of the blood (see "Blood")
and the control of enzyme activities (see "Enzymes"). But it is imprac-
ticable to enumerate all the other applications.

One of the most important applications of the principles discussed in
this book is in the adjustment of physiological salt solutions, perfusion
solutions, etc. Michaelis (1914) and others have called attention to the
fact that some of the older solutions were not adequately buffered or
adjusted. Improvement has been accomplished by the introduction of
phosphate buffers or by making use of the equilibria of bicarbonate solu-
tions under definite tensions of CO2.

Among numerous papers on the subject may be mentioned those by
A. C. Evans (1922), Fleisch (1922), Barkan, Broemser and Hahn (1922),
Chopra and Sudhamoy (1925), Mason and Sanford (1924), and such
discussions as are found in texts, e.g., Bayliss (1927).

In Recent Advances in Physiology (1926) Evans discusses the chemistry
and physiology of muscle contraction and refers to the effect of pH on the
recovery of muscle. See also McSwiney and Newton (1927) and Meyer-
hof (1923). Andrus and Carter (1927) conclude that cardiac tissue is
peculiarly sensitive to alterations of hydrion concentration and that per-
haps a difference of pH within and without the cell is a factor in excitation .
Katz, Kerridge and Long (1925) find the buffering capacity of cardiac
muscle is lower than that of skeletal muscle and that the critical level of
pH is higher for the former. Evans (1926) reviews the evidence relating
contraction to pH within and without the cell. On the zones of pH favor-
able to the several phases of heart action see Dale and Thacher (1914).

Gray (1922) finds that ciliary movement declines rapidly as the pH of
the solution is lowered from about 7.2 to 6.0. Organic acids are more
effective because of penetration. See Jacobs (1920). Pantin (1923) re-
views amoeboid movement. See also Hopkins (1926) on locomotion of
protozoa and Fenn (1922), Feringa (1923), and Jochims (1927) on phago-
cytosis. Clowes and Smith (1923) deal with the activity of spermatozoa
in relation to the hydrion concentration of the medium. See also Gel-
horn (1927), Kalwaryjski (1926), Anderson (1922), Healy (1922) and Vies
(1924) .

Lillie and Shepard (1923) find that heliotropism of arenicola larvae is
controlled by changes in the reaction of balanced isotonic solutions. See
also Rose (1924).

XXX PHYSIOLOGY 581

Two important methods of attack on various problems of cell physiol-
ogy are provided by the development on the one hand of Harrison's tissue
culture and on the other hand of Barber's micro manipulation methods.
Lewis and Felton (1922) and Fischer (1921) describe the uses of pH measure-
ments in tissue culture while Chambers (1926-1927) describes the revela-
tion of the pH of the cell interior which has come from the use of his im-
proved methods of micro-injection. In a recent paper Chambers shows
that the normal cytoplasmic pH of star fish eggs is 6.7 while that of
the nucleus is 7.5. For comments on the relation of pH and reduction
potentials of cell interior see Cohen, Chambers and Reznikoff (1928) . The
influence of pH on rates of reduction of methylene blue by tissues is dis-
cussed by Ahlgren (1925). The metabolism of the developing egg with
reference to pH is discussed by Needham (1925). For notes on hen's
eggs see Sharp and Whitaker (1927). For references on tumor cells see
Warburg (1926).

Rous (1925^1927) (see Drury et al. 1927) has carried out an extensive
study of the ' 'relative reaction" of living mammalian tissues. But see
Chambers. Mudd (1925) reports the effect of hydrion concentration upon
electroendosmosis through mammalian serous membranes. For a review
of plasmolysis see Prdt (1926), and hemolysis, Mond (1927), Rockwood
(1925).

The hydrion concentration of the medium is a controlling factor in the
culture (Morea, 1927, Saunders, 1924), growth and locomotion (Hopkins,
1926) reproduction and encystment (Beers, 1927, Koffman, 1924) of pro-
tozoa. Pruthi (1927) shows the relation to protozoan sequence in hay
infusions. Shapiro (1927), by feeding selected indicators to protozoa was
able to assign definite values to the acidity of food vacuoles. See Stoll
(1923) on hookworms and Jewell (1920) on tadpoles.

Bodine (1926) used a micro electrode in studying the blood of insects.
See ' 'Blood" for other references to the blood of lower animals.

On body fluids see brief mention in such texts as those of Hober (1927)
and Kopacewski (1926), comments on general principles of exchange by Van
Slyke (1926) ; McQuarrie and Shohl (1925) on cerebrospinal fluid; Talbert
(1922) on sweat, etc.

Brief reviews of the role of hydrion concentration in several other
phenomena must be sought in such general texts as that of Rogers (1927),
Hober (1927), Bayliss (1927), but more particularly in the special literature.

In the field of Plant Physiology the applications have been numerous.
Although it is dufficult to separate subjects in this field from those re-
ferred to in the sections "Soils" and "Ecology," there may be mentioned,
merely by way of illustration, the following subjects and references:
Absorption by plants : Robbins (1926) ; pH numbers of plant cells ; Pfeiffer
(1927), Haas (1917), Atkins (1922-1924), Small (1926), Rea and Small
(1927); pH gradient: Gustafsen (1924); Photoperiodism : Garner, Bacon
and Allard (1924); Turgor: Pfeiffer (1927); Staining: Naylor (1926);
Chlorosis : McCall and Haag (1921 ) . An excellent review of several aspects
of plant physiology in which pH measurements have been used is given

582

THE DETERMINATION OF HYDROGEN IONS

by Pfeiffer (1927). Numerous investigations have been made of the role
of reaction in the defense against parasites. Examples are: 'Gillespie and
Hurst (1918), Scott (1922-1924), Mclnnes, J. (1922), Berridge (1924) and
Kurd (1924), Atkins (1922).

Precipitations. Usually an acidic ionogen is less soluble than its alkali
salt and a basic ionogen is less soluble than its chloride. Figure 100
illustrates in elementary outline phenomena that may occur in titrating
the hydrochloride of a base. The abscissa represents percentage neu-
tralization of the hydrochloric acid combined with the base. The equilib-
rium is given approximately by:

(a)

I
CL

20 40 60 80 100

PERCENT NEUTRALIZATION
FIG. 100. TITRATION OF 100 cc. OP N/100 HYDROCHLORIDE OF A BASE

(14-Kb = 4) WITH NaOH
Solubility of free base 2 X 10~3 in one case and 2.2 X 10~2 in the other case

Accordingly the type curve is plotted with center at pH = 4.0.

Suppose the solubility of the free base, [B], is 2 X 10~3. Then when the
solid form has precipitated

pH = 4.0 - 2.7 - log [BH+] = 1.3 - log [BH+]

(b)

If 0.1 M hydrochloride of the base has been titrated to incipient pre-
cipitation, [BH+] = 0.1 - 0.002 = 0.098 (neglecting dilution). Hence
pH = 2.3 which is point a of figure 100. It may be that precipitation will
not occur at once and that the solution will remain supersaturated to
point b. Then, with the formation of a precipitate, the pH value jumps
back to c. From then on the curve is determined by equation (b) ap-
proximately.

If the solubility of the free base is 2.2 X 10~2 precipitation will determine
the following equation

pH = 4.0 - 1.66 - log [BH+] = 2.34 - log [BH

(c)

XXX

SPECIAL APPLICATIONS, P

583

Then at incipient precipitation [BH+] =0.1 - 0.02 = 0.078. Hence pH
= 3.54 approximately. The titration curve may continue to c instead of
"breaking" at d; but, with precipitation, the pH value will drop back to f .

The above description is approximate, not only because of the neglect
of dilution and the use of the first approximation equation, but particu-
larly because the activities were not used and no consideration was given
to the effect of ionic strength of the solution upon solubility. Nevertheless
the example illustrates how the "titration curve" is displaced to a greater
or lesser extent depending upon the magnitude of the solubility of the
precipitable component. It illustrates the flattening of the curve or in-
creased buffer index in a narrowed zone. It also illustrates a method of
determining solubility.

Recently Naegeli (1926) has given an extensive review of instances,
chiefly from the field of colloid chemistry. He proposed to elevate to
the rank of a new principle of acidimetry the employment of substances
which precipitate at low concentrations and at definite zones of pH. He
suggests in particular isonitrosoacetyl-p-amino azo benzene (indicator a)
and isonitrosoacetyl-p-toluoazo-p-toluidine (indicator b). For these
Naegeli finds the following ranges:

RAl

?GE

BUFFER SOLUTION

Indicator a

Indicator b

Borax-NaOH
Phosphate-
NaOH

turbid
turbid

10.95-11.01
10 80-10 90

clear
clear

turbid
turbid

11.30-11.36
11.55-11.63

clear
clear

Glycocol-
NaOH . . .

turbid

10.91-10.98

clear

turbid

11.68-11.74

clear

Note the extremely narrow range. Since the zone lies near those values
of pH which are required for the titration of certain weak acids by strong
bases (see page 535) Naegeli had some success in this application.

Proteins. From what is known of their chemical structure, proteins are
believed to be amphoteric. As such their conduct should be subject to
the state of the acid-base equilibria of the solution in which they are dis-
persed. Because of the high molecular weights of proteins and the ap-
parently numerous groups which can function as acids or bases, it is im-
practicable to formulate equations comparable to those of simple systems
and to subject these to experimental test. For the same reason experi-
mental progress in developing analogies with the equilibria of simple
systems has required the most painstaking work. Such work is well
exemplified in the classic papers of S0rensen and his coworkers which are
to be found chiefly in Compt. rend. trav. lab. Carlsberg, 1917 to date.
Beginning with the work of Hardy (1899-1905), Loeb (1909), Michaelis
(1909), Chick (1913), Pauli (1903-date) and continuing through the later

584 THE DETERMINATION OF HYDROGEN IONS

work of these same authors, and of Cohn, S0rensen and numerous others, a
large body of excellent working hypotheses and fundamental data has been
accumulated. See such reviews as that of Cohn (1925) and Lloyd's book.
Loeb reentered the field about 1918. His book (1922) contains interesting
material more precisely formulated elsewhere.

As an example of the application of the Debye-Htickel equation to pro-
tein solutions see Cohn and Prentiss (1927) and S0rensen and Linderstr0m-
Lang (1927).

Solubility, solubility product. The true solubility of a compound may
be regarded as independent of the hydrogen ion concentration of the solu-
tion; but if the compound is an acid, a base or an ampholyte, some of the
material present in solution may be ionized and the apparent solubility
will include both the ionized and unionized forms. Therefore, the total
or apparent solubility is a function of pH.

Since the presence of extraneous material often has a great influence
upon the true solubility of a substance there is some advantage in starting
the elementary formulation with the use of the activity-concept.

When the activities of a substance in two phases are the same the sub-
stance will not of itself pass from one phase to the other. Let the acid
HA be present in a solid phase where the activity is (HA)8.

(HA)S = a constant (a)

The activity in the liquid phase will be the same at equilibrium.

(HA)i = (HA). (b)

In the liquid phase

(H+), (A-),

(HA), K"

or by (a), (b) and (c):

(H+)i (A)i = a constant = Ka (d)

The constant Ks is called the solubility product.
Introducing activity coefficients, we have :

[H+] [A~] = ^— (e)

TH+ ?A-
or

(H+) = ~—, (e-2)

TA- [A-]

Chapter XXV deals with the calculation of activity coefficients and
indicates that a first order approximation of their evaluation for very
dilute solutions has been accomplished. See figure 86, page 504. This
accounts for the influence of neutral salts of various valence-types at high

XXX SPECIAL APPLICATIONS, S 585

dilution; but in the presence of high concentrations of salts and other
material the distribution of water is seriously affected and a "salting out"
process may be superimposed. Inexplicable effects such as are observed
when an organic solvent is but slightly altered by addition or withdrawal
of a minute quantity of some solute are often encountered.

Soils. A water extract of a soil will have taken up acids, bases and
salts in ratios conveniently described in terms of pH. A narrow range of
pH values may be determined by the mineral constituents of the soil
[see, for example, Kappen (1916)] by the products of leaf and wood de-
composition [see, for example, Od6n (1916)], by material excreted by plant
roots [see, for example, Duggar (1920), Davidson and Wherry (1924)], by
bacterial metabolism [see, for example, Waksman (1927)] or by artificial
additions. In the absence of artificial additions there may be reached a
natural balance in the contribution of each factor. This may permit
a correlation between pH and soil-type [see, for example, Gillespie and
Hurst (1918)] or between pH and plant-type [see references under Ecology].

The causal relation between the frequency of occurrence of a given
plant species in soils of a narrow range of pH and the pH may be direct in
some instances. More often it is probably indirect and is concerned with
the influence of soil-reaction upon the micro-organisms concerned in
supplying plant nutrition [see Waksman (1927)] or upon parasites [see,
for example, Gillespie (1918)]. However, the end result is a zone of pH
favorable for each given species of plant.

The importance of controlling the soil pH in agriculture is now
widely recognized. Lime is frequently used to increase pH [see, for
example, discussion by Hoagland and Christie (1918)] and sulfur (which
oxidizes to H2S04) to decrease pH [see discussion by Lipman, Waksman
and Joffe, 1921].

Some data have been obtained in recent years on the optimum pH values
for the production of individual crops. The most extensive of these
studies is that of O. Arrhenius (1926). The pH values of 70,000 samples
from 15,000 fields in which sugar beets were growing were determined.
Both the highest yields and the maximum sugar contents were found
uniformly in the range pH 7.0 to 7.5. A list of several hundred plants of
agricultural and horticultural interest, arranged according to their op-
timum pH values, has been published by Wherry (1926).

There is now an enormous literature on the manifold aspects of the
subject. The following reviews may be consulted. Fisher (1921), Knick-
mann (1925), Olsen (1923), Wherry (1922), Wiegner and Gessner (1926),
Trenel (1927).

Staining and dyeing. Most dyestuffs are of basic or acidic nature.
Many have ionization constants the values of which fall within the range
of ordinary hydrogen ion concentrations. Systematic evaluations remain
to be conducted. Many of the substances which "take" dyes are them-
selves basic or acidic. Consequently there are good grounds for believing
that dyeing is in some measure salt formation. However, the ordinary
equilibrium laws are inapplicable for account must be taken of the fact that

586 THE DETERMINATION OF HYDROGEN IONS

many dyes in the aqueous phase are dispersed in colloidial degree, of the
fact that the material dyed is often surface-active and of the fact that
dye-substrate "compounds" exhibit specific properties. There is here
another instance where progress requires the close cooperation of various
theoretical and experimental methods of approach.

Empirically, the control of hydrion concentrations and the study of
the acidic or basic nature of the substrate have yielded information of
considerable value, which should not be regarded as determinative of
theory nor neglected by the theorist.

Examples: Agulhon and L6obardy (1921), Boissevain (1927), Collier
(1924), Elod (1925-1926), Gellhorn (1927), Haden (1923), Marker and
Gordon (1924), Mommsen (1926), Naylor (1926), Pfeiffer (1927), Rohde
(1920), Ruhland (1923), Sheppe and Constable (1923), Speakman (1924),
Smith (1922), Steam and Steam (1924), Weiser and Porter (1927), Zirkle
(1927), Balint (1926).

Surface tension. See investigation and references by Hartridge and
Peters (1922), Egn6r and Hagg (1927) and general treatment by Rideal
(1926).

Taste. One of the original means of distinguishing acids. See page
1. There has been considerable discussion of the function of [H+j.
See review by Dietzel (1926).

Water, distilled and "conductivity." Review by Bencowitz and Hotch-
kiss (1925); cf. Bordas and Touplain (1926), Kolthoff (1926), and Bjerrum
(1927).

Waters, inland. The pH value of an inland water may be influenced by
the deposits with which it comes in contact. For an extreme see Wells
(1921). For the effect of stratification in lakes see Juday, Fred and Wilson
(1924). For the effect of industrial wastes and sewage see Buswell (1927).
See also "Ecology," Shelford (1925), Cowles and Schwitalla (1923), Saunders
(1921).

Water, sea. The carbonate equilibrium tends to maintain sea water at
a constant pH. This has doubtless varied with the CO2-tension of the
atmosphere in geological time. Locally it varies with temperature, the
photosynthetic action of the flora, accretions from rivers, and contact
with geologic deposits. The wider aspects have been described in Hen-
derson's Fitness of the Environment, The charting of the pH values of
different regions of the seas has been of aid in oceanographic surveys and
of value to the study of plant and animal distribution. See treatises by
Palitzsch (1922), Gaarder (1916-1917), Legendre (1926), Mayer (1922),
Bresslau (1926), Atkins et al. (1924).

BIBLIOGRAPHY

Knowledge is of two kinds. We know a subject ourselves, or we
know where we can find information upon it. — SAMUEL JOHNSON.

The references in this bibliography are classified either by notations
given in each chapter or else by the subjects briefly outlined in Chapter
XXX where cross references have been reduced to a minimum.

Abbreviations follow for the most part the system adopted by Chemical
Abstracts.
ABEGG, R. 1904 Elektrodenvorgange und Potentialbildung bei mini-

malen lonenkonzentrationen. Z. Elektrochem., 10, 607.
ABEGG, R., AUERBACH, F., AND LUTHER, R. 1909 Zur Frage des Null-

punktes der elektrochemischen Potentiale. Z. Elektrochem.,

16, 63.
ABEGG, R., AUERBACH, F., AND LUTHER, R. 1911 Messungen elektromo-

torischer Krafte galvanischer Ketten. Abhandl. d. Deutschen

Bunsen-Gesellschaft, No. 5. Halle, 1911. Supplement, 1915.
ABEL, J. J., CEILING, E. M. K., ROUILLER, C. A., BELL, F. K., WINTER-

STEINER, O. 1927 Crystalline insulin. J. Pharmacol., 31, 65.
ABT, G., AND LOISEAU, G. 1922 Reaction du milieu et production de la

toxine diphtherique. Ann. inst. Pasteur, 36, 535.
AGREE, S. F. 1908 On the theory of indicators and the reactions of phtha-

leins and their salts. Am. Chem. J., 39, 529.
AGREE, S. F., MELLON, R. R., AVERT, P. M., AND SLAGLE, E. A. 192] A

stable single buffer solution, pH 1-pH 12. J. Infect. Dis., 29, 7.
AGREE, S. F., AND SLAGLE, E. A. 1908 On the theory of indicators and the

reactions of phthaleins and their salts. Am. Chem. J., 39, 789;

1909, 42, 115.
ADAMS, E. Q. 1916 Relations between the constants of dibasic acids and

of amphoteric electrolytes. J. Am. Chem. Soc., 38, 1503.
ADAMS, E. Q. 1926 The electrostatic virial of strong electrolytes. J.

Am. Chem. Soc., 48, 621.
ADAMS, E. Q., AND ROSENSTEIN, L. 1914 The color and ionization of

crystal-violet. J. Am. Chem. Soc., 36, 1452.
AGULHON, AND LEOBARDY, J. DE 1921 Remarques sur Temploi en he"ma-

tologie des colorants complex base's sur la melhode de Romanow-

sky. Compt. rend. soc. biol., 84, 120.
AHLGREN, G. 1925 Zur Kenntnis der tierischen Gewebs oxydation.

Skand. Arch. Physiol. Supplement.

AIRILA, Y. 1921-22 The determination of the hydrogen-ion concentra-
tion in the range pH 8.45-10.5 by means of a series of colored

solutions. Acta soc. med. fennic, 3, 104 (cited).

587

588 THE DETERMINATION OF HYDROGEN IONS

ANDAUER, M. 1927 tJber absolute Werte von Elektrodenpotentialen.

Z. physik. Chem., 125, 135.
ANDERSON, W. S. 1922 Vitality of spermatozoa. Kentucky Agr. Expt.

Sta., Bull. 239, 36.

ANDRADE, E. N. DA C. 1926 The Structure of the Atom. 3rd ed.
ANDRESEN, V. 1922 tiber die Wasserstoffionenkonzentration des

Speichels. Ergebn. ges. Zahnheilk., 6, 59.
ANDREWS, J. C. 1924 Experimental studies on palladium electrodes. J.

Biol. Chem., 59, 479.
ANDRUS, E. C., AND CARTER, E. P. 1927 The mechanism of the action of

the hydrogen ion upon the cardiac rhythm. J. Clin. Investiga-
tion, 3, 555.
ANGELI, A., AND ERRANI, G. F. 1920 Acidity in smokeless powders.

Gazz. chim. ital., 50, 139 (cited).
ANONYMOUS 1927 The New Hellige Comparator for the determination of

hydrogen ion concentration. J. Sci. Instruments, 4, 327.
ARLOING, F., AND CHAVANNE. 1925 De 1'influence sur le bacteriophage,

des electrolytes et de la concentration en ions H du milieu.

Compt. rend. soc. biol., 93, 531.
ARND, T., AND SIEMERS, W. 1926 Zur Methodik der pH-Bestimmung

mit der Chinhydron-elektrode. Z. Pflanzenernahr. Diingung.

(A), 7, 191.
ARNDT, F., AND NACHTWEY, P. 1926 Reinisolierung von Pyridin iiber das

Perchlorat. Pyridin, Ammoniak und Indicatoren. Pyridinium-

perchlorat als saure Urtitersubstanz. Ber., 59, 448.
ARNOLD, E. L. 1924 o-Cresoltetrachlorophthalein and some of its deriva-
tives. J. Am. Chem. Soc., 46, 489.
ARRHENIUS, O. 1921 The hydrogen ion concentration of Egyptian soils

and the reclamation of alkaline land. Cairo Sci. J., 10, 3.
ARRHENIUS, O. 1921 Influence of soil reaction on earthworms. Ecology,

2, 255.
ARRHENIUS, O. 1922 Hydrogen ion concentration, soil properties and

growth of higher plants. Arkiv for Botanik, 18, No. 1.
ARRHENIUS, O. 1926 Kalkfrage, Bodenreaktion und Pflanzenwachstum.

Leipzig, Akademische Verlagsgesellschaft.
ARRHENIUS, O. 1928 The optimum soil reaction of the sugar beet. Ind.

Eng. Chem., 20, 219.
ARRHENIUS, S. 1887 tlber die Dissociation der in Wasser gelosten Stoff e.

Z. physik. Chem., 1, 631.
ARRHENIUS, S. 1888 Theorie der isohydrischen Losungen. Z. physik.

Chem., 2, 284.
ARRHENIUS, S. 1899 tlber die Anderung der Starke schwacher Sauren

durch Salzzusatz. Z. physik. Chem., 31, 197.
ARRHENIUS, S. 1914 The theory of electrolytic dissociation. (Faraday

Lecture.) J. Chem. Soc., 105, 1414.

ARTHUR, R. C., AND KEELER, E. A. 1922 A meter for recording the al-
kalinity of boiler-feed water. Power, 55, 768.

BIBLIOGRAPHY 589

ARZBERGER, C. F., PETERSON, W. H., AND FRED, E. B. 1920 Certain
factors that influence acetone production by Bacillus acetoethy-
licum. J. Biol. Chem., 44, 465.

ATEN, A. H. W. 1923 The hydrogen electrode in alkaline solutions.
Trans. Am. Electrochem. Soc., 43, 89.

ATEN, A. H. W., BRUIN, P., AND DE LANGE, W. 1927 The poisoning of
hydrogen electrodes. I. Rec. trav. chim., 46, 417.

ATEN, A. H. W., AND VAN DALFSEN, J. 1926 The elimination of liquid
potentials. Rec. trav. chim., 45, 177.

ATEN, A. H. W., AND VAN GINNEKEN, P. J. H. 1925 A hydrogen elec-
trode for flowing liquids. Rec. trav. chim., 44, 1012.

ATEN, A. H. W., VAN GINNEKEN, P. J. H., AND ENGELHARD, F. J. W. 1926
Studies on the carbonatation of sugar-lime-solutions. Rec.
trav. chim., 45, 753.

ATKINS, W. R. G. 1922 Some factors affecting the hydrogen ion concen-
tration of the soil and its relation to plant distribution. Sci.
Proc. Roy. Dublin Soc. (N. S.), 16, 369.

ATKINS, W. R. G. 1922 The hydrogen ion concentration of plant cells.
Sci. Proc. Roy. Dublin Soc. (N. S.), 16, 414.

ATKINS, W. R. G. 1922 Note on the occurrence of the finger and toe
disease of turnips in relation to the hydrogen ion concentration
of the soil. Sci. Proc. Roy. Dublin Soc. (N. S.), 16, 427.

ATKINS, W. R. G. 1922 Preparation of permanently non-acid formalin
for preserving calcareous specimens. J. Marine JBiol. Assoc.
United Kingdom, 12, 792.

ATKINS, W. R. G., AND LEBOUR, M. V. 1923 The hydrogen ion concen-
tration of the soil and of natural waters in relation to the distri-
bution of snails. Proc. Roy. Dublin Soc., 17, 233.

ATKINS, W. R. G. ET AL. 1924 List of papers by. J. Marine Biol. Assoc.
United Kingdom, 13.

ATKINS, W. R. G., AND PANTIN, C. F. A. 1926 A buffer mixture for the
alkaline range of hydrogen ion concentration determinations.
Biochem. J., 20, 102.

ATSUKI, K., AND NAKAMURA, M. 1927 The mechanism of the loading of
paper. Cellulose Ind., 2, 46.

ATZLER, E., AND LEHMANN, G. 1922 Influence of hydrion concentration
on blood vessels. Arch. ges. Physiol. (Pfliiger's), 193, 463 (cited).

AVERT, P. M., MELLON, R. R., AND AGREE, S. F. 1921 Uses in biological
science for standardized, sterile buffer tablets, and for a single
sterile buffer solution covering all pH values. Science, 53, 613.

AUERBACH, F. 1912 Die Potentiale der wichtigsten Bezugselektroden.
Z. Elektrochem., 18, 13.

AUERBACH, F., AND SMOLCZYK, E. 1924 Zur Theorie und Praxis der
elektrometrischem Sauretitration. Z. physik. Chem., 110, 65.

AUGER, V. 1921 Sur 1'emploi des indicateurs colorores en acidimetrie
et en alcalimetrie. Bull. soc. chim., 29, 329.

590 THE DETERMINATION OF HYDROGEN IONS

AUSTIN, J. H., AND CULLEN, G. E. 1926 Hydrogen Ion Concentration of

the Blood in Health and Disease. Baltimore.
AUSTIN, J. H., STADIE, W. C., AND ROBINSON, H. W. 1925 The relation

between colorimetric reading and true pH of serum or plasma.

J. Biol. Chem., 66, 505.
AVERT, 0. TM AND CULLEN, G. E. 1919 The use of the final hydrogen ion

concentration in the differentiation of Streptococcus haemolyticus

of human and bovine types. J. Exp. Med., 29, 215.
BACH, A. 1925 tJber aktiven Wasserstoff. Ber. 58B, 1388.
BAEYER, A., AND FRAUDE, G. 1880 Das Orthokresolphthalein und seine

Derivate. Ann. Chem., 202, 153.
BAGGESGAARD-RASMUSSEN, H., AND SCHOU, S. A. 1925 tlber die titra-

tion von alkaloiden. Z. Elektrochem., 31, 189.
BAILEY, C. H. 1920 A simple hydrogen electrode. J. Am. Chem. Soc.,

42, 45.

BAILEY, C. H. 1925 The Chemistry of Wheat Flour. New York.
BAKER, J. C., AND VAN SLYKE, L. L. 1918 A method for making electro-
metric titrations of solutions containing protein. J. Biol.

Chem., 36, 137.
BAKER, T. T., AND DAVIDSON, L. F. 1922 Spectroscopic measurements

of the hydrogen-ion concentration color changes in recent indi-
cators. Phot. J., 62, 375.

BALCH, R. T. 1925 The hydrogen ion in beet sugar work. Sugar, 27, 587.
BALINT, M. . 1926 Buffered solution for the Romanowsky-Giemsa Stain.

Klin. Wochschr., 5, 147 (cited).
BANCROFT, W. D. 1918 The sign of the zinc electrode. Trans. Am.

Electrochem. Soc., 33, 79.
BANCROFT, W. D. 1924 The electrolytic theory of corrosion. J. Phys.

Chem., 28, 786.
BARCROFT, J. 1925 The Respiratory Function of the Blood. Cambridge

University Press.
BARENDRECHT, H. P. 1915 A simple hydrogen electrode. Biochem. J.,

9, 66.
BARKAN, G., BROEMSER, P., AND HAHN, A. 1922 Eine gepufferte Durch-

stromungsflussigkeit fiir die tTberlebende Froschniere. Z. Biol.,

74, 1.
BARNETT, G. D., AND BARNETT, C. W. 1921 Colorimetric determination

of hydrogen ion concentration by means of a double-wedge

comparator. Proc. Soc. Exp. Biol. Med., 18, 127.
BARNETT, G. D., AND CHAPMAN, H. S. 1918 Colorimetric determination

of reaction of bacteriologic mediums and other fluids. J. Am.

Med. Assoc., 70, 1062.
BARRATT, J. O. W. 1925 Hydrolytic dissociation curves. Biochem. J.,

19, 875.
BAUMBERGER, J. P. 1924 Three hints on hydrogen electrode technic.

J. Lab. Clin. Med., 9, 720.

BIBLIOGRAPHY 591

BAUR, E. 1925 tTber die Messung einzelner Phasengrenz-potentiale.

Z. Elektrochem., 31, 514.
BAVER, L. D. 1926 The use of the quinhydrone electrode for measuring

the hydrogen-ion concentration of soils. Soil Science, 21, 167.
BAYLIS, J. R. 1923 Tungsten wire for hydrogen-ion determinations. J.

Ind. Eng. Chem., 15, 852.

BAYLISS, L. E., KERRIDGE, P. T., AND VERNEY, R. C. 1926 The deter-
mination of the hydrogen-ion concentration of the blood. J.

Physioi., 61, 448.

BAYLISS, W. M. 1927 Principles of General Physiology. London.
BEANS, H. T., AND HAMMETT, L. P. 1925 Experimental studies on the

hydrogen electrode. J. Am. Chem. Soc., 47, 1215.
BEANS, H. T., AND OAKES, E. T. 1920 The determination of the hydrogen

ion concentration in pure water by a method for measuring the

electromotive force of concentration cells of high internal

resistance. J. Am. Chem. Soc., 42, 2116.
BEATTIE, J. A. 1920 The activity coefficient of normal potassium chloride

solution and the potential of the normal calomel electrode.

J. Am. Chem. Soc., 42, 1128.
BEATTIE, J. A. 1924 The application of the phase rule to galvanic cells.

J. Am. Chem. Soc., 46, 2211.
BEATTIE, R. 1910-12 Simplified electrometer theory. Elect., 65, 729,

821, 910; 69, 233.
BEERS, C. D. 1927 The relation between hydrogen ion concentration

and encystment in Didinium nasutum. J. Morphol. Physioi.,

44,21.

BENCOWITZ, L, AND HOTCHKISS, H. T., JR. 1925 Preparation of conduc-
tivity water. J. Phys. Chem., 29, 705.
BENNETT, C. E. 1925 A new capillary electrometer, and the relation

between the mercury displacements and the radius of the tube.

J. Optical Soc. Am., 11, 411.
BENNEWITZ, K., AND GUNTHER, P. 1924 tJber den Zustand des in Platin

gelosten Wasserstoffs. Z. physik. Chem., Ill, 257.
BERRIDGE, E. M. 1924 The influence of hydrogen-ion concentration on

the growth of certain bacterial plant parasites and saprophytes.

Ann. Appl. Biol., 11, 73.
BIDDLE, H. C., AND PORTER, C. W. 1915 Temperature coefficients and

the effects of acids, bases and salts in reaction velocities of the

triphenylmethane dyes. J. Am. Chem. Soc., 37, 1571.
BIENFAIT, H. 1926 A deflection potentiometer. Rec. trav. chim., 45,

166.
BIGELOW, W. D., AND CATHCART, P. H. 1921 Relation of processing to

the acidity of canned foods. Bull. 17-LRes. Lab. Nat'l Canners'

Assoc., Wash., D. C.
BIGELOW, W. D., AND ESTY, J. R. 1920 The thermal death point in

relation to time of typical thermophilic organisms. J. Infect.

Dis., 27, 602.

592 THE DETERMINATION OF HYDROGEN IONS

BIILMANN, E. 1920 Kinhydroners Brintning. Ann. Univ. Copenhagen

(cited).
BIILMANN, E. 1921 Sur 1'hydrogenation des quinhydrones. Ann. chim.,

[9] 15, 109.

BIILMANN, E. 1923 Oxidation and reduction potentials of organic com-
pounds. Trans. Faraday Soc., 19, 676.
BIILMANN, E. 1924 On the measurement of hydrogen-ion concentration

in soil by means of the quinhydrone electrode. J. Agr. Sci.,

14, 232.
BlILHANN, E. 1927 L'electrode a quinhydrone et ses applications. Bull.

soc. chim. [4], 41, 213.
BIILMANN, E., AND HENRIQUES, O. M. 1924 Titrimetriske Studier over

det Evaldske Proevemaaltid. Biblio. for Laeger (Koebenhavn),

116, 569 (cited).
BIILMANN, E., AND JENSEN, A. L. 1927 Sur la preparation de 1'hydrogene

pur pour les electrodes a hydrogene. Bull. soc. chim., 41, 147.
BIILMANN, E., AND JENSEN, A. L. 1927 Sur le potentiel de 1'electrode

a quinhydrone par rapport a 1'electrode a hydrogene. Bull.

soc. chim., 41, 151.
BIILMANN, E., AND KATAGIRI, H. 1927 Influence of glucose, alcohol and

carbon dioxide at barometric pressure on the pH values of

phosphate and bicarbonate solutions, determined by means of

hydroquinhydrone electrodes. Biochem. J., 21, 441.
BIILMANN, E., AND KBARUP, I. 1924 The temperature coefficient of the

quinhydrone electrode. J. Chem. Soc., 125, 1954.
BIILMANN, E., AND KLIT, A. 1927 Kolloidales Palladium als Katalysator

in der Wasserstoffelektrode. Z. physik. Chem., Cohen-Fest-

band.
BIILMANN, E., AND LUND, H. 1921 Sur 1'electrode a quinhydrone. Ann.

chim. [9], 16, 321.
BIILMANN, E., AND TOVBORG-JENSEN, S. 1927 On the determination of

the reaction of soils by means of the quinhydrone electrode.

Proc. 2nd. Commission Internat. Soc. Soil Sci. B.
BIRCHER, L. J., AND HOWELL, G. D. 1926 Studies on the temperature

coefficients of reference electrodes. J. Am. Chem. Soc., 48, 34.
BIRGE, R. T., AND AGREE, S. F. 1919 On the quinone-phenolate theory of

indicators. J. Am. Chem. Soc., 41, 1031.
BISHOP, R. O. 1927 Studies on Hevea latex. VI. The proteins in serum

from frozen latex. Malayan Agr. J., 15, 27 (cited).
BISHOP, E. R., KITTREDGE, E. B., AND HiLDEBRAND, J. H. 1922 Titra-

tions in ethyl alcohol as solvent. J. Am. Chem. Soc., 44, 135.
BJERRUM, N. 1905 Uber die Elimination des Diffusionspotentials zwi-

schen zwei verdtinnten wasserigen Losungen durch Einschalten

einer konzentrierten Chlorkaliumlosung. Z. physik. Chem., 53,

428.
BJERRUM, N. 1909 A new form for the electrolytic dissociation theory.

7th Intern. Congress Applied Chem., Section 10, p. 59.

BIBLIOGRAPHY 593

BJBRRUM, N. 1911 Uber die Giiltigkeit der Planckschen Formel fur das

Diffusionspotential. Z. Elektrochem., 17, 58.
BJERRUM, N. 1911 tlber die Elimination des Fliissigkeitspotentials

bei Messungen von Elektrodenpotentialen. Z. Elektrochem.,

17, 389.
BJERRUM, N. 1914 Die Theorie der alkalimetrischen und azidimetrischen

titrierung. Stuttgart. Also in Sammlung chem. u. chem. tech.

Vortrage, 21, 1/3 H. p. 1.
BJBRRUM, N. 1917 Die moderne Auffassung der sauren und basischen

Reaktion und ihre Anwendung in der Analyse. Z. anal. Chem.,

66, 13, 81.
BJERRUM, N. 1921 Studien iiber Chromirhodanide. II. Z. anorg.

allgem. Chem., 119, 39.
BJERRUM, N. 1923 Die Konstitution der Ampholyte, besonders der

Aminosauren, und ihre Dissoziationskonstanten. Z. physik.

Chem., 104, 147.
BJERRUM, N. 1923 Dissoziationskonstanten von mehrbasischen Sauren

und ihre Anwendung zur Berechnung molekularer Dimensionen.

Z. physik. Chem., 106, 219.
BJERRUM, N. ]926 Die Verdiinnungswarme einer lonenlosung in der

Theorie von Debye und Huckel. Z. physik. Chem., 119, 145.
BJERRUM, N. 1926 Die elektrischen Krafte zwischen den lonen und

ihre Wirkungen. Ergebnisse exakten Naturwissensch., 5, 125.
BJERRUM, N. 1927 tlber titrimetrische Bestimmung der in distilliertem

Wasser vorhandenen kleinen Mengen von Kohlensaure und

Ammoniak. Ann. acad. sci. Fennicae [A] 29, 1.
BJERRUM, N., AND GJALDBAEK, J. K. 1919 Underspgelser over de fak-

torer, som bestemmer jordbundens reaktion. I. Determination

of acid-base equilibria in soil. II. Reaction of liquids saturat-
ed with CaC03. Kong. Vet.-og Landboh0jskole Aarskrift, 48.
BLACKADDER, T. 1925 Ripening of hydrogen electrodes. J. Am. Leather

Chem. Assocn., 20, 17.
BLATHERWICK, N. R. 1914 The specific role of foods in relation to the

composition of the urine. Arch. Intern. Med., 14, 409.
BLOWSKI, A. A., AND HOLVEN, A. L. 1925 Hydrogen-ion concentration

as a basis of refinery alkalinity control. Ind. Eng. Chem., 17,

1263.
BLUM, W. 1913-14 The constitution of aluminates. J. Am. Chem. Soc.,

35, 1499; 36, 2381.
BLUM, W. 1916 Determination of aluminium as oxide. J. Am. Chem.

Soc., 38, 1282.
BLUM, W., AND HOGABOOM, G. B. 1924 Principles of Electroplating and

Electroforming. McGraw-Hill Co.
BODENSTEIN, M. 1924 Ein Beitrag zur Theorie der katalytischen Hy-

drierung durch Platin. Ann., 440, 177.
BODFORSS, S. 1922 Uber die Beeinflussung von verschiedenen chemischen

Reaktionen durch Substituenten. Z. physik. Chem., 102, 41.

594 THE DETERMINATION OF HYDROGEN IONS

BODFORSS, S. 1923 tiber den absoluten Nullpunkt des elektrischen

Potentials. Z. Elektrochem., 29, 121.
BODINE, J. H. 1921 Hydrogen ion concentration of protozoan cultures.

Biol. Bull., 41, 73.
BODINE, J. H. 1926 The hydrogen ion concentration in the blood of

certain insects. Biol. Bull., 51, 363.
BODINE, J. H. 1927 Potentiometric studies on intracellular pH values of

single Fundulus egg cells. J. Gen. Physiol., 10, 533.
BODINE, J. H., AND FINK, D. E. 1925 A simple micro vessel with elec-
trode for determining the hydrogen ion concentration of small

amounts of fluid. J. Gen. Physiol., 7, 735.
BOD LANDER, G. 1904 Zeitgrossen der Komplexbildung, Komplexkonstan-

ten und atomistische Dimension. Z. Elektrochem., 10, 604.
BOGEN, E. 1927 A universal indicator for hydrogen ion concentration.

J. Am. Med. Assocn., 89, 199.
BOGERT, M. T., AND ScATCHARD, G. 1916 Researches on quinazolines,

XXXIII. A new and sensitive indicator for acidimetry and

alkalimetry, and for the determination of hydrogen ion concen-
trations between the limits 6 and 8 on the S0rensen scale. J.

Am..Chem. Soc., 38, 1606.
BOGUE, R. H. 1924 Theory and Application of Colloid Behavior. (Two

Vols.) N. Y.
BOISSEVAIN, C. H. 1927 The relation between loss of acid-fastness of the

tubercle bacillus and hydrogen ion concentration. Am. Rev.

Tuberculosis, 16, 758.

BOLTZMANN, L. 1898 Vorlesungen tiber Gastheorie, part II. Leipzig.
BONACORSI, L. 1923 tiber den Einfluss der Reaktion des Nahrbodens

auf die entwicklungshemmende Wirking Chemischer Substanzen.

Z. Hyg. Infektionskrankh., 99, 284.
BORDAS, F., AND TOUPLAIN. F. 1926 Pure neutral distilled water (pH =

7.07). Ann. fals., 19, 134 (cited).
BORELIUS, G. 1914 Die Oberflachenpotentiale von Losungen in Kontakt

mit Isolatoren. Ann. Physik. [4], 45, 929.
BOSE, E. 1900 Untersuchungen iiber die elektromotorische Wirksamkeit

der elementaren Gase. I. Z. physik. Chem., 34, 701; II, Z.

physik. Chem., 38, 1.
BOTTGER, W. 1897 Die Anwendung des Elektrometers als Indikator beim

Titrieren von Sauren und Basen. Z. physik. Chem., 24, 253.
BOVIE, W. T. 1915 A direct reading potentiometer for measuring and

recording both the actual and the total reactions of solutions.

J. Med. Res., 33, 295.
BOVIE, W. T. 1922 A new vessel for electrometric titration. J. Am.

Chem. Soc., 44, 2892.
BOVIE, W. T. 1923 Methods for making temperature corrections in

direct reading potentiometers for measuring hydrogen-ion con-
centrations. J. Optical Soc. Am., 7, 1235.

BIBLIOGRAPHY 595

BOVIE, W. T. AND HUGHES, W. S. 1923 A source of trouble in electro-
metric measurements of hydrogen-ion concentration. J. Am.
Chem. Soc., 45, 1904.

BRADFIELD, R. 1928 Factors affecting the coagulation of colloidal clay.
J. Phys. Chem., 32, 202.

BRADLEY, H., AND COHEN, A. 1924 The indicator paper test for acidity
in leather. Cited in Cuir tech., 14, 118 (1925).

BREDIG, G., AND FRAENKEL, W. 1905 Eine neue, sehr empfindliche Was-
serstoffionen-katalyse. Z. Elektrochem., 11, 525.

BRESSLAU, E. 1924 Ein einfacher, insbesondere fur kleine Fliissigkeits-
mengen geeigneter Apparat zur Bestimmung der Wasserstoffio-
nenkonzentration (Hydrionometer) mit den Michaelisschen
Indikatoren. Deut. med. Wochschr., 50, 164. Arch, f . Hydro-
biologie, 15, 585.

BRESSLAU, E. 1926 Die Bedeutung der Wasserstoffionenkonzentration
fur die Hydrobiologie. Verhand. Internat. Vereinigung theor.
angew, Limonologie, 3, 56.

BRIGHTMAN, C. L., HOPFIELD, J. J., MEACHAM, M. R., AND AGREE, S. F.
1918 The quinone phenolate theory of indicators. Spectro-
metric' study of the end points and fading of phenolsulphon-
phthalein indicators. J. Am. Chem. Soc., 40, 1940.

BRIGHTMAN, C. L., MEACHEM, M. R., AND ACREE, S. F. 1920 A spectro-
photometric study of the "salt effects" of phosphates upon the
color of phenolsulfonphthalein salts and some biological appli-
cations. J. Bact., 5, 169.

BRIOUX, C., AND PIEN, J. 1925 Emploi de P electrode a quinhydrone pour
la determination du pH des sols. Compt. rend., 181, 141.

British Association 1922 Report: Absorption Spectra and Chemical
Constitution of Organic Compounds. Reprints (new series) 12.

BRITTON, H. T. S. 1924 The electrometric titration of chromic acid using
(a) the hydrogen electrode, and (b) the oxygen electrode. J.
Chem. Soc., 125, 1572.

BRITTON, H. T. S. 1925 Electrometric studies of the precipitation of
hydroxides. I-IV. J. Chem. Soc., 127, 2110, 2120, 2142, 2148.

BRITTON, H. T. S. 1927 Electrometric methods of industrial importance
for the determination of hydrogen ions. Ind. Chemist, 3, 149.

BRITTON, H. T. S. 1927 The importance of hydrogen-ion estimation in
volumetric analysis. Ind. Chemist, 3, 220.

BRITTON, H. T. S. 1927 The importance of hydrogen-ion concentrations
in separation processes. Ind. Chemist, 3, 257.

BRITTON, H. T. S. 1927 The importance of hydrogen-ion concentration
in the electrodeposition of metals. Ind. Chemist, 3, 314.

BRODE, W. R. 1924 The determination of hydrogen-ion concentration
by a spectrophotometric method and the absorption spectra of
certain indicators. J. Am. Chem. Soc., 46, 581.

BROEMSER, P. 1922 tTber die zweckmassige Konstruktion von Capil-
larelektrometern. Z. Biol., 75, 309.

596 THE DETERMINATION OF HYDROGEN IONS

BRONFENBRENNER, J. 1918 A new indicator for direct reading of hydro-
gen ion concentration in growing bacterial cultures. J. Med.
Res., 39, 25.

BRONK, D. W., AND GESELL, R. 1926 Electrical conductivity, electrical
potential and hydrogen ion concentration measurements on the
submaxillary gland of the dog recorded with continuous photo-
graphic methods. Am. J. Physiol., 77, 570.

BR0NSTED, J. N. 1909 Die elektromotorische Kraft der Knallgaskette.
Z. physik. Chem., 66, 84, 744.

BR0NSTED, J. N. 1920 D. kgl. danske Videnskabernes Selskabs math.-
fys. Meddelelser. Ill no. 9 (cited).

BR0NSTED, J. N. 1920 Applicability of the gas laws to strong electrolytes.
Kgl. Danske Videnskab. Selskab, Math.-fys. Medd., 3, 21.

BR^NSTED, J. N. 1921 The influence of salts on chemical equilibria in
solutions. J. Chem. Soc., 119, 574.

BR^NSTED, J. N. 1922 Studies on solubility. IV. The principle of the
specific interaction of ions. J. Am. Chem. Soc., 44, 877.

BR0NSTED, J. N. 1922 Zur Theorie der chemischen Reaktionsge-
schwindigkeit. Z. physik. Chem., 102, 169.

BR^NSTED, J. N. 1923 The individual thermodynamic properties of
ions. J. Am. Chem. Soc., 45, 2898.

BR0NSTED, J. N. 1923 Einige Bemerkungen iiber den Begriff der Sauren
und Basen. Rec. trav. chim., 42, 718.

BR0NSTED, J. N. 1926 Zur Kinetik der Aquotisierung. Z. physik.
Chem., 122, 383.

BR0NSTED, J. N. 1926 Acid-basic function of molecules and its depend-
ency on the electric charge type. J. Phys. Chem., 30, 777.

BR0NSTED, J. N., AND GUGGENHEIM, E. A. 1927 Contribution to the
theory of acid and basic catalysis. The mutarotation of glu-
cose. J. Am. Chem. Soc., 49, 2554.

BR0NSTED, J. N., AND KING, C. V. 1925 Secondary kinetic salt effect in
the case of hydroxyl-ion catalysis. J. Am. Chem. Soc., 47,
2523.

BR^NSTED, J. N., AND LAMER, V. K. 1924 The activity coefficients of
ions in very dilute solutions. J. Am. Chem. Soc., 46, 555.

BR^NSTED, J. N., AND PEDERSEN, K. 1922 Uber die Gultigkeit des Mas-
senwirkungsgesetzes f iir lonengleichgewichte. Z. physik. Chem.,
103, 307.

BR^NSTED, J. N., AND TEETER, C. E., JR. 1924 On kinetic salt effect.
J. Ph/s. Chem., 28, 578.

BROOKS, S. C. 1920 The mechanism of complement action. J. Gen.
Physiol., 3, 185.

BROWN, J. H. 1923 The colorimetric determination of the hydrogen ion
concentration of small amounts of fluid. J. Lab. Clin. Med.,
9, 239.

BROWN, W. E. L. 1924 The measurement of hydrogen-ion concentrations
with glass electrodes. J. Sci. Instruments, 2, 12.

BIBLIOGRAPHY 597

BROWNE, F. L. 1923 The constitution of ferric* oxide hydrosol from
measurements of the chlorine- and hydrogen-ion activities.
J. Am. Chem. Soc., 45, 297.

BROWNING, C. H., GULBRANSEN, R., AND KENNAWAY, E. L. 1919 Hy-
drogen ion concentration and antiseptic potency, with special
reference to the action of acridine compounds. J. Path. Bact.,
23, 106.

BRUBAKER, H. W. 1914 Some natural indicators. J. Am. Chem. Soc.,
36, 1925.

BRUERE, DE LA 1925 La Spectrophotometrie des Extraits tannants dans
1'ultra-violet et les pH. J. Intern. Soc. Leather Trades' Chem.,
9, 427; Cuir tech., 14, 266.

BRUERE, P. 1926 Construction d'echelles colorimetriques stables pour
la mesure des indices pH. J. pharm. chim., [8], 3, 377; 4, 241.

BRUNIUS, E., AND KARSMARK, K. A. 1927 Determination of pH and the
effect of hydrogen ions on medicinals. Svensk Farm. Tid., 31,
201, 223, 257.

BUCH, K. 1926 Spectrophotometrie investigation of color indicators.
Soc. Sci. Fennica, Commentationen-Phys.-Math., 2, 26 (cited).

BUCHANAN, R. E., AND FULMER, E. I. 1928 Physiology and Biochemistry
of Bacteria. The Williams & Wilkins Co., Baltimore, Md.

BUCHI, P. F. 1924 Zur Bestimmung von Diffusionspotentialen. Z.
Elektrochem., 30, 443.

BUCKMASTER, G. A. 1923 A film method for the reaction of the liquids of
the body by indicators. J. Physiol. (proc.), 58, ii.

BUGARSZKY, S., AND LIEBERMANN, L. 1898 Ueber das Bindungsvermogen
eiweissartiger Korper fur Salzsaure, Natriumhydroxyd und
Kochsalz. Arch. ges. Physiol. (Pfliiger's), 72, 51.

BUGARSZKY, S., AND TANGL, F. 1898 Physikalisch-chemische Untersuch-
ungen iiber die molecularen Concentrationsverhaltnisse des
Blutserums. Arch. ges. Physiol. (Pfliiger's), 72, 531.

BURTON, E. F. 1926 Helmholtz double layer related to ions and charged
particles. Colloid Symposium, 4, 132.

BUSWELL, A. M. 1927 The Chemistry of Water and Sewage Treatment.
New York.

BUTLER, J. A. V. 1924 The seat of the electromotive force in the galvanic
cell. Phil. Mag. [6], 48, 927.

BUTLER, J. A. V. 1927 The equilibrium of heterogeneous systems includ-
ing electrolytes. II. Equilibrium at interfaces and the theory
of electrocapillarity. Proc. Roy. Soc., [A] 113, 594.

BUTLER, J. A. V., HUGH, W. E., AND HEY, D. H. 1926 The effect of the
electrode material on oxidation potentials. Trans. Faraday
Soc., 22, 24.

BUYTENDIJK, F. J. J., AND BRiNKMAN, R. 1926 On the reaction course of
physiological buffer mixtures examined by direct registration of
the pH changes. Proc. Roy. Acad. Amsterdam, 29, 816. Kon.
Akad. Wetensch. Amsterdam, 29, 1.

598 THE DETERMINATION OF HYDROGEN IONS

BUYTENDIJK, F. J. J./BRINKMAN, R., AND MOOK, H. W. 1927 A study of
the system carbonic acid, carbon dioxide and water. I. Deter-
mination of the true dissociation constant of carbonic acid.
Biochem. J., 21, 576.

BUYTENDIJK, F. J. J., AND WOERDEMAN, M. W. 1927 Die physico-chem-
ischen Erscheinungen wahrend der Eientwicklung. Roux's
Arch. Entwicklungsmechanik d. Org., 112, 387.

CALHANE, D. F., AND GUSHING, R. E. 1923 An application of the vacuum
tube to chemistry. Ind. Eng. Chem., 15, 1118.

CAMPBELL, N. R., AND GARDINER, H. W. B. 1925 Photo-electric colour-
matching. J. Sci. Instruments, 2, 177.

CANNAN, R. K. AND KNIGHT, B. C. J. G. 1927 Dissociation constants
of cystine, cysteine, thioglycolic acid and a-thiolactic acid.
Biochem. J., 21, 1384.

CARR, F. H. 1922 Demonstration of the use of a universal indicator.
Analyst, 47, 196.

CARSON, C. M. 1925 Determination of aniline in aqueous solutions.
Ind. Eng. Chem., 17, 62.

CARTER, S. R., AND LEA, F. M. 1926 Observations on liquid boundaries
and diffusion potentials. J. Chem. Soc., 834.

CENTNERSZWER, M., AND STRAUMANIS, M. 1925 t)bt Radiumstrahlung
einen Einfluss auf das Potential der Wasserstoffelektrode aus?
Z. physik. Chem., 118, 241.

CHABOT, G. 1925 Colorimetric method for pH determinations. Bull.
1'assocn. eleves Pinst. sup. fermentations Gand, 26, Ann. soc.
brasseurs, 34, 151 (cited).

CHAMBERS, R. 1926 The nature of the living cell as revealed by micro-
dissection. Harvey Lectures, 22, 41.

CHAMBERS, R., AND POLLACK, H. 1927 Micrurgical studies in cell phy-
siology. IV. Colorimetric determination of the nuclear and
cytoplasmic pH in the starfish egg. J. Gen. Physiol., 10, 739.

CHANDLER, E. E. 1908 The ionization constants of the second hydrogen
ion of dibasic acids. J. Am. Chem. Soc., 30, 694.

CHANOZ, A. M. 1906 On liquid junction potentials. Ann. Univ. Lyon,
n. s. 1, 18 (cited).

CHANOZ, M. 1926 Difference de potentiel des dissolutions aqueuses.
Obtention d'un contact liquide physiquement defini. Formule
de Gouy. Compt. rend. soc. biol., 95, 39.

CHESNEY, A. M. 1922 The use of phenol red and brom-cresol purple as
indicators in the bacteriological examination of stools. J.
Exp. Med., 35, 181.

CHICK, H. 1913 Some factors concerned in the solution and precipitation
of euglobulin. Biochem. J., 7, 318.

CHICK, H., AND MARTIN, C. J. 1911 On the "heat coagulation" of pro-
teins. II. The action of hot water upon egg-albumin and the
influence of acid and salts upon reaction velocity. J. Physiol.,
43,1.

BIBLIOGRAPHY 599

GHODAT, F. 1924 Concentration en ions hydrogene du sol et son im-
portance pour la constitution des formations vegetal. Univ.
Geneve, Inst. Bot. Ser 10 Fas 7.

CHOPRA, R. N., AND SUDHAMOY. 1925 A buffered solution for per-
fusion of isolated organs. Indian J. Med. Research, 13, 7.

CHOW, M. 1920 The free energy of potassium hydroxide in aqueous solu-
tion and the activities of its ions. J. Am. Chem. Soc., 42, 488.

CHOW, M. 1920 The activities of the ions in solutions of mixed electro-
lytes. J. Am. Chem. Soc., 42, 497.

CHRISTOPHERSEN, E. 1925 Soil reaction and plant distribution in the
Sylene National Park, Norway. Trans. Conn. Acad. Arts Sci.,
27, 471.

CHURCHMAN, J. W. 1922 The mechanism of bacteriostasis. Proc. Soc.
Exptl. Biol. Med., 20, 16.

CLARK, A. B., AND LUBS, H. A. 1918 The use of thymolsulfonphthalein
as an indicator in acidimetric titration. J. Am. Chem. Soc.,
40, 1443.

CLARK, G. W., AND CARTER, K. L. 1927 Factors involved in the reaction
changes of human saliva. J. Biol. Chem., 73, 391.

CLARK, W. M. 1913 An improved thermoregulator. J. Am. Chem. Soc.,
25, 1889.

CLARK, W. M. 1915 The "reaction" of bacteriologic culture media.
J. Infect. Dis., 17, 109.

CLARK, W. M. 1915 The final hydrogen ion concentrations of cultures of
Bacillus coli. J. Biol. Chem., 22, 87.

CLARK, W. M. ,1915 A hydrogen electrode vessel. J. Biol. Chem., 23, 475.

CLARK, W. M. 1920 Reduction potentials of mixtures of indigo and in-
digo white, and of mixtures of methylene blue and methylene
white. J. Wash. Acad. Sci., 10, 255.

CLARK, W. M. 1921 Reply to Wherry and Adams' article on methods of
stating acidity. J. Wash. Acad. Sci., 11, 199.

CLARK, W. M. 1922 Instability of phthalate potentials. J. Am. Chem.
Soc., 44, 1072.

CLARK, W. M. 1926 Standard buffer solutions and acid-base indicators.
International Critical Tables, 1, 81.

CLARK, W. M. 1927 Synthetic milk as a basis for research. J. Dairy
Sci., 10, 195.

CLARK, W. M., COHEN, B., SULLIVAN, M. X., GIBBS, H. D., CANNAN,

R. K. 1923-1927 Studies on Oxidation-reduction
I. Introduction. Public Health Reports, 1923, 38, 443. (Reprint

No. 823.)

II. An analysis of the theoretical relations between reduction po-
tentials and pH. Public Health Reports, 1923, 38, 666.
(Reprint No. 826.)

III. Electrode potentials of mixtures of l-naphthol-2-sulphonic acid
indophenol and the reduction product. Public Health Re-
ports, 1923, 38, 933. (Reprint No. 834.)

600 THE DETERMINATION OF HYDROGEN IONS

IV. Electrode potentials of indigo sulphonates, each in equilibrium
with its reduction product. Public Health Reports, 1923,

38, 1669. (Reprint No. 848.)

V. Electrode potentials of simple indophenols, each in equilibrium
with its reduction product. Public Health Reports, 1924,

39, 381. (Reprint No. 904.)

VI. A preliminary study of indophenols: (A) Dibromo substitution
products of phenol indophenol; (B) Substituted indophenols
of the ortho type ; < C) Miscellaneous. Public Health Reports,
1924, 39, 804. (Reprint No. 915.)

VII. A study of dichloro substitution products of phenol indophenols.
Public Health Reports, 1925, 40, 649. (Reprint No. 1001.)
VIII. Methylene blue. Public Health Reports, 1925, 40, 1131. (Re-
print No. 1017.)

IX. A potentiometric and spectrophotometric study of meriquinones
of the p-phenylene diamine and benzidine series. Supplement
No. 54 to Public Health Reports, 1926.
X. Reduction potentials in cell suspensions. Supplement No. 55

to Public Health Reports, 1926.

XI. Potentiometric and spectrophotometric studies of Bindsched-
ler's green and toluylene blue. Supplement No. 61 to Public
Health Reports, 1927.
XII. A note on the Schardinger reaction (in reply to Kodama).

Supplement No. 66 to Public Health Reports, 1927.
Reprints I-X Hygienic Laboratory Bulletin 151.

CLAEK, W. M., AND LUBS, H. A. 1915 The differentiation of bacteria of
the colon-aerogenes family by the use of indicators. J. Infect.
Dis., 17, 160.

CLARK, W. M., AND LUBS, H. A. 1916 Hydrogen electrode potentials of
phthalate, phosphate and borate buffer mixtures. J. Biol.
Chem., 25, 479.

CLARK, W. M., AND LUBS, H. A. 1917 The colorimetric determination of
hydrogen ion concentration and its applications in bacteriology.
J. Bact., 2, 1, 109, 191.

CLARK, W. M., AND LUBS, H. A. 1917 Improved chemical methods for dif-
ferentiating bacteria of the coli-aerogenes family. J. Biol.
Chem., 30, 209.
CLARK, W. M., AND LUBS, H. A. 1917 A substitute for litmus for use in

milk cultures. J. Agr. Research, 10, 105.

CLARKE, H. T., AND KIRNER, W. R. 1922 Methyl red. Organic Syn-
theses, 2, 47.

CLARKE, W. F., MYERS, C. N., AND AGREE, S. F. 1916 A study of the
hydrogen electrode, of the calomel electrode and of contact
potential. J. Phys. Chem., 20, 243.

CLIBBENS, D. A., AND FRANCIS, F. 1912 The catalytic decomposition of
nitrosotriacetonamine by alkalis. J. Chem. Soc., 101, 2358.

BIBLIOGRAPHY 601

CLOWES, G. H. A., AND SMITH, H. W. 1923 The influence of hydrogen ion
concentration on the fertilization and growth of certain marine
eggs. Am. J. Physiol., 64, 144.

COBRUN, S. E. 1927 Practical application of hydrogen-ion control in the
digestion of sewage sludge. Ind. Eng. Chem., 19, 235.

COGGESHALL, G. W. 1895 tlber die Konstanz der Kalomel-Elektrode. Z.
physik. Chem., 17, 62.

COHEN, A. 1922 Xylenol blue and its proposed use as a new and im-
proved indicator in chemical and biological work. Biochem.
J., 16, 31.

COHEN, A. 1922 The use of mixed indicators. J. Am. Chem. Soc., 44,
1851.

COHEN, A. 1923 Bromoxylenol blue. Biochem. J., 17, 535.

COHEN, B. 1922 The effects of temperature and hydrogen ion concen-
tration upon the viability of Bact. coli and Bad. typhosum in
water. J. Bact., 7, 183.

COHEN, B. 1922 Brom-cresol green a sulfonphthalein substitute for
methyl red. Proc. Soc. Exptl. Biol. Med., 20, 124.

COHEN, B. 1923 Indicators for pH control of alum dosage. U. S. Pub.
Health Repts., 38, 739.

COHEN, B. 1927 Synthesis and indicator properties of some new sulfon-
phthaleins. U. S. Pub. Health Repts., 41, 3051.

COHEN, B., CHAMBERS, R. AND REZNIKOFF, P. 1928 Intracellular oxida-
tion-reduction studies I. Reduction potentials of Amoeba
dubia by micro-injection of indicators. J. Gen. Physiol., 11,
585.

COHEN, B., AND CLARK, W. M. 1919 The growth of certain bacteria in
media of different hydrogen ion concentration. J. Bact., 4, 409.

COHEN, E., AND TOMBROCK, W. 1907 Die Bestimmung von Diffusions-
potentialen. Z. Elektrochem., 13, 612.

COHN, E. J. 1917 The relation between the hydrogen ion concentration
of sperm suspensions and their fertilizing power. Anat. Record,
11, 530.

COHN, E. J. 1925 The physical chemistry of the proteins. Physiol.
Rev., 5, 349.

COHN, E. J. 1927 The activity coefficients of the ions in certain phosphate
solutions. A contribution to the theory of buffer action. J.
Am. Chem. Soc., 49, 173.

COHN, E. J., CATHCART, P. H., AND HENDERSON, L. J. 1918 The measure-
ment of the acidity of bread. J. Biol. Chem., 36, 581.

COHN, E. J., HEYROTH, F. F., AND MENKIN, M. F. 1928 The dissociation
constant of acetic acid and the activity coefficients of the ions
in certain acetate solutions. J. Am. Chem. Soc., 50, 696.

COHN, E. J., AND PRENTISS, A. M. 1927 The activity coefficients of the
ions in certain oxyhemoglobin solutions. J. Gen. Physiol., 8,
619.

602 THE DETERMINATION OF HYDROGEN IONS

COHN, E. J., WALBACH, S. B., HENDERSON, L. J., AND CATHCART, P. H.

1918 On the control of rope in bread. J. Gen. PhysioL, 1, 221.
COKER, R. E. 1925 Observations of hydrogen-ion concentration and of

fishes in waters tributary to the Catawba river, etc. Ecology,

6, 52.
COLLIER, W. A. 1924 Ausschaltung des Wasserfehlers bei der Giemsa-

Farbung durch Phosphatpufferung. Deut. med. Wochschr.,

50, 1325.
COLLIP, J. B. 1920 The alkali reserve of marine fish and invertebrates.

The excretion of carbon dioxide. J. Biol. Chem., 44, 329.
COLLIP, J. B. 1921 The alkali reserve of the blood of certain of the

lower vertebrates. J. Biol. Chem., 46, 57.
Colloid Symposium Monographs. 1922-27 Vols. 1-5. Chem. Catal. Co.,

N. Y.
COLVIN, J. 1925 The ionic activity product of water in glycerol-water

mixtures. J. Chem. Soc., 127, 2788.
COLVIN, J. 1926 Decomposition of nitrosotriacetonamine in presence of

hydroxyl ion. Trans. Faraday Soc., 22, 241.
COMPTON, A. H., AND CoMPTON, K. T. 1919 A sensitive modification of

the quadrant electrometer; its theory and use. Phys. Rev.,

14, 85.
CONANT, J. B. 1926 The electrochemical formulation of the irreversible

reduction and oxidation of organic compounds. Chem. Re-
views, 3, 1.
CONANT, J. B., AND FIESER, L. F. 1922 Free and total energy changes in

the reduction of quinones. J. Am. Chem. Soc., 44, 2480.
CONANT, J. B., AND FIESER, .L. F. 1922 The relationship between struc-
ture and oxidation potential of quinones. Science, 56, 492.
CONANT, J. B., AND FIESER, L. F. 1923 Reduction potentials of quinones.

I. The effect of solvent on the potentials of certain benzo-
quinones. J. Am. Chem. Soc., 45, 2194.

CONANT, J. B., AND FIESER, L. F. 1924 Reduction potentials of quinones.

II. The potentials of certain derivatives of benzoquinone,
naphthoquinone and anthraquinone. J. Am. Chem. Soc., 46,
1858.

CONANT, J. B., KAHN, H. M., FIESER, L. F., AND KURTZ, S. S., JR. 1922
An electrochemical study of the reversible reduction of organic
compounds. J. Am. Chem. Soc., 44, 1382.

CONANT, J. B., AND LUTZ, R. E. 1923 An electrochemical method of
studying irreversible organic reductions. J. Am. Chem. Soc.,
45, 1047.

CONANT, J. B., SMALL, L. F., AND TAYLOR, B. S. 1925 The electro-
chemical relation of free radicals to halochromic salts. J. Am.
Chem. Soc., 47, 1959.

CONN, H. J., et al. 1919 Methods of pure culture study. Rept. 1918,
Committee Soc. Am. Bacteriologists. J. Bact., 4, 107.

BIBLIOGRAPHY 603

CONOVER, C., AND GIBBS, H. D. 1922 Phthalic anhydride V. J. Ind.
Eng. Chem., 14, 120.

CONSIDINE, F. J. 1924 Simple, useful forms of hydrogen electrode.
Analyst, 49, 332.

CONWAY-VERNEY, R., AND BAYLISS, L. E. 1923 A comparison between
the colorimetric and the electrometric methods of determining
the hydrogen ion concentration of blood. J. Physiol., 58, 101.

COOK, M. W., Mix, V., AND CULVYHOUSE, E. O. 1921 Hemotoxin pro-
duction by the streptococcus in relation to its metabolism. J.
Inf. Dis., 28, 93.

COOLEDGE, L. H. 1920 An improved comparator. J. Ind. Eng. Chem.,
12, 499.

COOPER, E. A., AND NICHOLAS, S. D. 1927 Chemical action of p-quinones
on proteins and other substances. J. Soc. Chem. Ind., 46, 59.

CORBINO, O. M. 1927 L'effetto Volta e il funzionamento della pila.
Atti accad. Lincei [6] 5, 68.

CORNEC, E. 1913 Contribution a Petude physico-chimique de la neutral-
isation. Ann. chim. phys. [8], 29, 490, 30, 63.

CORNOG, J. 1921 A simple method for the preparation of sodium hy-
droxide free from carbon dioxide. J. Am. Chem. Soc., 43, 2573.

CORNWELL, R. T. K., AND ESSELSTYN, A. J. 1927 Thymoltetrachloro-
phthalein and some of its derivatives. J. Am. Chem. Soc., 49,
826.

CORRAN, J. W., AND LEWIS, W. C. Me. 1924 The hydrogen ion concentra-
tion of the whole blood of normal males and of cancer patients
measured by means of the quinhydrode electrode. Biochem.
J., 18, 1358.

Corrosion Symposium 1925 Ind. Eng. Chem., 17, 335.

DA COSTA, S.-F. G. 1927 Sur une nouvelle cause d'erreur dans Petude
des actions des extraits hypophysaires sur les organes isoles.
Compt. rend. soc. biol., 96, 881.

COUDRES, T. DES 1892 Electromotorische Krafte zwischen verschieden
gekrummten Quecksilberelektroden in einer Quecksilbersalzlo-
sung. Ann. Physik., 46, 292.

COULTER, C. B. 1920 The isoelectric point of red blood cells and its
relation to agglutination. J. Gen. Physiol., 3, 309.

COULTER, C. B. 1921 The equilibrium between hemolytic sensitizer and
red blood cells in relation to the hydrogen ion concentration.
J. Gen. Physiol., 3, 513.

COULTER, C. B. 1921 The thermolability of complement in relation to
the hydrogen ion concentration. J. Gen. Physiol., 3, 771.

COULTER, C. B. 1922 The agglutination of red blood cells in the presence
of blood sera. J. Gen. Physiol., 4, 403.

COWLES, R. P., AND SCHWITALLA, A. M. 1923 The hydrogen-ion con-
centration of a creek, its waterfall, swamp and ponds. Ecology,
4, 402.

604 THE DETERMINATION OF HYDROGEN IONS

Cox, D. C. 1925 Differential electro-titration. J. Am. Chem. Soc., 47,
2138.

CRAY, F. M. 1926 The color change of Congo red in acidified acetone-
water solutions. J. Phys. Chem., 30, 1276.

CRAY, F. M., AND WESTRIP, G. M. 1925 The preparation of solutions of
standard hydrogen ion concentration and the measurement of
indicator ranges in an acetone-water mixture containing 10 per
cent by volume of water. Trans. Faraday Soc., 21, 1.

CREMER, M. 1906 tlber die Ursache der elektromotorischen Eigenschaf-
ten der Gewebe, zugleich ein Beitrag zur Lehre von den poly-
phasischen Elektrolytketten. Z. Biol., 47, 562.

CROTOGINO, F. 1900 Studien iiber Oxydationspotentiale. Z. anorg.
allgem. Chem., 24, 225.

CROZIER, W. J. 1916 Cell penetration by acids. II. Further observa-
tions on the blue pigment of Chromodoris zebra. J. Biol. Chem.,
26, 217.

CROZIER, W. J. 1918 On indicators in animal tissues. J. Biol. Chem.,
35, 455.

CROZIER, W. J. 1924 Hydrogen-ion concentrations within the alimen-
tary tract of insects. J. Gen. Physiol., 6, 289.

CRUZ, I. DAC. 1924 L'influence du pH sur la lyse par le bacte"riophage.
Compt. rend. soc. biol., 90, 878.

CS^.NYI, W. 1921 Uber die Indicatoreigenschaften zweier neuer Phtha-
leine (1-, 2-, 3-Xylenolphthalein und Ortho-a -Naphtholphtha-
lein). Z. Elektrochem., 27, 64.

CULLEN, G. E. 1922 The colorimetric determination of the pH of blood
plasma. J. Biol. Chem., 52, 501.

CULLEN, G. E. 1922 A modification of the Clark hydrogen electrode
vessel to permit accurate temperature control. J. Biol. Chem.,
52, 521.

CULLEN, G. E., AND AUSTIN, J. 1918 Hydrogen ion concentrations of
various indicator end points in dilute sodium hypochlorite solu-
tions. J. Biol. Chem., 34, 553.

CULLEN, G. E., AND BIILMANN, E. 1925 The use of the quinhydrone
electrode for hydrion concentration on serum. J. Biol. Chem.,
64, 727.

CULLEN, G. E., AND CHESNEY, A. M. 1918 A note on the production of
acid by pneumococci. J. Exper. Med., 28, 289.

CULLEN, G. E., AND EARLE, I. P. 1928 The accuracy of the quinhydrone
electrode for determining the pH of blood plasma or serum.
J. Biol. Chem., 76, 565.

CULLEN, G. E., AND HASTINGS, A. B. 1922 A comparison of colorimetric
and electrometric determination of the hydrogen ion concentra-
tion in solutions containing carbon dioxide. J. Biol. Chem.,
52, 517.

CULLEN, G. E., KEELER, H. R., AND ROBINSON, H. W. 1925 The pK' of
the Henderson-Hasselbalch equation for hydrion concentration
of serums. J. Biol. Chem., 66, 301.

BIBLIOGRAPHY 605

CULLEN, G. E., AND ROBINSON, H. W. 1923 The normal variations in
plasma hydrogen ion concentration. J. Biol. Chem., 57, 533.

GUMMING, A. C. 1912 The elimination of potential due to liquid contact.
II. A simple equation for the calculation of the diffusion poten-
tial. Trans. Faraday Soc., 8, 86.

GUMMING, A. C., AND ABEGG, R. 1907 Zur Eliminierung der Fliissigkeits-
potentiale. Z. Elektrochem., 13, 17.

GUMMING, A. C., AND GILCHRIST, E. 1913 On the potential due to liquid
contact. III. The effect of variations in the nature of the
liquid boundary on the E. M. F. Trans. Faraday Soc., 9, 174.

CUSHNY, A. R. 1926 The Secretion of the Urine. 2ded. Monographs on
Physiology, Longmans Green, London.

CZEPINSKI, V. 1902 Einige Messungen an Gasketten. Z. anorg. Chem.,
30, 1.

DALE, H. H., AND EVANS, C. L. 1920 Colorimetric determination of the
reaction of blood by dialysis. J. Physiol., 54, 167.

DALE, D., AND TRACKER, C. R. A. 1914 Hydrogen ion concentrations
limiting automaticity in different regions of the frog's heart. J.
Physiol., 47, 493.

DAM, W. VAN. 1908 Recherches sur la coagulation du lait au moyen de la
presure. Rev. g<§n. Lait, 7, 121, 145, 167.

DAM, W. VAN 1909 Beitrag zur Kenntnis der Labgerinnung. Z. physiol.
Chem., 58, 295.

DANIEL, L. 1927 The use of thiosulfate as an indicator in alkalimetry.
J. pharm. chim., 5, 487 (cited).

DANNEEL, H. 1904 Zeitgrossen der Komplexbildung, Komplexkonstan-
ten und atomistische Dimension. Z. Elektrochem., 10, 609.

DANNER, P. S. 1922 The degree of ionization of ethyl alcohol. II.
From measurements of electromotive force. J. Am. Chem. Soc.,
44, 2832.

DARMOIS, E. 1924 Proce"de"s d'dtude des corps actifs. J. Phys. [6], 5,
227.

DARMOIS, E., AND HONNELAITRE, A. 1924 Etude electrometrique de
1'acitide des melanges d'acide malique et d'acide molybdique.
Compt. rend., 178, 2183.

DAVIDSON, J., AND WHERRY, E. T. 1924 Changes in hydrogen-ion con-
centration produced by growing seedlings in acid solution. J.
Agr. Research, 27, 207.

DAVISON,W. G. 1922 Observations on the properties of bacteriolysants.
J. Bact., 7, 486.

DAWSON, L. E. 1925 Technic for measuring the hydrogen-ion concentra-
tion of distilled water and unbuffered solutions not in equilib-
rium with carbon dioxide of the air. J. Phys. Chem., 29, 551.

DAWSON, H. M. 1926 Acid and salt effects in catalysed reactions. J.
Chem. Soc., 2282, 2872, 3166.

DAWSON, H. M. 1927 Ibid., 213, 458, 756.

DEBYE, P. 1917 Konzentrationselement und Brownsche Bewegung.
Physik. Z., 18, 144.

606 THE DETERMINATION OF HYDROGEN IONS

DEBYE, P. 1923 Kinetische Theorie des Gesetze des osmotischen Drucks
bei starken Elektrolyten. Physik. Z., 24, 334.

DEBYE, P. 1923 Theorie cinetique des lois de la pression osmotique des
electrolytes forts. Rec. trav. chim., 42, 597.

DEBYE, P. 1924 Osmotische Zustandsgleichung und Aktivitat verdiinnter
Starker Elektrolyte. Physik. Z., 25, 97.

DEBYE, P. 1927 See Faraday Society 1927.

DEBYE, P., AND McAuLAY, J. 1925 D»as elektrische Feld der lonen und
die Neutralsalzwirkung. Physik. Z., 26, 22.

DEBYE, P., AND HUCKEL, E. 1923 Zur Theorie der Elektrolyte. I.
Gefrierpunktserniedrigung und verwandte Erscheinungen.
Physik. Z., 24, 185.

DEBYE, P., AND PAULING, L. 1925 The inter-ionic attraction theory of
ionized solutes. IV. The influence of variation of dielectric
constant on the limiting law for small concentrations. J. Am.
Chem. Soc., 47, 2129.

DEFRIES, R. D., AND McKiNNON, N. E. 1926 The effect of various hy-
drogen ion concentrations on the longevity of vaccine virus.
Trans. Roy. Soc. Can., 20 (V), 359.

DEKRUIF, P. H. 1922 Change of acid agglutination optimum as index
of bacterial mutation. J. Gen. Physiol., 4, 387.

DE KRUIF, P. H., AND NORTHROP, J. H. 1922 The stability of bacterial
suspensions. IV. The combination of antigen and antibody at
different hydrogen-ion concentrations. J. Gen. Physiol., 5, 127.

DENHAM, H. G. 1908 Anomalous behavior of the hydrogen electrode in
solutions of lead salts, and the existence of univalent lead
ions in aqueous solutions. J. Chem. Soc., 93, 424.

DENINA, E. 1926 Sulla forza elettromotrice di contatto tra due soluzioni
qualsiansi. Gazz. chim. ital., 66, 798.

DERNBY, K. G. 1918 A study on autolysis of animal tissues. J. Biol.
Chem., 35, 179.

DERNBY, K. G., AND ALLANDER, B. 1921 Studien iiber den Einfluss der
Wasserstoffionenkonzentration auf das Wachstum und die
Toxinbildung der Tetanusbazillen. Biochem. Z., 123, 245.

DERNBY, K. G., AND DAVIDE, H. 1922 Dae Beziehung zwischen Was-
serstoffionenkonzentration und Eucupinwirkung auf Diph-
theriebazillen. Z. Immunitats., Teil I, 35, 447.

DERNBY, K. G., AND WALBUM, L. E. 1923 Studien iiber die Bildung des
Diphtherietoxins. Biochem. Z., 138, 505.

DERRIEN, E., AND FONTES, G. 1925 Sur Tunite de mesure et le mode de
notation de la concentration en ions hydrogene des solutions
aqueues en biologic medicale. Compt. rend. soc. biol., 92,
503.

DESHA, L. J., AND AGREE, S. F. 1911 On difficulties in the use of the
hydrogen electrode in the measurement of the concentration of
hydrogen ions in the presence of organic compounds. Ann.
Chem. J., 46, 638.

BIBLIOGRAPHY 607

DESHA, L. J., SHERRILL, R. E., AND HARRISON, L. M. 1926 Fluorometry.
II. The relation between fluorescence and hydrogen-ion con-
centration. J. Am. Chem. Soc., 48, 1493.

DIETZEL, R. 1926 Saurer Geschmack und Wasserstoffionenkonzentra-
tion. Kolloid-Z., 40, 240.

DIETZEL, R., AND ROSENBAUM, E. 1927 The determination of hydrogen-
ion concentration in wine by the quinhydrone electrode. Z.
Untersuch. Lebensm., 53, 321.

DIXON, M. 1927 On the mechanism of oxidation-reduction potential.
Proc. Roy. Soc. (B), 101, 57.

DODGE, F. D. 1915-1920 The use of potassium hydrogen phthalate as a
standard in alkalimetry. J. Ind. Eng. Chem., 7, 29; J. Am.
Chem. Soc., 42, 1655.

DOLEZALEK, F. 1899 Beitrage zur Theorie des Blei-Akkumulators. Z.
Elektrochem., 5, 533.

DOLEZALEK, F. 1906 Uber ein hochempfindliches Zeigerelektrometer. Z.
Elektrochem., 12, 611.

DOMONTVICH, M. 1925 Adaptability of the hydroquinone electrode to the
determination of pH in expressed plant saps. Nauch. Agron.
Zhur., 2, 700.

DONNAN, F. G. 1911 Theorie der Membrangleichgewichte und Mem-
branpotentiale bei Vorhandensein von nicht dialysierenden
Elektrolyten. Ein Beitrag zur physikalisch-chemischen Physi-
ologic. Z. Elektrochem., 17, 572.

DONNAN, F. G., AND ALLMAND, A. J. 1911 A standard electrode with
alkaline electrolyte: Hg | HgO Alkali. J. Chem. Soc., 99, 845.

DONNAN, F. G., AND HARRIS, A. B. 1911 The osmotic pressure and con-
ductivity of aqueous solutions of congo-red and reversible
membrane equilibria. J. Chem. Soc., 99, 1554.

DOP AND CHALAUD 1926 C. A. F. A. S. Lyon (cited).

DRAVES, C. Z., AND TARTAR, H. V. 1925 Instability of phthalate solu-
tions toward the hydrogen electrode. J. Am. Chem. Soc., 47,
1226.

DRUCKER, C. 1922 Potentiometrische Bestimmung von lonenkonzen-
trationen. Abderhalden's Handb. biol. Arbeitsmeth. Abt III
A Heft 2, 527.

DRUCKER, C. 1927 tJber die Wirkung von Zwischenlosungen auf Dif-
fusionsspannungen. Z. physik. Chem., 125, 394.

DRUCKER, C. 1927 Versuche mit Diffusionselektroden am Palladium.
Z. Elektrochem., 33, 504 (cited).

DRUCKER, C., AND RIETHOF, G. 1924 Untersuchungen iiber die Kon-
stitution starker Elektrolyte. Z. physik. Chem., Ill, 1.

DRURY, D. R., BEATTIE, W. W., AND Rous, P. 1927 The relative reac-
tion within living mammalian tissues. J. Exptl. Med., 45, 41.

DUBOUX, M., AND TSAMADOS, D. 1924 Dissociation de quelques acides
organiques dissous dans des melanges d'eau et d'alcool ethylique.
Helv. Chim. Acta, 7, 855.

608 THE DETERMINATION OF HYDROGEN IONS

DUGGAR, B. M. 1920 H-ion concentration and the composition of nu-
trient solutions in relation to the growth of seed plants. Ann.

Missouri Botan. Gardens, 7, 1.
DUGGAR, B. M., SEVERY, J. W., AND SCHMITZ, H. 1917 Studies in the

physiology of the fungi. Ann. Missouri Bot. Garden, 4, 165.
DUTOIT, P., AND GROBET, E. 1921 Sur une nouvelle methode de volu-

metrie physico-chimique appliquee a quelques problems de

chimie minerale. J. chim. phys., 19, 324.
DUVAL, M. 1924 Reaction ionique du sang de quelques inverte"bre*s.

Compt. rend., 179, 1629.
EASTMAN, E. D. 1925 Theory of certain electrometric and conductimetric

titrations. J. Am. Chem. Soc., 47, 332.
EASTMAN, E. D. 1926 Thermodynamics of non-isothermal systems.

J. Am. Chem. Soc., 48, 1482.
EBERT, L. 1925 tlber die Geschwindigkeit der Addition von Chlorwas-

serstoff an Chinon in Methyl alkohol. Z. Elektrochem., 31, 113.
EBERT, L. 1925 tlber die Dissoziationskonstanten zweibasischer Carbon-

sauren und das Normalpotential der Chinhydron-Elektrode in

absolutem Methyl alkohol. Ber., 68, 175.
EDGAR, G., AND SHIVER, H. E. 1925 The equilibrium between creatine

and creatinine in aqueous solutions. The effect of hydrogen

ion. J. Am. Chem. Soc., 47, 1179.
EGGERTH, A. H. 1923-24 Changes in the stability and potential of cell

suspensions. J. Gen. Physiol., 6, 63, 547.
EGGERTH, A. H. 1926 The effects of the pH on the germicidal action of

soaps. J. Gen. Physiol., 10, 147.
EGGERT, J. 1914 tJber due Absorptionsgeschwindigkeit von Wasserstoff

und Sauerstoff durch Metallsalzlosungen. Z. Elektrochem.,

20, 370.

EGGERT, J. 1915 Zur Aktivierung von H2 und C>2 durch Platin. Z. Elek-
trochem., 21, 349.
EGNER, H., AND HAGG, G. 1927 The effect of the acidity of the support

on the structure of unimolecular films. Phil. Mag. [7], 4, 667.
EILERT, A. 1922 Konstruktion von Elektroden aus Glanzplatin und

Messmethoden mit denselben. Z. angew. Chem., 35, 445, 452.
EISENBERG, P. 1919 tlber Saureagglutination von Bakterien und iiber

chemische Agglutination in Allgemeinen. I. Cent. Bakt.

Parasitenk. I, Abt. (orig.), 83, 70; II, ibid., 83, 472; III, ibid.,

83, 561.
EISENMAN, A. J. 1927 Absorption curve of separated plasma and method

for determination of pH. J. Biol. Chem., 71, 611.
ELLIS, H. A. 1925 An Explanation of Hydrogen Ion Concentration. The

Capillator Method for the Determination of Acidity and Alkalinity

in General Practice. London.
ELLIS, J. H. 1916 The free energy of hydrochloric acid in aqueous

solutions. J. Am. Chem. Soc., 38, 737.

BIBLIOGRAPHY 609

ELOD, E. 1925-26 The theory of dyeing processes. Chem. Zentr., 2,

2632 (cited).
ELVEDEN, V., AND SINKINSON, E. 1925 Electrolytic generator for pure

hydrogen. J. Chem. Soc., 123, 2715.
ELVOVE, E., AND CLARK, W. M. 1924 A study of the acid-base equilibria

of arsphenamine solutions. Hygienic Laboratory Bull. 135.
EMSLANDER, F. 1915-1919 Die Wasserstoffionenkonzentration im Bier

und bei dessen Bereitung. Z. ges. Brauwesen, 37, 2, 16, 27, 37,

164; 38, 196; 42, 127, 135.
EMSLANDER, F. 1927 Eine neue gebrauchsfertige Apparatur zur elektro-

chemischen Messung der Wasserstoffionenkonzentration. Bio-

chem. Z., 184, 234.

EPPLEY, M. AND GRAY, W. R. 1922 A simple direct-reading potentiom-
eter for standard cell comparisons. J. Optical Soc. Am., 6, 859.
ESTY, J. R., AND CATHCART, P. H. 1921 The change in the hydrogen ion

concentration of various mediums during heating in soft and

Pyrex glass tubes. J. Infect. Dis., 29, 29.
ETIENNE, G., VERAIN, M., AND BOURGEAUD, M. 1925 Contribution a la

determination du pH du sang. Une nouvelle electrode a hydro-
gene. Compt. rend. soc. biol., 93, 765.
ETTISCH, G. 1925 Eine Mikrochinhydronelektrode. Z. wiss.Mikroskop.,

42, 302.

EULER, H. v. 1925 Chemie der Enzyme. I. Mimchen u. Wiesbaden.
EVANS, A. C. 1922 The toxicity of acids for leucocytes as indicated by

the tropin reaction. J. Immunol., 7, 271.
EVANS, A. C. 1922 A buffered physiologic salt solution. J. Infect.

Dis., 30, 95.
EVANS, C. L. 1921 A probable error in determinations by means of the

hydrogen electrode. J. Physiol., 64, 353.
EVANS, C. L. 1926 The physiology of plain muscle. Physiol. Rev., 6,

358.

EVANS, C. L. 1926 Recent Advances in Physiology.
EVANS, C. L., AND UNDERBILL, S. W. F. 1923 Studies on the physiology

of plain muscle. I. The effect of alteration of hydrogen-ion

concentration on the tone and contractions of plain muscle.

J. Physiol., 58, 1.
EVERS, N. 1921 The titration of certain alkaloids. J. Am. Pharm.

Assoc., 10, 676. Pharm. J., 106, 470.
EVERS, N. 1921 The colorimetric method of determining hydrogen ion

concentration: Some applications in the analytical laboratory.

Analyst, 46, 393.
EVERS, N. 1922 The extraction of quinine and strychnine from solutions

of varying hydrogen-ion concentration; a method for the separa-
tion of strychnine from quinine. Pharm. J., 109, 90.
G. E. 1920 Selection of glass for the manufacture of ampuls.

J. Franklin Inst., 189, 649.

610 THE DETERMINATION OF HYDROGEN IONS

EWING, W. W. 1925 The preparation of electrolytic mercurous chloride
in saturated potassium chloride for use in the calomel electrode.
J. Am. Chem. Soc., 47, 301.

FABIAN, F. W. 1921 The hydrogen-ion concentration of different kinds
of glassware when sterilized with buffered and nonbuffered solu-
tions. Mich. Sta. Kept., 173; Expt. Sta. Record, 48, 204.

FABRE, R., AND PARINAUD, E. 1925 Etude de la dissociation des sels de
narcotine et des conditions optima d'extraction de cet alca-
lo'ide en toxicologie. Compt. rend., 180, 2077.

FAJANS, K. 1923 Struktur und Deformation der Elektronenhullen in
ihrer Bedeutung fur die chemischen und optischen Eigenschaften
anorganischer Verbindungen. Naturwissenschaften, 11, 165.

FALES, H. A. 1925 Inorganic Quantitative Analysis. New York (The
Century Co.).

FALES, H. A., AND MORRELL, J. C. 1922 The velocity of inversion of
sucrose as a function of the thermodynamic concentration of
hydrogen ion. J. Am. Chem. Soc., 44, 2071.

FALES, H. A., AND MUDGE, W. A. 1920 A study of the saturated potas-
sium chloride calomel cell. J. Am. Chem. Soc., 42, 2434.

FALES, H. A., AND STAMMELMAN, M. J. 1923 Colloidal membrane for
liquid junctions. J. Am. Chem. Soc., 45, 1271.

FALES, H. A., AND WARE, G. M. 1919 A study of the conditions affecting
the precise determination of zinc as the sulfide. J. Am. Chem.
Soc., 41, 487.

FALES, H. A., AND VOSBURGH, W. C. 1918 Planck's formula for the po-
tential difference between solutions and the values of certain
important cells. J. Am. Chem. Soc., 40, 1291.

FALK, I. S. 1923 The role of certain ions in bacterial physiology. A
review. Abstracts Bact., 7, 33, 87, 133.

FALK, I. S., AND CAULFIELD, M. F. 1923 Some relations between hydro-
gen-ion concentration and the antigenic properties of proteins.
J. Immunol., 8, 239.

FALK, I. S., AND HARRISON, R. W. 1926 The influence of hydrogen ion
concentration upon the viscosity of bacterial suspensions. J.
Bact., 12, 97.

FALK, I. S., AND POWDERMAKER, F. 1925 The effect of hydrogen ion
concentration on certain antigenic properties of Clostridium
botulinum. J. Infectious Diseases, 37, 514.

FALK, K. G. 1922 Catalytic Action. New York.

FALK, K. G. 1924 The Chemistry of Enzyme Actions. New York.

Faraday Society 1924 Symposium on electrode reaction and equilibria.
Transactions 19, 667.

Faraday Society. 1927 Symposium on the theory of strong electrolytes.
Transactions 23, 343.

FARKAS, G. 1903 Ueber die Concentration der Hydroxylionen im Blut-
serum. Arch. ges. Physiol. (Pfliiger's), 98, 551.

BIBLIOGRAPHY 611

FARMER, R. C. 1920 The decomposition of nitric esters. J. Chem. Soc.,

117, 806.
FAURHOLT, C. 1924 Etudes sur les solutions aqueuses d'anhydride

carbonique et d'acide carbonique. J. chim. phys., 21, 401.
FELS, B. 1904 Studien iiber die Indicatoren der Acidimetrie und Alkali-
metric. Z. Elektrochem., 10, 208.
FELTON, L. D. 1921 A colorimetric method for determining the hydrogen

ion concentration of small amounts of fluid. J. Biol. Chem.,

46, 299.
FELTON, L. D., AND DOUGHERTY, K. M. 1924 Virulence. III. Influence

of hydrogen-ion concentration and of ingredients of plain broth

on the virulence of pneumococci. J. Exptl. Med., 39, 155.
FENN, W. O. 1922 Hemolysis of erythrocytes in contact with glass.

J. Exp. Med., 35, 271.

FENN, W. O. 1922 Effect of the hydrogen-ion concentration on the phago-
cytosis and adhesiveness of leucocytes. J. Gen. Physiol., 5, 169.
FERINGA, K. J. 1923 On the causes of the emigration of leukocytes.

Koninklijke Akad. Wetenschappen Amsterdam. Proc. Sec.

Sci., 25, 36.
FERNBACH, A. 1906 Influence de la reaction du milieu sur Pactivite des

diastases. Compt. rend., 142, 285.
FERNBACH, A., AND HUBERT, L. 1900 De 1'influence des phosphates et de

quelques autres matieres minerales sur la diastase proteolytique

du malt. Compt. rend., 131, 293.
FERNBACH, A., AND WOLFF, J. 1906 Sur le mechanisme de Pinfluence des

acides, des bases et des sels dans la liquefaction des empois de

fecules. Compt. rend., 143, 380.
FESSLER, A. H^., AND KRANER, H. M. 1927 Hydrogen-ion concentration

and electrical conductivity of clay slips. J. Am. Ceram. Soc.,

10, 501, 592.
FISCHER, A. 1921 Growth of fibroblasts and hydrogen ion concentration

of the medium. J. Exp. Med., 34, 447.
FISHER, E. A. 1921 Studies on soil reaction. I. A resume. J. Agr.

Sci., 11, 19. II. The colorimetric determination of the hydrogen

ion concentration in soils and aqueous soil extracts. Ibid., 45.
FLEISCH, A. 1922 Eine ausgeglichene sterilisierbare Nahrlosung von

physiologischer H-Ionenkonzentration. Arch, exptl. Path.

Pharmakol., 94, 22.
FLEISCHER, L., AND AMSTER, S. 1923 Ueber den Einfluss der Reaktion

des Mediums auf die Disinfektionswirkung organischer Farb-

stoffe. Z. Immunitats. I (orig.), 37, 327.
FODOR, A. 1926 Fermentwirkung und Wasserstofnonenkonzentration.

Kolloid-Z., 40, 234.
FOSTER, G. L., AND SCHMIDT, C. L. A. 1923 The separation of the hexone

bases from certain hydrolysates by electrolysis. J. Biol. Chem.,

56, 545.

612 THE DETERMINATION OF HYDROGEN IONS

FOULK, C. W., AND HOLLINGSWORTH, M. 1923 A precision measurement
of the composition of the constant-boiling mixture of hydrogen

chloride and water. J. Am. Chem. Soc., 45, 1220.
FRAENKEL, W. 1907 Zur chemischen Kinetik des Diazoessigesters. Z.

physik. Chem., 60, 202.

FRANCIS, F., AND GEAKE, F. H. 1913 A new method for the determina-
tion of the concentration of hydroxyl ions. J. Chem. Soc., 103,

1722.
FRANCIS, F., GEAKE, F. H., AND ROCHE, J. W. 1915 The determination

of the concentration of hydroxyl ions. J. Chem. Soc., 107. 1651 .
FRANKLIN, E. C. 1924 Systems of acids, bases and salts. J. Am. Chem.

Soc., 46, 2137.
FREUNDLICH, H. 1921 tJber Konzentrations- und Potentialgefalle an

Grenzflachen. Z. Elektrochem., 27, 505.

FREUNDLICH, H. 1922-1926 Kapillarchemie, 2nd Ed. Leipzig.
FREUNDLICH, H. 1926 Fortschritte d Kolloidchemie. Dresden.
FREUNDLICH, H. 1927 Elements of Colloidal Chemistry. Transl. by G.

Barger, New York.
FREUNDLICH, H., AND ETTISCH, G. 1925 Das elektrokinetische und das

thermodynamische Potential. Z. physik. Chem., 116, 401.
FREUNDLICH, H., AND HAUSER, E. A. 1925 Zur Kolloidchemie der Kaut-

schuk-milchsafte. Kolloid-Z. (Zsigmondy-Festschr.), 36, 15.
FREUNDLICH, H., AND NEUKIRCHER, H. 1926 Ueber den Einfluss der

Wasserstoffionenkonzentration auf die Viskositat und Elastizitat

von Gelatinelosungen. Kolloid-Z., 38, 180.
FREUNDLICH, H., AND RONA, P. 1920 Uber die Beziehungen zwischen

dem elektrokinetischen Potentialsprung und der elektrischen

Phasengrenzkraft. Sitzb. kgl. preuss. Akad. Wiss. Berlin, p.

397.
FRICKE, R. 1922 tlber Molekiil- und lonenhydrate. Z. Elektrochem.,

28, 161.
FRICKE, R. 1924 Zur Beeinflussung von Flussigkeitspotentialen durch

an den Fltissigkeitsgrenzen verwandte feinporige Materialien.

Z. Electrochem., 30, 577.
FRICKE, R., AND ROHMANN, C. 1924 tiber Fliissigkeitspotentiale an

Laugengrenzen. Z. Elektrochem., 30, 537.
FRIED, F. 1926 Messungen der EMK galvanischer Elemente vom Typus

Me | MeO | NaOH | H2(Pt) und ihre Verwertung zur Priifung

des Nernstschen Warmesatzes. Z. physik. Chem., 123, 406.
FRIEDENTHAL, H. 1904 Die Bestimmung der Reaktion einer Fliissigkeit

mit Hilfe von Indikatoren. Z. Elektrochem., 10, 113.
FRIEDENTHAL, H. 1910 Methoden zur Bestimmung der Reaktion tier-

ischer und pflanzlicher Fliissigkeiten. Abderhalden's Handbuch
der Biochemischen Arbeitsmethoden, 1, 534.

FULMER, E. I. 1926 The relation between pH and the reaction of aqueous
solutions at various temperatures. Iowa State College J. Sci.,
1, 37.

BIBLIOGRAPHY 613

FURMAN, N. H. 1922 Some applications of oxygen electrode and oxida-
tion potential measurements to acidimetry and alkalimetry.
J. Am. Chem. Soc., 44, 2685.

FURMAN, N. H. 1923 Electrotitration with the aid of the air electrode.
Trans. Am. Electrochem. Soc., 45, 79.

GABBE, E. 1923 tlber das Flockungsoptimum der durch Essigsaure
fallbaren Substanz des Tuberkulins. Biochem. Z., 139, 523.

GAARDER, T. 1916-1917 Die Hydroxylzahl des Meerwassers. Bergens Mu-
seum Aarbox Naturvidenskabelig Raekke. Nr. 3.

GAEDE, W. 1913 Die aussere Reibung der Gase. Ann. phys., 41, 302.

GAIL, F. W. 1919 Hydrogen ion concentration and other factors affect-
ing the distribution of Fucus. Pub. Puget Sound Biol. Sta., 2,
287; Botan. Abstracts, 5, 131.

GAMBLE, J. L. 1922 Carbonic acid and bicarbonate in urine. J. Biol.
Chem., 61, 295.

GARARD, I. D., AND SHERMAN, H. C. 1918 A study of the glucosazone
reaction. J. Am. Chem. Soc., 40, 955.

GARNER, W. W., BACON, C. W., AND ALLARD, H. A. 1924 Photoperiodism
in relation to hydrogen-ion concentration of the cell sap, etc.
J. Agr. Research, 27, 119.

GARRISON, A. 1923 A determination of absolute single electrode poten-
tials. J. Am. Chem. Soc., 45, 37.

GARRISON, A. D., NICHOLAS, H. O., AND PASTERNACK, J. G. 1926 A simple
hydrogen electrode for use in biochemistry. J. Lab. Clin.
Med., 11, 1091.

GAY, L. 1923 Application de la notion de tension d'expansibilit6 a
1'etude des forces electromotrices de contact. J. chim. phys.,
20, 263.

GAY, L. N. 1926 The effect of heat and hydrogen ion concentrations on
the extract of short ragweed. J. Immunol., 11, 371.

GELFAN, S. 1926 A non-polarizable micro-electrode. Preliminary re-
port. Proc. Soc. Exptl. Biol. Med., 23, 308.

GELLHORN, E. 1927 Befruchtungsstudien V. Arch. ges. Physiol.
(Pfluger's), 216, 198.

GELLHORN, E. 1927 Vitalfarbung und Permeabilitat. Arch. ges. Physiol.
(Pfluger's), 216, 234.

GELLHORN, E. 1927 Vergleichend-physiologische Untersuchungen iiber
die Pufferungspotenz von Blut and Karpersaften. Arch. ges.
Physiol. (Pfluger's), 216,253.

GELLHORN, E. 1927 Beitrage zur vergleichenden Physiologic der Sperma-
tozoen. Arch. ges. Physiol. (Pfluger's), 216, 267.

GERKE, R. H. 1922 Temperature coefficient of electromotive force of
galvanic cells and the entropy of reactions. J. Am. Chem. Soc.,
44, 1684.

GERKE, R. H. 1925 A summary of electrode potentials. Chem. Rev., 1,
377.

614 THE DETERMINATION OF HYDROGEN IONS

GERKE, R. H., AND GEDDES, J. R. 1927 An improved hydrogen electrode
vessel and the electromotive force of the mercury, mercurous
bromide, bromide ion electrode. J. Phys. Chem., 31, 886.

GERMANN, A. F. O. 1925 A general theory of solvent systems. J. Am.
Chem. Soc., 47,2461.

GERRETSEN, F. C. 1924 Determination of hydrogen-ion concentration
for biological purposes. Tijdschr. vergelijk Geneeskunde, 10,
162 (cited).

GESELL, R., AND HERTZMAN, A. B. 1925 Continuous recording changes in
hydrogen ion concentration of circulating blood: The relation
to respiration. Proc. Soc. Exptl. Biol. Med., 22, 298.

GESELL, R., AND HERTZMAN, A. B. 1926 The regulation of respiration.
Ill and IV. A continuous method of recording changes in
acidity applied to the circulating blood and other body fluids.
Am. J. PhysioL, 78, 206, 610.

GESELL, R., AND McGiNTY, D. A. 1926 Continuous electrometric
methods of recording changes in expired carbon dioxide and
oxygen. Am. J. PhysioL, 79, 72.

GIBBS, H. D. 1918 U. S. Pat. 1284887.

GIBBS, H. D. 1924 Apparatus for sublimation. U. S. Pat. 1484266.

GIBBS, J. W. 1877-1878 On the equilibrium of heterogeneous substances.
Trans. Connecticut Acad., III. The Scientific Papers of J.
Willard Gibbs, Vol. I. Longmans Green and Co. (1906).

GIBSON, K. S., et al. 1923 Spectrophotometry. J. Optical Soc. America,
10, 169,

GILLESPIE, L. J. 1914 .The acid agglutination of pneumococci. J. Exp.
Med., 19, 29.

GILLESPIE, L. J. 1916 The reaction of soil and measurements of hydrogen
ion concentration. J. Wash. Acad. Scb., 6, 7.

GILLESPIE, L. J. 1918 The growth of the potato scab organism at various
hydrogen ion concentrations as related to the comparative free-
dom of acid soils from the potato scab. Phytopathology, 8, 257.

GILLESPIE, L. J. 1920 Colorimetric determination of hydrogen ion con-
centration without buffer mixtures, with especial reference to
soils. Soil Science, 9, 115, also J. Am. Chem. Soc., 42, 742.

GILLESPIE, L. J. 1920 Reduction potentials of bacterial cultures and of
waterlogged soils. Soil Science, 9, 199.

GILLESPIE, L. J. 1921 Color standards for the colorimetric measure-
ment of H-ion concentration. J. Bact., 6, 399.

GILLESPIE, L. J., AND HALL, F. P. 1926 The palladium -hydrogen equi-
librium and palladium hydride. J. Am. Chem. Soc., 48, 1207.

GILLESPIE, L. J., AND HURST, L. A. 1917 Hydrogen-ion concentration
measurements of soils of two types; Caribou loam and Wash-
burn loam. Soil Science, 4, 313.

GILPIN, J. E. 1894 Orcin-sulphon-phthalem. Am. Chem. J., 16, 528.

GIRIBALDO, D. 1925 Ein neuer Ausdruck fur die aktuelle Reakton der
Losungen. Biochem. Z., 163, 8.

BIBLIOGRAPHY 615

GIRIBALDO, D. 1925 Expresion de la reaccion actual de las soluciones.
La noticion de Sorensen y sur desventajas. Nueva notaci6n
racional. An. Fac. Med., (cited).

GJALDBAEK, J. K. 1924 Uber das potential zwischen der 0.1 n und 3.5 n
Kalomelelektrode. Det. Kgl. Danske Videnskabernes Selskab.
Math.-fysiske Meddelelser, 9, 1.

GJALDBAEK, J. K. 1925 Untersuchungen liber die Loslichkeit des mag-
nesium hydroxyds. Z. anorg. allgem. Chem., 144, 145, 269.

GLASER, F. 1901 Indikatoren der Acidimetrie und Alkalimetrie. Wies-
baden.

GLASSTONE, S. 1925 Modified electrometric method for the determina-
tion of the hydrogen-ion concentration. Analyst, 50, 327.

GLASSTONE, S., AND SYMES, T. E. 1927 The electrodeposition of ion-
nickel alloys. Trans. Faraday Soc., 23, 213.

GLAZEBROOK, R. 1923 A Dictionary of Applied Physics. London.

GLAZER, R. W. 1925 Hydrogen ion concentrations in the blood of in-
sects. J. Gen. Physiol., 7, 599.

GOARD, A. K., AND RIDEAL, E. K. 1924 On the measurement of certain
"inaccessible" potentials with a controlled oxygen electrode.
Trans. Faraday Soc., 19, 740.

GOIFFON, R., AND HAUDiQUET. 1927 Denaturation des albumines et
"erreur de proteines." Compt. rend. soc. biol., 97, 434.

GOOCH, F. A., AND BURDICK, W. L. 1912 Ele.ctrolytic analysis with plati-
num electrodes of light weight. Am. J. Sci., 34, 107.

GOODE, K. H. 1922 A continuous-reading electrotitration apparatus.
J. Am. Chem. Soc., 44, 26.

GOODE, K. H. 1925 An improved, continuous-reading hydrogen-ion
meter. J. Am. Chem. Soc., 47, 2483.

GOUY, G. 1916 Sur les differences de potentiel au contact de deux elec-
trolytes. J. chim. phys., 14, 185.

GRABOWSKI, J. 1871 Ueber Naptholverbindungen. Ber., 4, 725.

GRAFF, S. 1924 Ein Verfahren zur Bestimmung der Wasserstoffionen-
konzentration im Gewebe mit Indikatoren. Beitr. path. Anat.;
72, 603.

GRAFF, S. 1924 Ein Verfahren zur Bestimmung der Wasserstoffionen-
konzentration im Gewebe mit Indikatoren. Klin. Wochschr.,
3, 451.

GRANT, J., AND PARTINGTON, J. R. 1923 Concentration cells in methyl
alcohol. Trans. Faraday Soc., 19, 414.

GRANT, M. H. 1920 The effect of varying the hydrogen ion concentra-
tion and of guanidine sulfate on the excitability of the neuro-
myon of the frog. J. Physiol., 54, 79.

GRAY, J. 1920 Effect of ions on ciliary motion. Proc. Cambridge Phil.
Soc., 19, 313.

GRAY, J. 1922 The mechanism of ciliary movement. Proc. Roy. Soc.,
B, 93, 104.

616 THE DETERMINATION OF HYDROGEN IONS

GREEN, E., AND BAILEY, C. H. 1927 Relation of hydrogen-ion concentra-
tion of dough to baking properties. Cereal Chem., 4, 261.

GREEK, W. N., AND PARKER, H. C. 1926 The potentiometric determina-
tion of hydrogen-ion concentrations as applied to boiler waters.
Mech. Eng., 48, 1129.

GREIG-SMITH, R. 1924 Note upon determining the hydrogen-ion con-
centration colorimetrically in small quantities of fluids. Proc.
Linnean Soc. New South Wales, 49, 504.

GROLLMAN, A. 1925 The combination of phenol red and proteins. J.
Biol. Chem., 64, 141.

GRONWALL, T. H. 1927 On the determination of the apparent diameters
of the ions in the Debye-Hiickel theory of strong electrolytes.
Proc. Acad. Natural Sci. Phila., 13, 198.

GROSS, P., AND HALPERN, O. 1925 tlber Mischelektroden zweiter Art.
Z. physik. Chem., 115, 54.

GROSS, P., AND HALPERN, O. 1925 tlber Mischelektroden zweiter Art.
Z. physik. Chem., 118, 255.

GROSS, P., AND HALPERN, O. 1925 tlber Elektrolyte in Losungen kleiner
Dielektrizitatskonstante. Physik. Z., 26, 636.

GROSSMAN, F. 1927 The use of the hydroquinhydrone electrode for pH
determination in the fluids of the organism. Biochem. J., 21,
267.

GRUBE, G., AND DULK, B. 1918 t)ber das elektromotorische Verhalten
des Sauerstoffes und seine anodische Entwicklung unterhalb
des reversiblen Sauerstoffpotentials. Z. Electrochem., 24, 237.

GRUBER, C. M. 1926 The influence of barbituric acid, of some benzyl
derivatives and of the pH of fluids on the tonus and rhythmic
movements of excised segments of intestine, uterus and ureters.
J. Pharmacol., 30, 149.

GRUNBERG, A. 1924 Beitrag zur Theorie der Indikatoren. Z. anorg.
allgem. Chem., 138, 333.

GUILD, J. 1926 A critical survey of modern developments in the theory
and technic of colorimetry and allied sciences. Proc. Optical
Convention, 1, 61.

GUILLAUMIN, C. O. 1922 Sur un chrdmoscope destine a la mesure de la
concentration en ions H des liquides par les indicateurs colorants.
J. pharm. chim., 26, 452.

GUILLAUMIN, C. O. 1926 Sur un mode de representation des variations
de la concentration en ions H des milieux organiques et du sang
en particular. Bull. soc. chim. biol., 8, 160.

GUNTELBERG, E. 1926 Untersuchungen iiber loneninteraktion. Z.
physik. Chem., 123, 199.

GUNTHERSCHULZE, A. 1925 Uber eine Beziehung zwischen der Ablose
arbeit der Elektronen und dem elektrochemischen Normal-
potential. Z. Physik., 32, 186.

GUSTAFSON, F. G. 1924 Hydrogen-ion concentration gradient in plants.
Am. J. Botany, 11, 1.

BIBLIOGRAPHY 617

GUTBIER, A., AND BRiNTziNGER, H. 1927 Ueber den Einfluss hydro-

philer Kolloide auf den Farbumschlag von Indikatoren. Kol-

loid-Z., 41, 1.
GYEMANT, A. 1922 Die Kataphorese von Wasser in organischen Fliissig-

keiten. Z. physik. Chem., 102, 74.
GYEMANT, A. 1923 Die elektrolytische Dissoziation ionogener Kolloide.

Kdlloid-Z., 33, 9.

HAAS, A, R. 1917 The reaction of plant protoplasm. Bot. Gaz., 63, 232.
HABER, F. 1904 Zeitgrossen der Komplexbildung, Komplexkonstanten

und atomistische Dimension. Z. Elektrochem., 10, 433.
HABER, F., AND KLEMENSIEWICZ 1909 tlber elektrische Phasengrenz-

krafte. Z. physik. Chem., 67, 385.
HABER, F., AND ZAWADZKI, J. 1911 tlber die Polarisierbarkeit fester

Elektrolyte. Z. physik. Chem., 78, 228.
HADEN, R. I. 1923 The use of buffer solutions in staining blood films

with Wright's stain. J. Lab. Clin. Med., 9, 64.
HAGGLUND, E., AND ROSENQVIST, T. 1927 tlber die Abhangigkeit der

alkoholischen Garung von der Wasserstoffionenkonzentration.

VI. Biochem. Z., 180, 61.
HAHN, F. L., AND FROMMER, M. 1927 Theorie und Praxis der Endpunkt-

bestimmung bei potentiometrischen Titrierungen. Z. physik.

Chem., 127, 1.
HAINSWORTH, W. R., AND MAC!NNES, D. A. 1922 The effect of hydrogen

pressures on the electromotive force of a hydrogen-calomel cell.

J. Am. Chem. Soc., 44, 1021.
HAINSWORTH, W. R., ROWLEY, H. J., AND MAC!NNES, D. A. 1924 The

effect of hydrogen pressure on the electromotive force of a hydro-
gen-calomel cell. II. The fugacity of hydrogen and hydrogen

ion at pressures to 1000 atmospheres. J. Am. Chem. Soc.,

46, 1437.
H ALB AN, H. v. 1923 tlber die Natur der Nichtdissoziierten Sauren. Z.

Elektrochem., 29, 434.
HALBAN, H. v., AND EBERT, L. 1924 tlber die optische Absorption

geloster Salze. Z. physik. Chem., 112, 321.
HALBAN, H. v., AND EBERT, L. 1924 Die elektrolytische Dissoziations

der Pikrinsaure in wasseriger Losung. Z. physik. Chem., 112,

359.
HALBAN, H. v., AND GEIGEL, H. 1920 tlber die Verwendung von photo-

elektrischen Zellen zur Messung der Lichtabsorption in Los-

ungen. Z. physik. Chem., 96, 214.
HALBAN, H. v., AND SIEDENTOPF, K. 1922 tlber die Verwendung von

photoelektrischen Zellen zur Messung der Lichtabsorption in

Losungen II. Z. physik. Chem., 100, 208.
HALBAN, H. v. AND ZIMPELMANN 1925 tlber die Dissoziationskonstanten

organischer Molekiilverbindungen. Z. physik. Chem., 117, 461.
HALDANE, J. S. 1922 Respiration. Yale Univ. Press.

618 THE DETERMINATION OF HYDROGEN IONS

HAMALAINEN, B,., LEIKOLA, E. E., AND ATRILA, Y. 1923 A simplified

method for the colorimetric determination of hydrogen-ion

concentrations within the limits of pH 2.8-8.0. Skand. Arch.

Physiol., 43, 244.
HAMMETT, L. P. 1922 Experimental studies on the hydrogen electrode.

Thesis, Columbia University, New York.
HAMMETT, L. P. 1924 The velocity of the hydrogen electrode reaction

on platinum catalysts. J. Am. Chem. Soc., 46, 7.
HANTZSCH, A. 1913 Uber die Natur der gelben und roten Helianthiri-

Losungen und die Chromoisomerie der Aminozosalze. Ber., 46,

1537.
HANTZSCH, A. 1914 Ueber die Kolloidchemie der Indikatoren. Kolloid-

Z., 15, 79.
HANTZSCH, A. 1915 Blaue und rote Kongofarbstoffsaure; ein Beitrag zur

Theorie der Indicatoren. Ber., 48, 158.
HANTZSCH, A. 1923 Die Theorie der lonogenen Bindung als Grundlage

der lonentheorie nach Versuchen iiber die Natur der nicht

lonisierten Sauren. Z. Elektrochem., 29, 221.
HANZLIK, P. J. 1920 Degree of alkalinity necessary for the phloro-

glucinol test for formaldehyde. J. Biol. Chem., 42, 411.
HARDEN, W. C. 1927 Salicylsulfonphthalein and its tetrabromo and

monomercury derivatives. J. Am. Chem. Soc., 49, 3139.
HARDING, E. A., AND SMITH, D. P. 1918 A study of the occlusion of

hydrogen and oxygen by metal electrodes. J. Am. Chem. Soc.,

40, 1508.
HARDMAN, R. T., AND LAPWORTH, A. 1911-1912 Electromotive forces in

alcohol. J. Chem. Soc., 99, 2242; 101, 2249.
HARDY, W. B. 1899 On the coagulation of proteid by electricity. J.

Physiol., 22, 288.
HARDY, W. B. 1905 Colloidal solution. The globulins. J. Physiol., 33,

251.
HARKINS, W. D., AND CLARK, G. L. 1925 The effect of sodium hydraxide

upon the surface tension of a solution of sodium nonylate. J.

Am. Chem. Soc., 47, 1854.

HARNED, H. S. 1915 The hydrogen- and hydroxyl-ion activities of solu-
tions of hydrochloric acid, sodium and potassium hydroxides in

the presence of neutral salts. J. Am. Chem. Soc., 37, 2460.
HARNED, H. S. 1916 The hydrogen and chlorine ion activities of solu-
tions of potassium chloride in 0.1 molal hydrochloric acid. J.

Am. Chem. Soc., 38, 1986.
HARNED, H. S. 1920 Thermoc^ynamic properties of the ions of some

strong electrolytes and of the hydrogen ion in solutions of tenth

molal hydrochloric acid containing uni-univalent salts. J. Am.

Chem. Soc., 42, 1808.
HARNED, H. S. 1922 Activity coefficients and colligative properties of

electrolytes. J. Am. Chem. Soc., 44, 252.
HARNED, H. S. 1925 Die Thermodynamik der Losungen einiger ein-

facher Elektrolyte. Z. physik. Chem., 117, 1.

BIBLIOGRAPHY 619

HARNED, H. S. 1925 The activity coefficient and ionic concentration
product of water in sodium chloride and potassium chloride.
J. Am. Chem. Soc., 47, 930.

HARNED, H. S. 1926 The activity coefficient of hydrochloric acid in con-
centrated solutions of strong electrolytes. J. Am. Chem. Soc..
48, 326.

HARNED, H. S. 1926 Individual thermodynamic behaviors of ions in
concentrated solutions, including a discussion of the thermo-
dynamic method of computing liquid-junction potentials. J.
Phys. Chem., 30, 433.

HARNED, H. S. 1927 The activity coefficients, ionic concentrations and
kinetic salt effects of formic acid in neutral salt solutions. J.
Am. Chem .Q Soc., 49, 1.

HARNED, H. S., AND AKERLOF, G. 1926 Experimentelle Untersuchungen
an wasserigen Losungen einfacher gewohnlicher Elektrolyte.
Physik. Z., 27, 411.

HARNED, H. S., AND BRUMBAUGH, N. J. 1922 The activity coefficient of
hydrochloric acid in aqueous salt solutions. J. Am. Chem. Soc.,
44, 2729.

HARNED, H. S., AND FLEYSHER, M. H. 1925 The activity coefficients of
hydrochloric acid in solutions of ethyl alcohol. J. Am. Chem.
Soc., 47, 82.

HARNED, H. S., AND FLEYPHER, M. H. 1925 The transference numbers
of hydrochloric acid in solutions of ethyl alcohol. J. Am. Chem.
Soc., 47, 92, 3105.

HARNED, H. S., AND STURGIS, R. D. 1925 The free energy of sulfuric
acid in aqueous sulfate solutions. J. Am. Chem. Soc., 47, 945.

HARRIS, L. J. 1923 Use of the quinhydrone electrode for the estimation
of amino-acids and of acid and basic functions. J. Chem. Soc.,
123, 3294.

HARRIS, L. J. 1923 The titration of amino- and carboxyl-groups in amino
acids, polypeptides, etc. I-III. Investigations with aqueous
solutions. Proc. Roy. Soc., 95B, 440.

HARRIS, L. J. 1923 The titration of amino- and carboxyl-groups in
amino acids, polypeptides, etc. IV-VI. Estimations in the
presence of formol and alcohol. Proc. Roy. Soc. 95B, 500.

HARTREE, W., AND HILL, A. V. 1924 The effect of hydrogen-ion concen-
tration on the recovery process in muscle. J. Physiol., 58, 470.

HARTRIDGE, H., AND PETERS, R. A. 1922 Interfacial tension and hy-
drogen-ion concentration. Proc. Roy. Soc., 101A, 348.

HARVEY, E. H. 1924 The pH value of some common foods. Am. Food
J., 19, 560.

HARVEY, E. N. 1920 The action of acid and of light in the reduction of
Cypridina oxyluciferin. J. Gen. Physiol., 2, 207.

HARVEY, R. B. 1920 Hydrogen-ion changes in the mosaic disease of
tobacco plants and their relation to catalase. J. Biol. Chem.,
42, 397.

620 THE DETERMINATION OF HYDROGEN IONS

HASKINS, H. D. 1919 Modifications of Henderson's Method of estima-
tion of the hydrogen-ion concentration of urine. J. Lab. Clin.
Med., 4,363.

HASSELBALCH, K. A. 1910 Elektrometrische Reaktionsbestimmung koh-
lensaurehaltiger Fliissigkeiten. Biochem. Z., 30, 317.

HASSELBALCH, K. A. 1911 Determination electrometrique de la reaction
des liquides renferment de 1'acide carbonique. Compt. rend.
Lab. Carlsberg, 10, 69.

HASSELBALCH, K. A. 1913 Methods for the electrometric determination
of the concentration of hydrogen ions in biological fluids. Bio-
chem. Bull., 2, 367.

HASSELBALCH, K. A. 1913 Verbesserte Methodik bei der elektrometri-
schen Reaktionsbestimmung biologischer Fliissigkeiten. Bio-
chem. Z., 49, 451.

HASTINGS, A. B. 1921 A hydrogen electrode vessel adapted for titra-
tions. J. Biol. Chem., 46, 463.

HASTINGS, A. B., MURRAY, C. D., AND SENDROY, J. JR. 1927 Studies of
the solubility of calcium salts. I. The solubility of calcium
carbonate in salt solutions and biological fluids. J. Biol. Chem.,
71, 723.

HASTINGS, A. B., SALVESEN, H. A., SENDROY, J., JR., AND VAN SLYKE,
D. D. 1927 Distribution of electrolytes between transudates
and serum. J. Gen. Physiol., 8, 701.

HASTINGS, A. B., AND SENDROY, J., JR. 1924 Studies of acidosis. XX.
The colorimetric determination of blood pH at body tem-
perature without buffer standards. J. Biol. Chem., 61, 695.

HASTINGS, A. B., AND SENDROY, J. 1925 The effect of variation in ionic
strength on the apparent first and second dissociation constants
of carbonic acid. J. Biol. Chem., 66, 445.

HASTINGS, A. B., SENDROY, J., AND ROBSON, W. 1925 The colorimetric
determination of the pH of urine. J. Biol. Chem., 65, 381.

HASTINGS, A. B., AND VAN SLYKE, D. D. 1922 The determination of the
three dissociation constants of citric acid. J. Biol. Chem., 53,
269.

HAUGE, S. M., AND WILLAMAN, J. J. 1927 Effect of pH on adsorption by
carbons. Ind. Eng. Chem., 19, 943.

HAWKINS, J. A. 1923 A micro method for the determination of the
hydrogen-ion concentration of whole blood. J. Biol. Chem.,
57, 493.

HAWKINS, J. A. 1924 Acid-base equilibrium of blood of normal guinea
pigs, rabbits and rats. J. Biol. Chem., 61, 147.

HAYWOOD, C. 1925 The relative importance of pH and carbon dioxide
tension in determining the cessation of ciliary movement in
acidified sea water. J. Gen. Physiol., 7, 693.

HEALY, D. J., AND ANDERSON, W. S. 1922 The hydrogen ion concentra-
tion of horse semen. Cornell Veterinarian.

BIBLIOGRAPHY 621

HEALY, D. J., AND PETER, A. M. 1925 The hydrogen ion concentration
ard basicity of egg yolk and egg white. Am. J. Physiol., 74, 363.

HEGGE, R. S. 1925 The dissociation constants of some indicators for
the determination of the pH by the Duboscq colorimeter. Proc.
Soc. Exptl. Biol. Med., 23, 235.

HEINTZ, W. 1877 Zersetzung des Nitrosotriacetonamins Mittelst Sauren.
Ann., 187, 250.

HELMHOLTZ, H. v. 1881 On the modern development of Faraday's con-
ception of electricity. J. Chem. Soc., 39, 292.

HELMHOLTZ, H. v. 1888 Weitere Untersuchungen, die Electrolyse des
Wassers betreffend. Ann. Physik., 34, 737.

HENDERSON, L. J. 1906 Equilibrium in solutions of phosphates. Am. J.
Physiol., 15, 257.

HENDERSON, L. J. 1908 A diagrammatic representation of equilibria
between acids and bases in solution. J. Am. Chem. Soc., 30, 954.

HENDERSON, L. J. 1908 Concerning the relationship between the strength
of acids and their capacity to preserve neutrality. Am. J.
Physiol., 21, 173.

HENDERSON, L. J. 1908 The theory of neutrality regulation in the
animal organism. Am. J. Physiol., 21, 427.

HENDERSON, L. J. 1909 On the neutrality equilibrium in blood and
protoplasm. J. Biol. Chem., 7, 29.

HENDERSON, L. J. 1909 Das Gleichgewicht zwischen Basen und Sauren
im tierischen Organismus. Ergeb. Physiol., 8, 254.

HENDERSON, L. J. 1910 Zur Kenntnis des lonengleichgewichts im Organ-
ismus. III. Messungen der normalen Harnaciditat. Biochem.
Z., 24, 40 (cited).

HENDERSON, L. J. 1911 A critical study of the processes of acid excretion.
J. Bjol. Chem., 9, 403.

HENDERSON, L. J. 1913 The Fitness of the Environment; an Inquiry into
the Biological Significance of the Properties of Matter. N. Y.

HENDERSON, L. J. 1914 The excretion of acid in health and disease.
Harvey Lectures, Series 10, 132.

HENDERSON, L. J. 1918 The prevention of rope in bread. Science, 48,
247.

HENDERSON, L. J. 1926 The synthetic description of blood as a physico-
chemical system. Lectures on certain aspects of biochemistry)
by Dale, Drummond, Henderson and Hill, London.

HENDERSON, L. J., BOCK, A. V., FIELD, H., JR., AND STODDARD, J. L.
1924 Blood as a physico-chemical system, II. J. Biol. Chem.,
59, 379.

HENDERSON, L. J., AND FORBES, A. 1910 On the estimation of the inten-
sity of acidity and alkalinity with dinitrohydroquinone. J.
Am. Chem. Soc., 32, 687.

HENDERSON, L. J., AND SPIRO, K. 1908 Zur Kenntnis des lonengleich-
gewichts im Organismus. I. tlber Basen- und Sauregleichge-
wicht im Harn. Biochem. Z., 15, 105.

622 THE DETERMINATION OF HYDROGEN IONS

HENDERSON, L. J., AND WEBSTER, H. B. 1907 The preservation of neu-
trality in culture media with the aid of phosphates. J. Med.

Research, 16, 1.
HENDERSON, P. 1907 Zur Thermo dynamik der Fliissigkeitsketten. Z.

physik. Chem., 59, 118.
HENDERSON, P. 1908 Ibid., 63, 325.
HENDERSON, Y. 1922 Reasons for believing that respiratory X is not

C+H. J. Biol. Chem., 50 (proc.), iii. Cf. Physiol. Rev., 5, 131.
HENDRIXSON, W. S. 1915 Acid potassium and acid sodium phthalates as

standards in acidimetry and alkalimetry. J. Am. Chem. Soc., 37,

2352.
HENDRIXSON, W. S. 1920 Further work on potassium hydrogen phthalate

as a standard in volumetric analysis. J. Am. Chem. Soc., 42,

724.
HENRI, V., AND FROMAGEOT, C. 1925 Spectre d'absorption de 1'acide

pyruvique. Existence de formes tautomeres. Bull. soc. chim.,

37, 845.
HENRICH, F. 1922 Theories of Organic Chemistry. Transl. by T. B.

Johnson and D. A. Hahn, N. Y.
HENRIQUES, M. 1922 Sur la determination de la concentration en ions

hydrogene dans les milieux de culture geloses. Compt. rend.

soc. biol., 87, 1220.
HERASYMENKO, P. 1925 Researches with the dropping mercury cathode.

IV. Changes in overvoltage with the concentration of hydrions.

Rec. trav. chim., 44, 503.
HERZFELD, K. F. 1915 Elektronentheorie der Metalle und Nernstsche

Formel. Physik. Z., 16, 354.
HERZFELD, K. F. 1918 Zur Berechnung der elektrochemischen Normal-

potentiale. Ann. Physik. [IV], 56, 133.
HESSELMAN, H. 1926 Studier ouer Barrskagens Humustacke-Studien

iiber die Humusdecke des Nadelwaldes. Medd. Statens Skogs-

forsokaustalt, 22, 169.
HETTERSCHIJ, C. W. G. 1922 Een verbetering van der voerelectrode.

Chem. Weekblad, 19, 294.
HETTERSCHIJ, C. W. G. 1926 Ein Potentiometer fur Massenarbeit.

Landw. Jahrb., 63, 216.
HEWITT, L. F. 1927 Combination of proteins with phthalein dyes.

Biochem. J., 21, 1305.
HEYDWEILLER, A. 1909 tlber lonisationswarme und lonisationskonstante

des Wassers. Ann. phys. [4], 28, 503.
HEYDWEILLER, A. 1925 Optische Untersuchungen an wasserigen Elek-

trolytlosungen. Physik. Z., 26, 526.
HEYROVSKY, J. 1925 The solvation of ions and the electrode potential.

Rec. trav. chim., 44, 447.

HEYROVSKY, J. 1925 The electrode, contact, and electro-kinetic poten-
tials of galvanic cells. J. Phys. Chem., 29, 344.
HICKMAN, K., AND HYNDMAN, D. 1928 An electrical solution-mixing

device. Ind. Eng. Chem., 20, 213.

BIBLIOGRAPHY 623

HICKMAN, K. C. D., AND LiNSTEAD, R. P. 1922 A modified methyl-
orange indicator. J. Chem. Soc., 121, 2502.
HIGLEY, H. P., AND MATHEWS, J. H. 1924 The absorption spectrum of

gelatin as a function of the hydrogen-ion concentration. J.

Am. Chem. Soc., 46, 852.
HILDEBRAND, J. 1908 Das Konigsche Spektralphotometer in neuer An-

ordnung und seine Verwendung zur Bestimmung chemischer

Gleichgewichte. Z. Elektrochem., 14, 349.
HILDEBRAND, J. H. 1913 Some applications of the hydrogen electrode in

analysis, research and teaching. J. Am. Chem. Soc., 35, 847.
HILDEBRAND, J. H., AND BOWERS, W. G. 1916 A study of the action of

alkali on certain zinc salts by means of the hydrogen electrode.

J. Am. Chem. Soc., 38, 785.
HILDEBRAND, J. H., AND HARNED, H. S. 1912 The rapid determination of

magnesia in limestone by means of the hydrogen electrode.

Orig. Com. 8th Intern. Cong. Applied Chem., 1, 217.

HILL, A. E. 1921 The distribution of a strong electrolyte between ben-
zene and water. J. Am. Chem. Soc., 43, 254.

HILPERT, S., AND BRAIDS, F. 1925 Quinone tannage. Collegium, 64.
HIRSCH, E. F. et al. 1922-1924 Hydrogen ion studies. J. Inf. Diseases

30, 263, 643, 658, 666; 32, 439; 33, 470; 34, 103, 390.
HIRSCH, E, F. 1925 The adsorption of indicator (cresol red) by serum

in the spectrophotometric determination of the pH. J. Biol.

Chem., 63, 55.
HIRSCH, P. 1924 Neue Moglichkeiten der Acidimetrie, besonders zur

Anwendung auf Eiweisskorper und deren Spaltungsprodukte.

Biochem. Z., 147, 433.
HIRST, L. F. 1926 Soil acidity and survival of hookworm larvae. A

critical commentary. Indian Med. Gaz., 61, 14.
HISSINK, D. J., AND VAN DER SPEK, J. 1926 The determination of the

pH of the soil by the Biilmann quinhydrone method. VerhandJ.

zweiten Komm. Intern. Bodenkund. Ges. Teil A. Groningen

(Holland), 29 (cited).
HITCHCOCK, D. I. 1926 The effect of pH on the permeability of collodion

membranes coated with protein. J. gen. physiol., 10, 179.
HJORT, E. V., LOWY, A., AND BLACKWOOD, O. 1924 The selenium optical

densimeter for colorimetric work. J. Optical Soc. Am., 9, 43.
HOAGLAND, D. R., AND CHRISTIE, A. W. 1918 The chemical effects of CaO

and CaCO3 on the soil. I. The effect on soil reaction. Soil Sci-
ence, 6, 379.

HOBER, R. 1900 Ueber die Hydroxylionen des Blutes. Arch. ges. Phys-
iol. (Pfluger's), 81, 522.
HOBER, R. 1903 Ueber die Hydroxylionen des Blutes. II. Arch. ges.

Physiol. (Pfliiger's), 99, 572.
HOBER, R. 1926 Physikalische Chemie der Zelle und der Gewebe. 6 Aufl.

Leipzig.
HOET, J. P., AND MARKS, H. P. 1926 Observations on the onset of rigor

mortis. Proc. Roy. Soc. B., 100, 72 and 116.

624 THE DETERMINATION OF HYDROGEN IONS

HOFMANN, K. A. 1922 Zur Kenntnis der Sauerstoff-Wasserstoff Katalyse
durch Platinmetalle und iiber die Potentiale der Kontakte bei
Gegenwart wassriger Elektrolyte. Ber., 56, 573.

HOLDEREB, M. 1911 Recherches sur la filtration des diastases. Thesis.
University of Paris, 1911.

HOLLER, H. D., AND RITCHIE, L. M. 1920 Hydrogen ion concentration in
dry cells. Bur. Standards Sci. Paper 364.

HOLLO, J., AND WEISS, ST. 1924 Einfache Methode zur direkten Festim-
mung der Wasserstoffzahl des Blutes mittels Indikatoren.
Biochem. Z., 144, 87.

HOLMES, W. C. 1924 The spectrophotometric determination of hydrogen-
ion concentrations and of the apparent dissociation constants
of indicators. J. Am. Chem. Soc., 46, 627.

HOLMES, W. C. 1924 The influence of constitutional variation upon the
absorption and stability of hydrogen ions of certain halogenated
derivatives of fluoroscein. J. Am. Chem. Soc., 46, 2770.

HOLMES, W. C., AND SNYDER, E. F. 1925 The spectrophotometric deter-
mination of hydrogen-ion concentrations and of the apparent
dissociation constants of indicators. II. Thymol Blue. J. Am.
Chem. Soc., 47, 221. III. Biomocresol green. Ibid., 226.
IV. l-naphthol-2-sodium sulfonate indo phenol. 47, 2232.

HOLT, A. 1914 The rate of solution of hydrogen by palladium. Proc.
Roy. Soc. (A), 90, 226.

HOLT, H. S. AND REID, E. E. 1924 The effect of sulfur on the color of
certain phthaleins. J. Am. Chem. Soc., 46, 2333.

HOMER, A. 1917 The reaction of sera as a factor in the successful con-
centration of antitoxic sera by the methods at present in use.
Biochem. J., 11, 21.

HOMER, A. 1917 A note on the use of indicators for the colorimetric de-
termination of hydrogen ion concentration in sera. Biochem.
J., 11, 283.

HOMER, A. 1918 Improvements in the technique of the concentration of
antitoxic sera. J. Hyg., 17, 51.

HOMER, A. 1919 A comparison between the precipitation of antitoxic
sera by sodium sulphate and by ammonium sulphate. Bio-
chem. J., 13, 278.

HOPKINS, D. L. 1926 Effect of hydrogen-ion concentration on locomotion
and other life-processes in Amoeba proteus. Proc. Nat. Acad.
Sci., 12, 311.

HOPKINS, R. H. 1925 Contributions to our knowledge of hydrogen ions
in brewing. J. Inst. Brewing, 31, 399.

HOROVITZ, K. 1923 Der lonenaustausch am Dielektrikum. I. Die
Elektrodenfunktion der Glaser. Z. physik., 15, 369.

HOROVITZ, K. 1924 Die Wasserstoffelektrodenfunktion des Platins.
Sitzb. Akad. Wiss. Wien, 132, Ha, 367.

HOROVITZ, K. 1925 tlber die Ausbildung von Mischelektroden an
Phasengrenzen. Z. physik. Chem., 115, 424.

BIBLIOGRAPHY 625

HOROVITZ, K., HORN, F., ZIMMERMANN, J., AND SCHNEIDER, J. 1925 Die
Charakterisierung der Glaser durch ihre elektromotorischen
Eigenschaften. Sitzungsb. Akad. Wissensch. Wien, Ha, 134,
335.

HOROVITZ, K., AND ZIMMERMANN, J. 1925 Untersuchungen uber lon-
enaustausch an Glasern. Sitzungsb. Akad. Wissensch. Wien.,
Ila, 134, 355.

HOTTINGER, R. 1914 Uber "Lackmosol," den empfindlichen Bestand-
teil des Indicators Lacmoid. Biochem. Z., 65, 177.

HOUBEN, J. 1919 Schwefeleisen als Indicator in der Acidimetrie und ein
neues Massanalytisches Verfahren zur Zinkbestimmung. Ber.,
62, 1613.

HOUSSLAU, A. 1927 Use of pH in the industrial control of the fermenta-
tion of molasses. Chimie et industria Special No. 663 (cited).

HOWARD, H., AND POPE, F. G. 1911 Indicators of the methyl-red type.
J. Chem. Soc., 99, 1333.

HUBBARD, R. S., AND MEEKER, D. O. 1924 The effect of high concentra-
tions of alkali upon the color of phenolsulphonephthalein. J.
Lab. Clin. Med., 10, 229.

HUCKEL, E. 1924 Zur Theorie der Elektrolyte. Ergebnisse d. Exakten
Naturwissenschaften, 3, 199.

HUCKEL, E. 1925 Zur Theorie konzentrierterer wasseriger Losungen
starker Elektrolyte. Physik. Z., 26, 93.

HUDIG, J., AND STURM, W. 1919 Een gewijzigde waterstof electrode. (A
modified hydrogen electrode.) Chem. Weekblad., 16, 473.

HUDSON, C. S. 1910 The inversion of cane sugar by invertase. VI. A
theory of the influence of acids and alkalies on the activity of
invertase. J. Am. Chem. Soc., 32, 1220.

HUGHES, W. S. 1922 The potential difference between glass and electro-
lytes in contact with glass. J. Am. Chem. Soc., 44, 2860.

HUGHES, W. S. 1928 On Haber's glass cell. J. Chem. SDC., 491.

HUGONIN, G. 1925 Observations sur une nouvelle methode de determina-
tion des concentrations en ions hydrogene. Cuir tech., 14,
210, 232.

HUGONIN, G. 1925 The use of quinhydrone electrodes for the measure-
ment of the hydrogen ion concentrations of tan liquors. J. Am.
Leather Chem. Assocn, 20, 52. From Cuir tech. (1924) 13, 385.

HULETT, G. A. 1906 The cadmium standard cell. Phys. Rev., 23, 166.

HULETT, G. A. 1911 The distillation of amalgams and the purification
of mercury. Phys. Rev., 33, 307.

HULETT, G. A. 1911 The construction of standard cells and a constant
temperature bath. Phys. Rev., 32, 257.

HULETT, G. A., AND MINCHIN, H. D. 1905 The distillation of amalgams
and the purification of mercury. Phys. Rev., 21, 388.

HULTON, H. F. E. 1924 The electrical measurement of available acidity
(pH) and its applications in English brewing. J. Inst. Brewing,
30, 57.

626 THE DETERMINATION OF HYDROGEN IONS

HUNDLEY, M., AND MCCLENDON, J. F. 1925 The dissociation constant of

orthocresol-tetrachlorophthalein. Proc. Soc. Exptl. Biol. Med.,

23, 236.
HURD, A. M. 1924 The course of acidity changes during the growth period

of wheat with special reference to stem-rust resistance. J.

Agr. Research, 27, 725.

HURD, C. B., ENGEL, E. W., AND VERNON, A. A. 1927 Studies of the con-
duction process in glass. J. Am. Chem. Soc., 49, 447.
HURWITZ, 8. H., MEYER, K. F., AND OSTENBERG, Z. 1915 On a colori-

metric method of adjusting bacteriological culture media to any

optimum hydrogen ion concentration. Proc. Soc. Exp. Biol.

Med., 13, 24. Also in Johns Hopkins Hospital Bull., 27, 16.
HUTTIG, G. F. 1914 Die Anwendung der Spektralanalyse auf chemische

Gleichgewichtsprobleme. Z. physik. Chem., 88, 172.
HUTTIG, G. F. 1920 Zur Theorie der azidimetrischen Indikatoren. Z.

physik. Chem., 95, 280.
ISGARISCHEV, N., AND KOLDAEWA, E. 1924 t)ber Potentiale vergifteter

Elektroden. Z. Elektrochem., 30, 83.
ITANO, A., ARAKAWA, S., AND HOSODA, K. 1926-1927. Biilmann's quinhy-

drone electrode. I. III. Bull. Agr. Chem. Soc. (Japan), 2, 163

(cited).
ITANO, A., AND HOSODA, K. 1926 Investigation on the Biilmann's quinhy-

drone electrode. J. Agr. Chem. Soc. Japan II, 2, 13 (cited).
ITANO, A., AND NEILL, J. 1919 Influence of temperature and hydrogen

ion concentration upon the spore cycle of Bacillus subtilis. J.

Gen. Physiol., 1, 421.
JACOBS, M. H. 1920 To what extent are the physiological effects of

carbon dioxide due to hydrogen ions? Am. J. Physiol., 51, 321.
JAHN, H. 1900 Uber den Dissociationsgrade und das Dissociations-

gleichgewicht stark dissociierter Elektrolyte. Z. physik. Chem.,

33, 545; 1901, ibid., 37, 490.
JAHN, H. 1901 tJber die Nernstschen Formeln zur Berechnung der elek-

tromotorischen Kraft von Konzentrationselementen. Eine

Erwiderung an Herrn Arrhenius. Z. physik. Chem., 36, 453.
JAMESON, A. P., AND ATKINS, W. R. G. 1921 On the physiology of the

silkworm. Biochem. J., 15, 209.
JANKE, A., AND KROPACSY, S. 1926 Zur kolorimetrischen Bestimmung

der Wasserstoffionenkonzentration. Biochem. Z., 174, 120.
JARISCH, A. 1922 tlber das Verhalten von Neutralrot in Seifenlosungen.

Biochem. Z., 134,177.
JARISCH, A. 1926 pH und pharmakologische Wirkung. Kolloid-Z., 40,

259.

JAUMAIN, D. 1925 Importance de Terreur de prot6ine dans la determina-
tion du pH a 1'aide du bleu de bromothymol. Compt. rend. soc.

biol., 93, 860.
JELLINEK, K., AND KREBS, P. 1923 "Dber neue Methoden in der Alkali-

und Acidimetrie, Oxydimetrie und Fallungsmassanalyse, Hy-

BIBLIOGRAPHY 627

drolytische Fallungsmassanalyse und Mercurimetrie. Z. anorg.

allgem. Chem., 130, 263.
JENNY, H. 1927 Kationen- und Anionenumtausch an Permutitgrenz-

flachen. Kolloidchem. Beihefte, 23, 428.

JEWELL, M. E. 1920 Effects of the hydrogen ion concentration and oxy-
gen content of water upon regeneration and metabolism in

tadpoles. J. Exp. Zoology, 30, 461.
JODLBAUER, A., AND HAFFNER, F. 1920 Einfluss von Na', K' und Ca",

auf Warmehamolyse bei verschiedener H'-Konzentration. Arch.

ges. Physiol. (Pfliiger's), 179, 140.
JOCHIMS, J. 1927 Physikalisch-chemische Untersuchungen iiber Leuko-

cytenwanderung. Arch. Physiol. (Pfliiger's), 216, 611.
JOHNSON, K. R. 1904 Zur Nernst-Planckschen Theorie iiber die Poten-

tialdifferenz zwischen verdiinnten Losungen. Drude Annal.,

14, 995.
JONES, G., AND JOSEPHS, R. C. 1928 The measurement of the conductance

of electrolytes. J. Am. Chem. Soc., 50, 1049.
JoNESco-MiHAESTi AND PopEsco, C. 1922 L'influence de la concentration

en ions H sur le developpement et la production de toxines par

le Bacille de Shiga. Compt. rend. soc. biol., 86, 893.
JORDAN, E. O., AND FALK, I. S. (editors) 1928 The Newer Knowledge of

Bacteriology and Immunology. Univ. Chicago Press.
J0RGENSEN, H. 1927 tlber die Verwendung von Chromatlosungen als

Vergleichslosungen bei kolorimetrischen Messungen. Biochem.

Z., 186, 485.

JUDAY, C., FRED, E. B., AND WILSON, F. C. 1924 The hydrogen ion con-
centration of certain Wisconsin lake waters. Trans. Am. Micro-
scop. Soc., October.
KAB, G. 1925 tlber den Einfluss von Gasbeladungen bei Platinkatalyse.

Z. physik. Chem., 115, 224.
KAHN, G., AND STOKES, J. 1926 The comparison of the electrometric and

colorimetric methods for determination of the- pH of gastric

contents. J. Biol. Chem., 69, 75.
KALWARYJSKI, B. E. 1926 tJber Samenfadenagglutination unter Einwir-

kung chemischer Agenzien. Biochem. Z., 169, 353.
KAPLAN, J. 1927 The Case "Thalofide Cell": Its use in spectroscopy.

J. Optical Soc. Am., 14, 251.
KAPPEN, H. 1916 Studien an sauren Mineralboden aus Nahe von Jena.

Landw. Vers. Sta., 88, 13.
KAPPEN, H., AND BELING, R. W. 1925 Ueber die Chinhydronmethode und

iiber die Beziehungen ihrer Resultate zu den Aziditatsformen der

Boden. Z. Pflanzenernahr. Diingung, A, 6, 1.
KARCZAG, L., AND BODO, R. 1923 Carbinole als Indikatoren. Biochem.

Z., 139, 342.
KASTLE, J. H. 1905 A method for the determination of the affinities of

acids colorimetrically by means of certain vegetable coloring

matters. Am. Chem. J., 33, 46.

628 THE DETERMINATION OF HYDROGEN IONS

KATZ, L. N., KERRIDGE, P. T., AND LONG, C. N. H. 1925 Lactic acid in

mammalian cardiac muscle. Proc. Roy. Soc., B, 99, 26.
KEELER, E. A. 1922 The application of ion concentration measurements

to the control of industrial processes. J. Ind. Eng. Chem.,

14, 395.
KELLER, R. 1921 Dielektrizitatskonstanten biochemischer Stoffe. Bio-

chem. Z., 115, 135.

KELLER, R. 1921 Aziditat und Basizitat. Z. physik. Chem., 98, 338.
KERRIDGE, P. M. T. 1925 Use of the glass electrode in biochemistry.

Biochem. J., 19, 611.

KERRIDGE, P. M. T. 1926 The use of glass electrodes. J. Sci. Instru-
ments, 3, 404.
KEUFFEL, C. W. 1925 A direct reading spectrophotometer. J. Optical

Soc. Am., 11, 403.
KILPATRICK, M., JR. 1926 Catalysis in buffer solutions I. J. Am. Chem.

Soc., 48, 2091.
KING, A. T. 1927 Use of indicator-dyed wool to control certain textile

operations. J. Soc. Dyers Colourists, 43, 321.
KING, R. W. 1924 Thermionic vacuum tubes and their applications. J.

Optical Soc. Am., 8.
KIPLINGER, C. C. 1921 Modified laboratory apparatus. J. Ind. Eng.

Chem., 13, 713.
KLEMENC, A. 1921 tlber das negative Wasserstoffion. Z. Elektrochem.,

27, 470.
KLIT, A. 1927 tlber die Anwendung der Chinhydronelektrode bei der

elektrometrischen Sauretitration. Z. physik. Chem., 131, 61.
KLOPSTEG, P. E. 1920 A simple method for titrating electrometrically

to a desired end-point in acid-alkaline reactions. Science, 62, 18.
KLOPSTEG, P. E. 1921 A calculator for converting gas-chain voltages into

equivalent CH+ or pH values. Science, 54, 153.
KLOPSTEG, P. E. 1922 Some practical aspects of hydrogen electrode

measurements. J. Ind. Eng. Chem., 14, 399.
KNICKMANN, E. 1925 Untersuchungen zur Frage der Bodenaziditat. Z.

Pflanzenernahr. Diingung, 5A, 1.
KNOBEL, M. 1923 The activities of the ions of potassium hydroxide in

aqueous solution. J. Am. Chem. Soc., 45, 70.
KNOBEL, M. 1923 Gas electrode. J. Am. Chem. Soc., 45, 1723.
KNUDSEN, S. 1925 Om bestemmelse af Brintionkoncentrationen i Ost

ved hjaelp af Kinhydronelektroden. [On the determination of

the concentration of hydrions in cheese with the quinhydrone

electrode.] Aarskr. K. Vet.-ogLandboh0jskole, 1925 (cited).
KOBER, P. A., AND HAW, A. B. 1916 Spectrophotometric study of copper

complexes and the biuret reaction. J. Am. Chem. Soc., 38, 457.
KOEHLER, A. E. 1920 A new 0.1N calomel electrode design. J. Biol.

Chem., 41, 619.
KOFFMAN, M. 1924 tiber die Bedeutung der Wasserstoffionenkonzentra-

tion fur die Encystierung bei einigen Ciliatenarten. Arch.

mikroskop. Anat. Entwicklungsmechk., 103, 168.

BIBLIOGRAPHY 629

KOHLRAUSCH, F., AND HEYDWEiLLER, A. 1894 Ucber reines Wasser.

Ann. Physik. Chem., 53, 209.
KOHN, M. 1926 Eine neue Chinhydronelektrode. Z. angew. Chem.,

39, 1073.
KOLTHOFF, I. M. De bepaling der waterstofionen — concentratie met de

water stof -electrode. Marius-Bibliotheek Nr. Ill, Utrecht.
KOLTHOFF, I. M. 1919 Kleurindicatorpapieren (Indicator test papers).

Pharm. Weekblad., 56, 175.

KOLTHOFF, I. M. 1921 La sensibilite d'indicateurs colorants a des tem-
peratures plus e levees que la temperature ordinaire. Rec. trav.

chim., 40, 775.
KOLTHOFF, I. M. 1922 De colorimetrische bepaling der waterstofionen-

concentratie zonder buffermengsels. Pharm. Weekblad, 59, 104.
KOLTHOFF, I. M. 1922 De titratie van middelmatig sterke zuren of

basen naast zeer zwakke. Pharm. Weekblad, 59, 129.
KOLTHOFF, I. M. 1922 L'erreur de sel des indicateurs colorants. Rec.

trav. chim., 41, 54.
KOLTHOFF, I. M. 1923 Die Verwendung der Chinhydron- statt der Was-

serstoffelektrode bei potentiometrischen Aciditatsbestimmungen.

Rec. trav. chim., 42, 186.
KOLTHOFF, I. M. 1923 Der Einfluss von Alkolhol auf die Empfindlichkeit

von Farbenindikatoren. Rec. trav. chim., 42, 251.
KOLTHOFF, I. M. 1923 Der Salzfehler von Nitramin (Pikrylmethylnitra-

min). Rec. trav. chim., 42, 964.

KOLTHOFF, I. M. 1923 Colorimetric determination of hydrogen-ion con-
centration by the method of Michaelis with one-color indica-
tors, with inorganic solutions for color comparison. Pharm.

Weekblad., 60, 949 (cited).
KOLTHOFF, I. M. 1923 Der Gebrauch von Farbenindicatoren, 2d aufl.

Julius Springer — Berlin. Translation by Furman (1926) in

English. Translation by Vellinger (1927) in French.
KOLTHOFF, I. M. 1923 Konduktometrische Titrationen. Dresden & Leipzig.
KOLTHOFF, I. M. 1924 Die colorimetrische Bestimmung der Wasserstoffi-

onenkonzentration, nach der Keil-Methode und die Dissozia-

tionskonstante verschiedener Indicatoren. Rec. trav. chim.,

43, 144.
KOLTHOFF, I. M. 1925 tJber den Zustand von Methylorange in seinem

Umschlagsinterval. Rec. trav. chim., 44, 68.
KOLTHOFF, I. M. 1925 tlber den Zustand von Methylrot in seinem Um-

wandlungsinterval. Rec. trav. chim., 44, 75.
KOLTHOFF, I. M. 1925 Der Salzfehler von Indicatoren in elektrolytarmen

Losungen. Rec. trav. chim., 44, 275.
KOLTHOFF, I. M. 1925 A new set of buffer mixtures that can be prepared

without the use of standardized acid or base. J. Biol. Chem.,

63, 135.
KOLTHOFF, I. M. 1925 Die Dissoziationskonstante, das Loslichkeitspro-

dukt und die Titrierbarkeit von Alkaloiden. Biochem. Z., 162,

289.

630 THE DETERMINATION OF HYDROGEN IONS

KOLTHOFF, I. M. 1925 Die Zuverlassigkeit der Chinhydronelektrode fur
die Messung der Wasserstoffionenkonzentration in verschiedenen
Losungen. Z. physiol. Chem., 144, 259.

KOLTHOFF, I. M. 1926 Die Reaktion vom neutral und destillierten was-
ser. Biochem. Z., 168, 110; 176, 101.

KOLTHOFF, I. M. 1926 Der Ausdruck fur die Reaktion von wasserigen
Losungen. Biochem. Z., 169, 490.

KOLTHOFF, I. M. 1926 The influence of boric acid on the electrolytic dis-
sociation of electrolytes. Rec. trav. chim., 45, 394.

KOLTHOFF, I. M. 1926 Der Methylorange-Fehler bei der colorimetri-
schen pH-Bestummung durch Vergleich mit den Clarkschen
Puffermischungen. Rec. trav. chim., 45, 433.

KOLTHOFF, I. M. 1927 The use of methoxytriphenyl carbinols as one-
color indicators. J. Am. Chem. Soc., 49, 1218.

KOLTHOFF, I. M. 1927 tlber die Anwendung von Mischindikatoren in
der Acidimetrie und Alkalimetries.. Biochem. Z., 189, 26.

KOLTHOFF, I. M., AND BOSCH, W. 1927 Ueber die abnormale pH-Aende-
rung in Borsaure-Natronlauge-Gemischen bei verschiedenen
Verdiinnungen und Temperaturen. Rec. trav. chim., 46, 180.

KOLTHOFF, I. M., AND BOSCH, W. 1927 The influence of neutral salts on,
acid-salt, equilibria. I. A contribution to the knowledge of the
standard value used for calculating the activity exponent paH
of the hydrogen ion concentration. Rec. trav. chim., 46, 430.

KOLTHOFF, I. M., AND BOSCH, W. 1927 Die Anwendung der Chinhydrone-
lektrode zur Messung der Wasserstoffionenkonzentration in
pufferarmen Losungen. Biochem. Z., 183, 434.

KOLTHOFF, I. M., AND FURMAN, N. H. 1926 Indicators. N. Y.

KOLTHOFF, I. M., AND FURMAN, N. H. 1926 Potentiometric titrations.
Wiley, N. Y.

KOLTHOFF, I. M., AND HARTONG, B. D. 1925 The antimony electrode as
an indicator for hydrogen ions and its application in potentio-
metric titrations of acids and bases. Rec. trav. chim., 44, 113.

KOLTHOFF, I. M., AND MENZEL, H. 1928 Die Myssanalyse. Berlin.

KOLTHOFF, I. M., AND TEKELENBURG, F. 1926-1927 The potentiometric
determination of the hydrogen ion concentration at higher tem-
peratures. Kon. Akad. Wetenschappen Amsterdam. Proc., 29,
766. Rec. trav. chim., 46, 18.

KOLTHOFF, I. M., AND TEKELENBURG, F. 1927 The change of the pH in
buffer mixtures at varying temperatures. Rec. trav. chim.,
46, 33.

KOLTHOFF, I. M., AND VLEESCHHOUWER, J. J. 1926 Eine neue Reihe
Pufferlosungen mit einem pH zwischen 2.2 and 6.0. Biochem.
Z., 179, 410.

KOLTHOFF, I. M., AND VLEESCHHOUWER, J. J. 1927 Eine Korrektur fur
die neue Reihe Pufferlosungen. Biochem. Z., 183, 444.

KOLTHOFF, I. M., and VLEESCHHOUWER, J. J. 1927 Eine Vervollstandi-
gung der JReihe Pufferlosungen im alkalischen Gebiet. Biochem.
Z., 189, 191.

BIBLIOGRAPHY 631

KOLTHOFF, I. M., AND VOGELENZANG, E. H. 1921 Le titrage acidimS-
trique du bichromate. Rec. trav. chim., 40, 681.

KONIKOFF, A. P. 1913 tlber die Bestiramung der wahren Blutreaktion
mittels der elektrischen Methode. Biochem. Z, 61, 200.

KOPACZEWSKI, W. 1926 Les ions d'hydrogene. Signification, mesure,
applications, donnees numeriques. Paris, Gauthier-Villars et
Cie.

KOPPEL, M., AND SPIRO, K. 1914 tlber die Wirkung von Moderatoren
(Puffern) bei der Verschiebung des Saure-Basengleichgewichtes
in biologischen Fliissigkeiten. Biochem. Z., 65, 409.

KRAMER, J. B. 1924 A new electronic battery. Electrician, 93, 497.

KUBELK.A, V., AND WAGNER, J. 1926 Zur elektrometrischen Bestimmung
der Wasserstoffionen Konzentration in kolloidalen Losungen.
Collegium, 25, 266.

KUHN, R., AND JACOB, P. 1924. tlber Mutarotation. Z. physik. Chem.,
113, 389.

KURODA, T. 1926 tlber den Einfluss der Wasserstoffionenkonzentration
auf die antiseptische Wirkung einiger Phenole und aromatischer
Sauren. Biochem. Z., 169, 281.

KUSTER, F. W. 1897 Kritische Studien zur volumetrischen Bestimmung
von karbonathaltigen Alkalilaugen und von Alkalikarbonaten,
sowie iiber das Verhalten von Phenolphthalem und Methylor-
ange als Indikatoren. Z. anorg. Chem., 13, 125.

I^AAR, C. 1885 tlber die Moglichkeit mehrerer Strukturformeln fiir
dieselbe chemische Verbindung. Ber., 18, 648.

LAMB, A. B., AND LARSON, A. T. 1920 The stability of the cobaltammines.
J. Am. Chem. Soc., 42, 2024.

LAMB, A. B., AND LARSON, A. T. 1920 Reproducible liquid junction po-
tentials; the flowing junction. J. Am, Chem. Soc., 42, 229.

LAMBERT, B., AND GATES, S. F. 1925 Relationships existing between hy-
drogen and palladium. Proc. Roy. Soc., 108A, 456.

LAMBLE, A., AND LEWIS, W. C. McC. 1915 Studies in catalysis. II.
The inversion of sucrose. J. Chem. Soc., 107, 233.

LAMBLING, E. Precis de biochimie, 3d ed. (Cited).

LAMER, V. K. 1921 Vitamines from the standpoint of physical chemistry.
J. Ino\T Eng. Chem., 13, 1108.

LAMER, V. K. 1921 The effect of temperature and hydrogen ion concen-
tration upon the rate of destruction of the antiscorbutic vitamin.
Thesis. Columbia Univ.

LAMER, V. K. 1927 Recent advances in the ionization theory as applied to
strong electrolytes. Trans. Am. electrochem. soc.

LAMER, V. K. AND BAKER, L. E. 1922 The effect of substitution on the
free energy of oxidation-reduction reactions. I. Benzoquinone
derivatives. J. Am. Chem. Soc., 44, 1954.

LAMER, V. K., CAMPBELL, H. L., AND SHERMAN, H. C. 1922 The effect of
temperature and the concentration of hydrogen ions upon the
rate of destruction of antiscorbutic vitamin (Vitamin C). J.
Am. Chem. Soc., 44, 172.

632 THE DETERMINATION OF HYDROGEN IONS

LAMER, V. K., KING, C. V., AND MASON, C. F. 1927 Activity coefficients
of electrolytes. I. The limiting law for a ter-tervalent salt.
J. Am. Chem. Soc., 49, 363.

LAMER, V. K., AND PARSONS T. R. 1923 The application of the quinhy-
drone electrode to electrometric acid-base titrations in the pres-
ence of air, and the factors limiting its use in alkaline solution.
J. Biol. Chem., 57, 613.

LAMER, V. K., AND RIDEAL, E. K. 1924 Influence of hydrogen concentra-
tion on the autoxidation of hydroquinol. A note on the stability
of the quinhydrone electrode. J. Am. Chem. Soc., 46, 223.

LANDOLT AND BORNSTEIN 1923 Physikalisch-chemische Tabellen. Ber-
lin.

LANGMUIR, I. 1916 The relation between contact potentials and elec-
trochemical action. Trans. Am. Electrochem. Soc., 29, 125.

LARSSON, E. 1922 Bestimmung der zweiten Dissoziationskonstanten
einiger^Sauren aus elektrometrischen Messungen. Z. anorg.
algem. Chem., 125, 281.

LARSSON, E. 1922 Untersuchungen iiber die elektrolytische Dissociation
einiger Elektrolyten in Aethylalkohol. Thesis. Lund (cited).

LARSSON, E. 1924 Zur elektrolytischen Dissoziation der zweibasischen
Sauren. Z. anorg. Chem. 140, 292.

LASCH, C. H. 1927 Eine neue Spritzenelektrode zur direkten pH-Mes-
sung mit stehender Wasserstoffblase. Z. ges. exptl. Med., 56, 157.

LAUBENGAYER, A. W. 1921 The apparent irreversibility of the calomel
electrode. J. phys. Chem., 25, 332.

LAXTON, F. C., PRIDEAUX, E. B. R., AND RADFORD, W. H. 1925 The col-
orimetric dissociation constants of 3,5-dinitrocatechol and 4,6-
dinitroresorcinol. J. Chem. Soc., 127, 2499.

LEEDS AND NORTHRUP COMPANY 1918 Moving coil galvanometers.
Catalogue No. 20.

LEGENDRE, R. 1925 La concentration en ions hydrogene de I'eau de mer.
Le pH. Methodes de mesure; importance oceanographique, geo-
logique, biologique. Paris, Pr. Univ. d,e France.

LEHFELDT, R. A. 1899 On the theory of the electrolytic solution-pres-
sure. Phil. Mag. (v), 48, 430.

LEHFELDT, R. A. 1900 Elecktromotorische Kraft und Osmotischer Druck
Z. physik. Chem., 35, 257.

LEHMANN, G. 1922 Die Messung der Pufferung. Biochem. Z., 133, 30.

LEHMANN, G. 1923 Ein einfaches Modell einer Mikroelektrode zur pH-
Bestimmung. Biochem. Z., 139, 213.

LEIGHTON, A. 1924 A convenient battery power-line circuit for the po-
tentiometer. Ind. Eng. Chem., 16, 1189.

LEPPER, E. H., AND MARTIN, C. J. 1926 The discrepancy between elec-
trometric and colorimetric (phenol red) determinations of Ch
according to the salt content of the solution. Biochem. J., 20, 45.

LEPPER, E. H., AND MARTIN, C. J. 1927 The protein error in estimating
pH with neutral red and phenol red. Biochem. J., 21, 356.

BIBLIOGRAPHY 633

LERCH, W., AND BOGUE, R. H. 1927 Studies on the hydrolysis of com-
pounds which may occur in portland cement. J. Phys. Ohem.,
31, 1627.

LESCHLY, W. 1916 Versuche iiber Komplement IV. Die Bedeutung der
Wasserstoffionenkonzentration. Z. Immunitat, 25, 203.

LESTER, V. 1924 The measurement of hydrion concentration in some
dairy products by means of Biilmann's quinhydrone electrode.
J. Agr. Sci., 14, 634.

LEVENE, P. A., BASS, L. W., STEIGER, R. E., AND BENCOWITZ, I. 1927 The
effect of ionization upon optical rotation. II. Relations in the
series of amino acids, polypeptides and ketopiperazines. J.
Biol. Chem., 72, 815.

LEVENE, P. A., AND SIMMS, H. S. 1923 Calculation of isoelectric points.
J. Biol. Chem., 65, 801.

LEVENE, P. A., SIMMS, H. S., AND BASS, L. W. 1926 The effect of ioniza-
tion upon optical rotation of nucleic acid derivatives. J. Biol.
Chem., 70, 243.

LEVINE, M., TOULOUSE, J. H., AND BUCHANAN, J. H. 1928 Effect of addi-
tion of salts on the germicidal efficiency of sodium hydroxide.
Ind. Eng. Chem., 20, 179.

LEVY, R. L., AND CULLEN, G. E. 1920 Deterioration of crystalline stro-
phanthin in aqueous solution. Its relation to hydrogen ion con-
centration and a method for its prevention. J. Exp. Med., 31,
267.

LEVY, R. L., ROWNTREE, L. G., AND MARRIOTT, W. Me. K. 1915 A simple
method for determining variations in the hydrogen-ion concen-
tration of the blood. Arch. Intern., Med., 16, 389.

LEWIS, G. N. 1906 The potential of the oxygen electrode. J. Am. Chem.
Soc., 28, 158.

LEWIS, G. N. 1907 Outlines of a new system of thermodynamic chem-
istry. Proc. Am. Acad., 43, 259.

LEWIS, G. N. 1913 The free energy of chemical substances. J. Am.
Chem. Soc., 35, 1.

LEWIS, G. N. 1923 Valence and the Structure of Atoms and Molecules.
N.Y.

LEWIS, G. N., BRIGHTON, T. B., AND SEBASTIAN, R. L. 1917 A study of
hydrogen and calomel electrodes. J. Am. Chem. Soc., 39, 2245.

LEWIS, G. N., AND RANDALL, M. 1914 The free energy of oxygen, hydro-
gen and oxides of hydrogen. J. Am. Chem. Soc., 36, 1969.

LEWIS, G. N., AND RANDALL, M. 1921 The activity coefficient of strong
electrolytes. J. Am. Chem. Soc., 43, 1112.

LEWIS, G. N., AND RANDALL, M. 1923 Thermodynamics and the Free
Energy of Chemical Substances. N. Y.

LEWIS, G. N., AND RUPERT, F. F. 1911 The potential of the chlorine
electrode. J. Am. Chem. Soc., 33, 299.

LEWIS, G. N., AND SARGENT, L. W. 1909 Note on the calomel electrode.
J. Am. Chem. Soc., 31, 362.

634 THE DETERMINATION OF HYDROGEN IONS

LEWIS, G. N., AND SAEGENT, L. W. 1909 Potentials between liquids. J.

Am. Chem. Soc., 31, 363.
LEWIS, M. R., AND FELTON, L. D. 1921 Hydrogen-ion concentration of

cultures of connective tissue from chick embryos. Science, 54,

636.
LEWIS, M. R., AND FELTON, L. D. 1922 The hydrogen-ion concentration

of tissue growth in vitro. Bull. Johns Hopkins Hospt., 33, 112.
LEWIS, W. C. McC. 1916 A System of Physical Chemistry, London.
LEWIS, W. C. McC. 1920 Contact potentials and dielectric capacities

of metals, in relation to the occlusion of hydrogen, and hydro-

genation. J. Chem. Soc., 117, 623.
LILLIE, R. S. AND SHEPARD, C. E. 1923 The influence of combinations of

inorganic salts and of variations in hydrogen-ion concentration

on the heliotropic response of Arenicola larvae. Am. J, Physiol.,

65, 450.
LINDEMANN, F. A., AND A. F., AND KsLLEY, T. C. 1924 A new form of

electrometer. Phil. Mag. [61 47, 577.
LiNDERSTR0M-LANG K. 1924 On the salting-out effect. Compt. rend.

trav. lab. Carlsberg 15, 1.

LiNDERSTR0M-LANG, K. 1927 Volumetric determination of amino ni-
trogen. Compt. rend. trav. lab. Carlsberg, 17, 1.
LiNDERSTR0M-LANG K., AND KODAMA, S. 1925 On the solubility of casein

in hydrochloric acid. Compt. rend. trav. lab. Carlsberg, 16, 1.
LINDHARD, J. 1921 Colorimetric determination of the concentration of

hydrogen ions in very small quantities of blood by dialysis.

Compt. rend. trav. lab. Carlsberg, 14, 13.

LINHART, G. A. 1917 A comparison of the activities of two typical elec-
trolytes. J. Am. Chem. Soc., 39, 2601.
LINHART, G. A. 1919 The applicability of the precipitated silver-silver

chlorid,e electrode to the measurement of the activity of hydro-
chloric acid in extremely dilute solutions. J. Am. Chem. Soc.,

41, 1175.
LIPMAN, J. G., WAKSMAN, S. A., AND JOFFE, J. S. 1921 The oxidation of

sulphur by soil organisms. Soil Science, 12, 475.
LIPSCOMB, G. F., AND HULETT, G. A. 1916 A calomel standard cell. J.

Am. Chem. Soc., 38, 21.
LIQUIER, J. 1927 Etude sur le pouvoir rotatoire des solutions aqueuses

des electrolytes en relation avec la concentration et I'activitS

des ions hyd^ogene. Ann. phys. [10] 8, 121.
Liu, S-K. 1927 tlber die Regulation der Wasserstoffipnenkonzentration

im Blute. Biochem. Z., 185, 242, 255, 263.
LIZIUS, J. L. 1921 The joint use of two indicators in the titration of acids

and bases. Analyst, 46, 355.
LIZIUS, J. L., AND EVERS, N. 1922 Studies in the titration of acids and

bases. Analyst, 47, 331.

LLOYD, D. J. 1926 Chemistry of the Proteins. London.
LODGE, 0. J. 1885 On Electrolysis. Rept. Brit. Assn. (Aberdeen), p.

723.

BIBLIOGKAPHY 635

LOEB, J. 1909 Elektrolytische Dissoziation und physiologische Wirk-

samkeit von Pepsin und Trypsin. Biochem. Z., 19, 534.
LOEB, J. 1922 Proteins and the Theory of Colloidal Behavior. N. Y.
LOEB, L. B. 1927 Kinetic Theory of Gases. N. Y.
LONG, J. H. 1916 A simple cell for the determination of hydrogen ion

concentration. J. Am. Chem. Soc., 38, 936.
LOOMIS, N. Bi 1915 Potentials of the calomel and hydrogen electrodes.

J. Phys. Chem., 19, 660.
LOOMIS, N. E*, AND AGREE, S. F. 1911 A stucty of the hydrogen electrode,

of the calomel electrode and of contact potential. Am. Chem.

J., 46, 585.
LOOMIS, N. E., AND AGREE, S. F. 1911 The application of the hydrogen

electrode to the measurement of the hydrolysis of aniline hy-

drochloride and the ionization of acetic acid in the presence of

neutral salts. Am. Chem. J., 46, 621.
LOOMIS, N. E., AND AGREE, S. F. 1916 The effect of pressure upon the

potential of the hydrogen electrode. J. Am. Chem. Soc., 38,

2391.
LOOMIS, N. E., ESPEX, J. L., AND MEACHAM, M. R. 1917 The applicability

of the isohydric principle to tenth-normal mixtures of hydro-
chloric acid and potassium chloride. J. Am. Chem. Soc., 39,

1133.
LOOMIS, N. E., AND MEACHAM, M. R. 1916 A study of the tenth-normal

hydrochloric acid calomel electrode. J. Am. Chem. Soc., 38,

2310.
LOOMIS, N. E., MYERS, C. N., AND AGREE, S. F. 1917 The potential of

the hydrogen electrode at different pressures. J. Phys. Chem.,

21, 334.
LOWRY, T. M. 1924 The electronic theory of valency. Part IV. The

origin of acidity. Phil. Mag., 47, 1021.

LOWRY, T. M. 1924 The origin of acidity. Trans. Faraday Soc., 20, 13.
LOWRY, T. M. 1927 Static and dynamic isomerism in prototropic com-
pounds. Chem. Rev., 4, 231.
LUBS, H. A. 1920 Indicators and their industrial application. J. Ind.

Eng. Chem., 12, 273.

LUBS, H. A., AND AGREE, S. F. 1916 On the sulfonphthalein series of indi-
cators and the quinone-phenolate theory. J. Am. Chem. Soc.,

38, 2772.
LUBS H. A., AND OLARK, W. M. 1915 On some new indicators for the col-

orimetric determination of hydrogen ion concentration. J.

Wash. Acad. Sci., 5, 609.
LUBS, H. A., AND CLARK, W. M. 1916 A note on the sulphonephthaleins

as indicators for the colorimetric determination of hydrogen ion

concentration. J. Wash. Acad. Sci., 6, 481.
LUCKIESH, M. 1917 The physical basis of color-technology. J. Franklin

Inst., 184, 227.
LUERS, H. 1920 Der Farbenumschlag des Knogorubins unter dem Ein-

fluss von Reaktion und Neutralsalzwirkung. Kolloid-Z., 26, 15.

636 THE DETERMINATION OF HYDROGEN IONS

LUERS, H., AND LOCHMULLER, K. 1927 Die Messung der Gelierkraft von

Fruchtpektinen. Kolloid-Z., 42, 154.
LUND, H. 1927 Methoxy-substituted triphenyl carbinols and their salts.

J. Am. Chem. Soc., 49, 1346.
LUTHER, R., AND BRISLEE, F. J. 1903 Zur Kenntnis des Verhaltens

"unangreif barer" Anoden insbesondere bei der Elektrolyse von

Salzsaure. Z. physik. Chem., 45, 216.
LYON, R., FRON, G. AND FOURNIER, M. 1927 Caracterisation des bois

vieux par rapport aux bois verts. Compt. rend., 184, 745, cf . 949.
MACARTHUR, J. W. 1920 Changes in acid and alkali tolerance with age in

planarians. Am. J. Physiol., 54, 138.
MACARTHUR, J. W. 1921 Gradients of vital staining and susceptibility in

planaria and other forms. Am. J. Physiol., 57, 350.
McBAiN, J. W. 1920 Colloidal chemistry of soap. Third Report of

Brit. Assoc. on Colloid Chemistry, 2.
McBAiN, J. W., AND EOLAM, T. R. 1918 The hydrolysis of soap solutions

measured by the rate of catalysis of nitrosotriacetonamine. J.

Chem. Sec., 113, 825.
McBAiN, J. W., DUBOIS, O. E., AND HAY, K. G. 1926 The salt error of

indicators caused by standard alkaline buffers themselves. J.

GEN. Physiol., 9, 451.
McBAiN, J. W., AND SALMON, S. C. 1920 Colloidal electrolytes. Soap

solutions and their constitution. J. Am. Chem. Soc., 42, 426.
McCALL, A. G., AND HAAG, J. R. 1921 The relation of the hydrogen ion

concentration of nutrient solutions to growth and chlorosis of

wheat plants. Soil Science, 12, 69.
McCLENDON, J. F. 1915 New hydrogen electrodes and rapid methods of

determining hydrogen ion concentrations. Am. J. Physiol., 38,

180.
MCCLENDON, J. F. 1915 Acidity curves in the stomachs and duodenums

of adults and infants, plotted with the aid of improved methods

of measuring hydrogen ion concentration. Am. J. Physiol.,

38, 191.
MCCLENDON, J. F. 1916 Improved gas chain methods of determining

hydrogen ion concentration in blood. J. Biol. Chem., 24, 519.
MCCLENDON, J. F. 1916 The composition, especially the hydrogen ion

concentration, of sea water in relation to marine organisms. J.

Biol. Chem., 28, 135.
MCCLENDON, J. F. 1917 The standardization of a new colorimetric

method for the determination of the hydrogen ion concentration,

CO2 tension, and CO2 and O2 content of sea water, of animal heat,

and of CC>2 of the air, with a summary of similar data on bicarbon-
ate solutions in general. J. Biol. Chem., 30, 265.
MCCLENDON, J. F. 1918 A new hydrogen electrode for the electrometric

titration of the alkaline reserve of blood plasma and other

frothing fluids. J. Biol. Chem., 33, 19.
MCCLENDON, J. F. 1920 Hydrogen-ion concentration of the contents of

the small intestine. Proc. Nat. Acad. Sci., 6, 690.

BIBLIOGRAPHY 637

McCLENDON, J. F. 1922 Chart for the conversion of colorimetric readings
into hydrogen ion concentration. J. Biol. Chem., 54, 647.

MCCLENDON, J. F. 1924 The determination of hydrogen ions in the gas-
tric contents. J. Biol. Chem., 59, 437.

MCCLENDON, J. F. 1924 The determination of the pH of the urine with
4-nitro-6-aminoguaicol. Proc. Soc. Exptl. Biol. Med., 21, 348.

McCLENDON, J. F., BlSSELL, F. S., LOWE, E. R., AND MEYER, P. F. 1920

Hydrogen-ion concentration of the contents of the small intestine
J. Am. Med. Assoc., 75, 1638.

MCCLENDON, J. F., AND MAGOON, C. A. 1916 An improved Hasselbalch
hydrogen electrode and a combined tonometer and hydrogen
electrode, together with rapid methods of determining the buffer
value of the blood. J. Biol. Chem., 25, 669.

MCCLENDON, J. F., MYERS, F. J., CULLIGAN, L. C., AND GYDESEN, C. S.
1919 Factors influencing the hydrogen ion concentration of the
ileum. J. Biol. Chem., 38, 535.

MCCLENDON, J. F., RUSSELL, S., AND TRACY, E. 1926 The determination
of hydrogen ions in the blood with the aid of the Duboscq colorim-
eter and ortho-chrom-T or para-nitro phenol. J. Biol. Chem., 70,
705.

MCCLENDON, J. F., AND SHARP, P. F. 1919 The hydrogen ion concentra-
tion of foods. J. Biol. Chem., 38, 531.

MCCLENDON, J. F., SHEDLOV, A., AND THOMSON, W. 1917 The hydrogen
ion concentration of the ileum content. J. Biol. Chem., 31, 269.

McCRAE, J. 1926 A modification of the Gillespie approximate method of
determining hydrogen-ion concentration. Analyst, 51, 287.

MACDOUGAL, D. T., AND MORAVEK, V. 1927 The activities of a con-
structed colloidal cell. Protoplasma, 2, 161.

McGiLL, W. J. 1922 The use of the newer indicators in titrations of
alkaloids. J. Am. Chem. Soc., 44, 2156.

MACHT, D. I., AND SHOHL, A. T. 1920 The stability of benzyl alcohol
solutions. J. Pharmacol., 16, 61.

MclLVAiNE, T. C. 1921 A buffer solution for colorimetric comparison.
J. Biol. Chem., 49, 183.

MAC!NNES, D. A. 1915 The potentials at the junctions of salt solutions.
Proc. Nat. Acad. Sci., 1, 526.

MAC!NNES, D. A. 1915 Liquid junction potentials. J. Am. Chem. Soc.,
37, 2301.

MAC!NNES, D. A. 1919 The activities of the ions of strong electrolytes.
J. Am. Chem. Soc., 41, 1086.

MAC!NNES, D. A. 1926 The ionization of weak electrolytes. J. Am.
Chem. Soc., 48, 2068.

MAC!NNES, D. A., AND BEATTIE, J. A. 1920 The free energy of dilution
and the transference numbers of lithium chloride solutions.
J. Am. Chem. Soc., 42, 1117

MAClNNES, D. A., COWPERTHWAITE, I. A., AND HUANG, T. C. 1927 MoV-

ing-boundary method for determining transference numbers.

638 THE DETERMINATION OF HYDROGEN IONS

VI. Further developments in experimental technic. J. Am.
Chem. Soc., 49, 1710.

MAC!NNES, D. A., AND JONES, P. T. 1926 A method for differential po-
tentiometric titration. J. Am. Chem. Soc., 48, 2831. See also
Z. physik. Chem. (Cohen Festband), 1927.

MAC!NNES, D. A., AND PARKER, K. 1915 Potassium chloride concentra-
tion cells. J. Am. Chem. Soc., 37, 1445.

MAC!NNES, D. A., AND YEH, Y. L. 1921 The potentials at the junctions
of monovalent chloride solutions. J. Am. Chem. Soc., 43, 2563.

MAC!NNES, J. 1922 The growth of the wheat scab organism in relation
to hydrogen-ion concentration. Phytopathology, 12, 290.

MclNTOSH, J., AND SMART, W. 1927 The determination of the reaction of
bacteriological culture media. Brit. J. Exptl. Path, 1, 9.

McQuARRiE, I., AND SnoHL, A. T. 1925 A colorimetric method for the de-
termination of the pH of cerebrospinal fluid. J. Biol. Chem.,
66, 367.

McSwiNEY,B. A., AND NEWTON, W.H. 1927 Reaction of smooth muscle to
the hydrogen-ion concentration. J. Physiol., 63, 51; 64, 144.

MADDISON, R. E. W. 1926 The electromotive behavior of cupric oxide.
Trans. Faraday Soc., 22, 27.

MALAPRADE, L. 1926 Titrage potentiometrique de quelques acides oxy-
dants. Bull. soc. chim., 39, 325.

MARKER, R. E., AND GORDON, N. E. 1924 Effect of hydrogen-ion concen-
tration on compound formation and adsorption of dyes by mor-
dants. Ind. Eng. Chem., 16, 1186.

MARSH, F. W. 1924 Indicator reaction as a source of error in pH deter-
minations. Science, 69, 216.

MARSHALL, E. K., JR. 1926 The secretion of urine. Physiol. Rev., 6, 440.

MARTIN, C. J. 1920 The preparation of S0rensen's phosphate solutions
when the pure salts are not available. Biochem. J., 14, 98.

MARTIN, C. J., AND LEPPER, E. H. 1926 A micro-method for the estima-
tion of the hydjogen-ion concentration of capillary blood. Bio-
chem. J., 20,37.

MARTIN, C. J., AND LEPPER, E. H. 1926 Observations on the extent to
which the electrometric determination of the [H'] of bicarbonate
solutions is interfered with by the production of formic acid
at the electrode. Biochem. J., 20, 1077.

MASON, E. C., AND SANFORD, A. H. 1924 A proposed buffered physiologic
salt solution to be used in serology. J. Lab. Clin. Med., 9, 313.

MASON, V. R. 1922 The relation of H-ion concentration to specific pre-
cipitation. Bull. Johns Hopkins Hosp., 33, 116.

MAXTED, E. B. 1919 The influence of hydrogen sulphide on the occlusion
of hydrogen by palladium. J. Chem. Soc., 115, 1050.

MAXTED, E. B. 1920 The influence of hydrogen sulphide on the occlusion
of hydrogen by palladium. J. Chem. Soc., 117, 1280.

MAXTED, E. B. 1921 On the relation between the occlusive power of
palladium for hydrogen and its activity for catalytic hydrogena-
tion. J. Chem. Soc., 119, 1280.

BIBLIOGRAPHY 639

MAXTED, E. B. 1921 The influence of mercury, sulphur, arsenic and zinc

on the catalytic activity of platinum. J. Chem. Soc., 119, 225.
MAXTED, E. B. 1925 Adsorption of catalytically poisonous metals by

platinum. I. Adsorption of lead and mercury. J. Chem. Soc.,

127, 73.

MAYER, A. G. 1922 Hydrogen-ion concentration and electrical conduc-
tivity of the surface water of the Atlantic and Pacific. Carnegie

Inst. Wash. Pub., 312.

MAYER, A. G. 1919 Detecting ocean currents by observing their hydro-
gen-ion concentration. Proc. Am. Phil. Soc., 68, 150.
MEDALIA, L. S. 1920 "Color Standards" for the colorimetric measure-
ment of H-ion concentration pH 1.2 to pH 9.8. J. Bact., 5, 441.
MEDALIA, L. S. 1922 Further observations on "Color Standards" for

the colorimetric determination of H-ion concentration. J.

Bact., 7, 589.
MEDICAL RESEARCH COMMITTEE (British) 1919 The reaction of media.

Special Report Series No. 35, V.
MEEKER, G. H., AND OSER, B. L. 1926 Titrimetric double hydrogen or

quinhydrone electrode systems for hydrion determination;

applications to urine and blood. J. Biol. Chem., 67, 307.
MEILLERE, G. 1920 Electrodes en verre platine pour dosages 61ectroly-

tiques. J. pharm. chim., 21, 311.
MELANDER, K. H. A. 1915 Beitrage zur Theorie der Fliissigkeitspoten-

tialdifferenzen. I. Z. physik. Chem., 90, 59.
MELLET, R., AND BISCHOFF, M. A. 1926 Reactions chimiques et titrages

volumetriques en lumiere de Wood. Compt. rend., 182, 1616.
MELLON, M. G. 1922 The use of solutions of inorganic salts as permanent

color standards. Proc. Indiana Acad. Sci., p. 164.
MELLON, M. G., AND MARTIN, F. D. 1927 Solutions for colorimetric

standards I. J. Phys. Chem., 31, 161.
MELLON, M. G., AND MORRIS, V. N. 1925 Potentiometric titrations with

hydrazine sulfate. Proc. Indiana Acad. Sci., 35, 155.
MELLON, R. R., AGREE, S. F., AVERY, P. M., AND SLAGLE, E. A. 1921

The ionization constants of glycerophosphoric acid and their

use as buffers, especially in culture mediums. J. Infect. Dis.,

29,1.
MENZEL, H., AND KRUGER, F. 1926 Notizen zur Methodik elektrometri-

schen pH-Bestimmungen. Z. Electrochem., 32, 93.
MERRILL, A. T. AND CLARK, W. M. 1928 Some conditions affecting the

production of gelatinase by proteus bacteria. J. Bact., 15, 267.
MEULEN, P. A. VAN DER, AND WILCOXON, F. 1923 Electrometric acid-

imetry and alkalimetry without the use of hydrogen. Ind.

Eng. Chem., 15, 62.
MEVITJS, W. 1927 Reaction des Bodens und Pfianzenwachstum. Freising-

Munchen.
MEYERHOF, O. 1918 Untersuchungen zur Atmung getoteter Zellen.

Arch. ges. Physiol. (Pfliiger's), 170, 327.

640 THE DETEEMINATION OF HYDROGEN IONS

MEYERHOF, O. 1923 Die chemischen und energetischen Verhaltnisse bei

der Muskelarbeit. Ergebn. Physiol., 22, 329.
MICHAELIS, L. 1909 Elektrische IJberfuhrung von Fermenten. I. Das

Invertin. Biochem. Z., 16, 81.
MICHAELIS, L. 1909 Die elektrische Ladling des Serumalbumins und der

Fermente. Biochem. Z., 19, 181.
MICHAELIS, L. 1911 Die Saureagglutination der Bakterien, insbesondere

der Typhusbazillen. Deut. med. Wochenschr., 37, 969.
MICHAELIS, L. 1911 Uber die Dissoziation der amphoteren Elektrolyte.

Biochem. Z., 33, 182.
MICHAELIS, L. 1912 Der isoelektrische Punkt der elektro-amphoteren

Kolloide. Festschrift. W. Nernst. Halle, 308.
MICHAELIS, L. 1914 Die Wasserstoffionenkonzentration. Berlin.
MICHAELIS, L. 1914 Zur Theorie der elektrolytischen Dissoziation der

Fermente. Biochem. Z., 60, 91.
MICHAELIS, L. 1920 Theoretische Untersuchungen iiber den Dissozia-

tionszustand der Ampholyte. I. Biochem. Z., 103, 225. II.

Ibid;, 106, 83.
MICHAELIS, L. 1920 Die Bestimmung der Wasserstoffzahl durch Indica-

toren. Deut. med. Wochschr., 46, 1238.
MICHAELIS, L. 1921 Vereinfachung der Indikatorenmethode. Deut.

med. Wochschr., 47, 465.
MICHAELIS, L. 1921 The titration of culture media. Z. Immunitats.,

32, 194.
MICHAELIS, L. 1921 Die Eestimmung der Wasserstoffzahl im Trink-,

Fluss-, und Meerwasser mit Indikatoren ohne Puffer. Z. Unter-

such. Nahrungs-Genussm., 42, 75.
MICHAELIS, L. 1921 Vereinfachung der Indicatorenmethode. Deut.

med. Wochschr., 47, 465.
MICHAELIS, L. 1921 Erweiterung der vereinfachten Indikatorenmethode.

Deut. med. Wochschr., 47, 673.
MICHAELIS, L. 1922 Die Wasserstoffionenkonzentration. 2nd Edition,

part I. Berlin.
MICHAELIS, L. 1922 Messung von pH mit indikatoren ohne Puffer. Ab-

derhalden's Handb. biol. Arbeitsmet. Abt. Ill, A, Heft 2, 487.
MICHAELIS, L. 1922 Die elektrometriwche titration. Abderhalden's

Handb. biol. Arbertsmeth., Abt. Ill, Heft 2A, 507.
MICHAELIS, L. 1924 General principles of ion effects on colloids. 2d

Colloid Symposium Monograph.

MICHAELIS, L. 1925 The Effects of Ions in Colloidal Systems. Baltimore.
MICHAELIS, L. 1926 Electric phenomena in colloid chemistry. Alexan-
der's Colloid Chemistry, p. 471, N. Y.
MICHAELIS, L. 1926 Praktikum der physikalischen Chemie insbesondere

der Kolloidchemie fur Mediziner und Biologen. Berlin.
MICHAELIS, L. 1926 Die Permeabilitat von Membranen. Die Natur-

wissenschaften, 14, 33.

MICHAELIS, L. 1927 Some problems concerning the gastric juice. Har-
vey Lectures, 22, 59,

BIBLIOGRAPHY 641

MICHAELIS, L. AND DAviDOFF, W. 1912 Methodisches und Sachliches

zur elektrometrischen Bestimmung der Blutalkalescenz. Bio-

chem. Z., 46, 131 and Note p. 148.
MICHAELIS, L., AND DAVIDSOHN, H. 1910 Zur Theorie des isoelektrischen

Punktes. Biochem. Z., 30, 143.
MICHAELIS, L., AND DAVIDSOHN, H. 1912 tlber die Kataphorese des Oxy-

hamoglobins. Biochem. Z., 41, 102.
MICHAELIS, L., AND DAVIDSOHN, H. 1912 Die Abhangigkeit spezifischer

Fallungsreaktionen von der Wasserstoffionenkonzentration.

Biochem. Z., 47, 59.
MICHAELIS, L., AND DAVIDSOHN, H. 1912 Zur Methodik der elektrischen

tJberfuhrung von Kolloiden. Z. physiol. Chem., 76, 385.
MICHAELIS, L., AND DAVIDSOHN, H. 1913 Weiterer Beitrag zur Frage nach

der Wirkung der Wasserstoffionenkonzentration auf Kolloid-

gemische. Erwiderung auf die Arbeit von Landsteiner. Bio-
chem. Z., 64, 323.
MICHAELIS, L., AND DAVIDSOHN, H. 1924 Verfahren zur Reinigung von

Toxinen, Fermenten und anderen biologisch wirksamen organi-

schen Kolloiden. Biochem. Z., 144, 294.
MICHAELIS, L., AND DERNBY, K. G. 1922 Der Einfluss der Alkalitat auf

die Wirksamkeit der Chininalkaloide. Z. Immunitat., I. Teil,

Orig., 34, 194.

MICHAELIS, L., AND FUJITA, A. 1923 Uber die Vernichtung des Diffusions-
potentials an Flussigkeitsgrenzen. Biochem. Z., 142, 398.
MICHAELIS, L., AND GYEMANT, A. 1920 Die Bestimmung der Wasser-

stoffzahl durch Indicatoren. Biochem. Z., 109, 165.
MICHAELIS, L., AND KAKINUMA, K. 1923 Einige elektrometrische Eichun-

gen mit Beriicksichtigung der lonenaktivitat. Biochem. Z.,

141, 394.
MICHAELIS, L., AND KRUGER, R. 1921 Weitere Ausarbeitung der Indika-

torenmethode ohne Puffer. Biochem. Z., 119, 307.

MICHAELIS, L., AND MARCORA, F. 1912 Die Saureproduktivitat des Bac-
terium coli. Z. Immunitat., Abt. I (orig.), 14, 170.
MICHAELIS, L., AND MIZUTANI, M. 1924 Der Einfluss der Neutralsalze

auf das Potential einer HCl-Losung gegen die Wasserstoffelek-

trode. Z. physik. Chem., 112, 68.
MICHAELIS, L., AND MIZUTANI, M. 1924 Die pH-Messung mit einfarbigen

Indikatoren in alkoholischen Losungen. Biochem. Z., 147, 7.
MICHAELIS, L., AND MIZUTANI, M. 1925 Die Dissoziation der schwachen

Elektrolyte in wasserig-alkaholischen Losungen. Z. physik.

Chem., 116, 135.
MICHAELIS, L., AND PERLZWEIG, W. A. (translator) 1926 Hydrogen Ion

Concentration L The Williams & Wilkins Co., Baltimore.
MICHAELIS, L., AND PERLZWEIG, W. A. 1927 Studies on permeability of

membranes. J. Gen. Physiol., 10, 575.
MICHAELIS, L., AND RONA, P. 1908 Zur Frage der Bestimmung der

H-ionenkonzentration durch Indikatoren. Z. Elektrochem.,

14, 251.

642 THE DETERMINATION OF HYDROGEN IONS

MICHAELIS, L., AND RONA, P. 1909 Der Einfluss der Neutralsalze auf die

Indikatoren. Biochem. Z., 23, 61.
MICHAELIS AND RONA, P. 1919 Erweiterung der Theorie des isoelek-

trischen Punktes. Die Konkurrenz der anderen lonen mit den

H' und OH'-ionen bei der Fallung des denaturierten Albumins.

Biochem. Z., 94,225.
MICHAELIS, L., AND RONA, P. 1920 Die Adsorbierbarkeit der ober-

flachenaktiven Stoffe durch verschiedene Adsorbenzien sowie

ein Versuch zur Systematik der Adsorptionserscheinungen.

Biochem. Z., 102, 268.
MICHAELIS, L., AND SKWIRSKY, P. 1909 Der Einfluss der Reaktion auf

die spezifische Hamolyse. Z. Immunitat., I Abt. (orig.), 4, 357,

629.

MILLER, E.J. 1928 Adsorption from solution by ash-free absorbent char-
coal. Colloid Symposium Monograph, 5, 55.
MILLET, H. 1927 See Faraday Society 1927.
MILNER, S. R. 1912 The virial of a mixture of ions. Phil. Mag., [6] 23,

551.
MILNER, S. R. 1913 The effect of interionic forces on the osmotic pressure

of electrolytes. Phil. Mag., [6] 25, 742.
MILOBEDZKI, T., AND JAJTE, S. 1926 Use of extracts of blue cabbage as

an indicator. Roczniki Chem., 6, 177 (cited).
MINES, G. R. 1910 The action of beryllium, lanthanum, yttrium and

cerium on the frog's heart. J. PhysioL, 40, 327.
MISLOWITZER, E. 1925 Zur H-Ionenmessung mit 'Chinhydron. Eine

neue Doppelelektrode in Becherglasform. Biochem. Z., 159, 72.
MISLOWITZER, E. 1925 Zur H-Ionenmessung von Blut. Die Spritze

als Ableitungselektrode. Biochem. Z., 159, 77.
MISLOWITZER, E. 1926 Zur Messung des pH von Plasma, Serum und Blut

mit der Chinhydronmethode. Klin. Wochschr., 5, 1863 and 2214.
MISLOWITZER, E. 1928 Die Bestimmung der Wasserstoffionenkonzentration

von Flussigkeiten. Berlin.
MIZTJTANI, M. 1925 The Determination of Hydrogen Ions. (In Japanese)

• Tokyo.
MIZUTANI, M. 1925 Die Dissoziation der Schwachen Elektrolyte in was-

serig-alkoholischen Losungen. Z. physik. Chem., 118, 318, 327.
MOIR, J. 1916 Spectra of the mixed phthaleins and of the sulfonephtha-

leins. Roy. Soc. South Africa J. Chem. Soc., 112, II (cited.)
MOIR, J. 1917 J. Chem. Met. Min. Soc. South Africa, 129 (cited).
MOIR, J. 1919-1920 Color and chemical constitution. Trans. Roy. Soc.

South Africa, 7, 183; 8, 41, 225, 303.
MOIR, J. 1920 A polychromatic indicator. J. S. African Assoc. Anal.

Chem., 3, No. 2, 6.
MOIR, J. 1923 An improved methyl orange. J. South African Chem.

Inst., 6, 69.
MOLONEY, P. J. 1921 A quick-acting hydrogen electrode. J. phys.

Chem., 25, 758.

BIBLIOGRAPHY 643

MOMMSEN, H. 1926 tlber den Einfluss der Wasserstoffionenkonzentration
auf die Farbung von Blutbildern. Klin. Wochschr., 6, 844.

MOMMSEN, H. 1926 "tfber den Einfluss der Wasserstoffionenkonzentration
auf die Diffusion von Farbstoffen in eine Gelatinegallerte. (Ein
Beitrag zum Zellpermeabilitatsproblem.) Biochem. Z., 168, 77.

MOND, R. 1926 Saurewirkung und H'-Konzentration in der Physiologic.
Kolloid-Z., 40, 228.

MOND, R. 1927 Die physiko-chemischen Grundlagen der unspezifischen
Hamolyse. Protoplasma, 2, 126.

MOND, L., RAMSAY, W., AND SHIELDS, J. 1898 On the occlusion of hydro-
gen and oxygen by palladium. Proc. Roy. Soc., 62, 290.

MoNiER-WiLLiAMS, G. W. 1921 Measurement of hydrogen ion concentra-
tion. Analyst, 46, 315.

MONIER-WILLIAMS, G. W. 1924 Hydrogen electrode for use with meat
pastes, etc. Analyst, 49, 224.

MONTILLON, G. H., AND GASSED N. S. 1924 Acidity of cobalt and nickel
plating baths. Use of the oxygen electrode. Trans. Am. Elec-
trochem. Soc., 45, 259.

MOORE, B., ALEXANDER, W., KELLY, R. E., AND ROAF, H. E. 1906 A
study of the pathological variations in the acidity of the gastric
contents, especially in relationship to malignant disease. Bio-
chem. J., 1, 274.

MOORE, B., ROAF, H. E., AND WHITLEY, E. 1905 On the effects of alkalies
and acids and of alkaline and acid salts, upon growth and cell
division in the fertilized eggs of Echinus esculentus. Proc. Roy.
Soc. (B), 77, 102.

MOORE, B., WHITLEY, E., AND WEBSTER, T. A. 1921 Studies of photo-
synthesis in marine algae. I. Fixation of carbon and nitrogen
from inorganic sources in sea water. II. Increase of alkalinity
of sea water as a measure of photosynthesis. Proc. Roy. Soc.
London (B), 92, 51.

MOREA, L. 1927 Influence de la concentration en ions H sur la culture de
quelques infusoires. Compt. rend. soc. biol., 97, 49.

MORSE, F. W. 1920 Effect of chemical fertilizers on the hydrogen ion
concentration of soils. Com. Fertilizer, 20, 84.

MORSE, H. N. 1905 Exercises in Quantitative Analysis. Boston, 1905.

MORTON, R. A., AND TIPPING. 1925 The correlation of absorption spectra
with ionisation in violuric acid. J. Chem. Soc., 127, 2514.

MOSER, L. 1920 Die Reinigung von verfliissigten und komprimierten
Gasen fur Laboratoriumszwecke. Z. anorg. allgem. Chem.,
110, 125.

MOZOLOWSKI, W., AND PARNAS, J. K. 1926 tlber eine neue Form der
Chinhydronelektrode. Biochem. Z., 169, 352.

MUDD, S. 1925 Electroendosmosis through mammalian serous mem-
branes. J. Gen. Physiol., 7, 389; 9, 73.

MULLER, E. 1926 Die Elektrometrische (Potentiometrische) Massanalyse.
4th ed. 246 pp. Dresden and Leipzig: Th. Steinkopff.

644 THE DETERMINATION OF HYDROGEN IONS

MiiLLER, E. 1924 Zur elektrometrischen Bestimmung der Chloride. Z.
Electrochem., 30, 420.

MULLER, F. 1924 Die potentiometrische Bestimmung von Alkaloiden
an der Wasserstoffelektrode. Z. Elektrochem., 30, 587.

MULLER, R. 1924 Elektrochemie der nichtwassrigen Losungen. Ahrens'
Sammlung Chem. Chem.-tech. Vortrage, 27, 243.

MULLER, R. H., AND PARTRIDGE, H. M. 1927 Precise colorimetric deter-
mination of hydrogen-ion concentration with the photo-electric
cell. Richmond meeting, Am. Chem. Soc.

MURRAY, C. D. 1923 The acid-base equilibrium in simple two-phase
systems. J. Biol. Chem., 56, 569.

MURRAY, D. C., AND HASTINGS, A. B. 1925 The maintenance of carbonic
acid equilibrium in the body, with special reference to the influ-
ence of respiration and kidney function on CO2, H+, HCO3~, and
COs~~ concentrations in plasma. J. Biol. Chem., 65, 265.

MYERS, C. N., AND AGREE, S. F. 1913 A study of the hydrogen electrode,
of the calomel electrode and of contact potential. Am. Chem.
J., 50, 396.

MYERS, V. C. 1922 A colorimeter for bicolorimetric work. J. Biol.
Chem., 54, 675.

MYERS, V. C., AND MUNTWYLER, E. 1927 Colorimetric estimation of
hydrogen ion concentration of blood. Proc. Soc. Exptl. Biol.
Med., 24, 789.

MYERS, V. C., SCHMITZ, W., AND BOOKER, L. E. 1923 A micro colorimetric
method of estimating the hydrogen ion concentration of the
blood. J. Biol. Chem., 57, 209.

NAEGELI, K. 1926 tlber ein neues Indikatorprinzip in der Azidimetrie
und Alkalimetrie. Tribimgsindikatoren. Kolloidchem. Bei-
hefte, 21, 305.

NARAY-SYAB6, St. v. 1927 Die Diffusions-Sauerstoffelektrode. Z. Elek-
trochem., 33, 15.

NAYLOR, E. E. 1926 The hydrogen-ion concentration and the staining
of sections of plant tissue. Am. J. Botany, 13, 265.

NEEDHAM, J. 1925 The metabolism of the developing egg. Physiol.
Rev., 5, 1.

NEEDHAM, J., AND NEEDHAM, D. M. 1927 The oxidation-reduction po-
tential of protoplasm. Protoplasma, 1, 255.

NEGBAUR, W. 1891 Experimentaluntersuchungen iiber Potentialdiffer-
enzen an den Beruhrungsflachen sehr verdiinnter Losungen.
Ann. Physik. Chem., 44, 737.

NEHRING, K. 1927 Vergleichende Untersuchung liber die Saurebestim-
mung in Sauerfutter. Z. angew. Chem., 40, 1058.

NERNST, W. 1888 Zur Kinetik der in Losung befmdlichen Korper.
I. Theorie der Diffusion. Z. physik. Chem., 2, 613.

NERNST, W. 1889 Die elektromotorische Wirksamkeit der Jonen. Z.
physik. Chem., 4, 129.

NERNST, W. 1894 Zur Dissociation des Wassers. Z. physik. Chem., 14,
155.

BIBLIOGRAPHY 645

NBRNST, W. 1897 Die elektrolytische Zersetzung wassriger Losungen.

Ber., 30, 1546.
NERNST, W. 1916 Theoretical Chemistry. Trans, by H. T. Tizard.

London.
NERNST, W., AND WILSMORE 1900 tlber Elektrodenpotentiale. Z. Elek-

trochem., 7, 252.
NIESE, G. 1923 Apparat zur elektrolytischen Reindarstellung von Was-

serstoff. Physik. Z., 24, 12.
NICHOLS, H. J., AND WOOD, C. B. 1922 The production of CO2 by the

typhoid bacillus and the mechanism of the Russell double sugar

tube. II. Phenol red as an indicator. J. Infect. Dis., 30, 320.
NIKLAS, H., AND HOCK, A. 1924 Universal indicator for the colorimetric

determination of pH values in the examination of soils. Z.

Pflanzenernahr. Dungung 3A, 402.
NORTHROP, J. H. 1923 The stability of bacterial suspensions. J. Gen.

Physiol., 6, 605.
NORTHROP, J. H., AND DE KRIUF, P. H. 1922 The stability of bactericidal

suspensions. J. Gen. Physiol., 4, 629, 639, 655.
NOTES, A. A. 1910 Quantitative application of the theory of indicators

to volumetric analysis. J. Am. Chem. Soc., 32, 815.
NOTES, A. A. 1924 The inter-ionic attraction theory of ionized solutes.

I. Critical presentation of the theory. J. Am. Chem. Soc., 46,
1080.

NOTES, A. A. 1924 The inter-ionic attraction theory of ionized solutes.

II. Testing of the theory with experimental data. J. Am.
Chem. Soc., 46, 1098

NOTES, A. A., AND BAXTER, W. P. 1925 The inter-ionic attraction theory

of ionized solutes III. Testing of the theory in alcoholic solvents.

J. Am. Chem. Soc., 47, 2122.
NOTES, A. A., AND ELLIS, J. H. 1917 The free energy of hydrochloric

acid in aqueous solution. II. J. Am. Chem. Soc., 39, 2532.
NOTES, A. A., AND FREED, E. S. 1920 A thermodynamic investigation

of reactions involving silver sulfide and silver iodide. J. Am.

Chem. Soc., 42, 476.
NOTES, A. A., AND MAC!NNES, D. A. 1920 The ionization and activity of

largely ionized substances. J. Am. Chem. Soc., 42, 239.
NULL, F. E. 1926 Linear amplification of galvanometer deflection by the

photoelectric cell. J. Optical Soc. Am., 12, 520.
NTE, R. N. 1921 A modified McClendon direct reading potentiometer

for use at varying room temperatures. J. Med. Research, 42, 303.
NTE, R. N. 1924 A simplified hydrogen electrode vessel. J. Immunol.,

9, 207.

OAKES, E. T., AND SALISBURT, H. M. 1922 The use of phthalate solu-
tions for hydrogen electrode standards. J. Am. Chem. Soc.,

44, 948.

OAKLET, H. B. 1927 The action of alkalies on clay. J. Chem. Soc., 2819.
OBLATA, J. 1921 Low-voltage standard cells. Proc. Phys.-Math. Soc.

Japan, [3] 3, 64, 136 (cited).

646 THE DETERMINATION OF HYDROGEN IONS

ODEN, S. 1916 Die Humussauren und die Bodenaziditat. Inst. Mitt. f.
Bodenkunde, 6, 81.

OD£N, S. 1920 Zur Frage der Aziditat von Humusboden und deren
Bestimmung. Intern. Mitt. Bodenk., 9, 361.

ODEN, S. 1921 Application of physico-chemical methods to study of
humus. Trans. Faraday Soc., May 31 (cited).

OLSEN, A. G. 1927 The relation of temperature to hydrogen-ion con-
centration of buffer solutions. Science, 65, 477.

OLSEN, C. 1923 Studies on the hydrogen ion concentration of the soil
and its significance to the vegetation, especially to the natural
distribution of plants. Compt. rend. trav. lab. Carlsberg, 15,
No. 1.

OLSEN, C., AND LINDERSTR^M-LANG, K. 1927 On the accuracy of the
various methods of measuring concentration of hydrogen ions
in soil. Compt. rend. trav. lab. Carlsberg, 17, 1.

ONSAGER, L. See Faraday Society 1927.

OPPENHEIMER, C. 1924 — Die Fermente und ihre Wirkungen. 5th Edition,
Leipzig.

ORNDORFF, W. R., AND PURDY, A. C. 1926 Meta-cresolsulfonephthalein,
3-6-dimethylsulfonefluoran and some of their derivatives.
J. Am. Chem. Soc., 48, 2212.

ORNDORFF, W. R., AND SHERWOOD, F. W. 1923 Phenolsulfonephthalein
and some of its derivatives. J. Am. Chem. Soc., 45, 486.

OSTERHOUT, W. J. V. 1918 A method of studying respiration. J. Gen.
Physiol., 1, 17, 171; Bot. Gaz., 68, 60.

OSTERHOUT, W. J. V. 1922 Injury, Recovery and Death in Relation to
Conductivity and Permeability. Philadelphia.

OSTERHOUT, W. J. V., AND HAAS, A. R. C. 1918 A simple method of meas-
uring photosynthesis. Science, 47, 420.

OSTERHOUT, W. J. V., AND HAAS, A. R. C. 1918 On the dynamics of pho-
tosynthesis. J. Gen. Physiol., 1, 1.

OSTWALD-LUTHER. 1925 Hand-und Hilfsbuch zur Ausfuhrung physiko-
chemischer Messungen. (C. Drucker) Leipzig.

OSTWALD, W. 1891 Lehrbuch der allgemeinen Chemie, 1, 799.

OSTWALD, W. 1892 tlber die Farbe der lonen. Z. physik. Chem.,

9, 579.

OSTWALD, W. 1893 Die Dissociation des Wassers. Z. physik. Chem., 11,

521.
OSTWALD, W. 1900 tlber die absoluten Potentiale der Metalle nebst

Bemerkungen uber Normalelektroden. Z. physik. Chem., 35,

333.
OSTWALD, Wo. 1912 Kolloidchemie der Indikatoren. I. Kolloid Z,,

10, 97.

OSTWALD, Wo. 1926 Saureflockung von schwach solvatisierten Solen.
Kolloid-Z., 40, 201.

O'SULLIVAN, J. B. 1927 Behavior of the quinhydrone electrode in solu-
tions of neutral copper sulfate. Trans. Faraday Soc., 23, 52.

, BIBLIOGRAPHY 647

PAINE, H. S., AND BALCH, R. T. 1927 Some relations between hydrogen-
ion concentration and defecation of cane juice. Planter Sugar
Mfg., 78, 127, 148, 173; Sugar, 29, 206.

PAINE, H. J., AND KEANE, J. C. 1927 A study of cane juice defecation at
various pH values. Planter Sugar Mfr., 78, 168.

PALITZSCH, S. 1911 Sur le mesurage et la grandeur de la concentration
en ions hydrogene de 1'eau salee. Compt. rend. Lab. Carlsberg,
10, 85.

PALITZSCH, S. 1911 Uber die Messung und die Grosse der Wasserstoffion-
enkonzentration des Meerwassers. Biochem. Z., 37, 116.

PALITZSCH, S. 1911 Sur I'emploi du rouge de methyle au mesurage color-
imetrique de la concentration en ions hydrogene. Compt.
reno^ Lab. Carlsberg, 10, 162.

PALITZSCH, S. 1911 tlber die Verwendung von Methylrot bei der colori-
metrischen Messung der Wasserstoffionenkonzentration. Bio-
chem. Z., 37, 131.

PALITZSCH, S. 1912 Measurement of the hydrogen ion concentration of
sea water. Report on the Danish Oceanographical Expeditions
1908-09, 1, No. 6.

PALITZSCH, S. 1915 IJber die Anwendung von Borax und Borsaure-losun-
gen bei der colorimetrischen Messung der Wasserstoffionenkon-
zentration des Meerwassers. Biochem. Z., 70, 333.

PALITZSCH, S. 1916 Sur Pemploi de solutions de borax et d'acide borique
dans la determination colorimetrique de la concentration en ions
hydrogene de 1'eau de mer. Compt. rend. Lab. Carlsberg, 11, 199.

PALITZSCH, S. 1922 Manuel pratique de I'analyse de I'eau de mer. III.
Determination des ions hydrogene par la methode colorimetrique.
Bull. Inst. Oceanographique, No. 409, Monaco.

PALMAER, W. 1898 Uber die Wirkungsart der Tropfelektroden. Z.
physik. Chem., 25, 265.

PALMAER, W. 1907 Uber das absolute Potential der Kalomelelektrode.
Z. physik. Chem., 59, 129.

PALMER, W. W. 1926 The titration of organic acids in urine. J. Biol.
Chem., 68, 245.

PALMER, W. W., SALVESEN, H., AND JACKSON, H. 1920 Relationship
between the plasma bicarbonate and urinary acidity following
the administration of sodium bicarbonate. J. Biol. Chem., 45,
101.

PALMER, W. W., AND VAN SLYKE, D. D. 1917 Relationship between alkali
retention and alkali reserve in normal and pathological individ-
uals. J. Biol. Chem., 32, 499.

PANTIN, C. F. A. 1923 On the physiology of amoeboid movement. I.
J. Marine Biol. Assocn. United Kingdom, 13, 24.

PANTIN, C. F. A. 1923 The determination of pH of microscopic bodies.
Nature 111, 81.

PARKER, H. C. 1925 Potentiometric hydrogen-ion measurement with
non-gas electrodes. Ind. Eng. Chem., 17, 737.

648 THE DETERMINATION OF HYDROGEN IONS

PARKER, H. C. 1927 Progress of electrometric control methods in in-

d^ustry. Ind. Eng. Chem., 19, 660.
PARKER, H. C., AND BAYLIS, J. R. 1926 Recording the hydrogen ion

concentration of potable water. J. Am. Water Works Assoc.,

15, 22.
PARKER, H. C., AND DANNERTH, C. A. 1925 New calomel half-cells for

industrial hydrogen-ion measurements. Ind. Eng. Chem., 17,

637.
PARKER, H. C., AND GREER, W. N. 1926 Automatic hydrogen-ion control

of boiler feed water. J. Am. Water Works Assoc., 16, 602.
PARKER, H. C., AND GREER, W. N. 1926 Hydrogen ion control of nickel

plating baths with the quinhydrone electrode. Trans. Am.

Electrochem. Soc., 49, 451.
PARSONS, L. B., AND DOUGLAS, W. F. 1926 The influence of sodium

chloride on the colorimetric determination of pH. J. Bact.,

12, 263.
PARSONS, N. M. 1924 Electric measurement of available acidity (pH)

and its applications in English brewing. J. Inst. Brewing, 30, 30.

PATTEN, H. E., JOHNSON, A. J., AND MAINS, G. H. 1918 A study of the

.electrical conductance of aqueous phthalate solutions. J. Am.

Chem. Soc., 40, 1156.
PATTEN, H. E., AND MAINS, G. H. 1917 An apparatus for the purification

of mercury. J. Ind. Eng. Chem., 9, 600.
PAUL, T. 1914 Uber den gegenwartigen Stand der chemischen Unter-

suchung des Weins. Z. Untersuch. Nahr. Genussm., 28, 509.
PAUL, T. 1924 Die Bestimmung der zweiten Dissoziationskonstanten

zweibasischer Sauren, insbesondere der Weinsaure. Z. physik.

Chem., 110, 417.
PAULI, W. 1903 Untersuchungen uber physikalische Zustandsanderun-

gen der Kolloide. II. Verbal ten der Eiweisskorper gegen Elek-

trolyten. Beitr. chem. Physiol. Path., 3, 225.
PAULI, W. 1920 Kolloid-Chemie der Eiweisskorper. I. Halfte. Dresden,

Leipzig.
PAULI, W. 1921 The general structure of colloids. Trans. Faraday Soc.,

16,1.

PAULI, W. 1926 Eiweisskorper und Sauren. Kolloid-Z., 40, 185.
PAULUS, M. G., HUTCHINSON, J. F., AND JONES, H. C. 1915 Radiometric

measurements of the ionization constants of indicators (2). J.

Am. Chem. Soc., 37, 1694.

PELLING, A. J. 1925 The hydrolysis of aluminum sulfate — an applica-
tion of the quinhydrone electrode. J. Chem. Met. Mining

Soc. S. Africa, 26, 88 (cited).
PENNYCUICK, S. W., AND BEST, R. J. 1926 The electrolytic preparation

of calomel for use in the calomel electrode. Australian J.

Exptl. Biol. Med. Sci., 3, 173 (cited).
PERKINS, H. Z. E. 1923 Hydrogen-ion determination as a method of

refinery control. Ind. Eng. Chem., 15, 623.

BIBLIOGRAPHY 649

PERLZWEIG, W. A. See Michaelis and Perlzweig, 1926.

PETERS, R. 1898 Ueber oxydations- und Reduktions-ketten und den

Einfluss komplexer lonen auf ihre elektromotorische Kraft. Z.

physik. Chem., 26, 193.
PFEIFFER, H. 1925 Uber die Wasserstoffionenkonzentration [H'] als

Determinationsfaktor physiologischer Gewebegeschehen in der

sekundaren Rinde der Pflanzen. New Phytologist, 24, 65.
PFEIFFER, H. 1926 Eine Methode zur kolorimetrischen Bestimmung

der Wasserstoffionenkonzentration in pflanzlichen Gewebeschnit-

ten ohne Anwendung von Moderatoren. Z. wiss. Mikroskop.,

42, 396.
PFEIFFER, H. 1927 Der gegenwartige Stand der kolorimetrischen

Azidimetrie in der Gewebephysiologie. Protoplasma, 1, 434.
PFEIFFER, H. 1927 Beitrage zur physiko-chemischen Analyse desTurgor-

Mechanismus in pflanzlichen Trennungszellen. Protoplasma,

2, 206.
PINCUSSEN, L. 1927 Methodische Mitteilungen. VII. Biochem. Z.,

186, 28.
PINKHOF, J. 1919 Over de Toepassing der elektrometrische Titraties.

(On the applications of electrometric titrations.) Chem. Week-

blad, 16, 1162.

PINKHOF, J. 1919 De Bepaling van den Waterstof-exponent. (The de-
termination of the hydrogen ion exponent.) Chem. Weekblad,

16, 1168.
PLANCK, M. 1890 Ueber die Potentialdifferenz zwischen zwei verdiinnten

Losungen binarer Electrolyte. Ann. Physik. Chem., 40, 561.
Plant Research Lab., (Lehn and Fink.) 1925 A study of the influence

of the pH concentration (sic.) upon the stability of digitalis

infusion and potassium citrate mixtures. Am. J. Pharm., 97,

456.
PLEIJEL, H. 1910 Die Potentialdifferenz zwischen zwei elektrolytischen

Losungen. Z. physik. Chem., 72, 1.
POMA, G. 1914 Neutralsalzwirkung und Zustand der lonen in Losung.

Z. physik. Chem., 83, 671.
PONSELLE, A. 1919 Precede simple de neutralization de Peau distillSe

destinee aux colorations derivees de la methode de Romanowsky.

Compt. rend. soc. biol., 82, 1328.
POPE, C. G., AND GOWLETT, F. W. 1927 A direct-reading hydrogen-ion

meter. J. Sci. Instruments, 4, 380.

POPOFF, S. 1927 Quantitative analysis. 2nd ed. Blakiston, Phila-
delphia.
POPOFF, S., AND McHENRY, M. J. 1925 A simple and rapid electrometric

determination of alkaloids without the use of hydrogen elec-
trode. J. Am. Pharm. Assoc., 14, 473.
PORTER, A. W. 1921 Electric endosmosis and cataphoresis. Trans.

Faraday Soc., 16, 134.

650 THE DETERMINATION OF HYDROGEN IONS

PORTER, A. W. 1924 The standardization of the sign of electric poten-
tial. Trans. Faraday Soc., 19, 703.

POWERS, E. B. 1921 The variation of the condition of sea-water, es-
pecially the hydrogen ion concentration, and its relation to
marine organisms. Pub.-Puget Sound Biol. Sta., 2, 369.

POWERS, E. B. 1922 The physiology of the respiration of fishes in rela-
tion to the hydrogen ion concentration of the medium. J.
Gen. Physiol., 4, 305.

PRA"T, S. 1926 Wasserstoffionenkonzentration und Plasmolyse. Kolloid-
Z., 40, 248.

PRIDEAUX, E. B. R. 1911 The sodium phosphate standards of acidity.
Biochem. J., 6, 122.

PRIDEAUX, E. B. R. 1911 The second and third dissociation constants of
orthophosphoric acid. J. Chem. Soc., 99, 1224.

PRIDEAUX, E. B. R. 1914 Diffusion and membrane potentials. Trans.
Faraday Soc., 10, 160; also in Chem. News, 109, 291.

PRIDEAUX, E. B. R. 1915 General equations for the neutralization of di-
basic acids and their use to calculate the acidity of dilute car-
bonate solutions. Proc. Roy. Soc. (A), 91, 535.

PRIDEAUX, E. B. R. 1916 On the use of partly neutralized mixtures of
acids as hydrion regulators. Proc. Roy. Soc. (A), 92, 463.

PRIDEAUX, E. B. R. 1917 The Theory and Use of Indicators. An Account
of the Chemical Equilibria of Acids, Alkalies and Indicators in
Aqueous Solution, with Applications. London.

PRIDEAUX, E. B. R. 1919 The effect of sea salt on the pressure of carbon
dioxide and alkalinity of natural waters. J. Chem. Soc., 115,
1223.

PRIDEAUX, E. B. R. 1923 The theory of acid-alkali solution equilibrium
as applied to salts of moderately strong but sparingly soluble
acids. J. Chem. Soc., 123, 1624.

PRIDEAUX, E. B. R. 1924r-1925 The measurement of hydrogen-ion con-
centration. J. Sci. Instruments, 2, 33, 113.

PRIDEAUX, E. B. R. 1926 The spectrophotometric examination of dyes
and indicators. Chemistry Industry, 45, 664, 678.

PRIDEAUX, E. B. R., AND CROOKS, W. E. 1924 The diffusion potentials
and ionic mobilities of benzoates and salicylates and their
modification by a membrane of parchment paper. Trans.
Faraday Soc., 20, 37.

PRIDEAUX, E. B. R., AND GILBERT, F. L. 1927 The application of the
hydrogen electrode to organic bases. J. Chem. Soc., 2164.

PRIDEAUX, E.B.R., AND NUNN, G.R. 1924 The colorimetric dissociation
constants of the mono- and di-nitro quinols. J. Chem. Soc.,
125, 2110.

PRIDEAUX, E. B. R., AND WARD, A. T. 1924 The dissociation constants
of phosphoric acid. J. Chem. Soc., 125, 423.

PRIDEAUX, E. B. R., AND WARD, A. T. 1924 Calculations on the neu-
tralization of mixtures of acids, and a universal buffer mixture.
J. Chem. Soc., 125, 426.

BIBLIOGRAPHY 651

PBING, J. N. 1924 Determination of the affinity constants of bases by
the hydrogen and quinhydrone electrodes. Trans. Faraday
Soc., 19, 705.

PRINGSHEIM, P. 1923 Fluoreszenz und Phosphoreszenz im Lichte der
neuren Atomtheorie. 2d. Aufl. (Springer) Berlin.

PRUTHI, H. S. 1927 On the hydrogen-ion concentration of hay infusions,
with special reference to its influence on the protozoan sequence.
Brit. J. Exptl. BioL, 4, 292.

RABINOWITSCH, A. J., AND KARGIN, V. A. 1927 tTber Anwendung der
Chinhydronelektrode bei elektrometrischen Titrationen. Z.
Elektrochem., 33, 11.

RADSIMOWSKA, W. 1924 Eine Ansatzelektrode zur pH-Bestimmung in
festen Nahrboden. Biochem. Z., 154, 49.

RAMAGE, W. D., AND MILLER, R. C. 1925 The salt error of cresol red.
J. Am. Chem. Soc., 47, 1230.

RANDALL, M. 1927 See Faraday Society 1927.

RANDALL, M., AND FAILEY, C. F. 1927 The activity coefficient of gases
in aqueous salt solutions. Chem. Rev., 4, 271.

RANDALL, M., AND VANSELOW, A. P. 1924 The activity coefficients of
dilute aqueous solutions of hydrogen chloride, thallous chloride
and lead nitrate. J. Am. Chem. Soc., 46, 2418.

RANDALL, M., AND YOUNG, L. E. 1928 The calomel and silver chloride
electrodes in acid and neutral solutions. The activity coeffi-
cient of aqueous hydrochloric acid and the single potential of
the deci-molal calomel electrode. J. Am. Chem. Soc., 60, 989.

RANDOLPH, D. W., AND DONNENWIRTH, A. L. 1926 Hydrogen-ion meas-
urements on clay slips. J. Am. Ceram. Soc., 9, 541.

RASMUSSEN, H. B., AND SCHOU, S. A. 1924 Zur Titration von Alkaloiden.
Pharm. Zentr., 65, 729.

RAWLINGS, S. O. 1926 Photo. J., 66, 495 (cited).

RAWLINGS, S. O. 1926 An electrode vessel jacketed for work at various
temperatures. Chemistry Industry, 45, 73.

REA, M. W., AND SMALL, J. 1927 The hydrion concentration of plant
tissues. Protoplasma, 2, 45.

REBELLO, S. 1922 Le controle de la "reaction actuelle" des tissus an-
imaux par les fils-indicateurs. Une me'thode pour le diagnostic
de la mort. Arch, intern, pharmacodynamie, 26, 395.

REDMAN, T., WILLIMOTT, S. G., AND WOKES, F. 1927 The pH of the
gastrointestinal tract of certain rodents used in feeding experi-
mentSj and its possible significance in rickets. Biochem. J.,
21, 589.

REED, G., AND MACLEOD, D. J. 1924 The motility of bacteria as affected
by the hydrogen-ion concentration. J. Bact., 9, 119.

REED, G., AND ORR, J. H. 1923 The influence of hydrogen-ion concen-
tration upon structure. I. Hemophilis influenzae. J. Bact.,
8, 103.

REHBERG, P. B. 1925 A method of micro titration. Biochem. J., 19, 270.

652 THE DETERMINATION OF HYDROGEN IONS

REICHINSTEIN, D. 1924 Der Mechanismus der Ausbildung einer Poten-

tialdifferenz an der Grenze zweier Phasen. Z. Elektrochem.,

30, 239.
REIMANN, S. P. 1926 The photoelectric cell as a colorimeter. Proc.

Soc. Exptl. Biol. Med., 23, 520.

REISS, P. 1925 Le pH interieur cellulaire. Paris (cited).
REISS, P. 1926 La reduction des indicateurs comme cause d'erreur des

mesures colorimetriques du pH. Compt. rend. soc. biol., 94,

289
Report of O. S. A. Progress Committee for 1922-23 (1925) Spectrophoto-

metry. J. Optical Soc., 10, 169.
RHODE, H., AND SAITO, Y. 1923 tJber die Herstellung einer physiolo-

gischen Salzlosung von verschiedener CH fur Warm- und Kalt-

bliiter. Z. ges. exptl. Med., 38, 503.
RICE, F. E., AND RIDER, A. J. 1923 Simplified apparatus and technique

for the electrometric determination of H-ion concentration in

milk and other biological liquids. N. Y. Cornell Sta. Mem., 66.

Exp. Sta. Record, 49, 712.
RICHARDS, T. W. 1897 tJber den Temperaturkoemzienten des Potentials

der Kalomelektrode mit verschiedenen gelosten Elektrolyten.

Z. physik. Chem., 24, 39.
RICHARDS, T. W., AND ARCHIBALD, E.H. 1902 Die Zersetzung von Queck-

silberchloriir durch geloste Chlorid. Z. physik. Chem., 40, 385.
RICHTER, A. 1924 Massanalytische Studien iiber den Einfluss von Salz-

und Alkoholgegenwart sowie Temperaturveranderung auf das

Umschlagsgebiet einiger Indikatoren und die Ausschaltung der

hierdurch bedingten Abweichungen bei acidimetrischen Titra-

tionen. Z. anal. Chem., 65, 209.
RICHTER, A. F. 1926 Beitrag zur Begriindung der Ausdriiche r(n) and

r(p) von D. Giribaldo. Biochem. Z., 174, 271.
RIDEAL, E. K. 1924 The mechanism of the reversible electrode. Trans.

Faraday Soc., 19, 667.

RIDEAL, E. K. 1926 An Introduction to Surface Chemistry. Cambridge.
RIFFART, K. 1922 Die Triketonhydrindenhydrat (Ninhydrin)— Reaktion

als quantitative kolorimetrische Bestimmungsmethode des

Ammosaurenstickstoffes. Biochem. Z., 131, 78.
RINGER, W. E. 1909 De waterstofionenconcentratie in verdunde oplos-

singen van phosphorzuur, mono- en dinatriumphosphaat. Chem.

Weekblad, 6, 446.
Risen, C. 1924 Eine titrimetrische Bestimmung der Wasserstoffionen-

Jionzentration. Biochem. Z., 148, 147.

ROAF, H. E. 1913 The liberation of ions and the oxygen tension of tis-
sues during activity. Proc. Roy. Soc. B., 86, 215.
ROAF, H. E. 1914 The time relations of acid production in muscle during

contraction. J. Physiol., 48, 380.

ROBBINS, W. J. 1926 The isoelectric point for plant tissue and its im-
portance in absorption and toxicity. Univ. Missouri Studies,

1, 1.

BIBLIOGKAPHY 653

ROBERTS, E. J., AND FENWICK, F. 1927 A simple type of flowing junction.

J. Am. Chem. Soc., 49, 2787.
ROBINSON, C. S. 1923 Neutral solution of ammonium citrate. J. Assoc.

Official Agr. Chem., 6, 384.
ROBINSON, C. S. 1925 The use of the quinhydrone electrode for the

determination of the hydrion concentration of feces. J. Biol.

Chem., 66, 811.
ROBL, R. 1926 Umbelliferon als fluorescierender Indicator. Ber., 59,

1725.
ROCKWOOD, R. 1925 Physichochemical aspects of hemolysis. IV. The

relation of the acidity of phosphate buffers to biologic hemoly-
sis. J. Immunol., 10, 741.
RODEBUSH, W. H. 1927 Thermal equilibrium of electrons in metals.

Contact potentials and thermoelectric force. Chem. Rev., 4,

255.

ROGERS, C. G. 1927 Textbook of Comparative Physiology. New York.
ROGERS, L. A., associates of, 1928 Fundamentals of Dairy Science.

New York.
ROGERS, L. A., DEYSHER, E. F., AND EVANS, F. R. 1921 The relation of

acidity to the coagulation temperature of evaporated milk.

J. Dairy Sci., 4, 294.
ROHDE, K. 1917 Untersuchungen iiber den Einfluss cter freien H-Ionen

im Innern lebender Zellen auf den Vorgang der vitalen Farbung.

Arch. ges. Physiol., 168, 411.
ROHDE, K. 1920 Zur Physiologic der Aufnahme und Ausscheidung

saurer und basischer Farbsalze durch die Nieren. Archiv. ges.

Physiol. (Pfliiger's), 182, 114.
RONA, P. 1926 Praktikum d. Physiologischen Chemie, in 3 vols. Vol. I.

Fermentmethoden. J. Springer, Berlin.
R0RDAM, H. N. K. 1925 Studies on activity. K0benhavn.
ROSE, M. 1924 Action du pH exterieur sur le phototropisme des Cope-

podes pelagiques marins. Arch. phys. biol., 3, 33.
ROSENSTEIN, L. 1912 The ionization constant of phenolphthalein and

the effect upon it of neutral salts. J. Am. Chem. Soc., 34, 1117.
Ross, W. H., JONES, R. M., AND DURGIN, C. B. 1925 The purification of

phosphoric acid by crystallization. Ind. Eng. Chem., 17, 1081.
ROSSEE, AND v. MORGENSTERN 1927 Ein vcreinfachtes colorim-

etrisches Verfahren nach Dr Todt zur Messung der Wasser-

stoffionenkonzentration geringer Mengen stark gefarbter oder

triiber Losungen. Chem. Z., 51, 302.
Rous, P. 1925 Relative reaction within living mammalian tissues.

J. Exptl. Med., 41, 399, 739; 45, 41.
ROWE, F. M. 1924 Colour Index, Society of Dyers and Colourists,

Bradford.
RUDNICK, P. 1921 The preparation of chloroplatinic acid by means

of hydrogen peroxide. J. Am. Chem. Soc., 43, 2575.

654 THE DETEKMINATION OF HYDKOGEN IONS

RUHLAND, W. 1923 tlber die Verwendbarkeit vitaler Indikatoren zur

Ermittlung der Plasmareaktion. Ber. deut. botan. Ges., 41, 252.
RTJNGE, H., AND SCHMIDT, O. 1926 Ueber die Verwendbarkeit der Chin-
hydro nelekt rode fiir die Messung der aktuellen Blutreaktion.

Deut. med. Wochschr., 62, 2077.
RUPP, E. 1915 Ueber das Methylrot und verwandte Azokombinationen.

Arch. Pharm., 253, 3.67.
RUPP, E., AND LOOSE, R. 1908 Uber einen alkalihochempfindlichen, zur

Titration mit Hundertstelnormallosungen geeigneten Indicator.

Ber., 41, 3905.
R CJPPEL, W. G. 1920 Das Verhalten von Eiweiss und Antitoxin gegeniiber

dem elektrischen Strom und die Isolierung von reinem anti-

toxischen Eiweiss aus Diphtherieserum auf elektro-osmotischem

Wege. Ber. pharm. Ges., 30, 314.
SACHER, J. F. 1910 tJber einen sehr empfindlichen Indicator. Chem. Z.,

34, 1192.
SACHS, A. P. 1927 Hydrogen-ion control and measurement and its

application to the textile industry. Textile Colorist, 49, 92

(cited).
SAKAMURA, T. 1924 tlber die Kultur von Aspergillus niger mit besonderer

Riicksicht auf das Puffervermogen der Nahrlosung. J. Coll.

Agr., Hokkaido Imp. Univ., 14, 65.
SALESSKY, W. 1904 tlber Indikatoren der Acidimetrie und Alkalimetrie.

Z. Elektrochem., 10, 204.
SALM, E. 1904 Die Bestimmung des H'-Gehaltes einer Losung mit Hilfe

von Indikatoren. Z. Elektrochem., 10, 341.
SALM, E. 1906 Kolorimetrische Affinitatsmessungen. Z. Elektrochem.,

12, 99.

SALM, E. 1906 Studie iiber Indikatoren. Z. physik. Chem., 57, 471.
SALM, E. 1908 Messungen der Affinitatsgrossen organischer Sauren mit

Hilfe von Indikatoren. Z. physik. Chem., 63, 83.
SALM, E., AND FRIEDENTHAL, H. 1907 Zur Kenntnis der acidimetrischen

und alkalimetrischen Indikatoren. Z. Elektrochem., 13, 125.
ST. JOHNSON, J. H., AND PEARD, G. T. 1926 The surface tension of

gelatine solutions. Biochem. J., 20, 816.
SAND, H. J. S., AND LAW, D. J. 1911 The employment of the electrometric

method for the estimation of the acidity of tan liquors. I.

J. Soc. Chem. Ind., 30, 3.
SANNIE, G. 1924 Description d'une electrode a hydrogene pour la

mesure du pH sur de petites quantites de liquides biologiques.

Compt. rend. soc. biol., 90, 84.

SARTORY, A., SARTORY, R., AND MEYER, J. 1927 fitude de la concen-
tration optima en ions H des milieux dans la culture de quelques

champignons inferieurs. Bull. sci. pharmacol., 34, 74.
SAUER, L. 1904 Bezugselektroden. Z. physik. Chem., 47, 146.
SAUNDERS, J. T. 1921 A note on the hydrogen ion concentration of some

natural waters. Proc. Cambridge Phil. Soc., 20, 350.

BIBLIOGRAPHY 655

SAUNDERS, J. T. 1923 The determination of the salt error of indicators
and the accurate estimation of the pH of solutions by colori-
metric methods. Proc. Cambridge Phil. Soc., Biol. Sci., 1, 30.

SAUNDERS, J. T. 1923 The measurement of the carbon dioxide output
of fresh water animals by means of indicators. Proc. Cambridge
Phil. Soc., Biol. Sci., 1, 43.

SAUNDERS, J. T. 1924 The effect of the hydrogen ion concentration on
the behavior, growth and occurrence of spirostomum. Proc.
Cambridge Phil. Soc., 1, 189.

SAYLOR, C. H. 1928 Adsorption and Crystal Form. Colloid Symposium
Monograph, 6, 49.

SCATCHARD, G. 1921 The speed of reaction in concentrated solutions;
and the mechanism of the inversion of sucrose. J. Am. Chem.
Soc., 43, 2387.

SCATCHARD, G. 1923 Electromotive force measurements with a saturated
potassium chloride bridge or with concentration cells with a
liquid junction. J. Am. Chem. Soc., 46, 1716.

SCATCHARD, G. 1925 The activities of strong electrolytes. I. The
activity of hydrochloric acid derived from the electromotive
force of hydrogen-silver chloride cells. J. Am. Chem. Soc.,
47, 641.

SCATCHARD, G. 1925 The activities of strong electrolytes. II. A re-
vision of the activity coefficients of potassium, sodium and
lithium chlorides and potassium hydroxide. J. Am. Chem. Soc.,
47, 648.

SCATCHARD, G. 1925 The activities of strong electrolytes. III. The use
of the flowing junction to study the liquid-junction potential
between dilute hydrochloric acid and potassium chloride solu-
tions; and the revision of some single electrode potentials. J.
Am. Chem. Soc., 47, 696.

SCATCHARD, G. 1925 The activity of strong electrolytes. IV. The appli-
cation of the Debye-Hiickel equation to alcoholic solutions.
J. Am. Chem. Soc., 47, 2098.

SCATCHARD, G. 1926 Electromotive-force measurements in aqueous
solutions of hydrochloric acid containing sucrose. J. Am. Chem.
Soc., 48, 2026.

SCATCHARD, G. 1926 The unimolecularity of the inversion process. J.
Am. Chem. Soc., 48, 2259.

SCATCHARD, G. 1927 The interaction of electrolytes with non«-electro-
lytes. Chem. Rev., 3, 383.

SCHADE, H., NEUKIRCH, P., AND HALPERT, A. 1921 tlber lokale Acidosen
des Gewebes und die Methodik ihre intravitalen Messung,
zugleich ein Beitrag zur Lehre der Entziindung. Z. ges. exptl.
Med., 24, 11.

SCHAEFER, R. 1926 Die Messung der aktuellen Reaktion des Kapil-
larblutes mittels Chinhydronelektrode. Biochem. Z., 167, 433.

SCHAEFER, R., AND SCHMIDT, F. 1925 Die Chinhydronelektrode bei klin-
ischen pH-Messungen. Biochem. Z., 166, 63.

656 THE DETERMINATION OF HYDROGEN IONS

SCHEITZ, P. 1910 tiber das Azolitmin des Handels. Z. analyt. Chem.,

49, 735.
SCHLEGEL, J. W., AND STUBBED A. H. 1927 Some sources of error in the

colorimetric determination of pH values. Ind. Eng. Chem.,

19, 631.
SCHILLER, H. 1924 tiber die elektromotorischen Eigenschaften der

Glaser. Ann. Physik [4], 74, 105.

SCHMID, A. 1924 Die Diffusionsgaselektrode. Helv. Chim. Acta, 7, 370.
SCHMIDT, C. L. A. 1916 Changes in the H+ and OH~ concentration

which take place in the formation of certain protein compounds.

J. Biol. Chem., 25, 63.

SCHMIDT, C. L. A., AND FINGER, C. P. 1908 Potential of a hydrogen elec-
trode in acid and alkaline borate solutions. J. Phys. Chem.,

12, 406.
SCHMIDT, F. 1925 Die Verwendbarkeit der Chinhydronelektrode zur

Bestimmung der Wasserstoffionenkonzentration in den Nahr-
• boden. Centr. Bakt., Parasitenk. I Abt., Orig., 96, 262.
SCHMIDTMANN, M. 1924 Uber eine Methode zur Bestimmung der Was-

serstoffzahl im Gewebe und in einzelnen Zellen. Biochem. Z.,

150, 253.
SCHMITT, W. 1926 Eine neue Wasserstoffelektrode zur Messung kohlen-

saurehaltiger Korperfliissigkeiten, insbesondere des Liquors.

Biochem. Z., 170, 391.
SCHMITZ, H. 1919 Studies in the physiology of the fungi. VI. The

relation of bacteria to cellulose fermentation induced by fungi,

with special reference to the decay of wood. Ann. Missouri

Botan. Gardens, 6 (cited).
SCHOCH, E. P. 1910 The potential of the oxygen electrode. J. Phys.

Chem., 14, 665.

SCHOFIELD, R. K. 1926 An experimental verification of Gibb's adsorp-
tion equation by observing the adsorption by mercury of its

own ions from solution, and its bearing on Nernst's theory of

electrode potential. Phil. Mag. [7], 1, 641.
SCHOLLENBERGER, C. J. 1925 An improved calomel electrode. J. Ind.

Eng. Chem., 17, 649.
SCHORGER, A. W. 1923 Preparation of methyl red. J. Ind. Eng. Chem.,

15, 742.
SCHREINER, E. 1921 Der Dissoziationszustand der Essigsaure in Was-

ser und in Salzlosungen. Z. anorg. allgem. Chem., 115, 181.
SCHREINER, E. 1922 Die Hydration des Wasserstoffions. Z. anorg.

allgem. Chem., 121, 321.
SCHREINER, E. 1922 Der Dissoziationszustand von mittelstarken Sauren,

besonders der Dichloressigsaure, in Wasser und in Salzlosungen.

Z. anorg. allgem. Chem., 122, 201.
SCHREINER, E. 1924 Der Dissoziationszustand von Sauren in Alkoholen.

Z. physik. Chem., Ill, 419.
SCHREINER, E. 1924 Zur Hydration einwertiger lonen. Z. anorg.

allgem. Chem., 135, 333.

BIBLIOGEAPHY 657

SCHREINER, E. 1925 Thermo dynamik der Chinhydronelektroden die
chemische Konstante des Wasserstoffs. Z. physik. Chem.,
117, 57.

SCHREINER, E., AND FRIVOLD, O. E. 1926 Cryoscopic measurements of
very dilute solutions of strong electrolytes in cyclohexanol for
verification of the osmotic theory of Debye and Hiickel. Z.
physik. Chem., 124, 1 (cited).

SCHULTZ, G. 1914 Farbstofftabellen. 5th edition. Berlin.

SCHUHMANN, R. 1924 The free energy of antimony trioxide and the re-
reduction potential of antimony. J. Am. Chem. Soc., 46, 52.

SCHWARZ, C. et al. 1924 Beitrage zur Physiologic der Verdauung. Arch,
ges. Physiol. (Pfluger's), 202, 475, 478, 488.

SCOTT, I. T. 1924 The influence of hydrogen-ion concentration on the
growth of Ausarium hycopersici and on tomato wilt. Univ.
Missouri Agr. Exptl. Sta. Res. Bull. 64.

SCUDDER, H. 1914 The Electrical Conductivity and lonization Constants of
Organic Compounds. New York.

SENDROY, J., JR., AND HASTINGS, A. B. 1927 Studies of the solubility of
calcium salts. II. The solubility of tertiary calcium phosphate
in salt solutions and biological fluids. J. Biol. Chem., 71, 783.

SENDROY, J., JR., AND HASTINGS, A. B. 1927 Studies of the solubility
of calcium salts. III. The solubility of calcium carbonate and
tertiary calcium phosphate under various conditions. J. Biol.
Chem., 71, 797.

SHACKELL, L. F. 1923 Dye-protein aggregates. I. Congo fibrin. J.
Biol. Chem., 66, 887.

SHAEFPER, E. J., PAULUS, M. G., AND JONES, H. C. 1915 Radiometric
measurements of the ionization constants of indicators. J. Am.
Chem. Soc., 37, 776.

SHAFFER, L. W. 1924 The effect of hydrogen-ion concentration on the
precipitation of colloidal benzoin and gold solutions by cerebro-
spinal fluid. J. Lab. Clin. Med., 9, 757.

SHAPIRO, N. N. 1927 The cycle of hydrogen ion concentration in the
food vacuoles of paramecium, vorticella and stylomychia. Trans.
Am. Micro. Soc., 46, 45.

SHARP, P. F., AND MACDOUGALL, F. H. 1922 A simple method of electro-
metric titration in acidimetry and alkalimetry. J. Am. Chem.
Soc., 44, 1193.

SHARP, P. F., AND MC!NERNEY, T. J. 1926 The colorimetric determina-
tion of the hydrogen ion concentration of milk, whey and cream.
J. Biol. Chem., 70, 729.

SHARP, P. F., AND WHITAKER, R. 1927 The relation of the hydrogen-ion
concentration of egg white to its germicidal action. J. Bact.,
14, 17.

SHAW, M. B. 1925 Hydrogen-ion concentration in the paper mill. Paper
Trade J., 81, 59.

SHELFORD, V. E. 1925 The hydrogen ion concentration of certain western
American inland waters. Ecology, 6, 279.

658 THE DETERMINATION OF HYDROGEN IONS

SHELFORD, V. E., AND POWERS, E. B. 1915 An experimental study of

the movements of herring and other marine fishes. Biol. Bull.

28, 315 (cited).
SHEPHERD, M., AND LEDIG, P. G. 1927 Rubber stopcock lubricants for

high vacuum and other uses. Ind. Eng. Chem., 19, 1059.
SHEPPARD, S. E. 1925 Photographic Sensitivity. Colloid Symposium

Monograph, 3, 76.
SHEPPARD, S. E., AND ELLIOTT, F. A. 1922 The potentials of silver:

Silver halide — halide electrodes in light. Part I. Science, 56,

578.
SHEPPARD, S. E., AND ELLIOTT, F. A. 1923 Knowns and unknowns in

the theory of development. Trans. Faraday Soc., 19, 355.
SHEPPARD, S. E., ELLIOTT, F. A., AND SWEET, S. S. 1923 Notes on the

photographic 'chemistry of gelatin. Trans. Faraday Soc., 19,

261.
SHEPPARD, S. E., ELLIOTT, F. A., AND SWEET, S. S. 1923 Chemistry of

the acid fixing bath. J. Franklin Inst., 196, 45.
SHEPPE, W. M., AND CONSTABLE, M. G. 1923 An unsuspected source of

error in the gram stain. J. Lab. Clin. Med., 8, 757.

SHERMAN, H. C., AND BURTON, G. W. 1926 Effect of hydrogen-ion con-
centration upon the rate of destruction of vitamin B upon

heating. J. Biol. Chem., 70, 639.
SHERRILL, M. S., AND NOTES, A. A. 1926 The inter-ionic attraction

theory of ionized solutes. VI. The ionization and ionization

constants of moderately ionized acids. J. Am. Chem. Soc.; 48,

1861.
SHOHL, A. T. 1920 Determination of the acidity of gastric contents.

I. Johns Hopkins Hosp. Bull., 31, 151.
SHOHL, A. T. AND DEMING, C. L. 1921 Hexamethylenetetramine: its

quantitative factors in therapy. J. Urol., 4, 419.

SHOHL, A. T., AND KING, J. H. 1920 Determination of the acidity of
"gastric contents. II. The colorimetric determination of free

hydrochloric acid. Johns Hopkins Hosp. Bull., 31, 158. III.

Combined acidity and buffer value. Ibid., 162.
SIDERIS, C. P. 1925 The role of the hydrogen-ion concentration on the

development of pigment in Fusaria. J. Agr. Res., 30, 1011.
SIEGLER-SORU, E. 1927 Le spectre ultra-violet de 1'acide nitrique et des

nitrates en fonction du pH. Arch. phys. biol., 5, 237.
SIMMS, H. S. 1923 A water-jacketed hydrogen electrode. J. Am. Chem.

Soc., 45, 2503.
SIMMS, H. S. 1926 Dissociation of multivalent substances. J. Am.

Chem. Soc., 48, 1239, 1251.
SIMMS, H. S., AND LEVENE, P. A. 1926 Graphical interpretation of

electrometric titration data by use of comparison curves. J.

Biol. Chem., 70, 319.
SIMON, L-J. 1925 Neutralisation viscosimetrique des monoacides par les

alcalis. Compt. rend., 180, 1169.

BIBLIOGRAPHY 659

SIVE, B. J., AND JONES, L. W. 1915 Private communication on mono-

methylred.
SJOSTROM, O. A. 1922 The determination of the pH value of commercial

glucose as a substitute for the candy test. J. Ind. Eng. Chem.,

14, 94.
SLAGLE, E. A., AND AGREE, S. F. 1921 A simplified hydrogen electrode

potentiometer outfit. Abstracts Bact., 5, 5 (proc.).

SMALE, F. J. 1894 Studien iiber Gasketten. Z. physik. Chem., 14, 577.
SMALL, J. 1926 The hydrion concentration of plant tissues. Proto-

plasma, 1, 324.

SMITH, D. P. 1921 Experiments on the electrical conduction of a hydro-
gen alloy. Proc. Nat. Acad. Sci., 7, 28.
SMITH, H. W. 1922 The biochemical differentiation of bacteria. Am. J.

Hyg., 2, 607.
SMITH, H. W. 1925 Action of acids on cell division with reference to

permeability to anions. Am. J. Physiol., 72, 347.
SMITH, R. B., AND GIESY, P. M. 1923 The titration of ferric chloride with

sodium hydroxide, using the oxygen electrode, a proof of the

non-existence of iron oxychloride. J. Am. Pharm. Assocn., 12,

855.
SMITH, W. A. 1896 Zu O. F. Towers " Studien uber Superoxyd-Elek-

troden." Z. physik. Chem., 21, 93.

SMITS, A. 1921 Die Theorie der Allotropie. Barth, Leipzig.
SMITS, A., AND ATEN, A. H. W. 1916 Die Anwendung der Theorie der

Allotropie auf elektromotorische Gleichgewichte. III. Z.

physik. Chem., 92, 1.
SMOLIK, L. 1926 Eine neue E*lektrode zur H-Ionenbestimmung mit

Chinhydron. Biochem. Z., 172, 171.

SNYDER, E. F. 1927 A comparative study of the quinhydrone and hy-
drogen electrodes for determining the hydrogen-ion concentra-
tion of soils. J. Agr. Research, 35, 825.
SOBOTKA, H., AND FRiEDLANDER, M. 1928 Precipitin reaction of anti-

pneumococcus sera. J. Exptl. Med., 47, 57.
SOHON, M. D. 1898 An investigation of some derivatives of orthosulpho-

benzoic anhydride. Am. Chem. J., 20, 257.
SOLOWIEW, B. 1926 Eine Multimikroelektrode zu gleichzeitiger pH-

Bestimmung in vielen und verschieden Objekten. Biochem.

Z., 167, 54.
SONDEN, K. 1921 Zur Anwendung Gefarbter Glaser statt Flussigkeiten

bei kolorimetrischen Untersuchungen. Arkiv kemi, Mineral.

Geol. 8, no. 7.
S0RENSEN, S. P. L. 1909 Etudes enzymatiques; II. Sur la mesure et

1'importance de la concentration des ions hydrogene dans les

reactions enzymatiques. Compt. rend. Lab. Carlsberg, 8, 1.
S0RENSEN, S. P. L. 1909 Note supplementaire au m6moire intitule:

Etudes enzymatiques. II. Compt. rend. Lab. Carlsberg, 8,

396.

THE DETERMINATION OF HYDROGEN IONS

S0RENSEN, S. P. L. 1909 Enzymstudien. II. "Uber die Messung und die
Bedeutung der Wasserstoffionenkonzentration bei enzyma-
tischen Prozessen. Biochem. Z., 21, 131, 201.

S0RENSEN, S. P. L. 1909 Erganzungzu der Abhandlung: Enzymstudien.
II. Biochem. Z., 22, 352.

S0RENSEN, S. P. L. 1912 tlber die Messung und Bedeutung der Wasser-
stoffionenkonzentration bei biologischen Prozessen. Ergeb.
Physiol., 12, 393.

S0RENSEN, S. P. L. 1917 Studies on proteins. Compt. rend. Lab. Carls-
berg, 12, 1. See also Z. Physiol., 103, 1.

S0RENSEN, S. P. L. 1921 Sur Valbumine du blanc d'oeuf de poule. Con-
f6rence Soc. Chim. France. Paris.

S0RENSEN, S. P. L. 1924 Hydrogen-ion concentration in bread-making.
Am. Food J., 19, 556.

S0RENSEN, S. P. L., AND LiNDERSTR0M-LANG, K. 1924 The determina-
tion and value of TTO in electrometric measurements of hjdrogen-
ion concentrations. Compt. rend. trav. lab. Carlsberg, 16, 40.

S0RENSEN, S. P. L., LINDERSTR0M-LANG, K., AND LUND, L. 1926 Studies

on proteins. IX. The influence of salt concentration on the
acid-binding capacity of egg albumin. Compt. rend. trav. lab.
Carlsberg, 16, 1.

S0RENSEN, S. P. L., LINDERSTR0M-LANG, K., AND LlJND, E. 1927 The

influence of salts upon the ionisation of egg albumin. J. Gen.
Physiol., 8, 543.

S0RENSEN, S. P. L., AND PALiTzscH, S. 1910 Sur un indicateur nouveau,
a-naphtholphthaleine, ayant un virage au voisinage du point
neutre. Compt. rend. Lab. Carlsberg, 9, 1.

S0RENSEN, S. P. L., AND PALITZSCH, S. 1910 Uber ein neuen Indicator,
a-naphtholphthalein mit Umschlag in der Nahe des Neutral-
punktes. Biochem. Z., 24, 381.

S0RENSEN, S. P. L., AND PALITZSCH, S. 1910 Sur le mesurage de la con-
centration en ions hydrogene de Peau de mer. Compt. rend.
Lab. Carlsberg, 9, 8.

S0RENSEN, S. P. L., AND PALITZSCH, S. 1910 tlber die Messung der
Wasserstoffionenkonzentration des Meerwassers. Biochem. Z.,
24, 387.

S0RENSEN, S. P. L., AND PALITZSCH, S. 1913 Sur "l'erreur de sel" dans
la mesure colorimetrique de la concentration des ions hydrogene
de 1'eau de mer. Compt. rend. Lab. Carlsberg, 10, 252.

S0RENSEN, S. P. L., AND PALITZSCH, S. 1913 tTber den "Salzfehler" bei
der colorimetrischen Messung der Wasserstoffionenkonzentra-
tion des Meerwassers. Biochem. Z., 51, 307.

S0RENSEN, S. P. L., S0RENSEN, M., AND LlNDERSTR0M-LANG, K. 1921

Sur l'erreur de sel inh6rente a P61ectrode de quinhydrone.
Compt. rend. Lab. Carlsberg, 14, 1. Ann. de Chim., 16, 283.
SPEAKMAN, J. B. 1924 The behavior of wool as an amphoteric colloid:
a contribution to the theory of dyeing. J. Soc. Dyers Colour-
ists, 40, 408.

BIBLIOGRAPHY 661

SPIRO, K., AND HENDERSON, L. J. 1908 Zur Kenntnis des lonengleich-
gewichts im Organismus. II. Einfluss der Kohlensaure auf die
Verteilung von Elektrolyten zwischen roten Blutkorperchen
und Plasma. Biochem. Z., 15, 114.

STADIE, W. C. AND HAWES, E. R. 1928 The validity of hydrogen ion
activity determinations by the hydrogen electrode in systems
containing carbonic acid, carbonates, hemoglobin, carbon
monoxide hemoglobin, and methemoglobin. J. Biol. Chem.,
77, 241.

STASIAK, A. 1926 Effect of the acidity of the solvent on the stability of
the active principle of the infundibulum. J. Pharmacol., 28, 1.

STEARN, E. W., AND STEARN, A. E. 1924 The chemical mechanism of
bacterial behavior. I. Behavior towards dyes. Factors con-
trolling the gram reaction. J. Bact., 9, 463.

STEARN, E. W., AND STEARN, A. E. 1924 The role of hydrogen ion con-
centration in the action of dyes on bacteria. Am. J. Pub.
Health, 14, 409.

v. STEIGER, A. L. 1924 tJber die Bestimmung der Wasserstoffionen-
konzentration saurer Losungen mit Hilfe der Glaselektrode.
Z. Elektrochem., 30, 259.

STEINBERG, R. A. 1919 A study of some factors in the chemical stimula-
tion of the growth of Aspergillus niger. Am. J. Bot., 6, 330.

STENSTROM, W., AND REINHARD, M. 1925 The influence of the pH upon
the ultraviolet absorption spectra of certain cyclic compounds,
J. Phys. Chem., 29, 1477.

STERN, H. T. 1925 The colorimetric pH test of water or unbuffered
solutions. J. Biol. Chem., 65, 677.

STERN, H. T. 1925 An improved salt bridge. J. phys. Chem., 29, 1583.

STEVENS, F. A., AND KOSER, S. A. 1919 ,Streptolysin production in
carbohydrate media. J. Exp. Med., 30, 539.

STIEGLITZ, J. 1903 The theories of indicators. J. Am. Chem. Soc., 25,
1112.

STIEGLITZ, J. 1917 The Elements of Qualitative Chemical Analysis. Vol.
I, (Theory), New York.

STILES, W. 1924 Permeability. New Phytologist, Reprint 13, London.

STOLL, N. R. 1923 Investigations on the control of hookworm disease.
Am. J. Hyg., 3, 137.

STRACHAN, E. K. 1926 The accurate measurement of hydrogen-ion con-
centration as an aid to the textile chemist. Proc. Am. Assoc.
Textile Chem. Colorists, 139. Am. Dyestuff Reporter, 15, 291.

STURM, W. 1918 Eenige mededeelingen over het meten van de water-
stofionen-concentratie en een nieuwe vorm van kalomel-elec-
trode. (Measurement of hydrogen ion concentration and a new
form of calomel electrode.) Chem. Weekblad., 15, 912.

SWEENEY, O. R., AND RILEY, R. 1926 Effect of hydrogen-ion concentra-
tion in revivifying zeolites. Ind. Eng. Chem., 18, 1214.

SWYNGEDAUW, J. 1927 Electrode a saturation permanent pour la mesure
en sSrie des pH. Compt. rend. soc. biol., 96, 693.

662 THE DETERMINATION OF HYDROGEN IONS

TAINTER, M. L. 1926 The pH and potency of digitalis infusions. J. Am.

Pharm. Assocn., 15, 255.
TALBERT, G. A. 1919 The effect of work and heat on the hydrogen ion

concentration of the sweat. Am. J. PhysioL, 60, 433.
TALBERT, G. A. 1922 Further studies on the hydrogen ion concentration

of human sweat. Am. J. PhysioL, 61, 493.
TAMMANN, G., AND DIEKMANN, H. 1926 Die Abhangigkeit des Potentials

der Wasserstoffelektrode vom Druck. Z. anorg. Chem., 150,

129.
TANNER, H. G. 1922 The decolorizing action of adsorptive charcoals.

J. Ind, Eng. Chem., 14, 441.
TARR, L. W. 1923 Fruit Jellies. I. The role of acids. Univ. Delaware

Agr. Exptl. Sta. Bull. 134.

TAUB, A. 1927 Permanent standards for the determination of hydrogen-
ion concentration. J. Am. Pharm. Assocn., 16, 116.
TAUFEL, K. 1927 Sabre las curvas de neutralizaci6n y su significaci6n

en la alcalimetria y acidimetria. An. Soc. Espafiora Fisica. y

Quimica, 25, 13.
TAUFEL, K., AND WAGNER, C. 1926 tlber die Pufferung in homogenen und

heterogenen Systemen. Biochem. Z., 177, 389.
TAYLOR, C. V. 1925 Microelectrodes and micromagnets. Proc. Soc.

Exptl. Biol. Med., 23, 147.

TAYLOR, H. S. 1924 A Treatise on Physical Chemistry, New York.
TAYLOR, P. B. 1927 Electromotive force of the cell with transference

and theory of interdiffusion of electrolytes. J. Phys. Chem.,

31, 1478.

TAYLOR, T. W. J., AND BOMFORD, R. F. 1924 The apparent concentra-
tion of the hydrogen-ion in solutions containing sucrose. J.

Chem. Soc., 125, 2016.
TAYLOR, W. A. 1928 The A B C of Hydrogen Ion Control, 4th ed.

LaMotte Chemical Products Co., Baltimore.
TERTSCH, H. 1926 Trachten der Krystalle. Forschungen der Kristall-

kunde H. 1. Berlin, p. 114 (cited).
THIEL, A. 1911 Der Stand der. Indikatorenfrage. Zugleich ein Beitrag

zur chemischen Theorie der Farbe. Sammlung chem. chem-

tech. Vortrage., 16, 307.
THIEL, A. 1922 Zur Frage nach dem Mechanismus der Farbumschlags

einiger Phthaleine. Z. physik. chem., 100, 479.
THIEL, A. 1924 Beitrage zur systematischen Indikatorenkunde. Z.

anorg. allgem. Chem., 135, 1.
THIEL, A., AND DASSLER, A. 1923 tlber dur Zustand von Methylorange

und Methylrot im Umschlagsintervall. Ber., 56, 1667; 56B,

2082.
THIEL, A., AND DASSLER, A. 1924 tTber das Zwitterion des Helianthins

und das dielektrische Verhalten seiner Losungen, Z. physik.

Chem., 108, 298.

BIBLIOGRAPHY 663

THIEL, A., DASSLER, A., AND WULFKEN, F. 1924 tlber Azo-Indikatoren

von Typus des Methylgelb, Methylorange und Methylrot.

Fortschritte Chem. Physik physik. Chem., 18, H. 3.
THIEL, A., AND DIEHL, R. 1927 Beitrage zur systematischen Indikator-

enkunde. II. tlber Phenolphthalein und Phenolphthalein-

Derivate. Sitzb. Ges. Beforderung ges. Naturwissensch. Mar-
burg, 62, 472.
THIEL, A., AND MULLER, F. 1922 tlber Chlor- und Brom-Derivate des

Phenolphthaleins. Ber., 55, 1312.
THIEL, A., AND WULFKEN, F. 1924 Systematic study of indicators. IX.

Azo indicators with unsymmetrical kernels. Z. anorg. allgem.

Chem., 136, 393 (cited).

THIEL, A., WULFKEN, F., AND DASSLER, A. 1924 Beitrage zur Systema-
tischen Indikatorenkunde 10. Vorlaufiges iiber Losungsmit-

teleinfliisse, insbesondere den "Alkoholfehler," bei Indikatoren.

Z. anorg. allgem. Chem., 136, 406.
THOMPSON, M. R. 1922 The acidity of nickel depositing solutions.

Trans. Am. Electrochem. Soc., 41, 333.

TIAN, A. 1923 Recherches sur les thermostats. J. chim. phys., 20, 132.
TILLEY, G. S., AND RALSTON, O. C. 1923 An electrometric method of

following certain inorganic hydrolytic reactions. Trans. Am.

Electrochem. Soc., 44, 31.
TINGLE, A. 1918 The acidimetry of colored solutions: An application of

the pocket spectroscope. J. Am. Chem. Soc., 40, 873.
TIZARD, H. T. 1910 The color changes of methyl-orange and methyl-red

in acid solutions. J. Chem. Soc., 97, 2477.
TIZARD, H. T., AND WHISTON, J. R. H. 1920 The effect of a change in

temperature on the color changes of methyl orange and on the

accuracy of titrations. J. Chem. Soc., 117, 150.
TODD, C. 1927 On the electrical behaviour of the bacteriophage. Brit.

J. Exptl. Path., 8, 369.
TOWER, O. F. 1895 Studien iiber Superoxyd-Elektroden. Z. physik.

Chem., 18, 17.
TOWER, O. F. 1896 tlber Potentialdifferenzen an den Beruhrungsflachen

verdunnter Losungen. Z. physik. Chem., 20, 198.
TRATMAN, E. R. 1926 Hydrogen ion concentration and its application

to textile industries. Am. Dyestuff Reporter, 15, 577.
TRAUBE, J. 1921 Nochmals die Wasserstoffionen. Biochem. Z., 120, 108.
TREAD WELL, W. D. 1925 tlber die Verwendung der Radioempfanger-

rohre zur elektrometrischen Titrationen. Helv. Chim. Acta,

8, 89.
TRENEL, M. 1924 tlber eine einfache Vorrichtung fur elektrochimische

Potentialmessungen. Z. Elektrochem., 30, 544. Cf. Biochem.

Z., 165, 500.
TRENEL, M. 1927 Die wissenschaftlichen Grundlagen der Bodensaure-

frage. Berlin.

664 THE DETERMINATION OF HYDROGEN IONS

TREVAN, J. W., AND BOOCK, E. 1927 The relation of hydrogen ion con-
centration to the action of the local anaesthetics. Brit. J.

Exptl. Path., 8, 307.
TRILLAT, A. 1916 Sur un precede" colorimStrique utilise" par les Romains

pour characterise! les eaux douces. Compt. rend., 162, 486.
TROLAND, L. T. et al. 1922 Report of Committee on Colorimetry for

1920-1921. J. Optical Soc. Am., 6, 527.
TROTMAN, E. R. 1926 Hydrogen-ion concentration and its application

to textile industries. J. Soc. Dyers Colourists, 42, 208.
UHL, A., AND KESTRANEK, W. 1924 Die elektrometrische Titration

von Sauren und Basen mit der Antimon-Indikatorelektrode.

Monatsh., 44, 29.
UMETSU, K. 1923 Untersuchungen iiber die Bindungsfahigkeit der

Eiweisskorper fiir Farbstoff. Biochem. Z., 137, 258.
USHER, F. L. 1926 Electrokinetic behavior and electrode potential.

J. Phys. Chem., 30, 954.
VANA, A. 1926 O zmenach koncentrace vodikovych jontu a alkalicke"

reservy v krvi pfi nekterych chorobach chirurgickych. Spisy

Lekafske Fakulty Masarykovy Univ., 4, 15.
VAN-ALSTINE, E. 1920 The determination of H-ion concentration by

the colorimetric method and an apparatus for rapid and accurate

work. Soil Science, 10, 467.

VAN DER BIJL, H. J. 1920 The Thermionic Vacuum Tube and its Applica-
tions. New York.
VAN DER MEULEN, AND WILCOXON 1923 Electrometric acidimetry and

alkalimetry without the use of hydrogen. Ind. Eng. Chem.,

15, 62.
VAN NAME, R. G., AND FENWICK, F. 1925 The behavior of electrodes of

platinum and platinum alloys in electrometric analysis. I.

Dissimilar electrodes. II. Polarized electrodes. J. Am. Chem.

Soc., 47, 9.
VAN SLYKE, D. D. 1921 Studies of acidosis. XVII. The normal and

abnormal variations in the acid-base balance of the blood. J.

Biol. Chem., 48, 153.
VAN SLYKE, D. D. 1921 The carbon dioxide carriers of the blood.

Physiol. Reviews, 1, 141.
VAN SLYKE, D. D. 1922 On the measurement of buffer values and on the

relationship of buffer value to the dissociation constant of the
^ , buffer and the concentration and reaction of the buffer solution.

J. Biol. Chem., 42, 525.
VAN SLYKE, D. D. 1926 Factors Affecting the Distribution of Electrolytes,

Water, and Gases in the Animal Body. Philadelphia.
VAN SLYKE, D. D., AND CULLEN, G. E. 1917 Studies of acidosis. I. The

bicarbonate concentration of the blood plasma, its significance,

and its determination as a measure of acidosis. J. Biol. Chem.,

30, 289.

BIBLIOGRAPHY 665

VAN SLYKE, D. D., HASTINGS, H. B., MURRAY, C. D., AND SENDROY, J. JR.

1925 Studies of gas and electrolyte equilibria in blood. J.

Biol. Chem., 65, 701.
VAN SLYKE, D. D., AND NEILL, J. M. 1924 The determination of gases

in blood and other solutions by vacuum extraction and mano-

metric measurement. J. Biol. Chem., 61, 523.
VAN SLYKE, D. D., AND PALMER, W. W. 1920 Acidosis. XVI. The titra-

tion of organic acids in urine. J. Biol. Chem., 41, 567.
VAN SLYKE, D. D., AND SENDROY, J., JR. 1927 Carbon dioxide factors

for the manometric blood gas apparatus. J. Biol. Chem., 73,

127.
VAN SLYKE, D. D., AND STADIE, W. C. 1921 The determination of the

gases of the blood. J. Biol. Chem., 49, 1.
VAN SLYKE, D. D., STILLMAN, E., AND CULLEN, G. E. 1917 Studies of

acidosis. V. Alveolar carbon dioxide and plasma bicarbonate

in normal men during digestive rest and activity. J. Biol.

Chem., 30, 401.
VAN SLYKE, D. D., STILLMAN, E., AND CULLEN, G. E. 1919 Studies of

acidosis. XIII. A method for titrating the bicarbonate content

of the plasma. J. Biol. Chem., 38, 167.
VEIBEL, S. 1923 Quinhydrone electrode as a comparison electrode. J.

Chem. Soc., 123, 2203.
VELLINGER, E. 1926 La pouvoir rotatorie des corps organiques en fonc-

tion du pH. Compt. rend., 182, 1625; 184, 94.
VELLINGER, E. 1926 Le potentiel de P electrode au calomel saturee

entre 0° et 40°. Arch. phys. biol., 5, 119.
VELLINGER, E. 1927 Recherches potentiometriques sur le pH interieur

et sur le potential d'oxydation reduction de Poeuf d'oursin.

Arch. phys. biol., 6, 141.
VELLINGER, E., AND ROCHE, J. 1925 Remarques sur la mesure du pH du

sang total et du plasma a Paide de 1'electrode a quinhydrone.

Bull. soc. chim. biol., 7, 1004.

VENTRE, J. 1925 Du rdle de I'acidite reelle dans la preparation et la con-
servation des vins. Montpellier. (Cited.)
VICKERY, H. B., AND LEAVENWORTH, C. S. 1927 On the separation of

histidine and arginine. II. The separation of the silver com-
pounds at pH 7.0. J. Biol. Chem., 72, 403.

VINAL, G. W. 1925 Storage batteries. J. Optical Soc., 11, 263.
VINAL, G. W., AND BATES, S. J. 1914 Comparison of the silver and

iodine voltameters and the determination of the value of the

faraday. Scientific Paper 218, U. S. Bureau Standards.
VINCENT, M. 1926 La concentration en ions hydrogene et sa mesure par la

methode electrometrique. Application aux variations de I'equi-

libre acide-base du sang, a I'etat physiologique et a I'etat patho-

logique. — Action de colloldes electriques en injection intra-

veineuse. Paris.

666 THE DETERMINATION OF HYDROGEN IONS

VIRTANEN, A. I., AND BXRLUND, B. 1926 Die Oxydation des Glycerins
zu Dioxyaceton durch Hakterien. Biochem. Z., 169, 169.

VLES, F. 1924 Recherches sur les propri6t-6s physico-chimiques des
products sexuels de 1'Oursin. Arch. phys. biol., 3, 42.

VLES, F. 1925-1926 Sur la mesure du pH par les methodes spectrophoto-
metriques. Bull. Soc. Chim., 37, 558; Arch. phys. biol., 4, 285.

VLES, F. 1926 Microcolorimctre pour les mesures microscopiques de
pH on de rH. Compt. rend. soc. biol., 94, 879.

VLES, F. 1927 Notes sur 1'electrode d'antimoine. Arch. phys. biol.,
6, 92.

VLES, F. et al. 1926 Recherches sur les proprirtcs phvsico-chemiques
des corps organiques en fonction du pH. Arch. phys. biol., 6, 1.

VLES, F., AND GEX, M. 1927 I/absorption ultra-violett, en fonction du
pH. Arch. phys. biol., 6, 62.

VLES, F., AND VELLINGER, E. 1925 Le pouvoir rotatoire des corps
organiques en fonction du pH: 1'acide tartarique. Bull. Soc.
Chim., 37, 841.

VLES, F., AND VELLINGER, E. 1925 Sur un modele pratique d'61ectrode
a hydrogene. Bull. soc. chim., 37, 771.

VLES, F., AND VELLINGER, E. 1927 Notes pr61iminaries sur 1'electrode
d'antimoine. Arch. phys. biol., 6, 38.

VOEGTLIN, C., AND DE EDS, F. 1928 A method for the continuous meas-
urement of the electrical potential in living cells. U. S. Public
Health Repts., 43, 380.

VOLMAR, Y. 1927 Les phenom£nes de fluorescence en analyse chimique :
volumetric par fluorescence. Arch. phys. biol., 6, 61.

VOSBURGH, W. C. 1925 Saturated standard cells with small tempera-
ture coefficients. J. Am. Chem. Soc., 44, 2531.

VOSBURGH, W. C. 1925 Conditions affecting the reproducibility and
constancy of Weston standard cells. J. Am. Chem. Soc., 47,
1255.

VOSBURGH, W. C. 1925 The decrease in electromotive force of un-
saturated Weston cells. J. Optical Soc. Am., 11, 59.

VOSBURGH, W. C. 1926 Eppley unsaturated standard cells at high tem-
peratures. J. Optical Soc. Am., 12, 393.

VOSBURGH, W. C. 1927 The electrode equilibrium in the Weston Stand-
ard Cell. J. Am. Chem. Soc., 49, 78.

VOSBURGH, W. C., AND EPPLEY, M. 1923 Temperature coefficients of
unsauirated Weston cells. J. Am. Chem. Soc., 45, 2268.

VOSBURGH, W. C., AND EPPLEY, M. 1924 Portable unsaturated Weston
cells. J. Optical Soc. Am., 9, 65.

VOSBURGH, W. C., AND EPPLEY, M. 1924 The effect of various prepara-
tions of mercurous sulfate on the electromotive force and
hysteresis of Weston standard cells. J. Am. Chem. Soc., 46,
104.

WAGENER, L. R., AND McGiLL, W. J. 1925 The electrometric titration
of alkaloids; application of the quinhydrone electrode to alka-
loidal titration. J. Am. Pharm. Assocn., 14, 288.

BIBLIOGRAPHY 667

WAKHMAN, 8. 1924 Influence of soil reaction upon the distribution of
filamentous fungi in the soil. Ecology, 5, 54.

WAKHMAN, »S. A. 1027 rrinr/ipifw <>J Xoil M-irroliinloyy. Baltimore.

WAKSMAN, S. A., AND DAVIBON, W. C. 1926 Enzymes. Williams and
Wilkins.

WALBUM, L. E. 1913 Sur 1'ernploi de 1'extrait de choux rouge comme in-
dicateur dans la mesure eolorim6trique de la concentration des
ions hydrog(:n<!. (Jornpt. rend. Lab. Carlsberg, 10, 227.

WALBUM, L. E. T913 tlber die Verweridung von Rotkohlauszug als Indi-
cator bei der colorimetrischen Messung der Wasserstoffionen-
konzentration. Biochem. Z., 48, 291.

WALBUM, L. E. 1913 Nachtrag zu meiner Arbeit: tlber die Verwendung
von Rotkohlauszug. Biochem. Z., 50, 346.

WALBUM, L. E. 1914 Die Bedeutung der Wasserstoffionenkonzentration
fur die; I I;imoly.se. Biochem. Z., 63, 221.

WALBUM, L. E. 1920 tlber die Wassstoffionenkonzentration einiger
Standard losungen bei verschiedenen Temperaturen. Biochem.
Z., 107, 219.

WALBUM, L. E. 1921 L'influence de la temp6rature sur la concentration
en ions hydrogene de quelques solutions Stalons. Compt. rend,
soc. biol., 83, 707.

WALBUM, L. E. 1922-1923 Studien uber die Bildung der bakteriellen
Toxine. Biochem. Z., 129, 367; 130, 25; 134, 601.

WALDEN, P. 1924 Elektrochemie nichtwassriyer Losungen, Lepizig.

WALES, H. 1926 Choice of indicators for alkaloidal titrations. Ind.
Eng. Chem., 18, 390.

WALKER, A. C., BKAY, U. B., AND JOHNSTON, J. 1927 Equilibria in solu-
tions of alkali carbonates. J. Am. Chem. Soc., 49, 1235.

WALPOLE, G. S. 1910 Chart presentation on recent work on indicators.
Biochem. J., 6, 207.

WALPOLE, G. S. 1913 The use of litmus paper as a quantitative indicator
of reaction. Biochem. J., 7, 260.

WALPOLE, G. 8. 1913 Gas-electrode for general use. Biochem. J., 7, 410.

WALPOLE, G. S. 1914 An improved hydrogen electrode. Biochem. J., 8,
131.

WALPOLE, G. S. 1914 Diagrammatic co-ordination of phenomena relat-
ing to aggregation of sols. Biochem. J., 8, 170.

WALPOLE, G. S. 1914 Notes on regulator mixtures, recent indicators, etc.
II. Biochem. J., 8, 628.

WALPOLE, G. S. 1914 Hydrogen potentials of mixtures of acetic acid and
sodium acetate. J. Chem. Soc., 106, 2501.

WALPOLE, G. S. 1914 The effect of dilution on the hydrogen potentials
of acetic acid and "standard acetate" solution. J. Chem. Soc.,
106, 2521.

WALSH, J. W. T. 1926 Photometry. N. Y.

WALTHER, O. A., AND ULRICH, J. 1926 Une microm6thode colorim6trique
de mesure du pH. Bull. soc. chim. biol., 8, 1106.

668 THE DETERMINATION OF HYDROGEN IONS

WAKBURG, E. J. 1922 Carbonic acid compounds and hydrogen ion
activities in blood and salt solutions. Biochem. J., 16, 153.

WARBURG, O. 1926 Ober den Stoffwechsel der Tumoren. Berlin.

WASHBURN, E. W. 1908 The theory and practice of the iodometric deter-
mination of arsenious acid. J. Am. Chem. Soc., 30, 31.

WATERMAN, H. S., AND KNIPER, P. 1924 The antiseptic action of benzoic
acid, salicylic acid, cinnamic acid and their salts. Rec. trav.
chim. (4), 5, 323.

WATSON, A. F., AND WALLACE, U. 1924 The concentration of diphtheria
toxin by acid precipitation. J. Path. Bact., 27, 289.

WATSON, G. N. 1913 The juice of the blueberry as an indicator. Am.
J. Pharm., 85, 246.

WATSON, P. D. 1927 Use of quinhydrone electrode for following changes
of pH in Swiss cheese. Ind. Eng. Chem., 19, 1272.

WEAVER, H. E. 1925 Hydrogen ions and their application to mill control.
Cereal Chemistry, 2, 209.

WEBB, R. W. 1919 Studies in the physiology of the fungi. X. Germina-
tion of the spores of certain fungi in relation to H-ion concen-
tration. Ann. Missouri Botan. Gardens, 6 (cited).

WEBB, R. W., AND FELLOWS, H. 1926 The growth of Ophiobolus graminis
Sacc. in relation to hydrogen-ion concentration. J. Agr.
Research, 33, 845.

WEBER, F. 1926 Permeabilitat der Pflanzenzelle und kunstlicher Mem-
branen (Permeabilitatstheorien) Literatur seit 1922. Proto-
plasma, 1, 486.

WEGSCHEIDER, R. 1908 tlber den Farbenumschlag des Phenolphthaleins.
Z. Elektrochem., 14, 510.

WEGSCHEIDER, R. 1915 Theorie der azidimetrischen Indikatoren. Z.
physik. Chem., 90, 641.

WEHRLE, E. 1927 Studien iiber Wasserstoffionenkonzentrationsverhalt-
nisse und Besiedlung an Algenstand.orten von Freiburg. Z.
Botanik., 19, 209.

WEISER, H. B., AND PORTER, E. E. 1927 Physical chemistry of color-lake
formation. J. Phys. Chem., 31, 1383, 1704.

WELLS, H. G. 1925 The Chemical Aspects of Immunity. N. Y.

WELLS, R. C. 1920 The salt error of cresol red. J. Am. Chem. Soc.,
42, 2160.

WELLS, R. C. 1921 The alkalinity of Searles Lake brine. J. Ind. Eng.
Chem., 13, 691.

WENDT, G. 1927 On recording acidity. Tech. Assocn. Pulp Paper Ind.,
Tech. Papers series X.

WENNER, F., AND WEIBEL, E. 1914 The testing of potentiometers. Sci-
entific paper 223, U. S. Bureau of Standards.

WESTHAVER, J. B. 1905 Aufgebrannte Elektrode. Z. physik. Chem., 51,
90.

WEYL, A. 1905 Messung von Diffusions-potentialen konzentrierter
Chloridlosungen. Dissertation, Karlsruhe.

BIBLIOGRAPHY

WHERRY, E. T. 1916 A chemical study of the habitat of the walking fern.

J. Wash. Acad. Sci., 6, 672.
WHERRY, E. T. 1919 The statement of acidity and alkalinity, with

special reference to soils. J. Wash. Acad. Sci., 9, 305.
WHERRY, E. T. 1920 Determining soil acidity and alkalinity by indica-
tors in the field. J. Wash. Acad. Sci., 10, 217.
WHERRY, E. T. 1920 Plant distribution around salt marshes in relation

to soil acidity. Ecology, 1, 42.
WHERRY, E. T. 1920 Soil acidity and a field method for its measurement.

Ecology, 1, 160.
WHERRY, E. T. 1920 Observations on the soil acidity of ericaceae and

associated plants in the middle Atlantic states. Proc. Acad.

Natural Sci. Phila., 84.
WHERRY, E. T. 1920 Correlation between vegetation and soil acidity in

southern New Jersey. Proc. Acad. Natural Sci. Phila., 113.
WHERRY, E. T. 1920 Soil tests of ericaceae and other reaction-sensitive

families in northern Vermont and New Hampshire. Rhodora,

22, 33.
WHERRY, E. T. 1920 The soil reactions of certain rock ferns. Am.

Fern J., 10, 15, 45.
WHERRY, E. T. 1921 The soil reactions of the ferns of woods and swamps.

Am. Fern J., 11, 5.
WHERRY, E. T. 1921 The soil reactions of Spiranthes cernua and its

relatives. Rhodora, 23, 127.

WHERRY, E. T. 1922 Recent work on soil acidity. Science, 65, 568.
WHERRY, E. T. 1922 Soil acidity: Its nature, measurement and relation

to plant distribution. Smithsonian Rept., 1920, p. 247. Pub.

2630.
WHERRY, E. T. 1923 A soil acidity map of a Long Island wild garden.

Ecology, 4, 395.
WHERRY, E. T. 1926 Soil reaction in relation to horticulture. Bull. 4,

Am. Horticultural Soc., Washington.
WHERRY, E. T. 1927 New method of stating hydrion concentration.

Bull. Wagner Free Inst. Sci., 2, 59.
WHERRY, E. T., AND ADAMS, E. Q. 1921 Methods of stating acidity.

J. Wash. Acad. Sci., 11, 197.

WHITE, E. C. 1915 Dissertation on the sulfon phthaleins. Univ. Wis-
consin.
WHITE, E. C., AND AGREE, S. F. 1918 On the quinone-phenolate theory

of indicators. J. Am. Chem. Soc., 40, 1092.
WHITE, E. C., AND AGREE, S. F. 1919 On the quinone-phenolate theory of

indicators. J. Am. Chem. Soc., 41, 1190.
WHITE, W. P. 1906 Every-day problems of the moving coil galvanometer.

Phys. Rev., 23, 382.

WHITE, W. P. 1914 Leakage prevention by shielding, especially in poten-
tiometer systems. J. Am. Chem. Soc., 36, 2011.
WICHERS, E. 1921 The preparation of pure platinum. J. Am. Chem.

Soc., 43, 1268.

670 THE DETERMINATION OF HYDROGEN IONS

WIEGNER, G. 1920 Kolloidchemische Betrachtungen zur Indikatoren-

theorie. Mitt. Lebensm. Hyg., 11, 216.
WIEGNER, G., AND GESSNER, H. 1926 Die Bedeutung der pH-Bestim-

mung in der Bodenkunde. Kolloid-Z., 40, 209.

WIGHTMAN, E. P., TRIVELLI, A. P. H., AND SHEPPARD, S. E. 1923 Struc-
ture of the photographic emulsion. Trans. Faraday Soc., 19,
270.
Wus, J. J. A. 1893 Die Dissociation des Wassers. Z. physik. Chem.,

12, 514.
WILKE, E. 1913 tlber eine neue Wasserstoffelektrode und ihre Verwend-

barkeit. Z. Elektrochem., 19, 857.

WILLARD, H. H., AND FENWicK, F. 1923 The bimetallic electrode system

applied to neutralization reactions. J. Am. Chem. Soc., 45, 715.

WILLIAMS, J. W., AND WHITENACK, T. A. 1927 The application of the

electron tube to potentiometric titrations. J. Phys. Chem.,

31, 519.

WILLIAMSON, F. S. 1924 Sodium alizarate and alumina. J. Phys. Chem.,

28, 891.
WILSMORE, N. T. M. 1900 tlber Elektroden-Potentiale. Z. physik.

Chem., 35, 291.
WILSMORE, N. T. M., AND OSTWALD, W. 1901 tlber Elektrodenpotentiale

und absolute Potentiale. Z. physik. Chem., 36, 91.

WILSON, J. A. 1928 Chemistry of Leather Manufacture. A. C. S. Mono-
graph No. 12, Vol. 1.

WILSON, J. A., COPELAND, W. R., AND HEISIG, H. M. 1923 A practical
solution of the problem of dewatering activated sludge. Ind.
Eng. Chem., 15, 956.

WINDISH, W., AND DIETRICH, W. 1919 Neue Wege zur Bestimmung der
Aciditat in Wiirzen, Bieren und anderen physiologischen Fliissig-
keiten. Ws. Brau., 36, 189, 201, 209 (cited).

WINDISCH, W., AND DIETRICH, W. 1919-1920 Titrationen mit oberflachen-
aktwen Stoffen als Indicator. Biochem. Z., 97, 135; 100,
130; 101, 82; 106, 92.

WINDISCH, W., AND DIETRICH, W. 1920 tlber das Puffersystem primares
Phosphat-Bicarbonat-freie Kohlensaure an Stelle des Puffer-
systems primares Phosphat-sekundares Phosphat. Biochem. Z.,
102, 141.

WINDISCH, W., DIETRICH, W., AND KOLBACH, P. 1922 Hydrogen-ion
concentration in the brewery. Wochschr. Brau., 38, 275, 283,
289; 39, 145, 151, 157, 165, 171, 177 (cited).

WINSLOW, C.-E. A., FALK, I. S., AND CAULFIELD, M. F. 1923 Electro-
phoresis of bacteria as influenced by hydrogen-ion concentra-
tion and the presence of sodium and calcium salts. J. Gen.
Physiol., 6, 177.

WINSLOW, C.-E. A., AND LOCHRIDGE, E. E. 1906 The toxic effect of cer-
tain acids upon typhoid and colon bacilli in relation to the de-
gree of their dissociation. J. Infect. Dis., 3, 547.

BIBLIOGRAPHY 671

WINSLOW, C.-E. A., AND SHAUGHNESSY, H. J. 1924 The alkaline iso-

potential point of the bacterial cell. J. Gen. Physiol., 6, 697.
WINTERSTEIN, H. 1927 Mikroelektrode zur Bestimmung der aktuellen

cH. Arch. Physiol. (Pfliiger's), 216, 267.
WLADIMIROFF, G. E., AND GALWIALO, M. J. 1925 Zur Bewertung der

Lehmannschen Mikroelektrode. Biochem. Z., 160, 101.
WOLF, K. 1927 Eine neue Methode der pH-Bestimmung. Collegium, 8,

370.
WOLFF, F. A. 1908 The temperature formula of the Weston standard

cell. Scientific paper 104, U. S. Bureau Standards; Bull.

Bur. Standards, 5, 309.
WOLFF, F. A., AND WATERS, C. E. 1907 Clark and Weston standard cells.

Scientific Paper 70, U. S. Bureau Standards.
WOLFF, F. A., AND WATERS, C. E. 1907 The electrode equilibria of the

standard cell. Scientific paper 71, U. S. Bureau Standards.
WOOD, C. J., AND MURDICK, P. P. 1922 The stability of phthalate solu-
tions as standards in hydrogen-ion work. J. Am. Chem. Soc.,

44, 2008.
WOOD, J. K. 1903 The affinities of some feebly basic substances. J.

Chem. Soc., 83, 568.
WOOD, J. T., SAND, H. J. S., AND LAW, D. J. 1911 The employment of

the electrometric method for the estimation of the acidity of

tan liquors. J. Soc. Chem. Ind., 30, 872.
WOOD, R. W. 1921 Physical Optics. New York.
WRIGHT, J. H. 1917 The importance of uniform culture media in the

bacteriological examination of disinfectants. J. Bact., 2, 315.
WRIGHT, S. L., JR. 1925 Note on the preservation of hydrogen ion

standards. Bull. Ayer Clin. Lab. Penn. Hospt., No. 9, 63.
WRIGHT, W. H., AND HARDING, H. G. 1927 A modification of the Brown

apparatus for the determination of colorimetric pH. J. Bact.,

13, 10.
Wu, H. 1923 A modification of Duboscq-Pellin colorimeter for bicolori-

metric work. Pr.oc. Soc. Exptl. Biol. Med., 21, 111.
WULF, T. 1904 tlber den Einfl.usp des Druckes auf die elektromotorische

Kraft der Gaselektroden. Z. physik. Chem., 48, 87.
WULFF, P. 1926 Bestimmung der Wasserstaffionenkonzentration mit

indikatorhaltigen Kolloidschichten. Kolloid-Z., 40, 341.
YONGE, C. M. 1925 The hydrogen ion concentration in the gut of certain

lamellibranches and gastropods. J. Marine Biol. Assocn.

United Kingdom, 13, 938.

ZILVA, S. S. 1923 The influence of reaction on the oxidation of the anti-
scorbutic factor in lemon juice. Biochem. J., 17, 410.
ZIRKLE, C. 1927 Some fixatives for both nuclei and mitochondria.

Science, 66, 400.
ZOLLER, H. F. 1921 Phthalate buffers — some incompatibilities. J. Am.

Chem. Soc., 43, 914.
ZSIGMONDY, R. 1924 Uber den Zerteilungszustand hochmolekularen

Farbstoff in wasseriger Losung. Z. physik. Chem., Ill, 211.

APPENDIX

TABLE A

ARBITRARILY STANDARDIZED VALUES FOR HALF-CELLS
See Chapter XXIII and especially page 488.

|| (H+) = 1 | H8(l atmos.), Pt.

KC1 (sat.) | KC1 (0.1 N), HgCl | Hg

KC1 (sat.), HgCl | Hg

KC1 (sat.) I HC1 (0.1 N) | H2(l atmos.), Pt.

KC1 (sat.) I KHPhthalate (0.05 M) j H2(l atmos.), Pt.

fa«+ i I Acetic acid (0.1 N) I H /, nfm q N Pf
(sat.) | Na Acetate (0 ! M) I Ha(l atmos.), Pt.

(H+) = 1, quinhydrone I Pt.

Half -Cell I
Half -Cell II
Half -Cell III
Half -Cell IV
Half -Cell V

Half -Cell VI

Half-Cell VII

Half-Cell VIII KC1 (sat.) | HC1 (0.1 N), quinhydrone | Pt.

L H

HALF-CELL

III

Iva

VII

VIII

°C.

volts

volt*

0.0000

0.3380

0.251

-0.0621

(-0.229)

-0.2668

0.7044

0.6423

0.0000

0.3379

0.250

-0.0625

-0.2310

-0.2686

0.7029

0.6404

0.0000

0.3376

0.2458

-0.0636

(-0.235)

-0.2732

0.6992

0.6356

0.0000

0.3371

0.242

-0.0647

(-0.239)

0.6955

0.6308

0.0000

0.3365

0.238

-0.0657

0.6918

0.6261

0.0000

0.3361

0.236

-0.0664

0.6896

0.6232

0.0000

0.3358

0.234

-0.0668

0.6881

0.6213

Examples of experimental values (see page 479)

CELL

CITATION

CELL

TEMPER-
ATURE

CITATION

II -III

0.087

Table

III: IV

0.3094

Table

0.0885

Walpole, 1914

0.3103

Fales and Mudge, 1920

0.0874

Michaelis, 1914

0.3102S

Harned, 1926

0.0918
0.0918
0.0916b

Table
Fales and Mudge, 1920
Ewing, 1925

0.3024
0.3024

Table
Stadie and Hawes, 1928,
maximum

0 3010

Stadie and Hawes 1928

II: IV

0.4001

Table

minimum

0.4011°

S0rensen and Linder-
str0m-Lang, 1924

0.3008
0.3016

Table
Fales and Mudge, 1920

0.4012d
0.4010
0.4000

Table
Myers and Acree, 1913
Loomis and Acree, 1911

III:V

0.481
0.482

Table
Author

0.4004
0.3995

Harned, 1915
Fales and Vosburgh,
1918

III: VI

0.5178
0.5175

Table
Michaelis, 1914

O'.3985e

Cohn and Berggren,
1925

0.5190
0.5195

Table
Michaelis, 1914

II: VI

0.6048

Table

VI: IV

0.2047

Table

0.6046f

Walpole, 1914

0.2095h

Michaelis and Kaki-

numa, 1923

0.2085h

Michaelis and Fujita,

1923

a Calculated with assumption that yH+ = 0.84 and neglect of junction potential. ^ Calcu-
lated from data for Hg | HgCl, KC1 (sat.) | KC1 (1. N), HgCl | Hg. c With 3.5 N KC1 as
bridge. d 0.4009^ calculated from Scatchard's data. e Calculated. * Unconnected for
barometer? Add 0.3 m.v.? * Unconnected for change from molal to molar. ^ Special
liquid junction.

672

APPENDIX

673

TABLE B

SHOWING RELATION OF [H+] TO pH (ON THE ASSUMPTION THAT

See Chapter XXIII

[H+]

x.OO

1.000 X 10~x

x.35

0.447 X 10~x

x.70

0.200 X 10~x

x.Ol

0.977 X 10~x

x.36

0.437 X 10~x

x.71

0.195 X 10~x

x.02

0.955 X 10~x

x.37

0.427 X 10~x

x.72

0.191 X 10~x

x.03

0.933 X 10~x

.38

0.417 X 10~x

x.73

0.186 X 10~x

x.04

0.912 X 10~x

.39

0.407 X 10~x

x.74

0.182 X 10~x

x.05

0.891 X 10~x

.40

0.398 X 10~x

x.75

0.178 X 10~x

x.06

0.871 X 10~x

.41

0.389 X 10~x

x.76

0.174 X 10~x

x.07

0.851 X 10~x

.42

0.380 X 10~x

x.77

0. 170 X 10~x

x.08

0.832 X 10~x

.43

0.372 X 10~x

x.78

0.166 X 10~x

x.09

0.813 X 10~x

.44

0.363 X 10"~x

x.79

0.162 X 10~x

x.10

0.794 X 10~x

.45

0.355 X 10~x

x.80

0.158 X 10~x

x.ll

0.776 X 10~x

.46

0.347 X 10~x

x.81

0.155 X 10~x

x.12

0.759 X 10~x

.47

0.339 X 10~x

x.82

0.151 X 10~x

x.13

0.741 X 10~x

.48

0.331 X 10~x

x.83

0.148 X 10~x

x.14

0.725 X 10~x

.49

0.324 X 10~x

x.84

0.144 X 10~x

x.15

0.708 X 10~x

.50

0.316 X 10~x

x.85

0.141 X 10~x

x.16

0.692 X 10~x

.51

, 0.309 X 10~x

x.86

0.138 X 10~x

x.17

0.676 X 10~x

.52

0.302 X 10~x

x.87

0.135 X 10~x

x.18

0.661 X 10~x

.53

0.295 X 10~x

x.88

0.132 X 10~x

x.19

0.646 X 10~x

0.288 X 10~x

x.89

0.129 X 10~x

x.20

0.631 X 10~x

0.282 X 10~x

x.90

0.126 X 10~x

x.21

0.617 X 10~x

0.275 X 10~x

x.91

0.123 X 10~x

x.22

0.603 X 10~x

0.269 X 10~x

x.92

0.120 X 10~x

x.23

0.589 X 10~x

0.263 X 10~x

x.93

0. 117 X 10~x

x.24

0.575 X 10~x

0.257 X 10~x

x.94

0.115 X 10~x

x.25

0.562 X 10~x

0.251 X 10~x

x.95

0.112 X 10~x

x.26

0.549 X 10~x

0.245 X 10~x

x.96

0.110 X 10~x

x.27

0.537 X 10~x

0.240 X 10~x

x.97

0.107 X 10~x

x.28

0.525 X 10~x

0.234 X 10~x

x.98

0.105 X 10~x

x.29

0.513 X 10~x

0.229 X 10~x

x.99

0.102 X 10~x

x.30

0.501 X 10~x

0.224 X 10~x

1 + x.OO

0.100 X 10"x

x.31

0.490 X 10~x

0.219 X 10~x

1 + x.Ol

0.0977 X 10~x

x.32

0.479 X 10~x

0.214 X 10~x

1 +X.02

0.0955 X 10~x

x.33

0.468 X 10~x

0.209 X 10~x

x.34

0.457 X 10~x

0.204 X 10~x

Examples: pll = 7.00;[H+] = 1.000 X 10~7
pH = 6.63; [H+] = 0.234 X 10~6
[H+] = 1.23 X 10~8; pH = 7.91

2.34 X 10"

See Klopsteg (1921).

TABLE C

FACTORS FOR CONCENTRATION CELLS 0°C TO 70°C.

E = 0.000,198,322 T log ! (when valence = 1). A

V^2

See discussion page 250 for uncertainties.

0.000,198,322 T.

1 *

t (CENTIGRADE)

T (ABSOLUTE)

LOG A

273.1

0.054162

18.463

2.7336935

274.1

0.054360

18.396

2.7352808

275.1

0.054558

18.329

2.7368624

276.1

0.054757

18.263

2.7384382

277.1

0.054955

18.197

2.7400083

278.1

0.055153

18.131

2.7415728

279.1

0.055352

18.066

2.7431316

280.1

0.055550

18.002

2.7446849

281.1

0.055748

17.938

2.7462326

282.1

0.055947

17.874

2.7477749

283.1

0.056145

17.811

2.7493117

284.1

0.056343

17.748

2.7508430

285.1

0.056542

17.686

2.7523690

286.1

0.056740

17.624

2.7538897

287.1

0.056938

17.563

2.7554050

288.1

0.057137

17.502

2.7569151

289.1

0.057335

17.441

2.7584199

290.1

0.057533

17.381

2.7599195

291.1

0.057732

17.321

2.7614140

292.1

0.057930

17.262

2.7629034

293.1

0.058128

17.203

2.7643876

294.1

0.058327

17.145

2.7658668

295.1

0.058525

17.087

2.7673410

296.1

0.058723

17.029

2.7688102

297.1

0.058921

16.972

2.7702745

298.1

0.059120

16.915

2.7717338

299.1

0.059318

16.858

2.7731882

300.1

0.059516

16.802

2.7746378

301.1

0.059715

16.746

2.7760826

302.1

0.059913

16.691

2.7775225

303.1

0.060111

16.636

2.7789577

304.1

0.060310

16.581

2.7803882

305.1

0.060508

16.527

2.7818140

306.1

0.060706

16.473

2.7832351

307.1

0.060905

16.419

2.7846516

308.1

0.061103

16.366

2.7860635

309.1

0.0613C1

16.313

2.7874708

310.1

0.061500

16.260

2.7888736

311.1

0.061698

16.208

2.7902718

312.1

0.061896

16.156

2.7916656

313.1

0.062095

16.104

2.7930549

318.1

0.063086

15.851

2.7999355

323.1

0.064078

15.606

2.8067088

328.1

0.065069

15.368

2.8133780

333.1

0.066061

15.137

2.8199464

338.1

0.067053

14.914

2.8264170

343.1

0.068044

14.696

2.8327925

* Useful in machine calculations.

674

APPENDIX

675

TABLE D

CORRECTION OF BAROMETER READING FOR TEMPERATURE

When the mercury in the barometer is at the temperature t subtract the
following millimeters to obtain the barometic height in terms of mercury
at zero degrees centigrade.

BAROMETER READINGS IN MILLIMETERS

720

730

740

750

760

770

780

2.0

2.1

2.2

2.1

2.2

2.3

2.2

2.3

2.4

2.3

2.4

2.5

2.6

2.7

2.6

2.7

2.8

2.7

2.8

2.9

2.8

2.9

3.0

3.1

2.9

3.0

3.1

3.2

3.0

3.1

3.2

3.3

3.2

3.3

3.4

3.3

3.4

3.5

3.6

3.4

3.5

3.6

3.7

3.5

3.6

3.7

3.8

3.7

3.8

3.9

For various refined corrections of barometric readings see article on
Barometry and Manometry by Kimball in International Critical Tables,
Vol. 1, p. 68.

676

THE DETERMINATION OF HYDROGEN IONS

TABLE E

BAROMETRIC CORRECTIONS FOR H-ELECTRODE POTENTIALS
(Data for use in plotting correction curves)

Ebar.

0.000,198322 T ]o 760

TEMPER-
ATURE

CORRECTED

PRESSURE

VAPOR

PRESSURE

760
LOO —

Ebar.

•c.

mm.

WOT.

millivolts

780

769.5

-0.00537

-0.15

760

10.5

749.5

+0.00604

+0.17

740

729.5

0.01779

0.50

780

15.5

764.5

-0.00256

-0.07

760

744.5

+0.00895

+0.26

740

724.5

0.02078

0.60

780

17.5

762.5

-0.00143

-0.04

760

742.5

+0.01012

+0.29

740

722.5

0.02198

0.64

(

780

23.8

756.2

0.00218

0.06

760

736.2

0.01382

0.41

740

716.2

0.02578

0.76

780

31.8

748.2

0.00680

0.20

760

728.2

0.01856

0.56

740

708.2

0.03066

0.92

780

42.2

737.8

0.01288

0.39

760

717.8

0.02481

0.76

740

697.8

0.03708

1.13

780

55.3

724.8

0.02060

0.64

760

704.8

0.03275

1.02

740

684.7

0.04525

1.41

E. M. F. + Ebar. - Ecal.
0.000,198322 T

APPENDIX

677

VALUES OF Loo

AND OF Loo

TABLE F
a

MULTIPLIED BY THE TEMPERA-

TURE FACTORS FOR CONCENTRATION CELLS AT 20°, 25°, 30° AND 37.5°C.

/v
• +*.** .»

Cn/TIPLIED BY

1 —a

1 — a

0.058128

(20)

0.059120

(25)

0.060111
(30)

0.061599
(37.5)

0.001

-2.9996

-0.1744

-0.1773

-0.1803

-0.1848

0.005

-2.2989

-0.1336

-0.1359

-0.1382

-0.1416

0.01

- .9956

-0.1160

-0.1180

-0.1200

-0. 1229

0.02

- .6902

-0.0982

-0.0999

-0.1016

-0.1041

0.03

- .5096

-0.0878

-0.0892

-0.0907

-0.0930

0.04

- .3802

-0.0802

-0.0816

-0.0830

-0.0850

0.05

- .2788

-0.0743

-0.0758

-0.0769

-0.0788

0.06

- .1950

-0.0695

-0.0706

-0.0718

-0.0736

0.07

- .1234

-0.0653

-0.0664

-0.0675

-0.0692

0.08

- .0607

-0.0617

-0.0627

-0.0638

-0.0653

0.09

- .0048

-0.0584

-0.0594

-0.0604

-0.0619

0.10

-0.9542

-0.0555

-0.0564

-0.0574

-0.0588

0.11

-0.9080

-0.0528

-0.0537

-0.0546

-0.0559

0.12

-0.8653

-0.0503

-0.0512

-0.0520

-0.0533

0.13

—0.8256

-0.0480

-0.0488

-0.0496

-0.0509

0.14

-0.7884

-0.0458

-0.0466

-0.0474

-0.0486

0.15

-0.7533

-0.0438

-0.0445

-0.0453

-0.0464

0.16

-0.7202

-0.0419

-0.0426

-0.0433

-0.0444

0.17

-0.6886

-0.0400

-0.0407

-0.0414

-0.0424

0.18

-0.6585

-0.0383

-0.0389

-0.0396

-0.0406

0.19

-0.6297

-0.0366

-0.0372

-0.0379

-0.0388

0.20

-0.6021

-0.0350

-0.0356

-0.0362

-0.0371

0.21

-0.5754

-0.0334

-0.0340

-0.0346

-0.0354

0.22

-0.5497

-0.0320

-0.0325

-0.0330

-0.0339

0.23

-0.5248

-0.0305

-0.0310

-0.0315

-0.0323

0.24

-0.5006

-0.0291

-0.0296

-0.0301

-0.0308

0.25

-0.4771

-0.0277

-0.0282

-0.0287

-0.0294

0.28

-0.4543

-0.0264

-0.0269

-0.0273

-0.0280

0.27

-0.4320

-0.0251

-0.0255

-0.0260

-0.0266

0.28

-0.4102

-0.0238

-0.0243

-0.0247

-0.0253

0.29

-0.3888

-0.0226

-0.0230

-0.0234

-0.0239

0.30

-0.3680

-0.0214

-0.0218

-0.0221

-0.0227

0.31

-0.3475

-0.0202

-0.0205

-0.0209

-0.0214

0.32

-0.3274

-0.0190

-0.0194

-0.0197

-0.0202

0.33

-0.3076

-0.0179

-0.0182

-0.0185

-0.0189

0.34

-0.2880

-0.0167

-0.0170

-0.0173

-0.0177

0.35

-0.2688

-0.0156

-0.0159

-0.0162

-0.0166

0.36

-0.2499

-0.0145

-0.0148

-0.0150

-0.0154

0.37

-0.2311

-0.0134

-0.0137

-0.0139

-0.0142

0.38

-0.2126

-0.0124

-0.0126

-0.0128

-0.0131

0.39

-0.1943

-0.0113

-0.0115

-0.0117

-0.0120

0.40

-0.1761

-0.0102

-0.0104

-0.0106

-0.0108

0.41

-0.1581

-0.0092

-0.0093

-0.0095

-0.0097

0.42

-0.1402

-0.0081

-0.0083

-0.0084

-0.0086

0.43

-0.1224

-0.0071

-0.0072

-0.0074

-0.0075

0.44

-0.1047

-0.0061

-0.0062

-0.0063

-0.0064

0.45

-0.0871

-0.0051

-0.0052

-0.0054

0.46

-0.0696

-0.0040

-0.0041

-0.0042

-0.0043

0.47

-0.0522

-0.0030

-0.0031

-0.0032

0.48

-0.0347

-0.0020

-0.0021

0.49

-0.0174

-0.0010

-0.0011

0.50

±0.0000

0.51

+0.0174

+0.0010

+0.0011

0.52

+0.0347

+0.0020

+0.0021

For values beyond a = 0.50 the table progresses inversely as above but with sign +. Exam-
ple: a = 0.53, (1 - a = 0.47), read row for a = 0,47, i.e., log ,—^— = + 0.0522, etc. If a = 0.80,

1 — a

(1 - a = 0.20), read row for a - 0.20, i.e., log ^—^ — =* + 0.6021, etc.

678

THE DETERMINATION OF HYDROGEN IONS

TABLE G

DISSOCIATION EXPONENTS OF ACIDS

Important: Values are to be regarded as approximate. It is impracticable
to state conditions in every case. Note distinction between pK and pK' .

ACID

pK'

AUTHOR-
ITY

ACID

pK'

AUTHOR-
ITY

Acetic pK

4 73*

(4)

Malonic

2 80

Alloxan

6 6

(3)

Malonic 2d

5 68

(1)

Arsenic

2 3

(3)

Mucic . .

3 2

(6)

Arsenic 2d

4 4

(3)

Nitrous

3 4

(3) 18°

Arsenic 3d

9 2

(3)

Oxalic

1 42

9 2

(3)

Oxalic 2d

4 39

(6)

Azelaic

4 6

(1)

Phenol

10 0

(3)

Azelaic 2d

5 6

(6) 18°

Phosphoric pKi

2 11*

(10)

Barbituric

4 0

(3)

Phosphoric pK.2

7 16*

(9)

Benzoic

4 2

(3)

Phosphoric pKs

12 66*

(10)

Boric . .

9 2

(3)

o-phthalic

2 92

(1)

Butyric

4 8

(3)

o-phthalic 2d

5 41

(1)

Carbonic pKi

6 33*

(5)

m-phthalic

3 54

(1)

Carbonic . . pK2

10 22*

(5)

m-phthalic 2d

4 62

(i)

Citric

3 08

(8)

Pinaelic

2 92

(1)

Citric 2d

4 39

(8)

Pimelic 2d

5 41

(1)

Citric 3d

5 49

(8)

4 8

(3)

Formic

3 7

(3)

4 1

(6)

Fumaric

3 03

(1)

5 63

(2)

Fumaric 2d

4 49

(1)

3 0

(3)

Glucose

12 3

(3) '

4 62

Glutaric

4 32

(1)

Sebacic 2d

5 60

Glutaric2d .~7r...

5.54

(1)

Succinic

4 18

(i)

Hippuric

3 7

(3)

5 57

Hydrocyanic

9.1

(3)

Sulfanilic

3 2

(3)

Hydrogen sulphide

7 2

(3) 18°

Sulfurous

1 8

(3)

Hydrogen sulphide 2d

14.7

(7) 0°

Sulfurous 2d . ..

5.3

(3)

Itaconic .

3 8

(6)

2 56

(1)

Itaconic 2d

5 7

(6)

4 41

(1)

Lactic

3.85

(6)

d-Tartaric

3 0

(6)

Maleic

1 93

(1)

d-Tartaric 2d

4 39

(2)

Maleic 2d

6 58

(I)

Thiodiglycollic

3 31

(R)

1-malic

3 48

(6)

Thiodiglycollic 2d

4 46

(2)

1-malic 2d

5 11

(2)

Uric

5 8

(6^ 18°

* pK value.

Authorities

(1) Chandler (1908) 25°.

(2) Larsson (1922) 18°.

(3) Landolt-Bornstein (1923) 25°.

(4) Cohn, Heyroth and Menkin (1928) see page 509.

(5) Hastings and Sendroy (1925). pKi' = 6.33 - 0.5

at 38°.

(6) Scudder (1914) 25°.

(7) Jellinek and Czerwinski (1922).

(8) Hastings and Van Slyke (1922).

at 38°. pK'2 = 10.22 - 1.

(9) Cohn (1927). pKs' = 7.16

1 + 1.5

(10) Sendroy and Hastings (1927). pKi'
at 38°.

+ KSM (see page 506).
/x

2.11 -0.5 VM at 18°. pK»'

12.60 - 2.25

APPENDIX

679

TABLE H

DISSOCIATION CONSTANTS AND ASSOCIATION EXPONENTS OF BASES

[B+l [OH-]
[BOH]

= Kb

[B] [H

Kab

pKab = log

[BH]
Assumptions :

= Kw — pKb
Values of Kw taken from table 6, page 45
Values of Kb taken from Kolthof? and Furman (1926)

' BASE

Kb TEMPERATURE °C.

PKab

Ammonia

1 75 X 10*5 18°

9 37

Aniline

4 6 X lO"10 25°

4 56

Ethylamine

5 6 X 10~4 25°

10 64

Diethylamine

1 26 X 10~3 25°

11 00

Triethylamine

6 4 X 10~4 25°

10 70

Methylamine

SOX 10~4 25°

10 59

Dime thy lamine .... . .

7 4 X 10~4 25°

10 76

Trimethylamine

7 4 X 10~B 25°

9 76

Pyridine

2 3 X 10~9 25°

5 26

Urea

about (1 5 X 10~14 ?)

(0 1)

680

THE DETEKMINATION OF HYDROGEN IONS

TABLE I
DISSOCIATION EXPONENTS AND ASSOCIATION EXPONENTS OF AMINO

ACIDS AT 25°
(After Bjerrum (1923))

pKw

pK = log —

[NH2RCOQ-]

[NH2RCOOH]
[NH+RCOOH] [OH-]
[NH2RCOOHJ

13.90

[NH+RCOO-] [H+]
[NH+RCOOH]

[NH+RCOO-] [OH]
[NH2RCOO-]

P*a

PKW-
PKb

PKA

PKW-
PKB

Aliphatic:
Glycine . ...

9 75

2 33

Q 75

IVlethyl glycine

9 89

2 15

9 on

Dimethyl glycine

9 85

1 93

Q 85

Betaine

ca!4

1 34

ca!4

Alanine

9 72

2 61

972

L/eucine

9 75

2 26

9 75

Phenylalanin

8 60

2 01

C Af)

Tyrosine

8 40

2 51

8 40

Glycyl glycine .

7 74

3 20

7 74

Alanyl glycine

7 74

3 20

7 74

Leucyl glycine . .

7 82

3 38

7 82

Taurine

8 8

caO

cctO

8 8

Asparagine

8 87

2 08

c 07

[First step . .

<6 94

1 94

Lysine < 0 , *
I feecond step

1 94

fi Q4

[First step

>13 96

6 9

2 24

ca!4

Argmme \Second step

2 24

7 0

Histidine (*irst •te?
(Second step

8.66

5.66
1 60

1.60

8.66
.5 fifi

. , [First sten

3 82

1 Q8

10 1

Aspartic acid < 0
[becond step

12 1

3 82

Aromatic :
o-amino benzoic

4 98

2 04

4 98

m-amino benzoic

4 92

3 27

4 92

p-amino benzoic

4 80

1 Q8

4 80

o-benzbetaine

>14

1 35

—0 1

m-benzbetaine

>14

3 43

—0 1

p-benzbetaine

ca!4

3 41

ca— 0 1

o-amino benzene sulfonic acid,
m-amino benzene sulfonic acid. .
p-amino benzene sulfonic acid. . .

2.48
3.73
3.24

APPENDIX

681

TABLE J

ALKALOIDS— HALF TRANSFORMATION POINTS AT 15°C. AS DETERMINED
ROUGHLY BY KOLTHOFF (1925)

pK = 14.2 - log

ALKALOID

pK'

ALKALOID

Aconitine

8 32

Brucine

8 16

2 50

Atropine

9 85

Cinchonine

8 35

4 28

Cocaine

8 61

Emetine

8 43

7 56

Codeine

8 15

Nicotine

8 04

3 24

Coniine

11 10

Novocaine

9 05

2 47

Morphine .

8 07

Quinine

8 23

4 50

Thebaine

8 15

Strychnine

8 20

2 50

682

THE DETERMINATION OF HYDROGEN IONS

TABLE K

RELATION OF PERCENTAGE REDUCTION TO POTENTIAL AT CONSTANT pH

[Sr]

DETERMINED BY Eh = E'0 - 0.03006 LOG

[So]

AT 30°C.

(Values rounded to nearest millivolt)

EBDXJCTION

-0.03006 LOG ||4

[CO]

REDUCTION

- 0.03006 LOG |^j

per cent

volts

per cent

volts

+0.060

-0.003

0.051

0.005

0.038

0.008

0.029

0.011

0.023

0.014

0.018

0.014

0.023

0.011

0.029

0.008

0.038

0.005

0.051

+0.003

-0.060

±0.000

APPENDIX

683

TABLE L

Eo' VALUES FOR SEVERAL OXIDATION-REDUCTION INDICATORS, 30°C.
(Values rounded to nearest millivolt)

o
a

DLPHONA1

H
p

JULPHONJ

HENOL IN

o
§

8 GREEN

OL INDO-

eji 3

•

ifc

«S

*3 O

ft J

i
s

•LTJYLE

III

6-DICH
0-CRE8

6-DICH
PHENO

NDSCH:

CHLORi
PHENO

•BROMC

PHENO:

<N~

5.0

-0.010

0.032

0.065

0.101

0.221

0.262

0.335

0.366

0.335

5.2

0.022

0.020

0.053

0.088

0.208

0.249

0.322

0.352

0.320

5.4

0.034

+0.008

0.041

0.077

0.196

0.236

0.307

0.339

0.307

•

5.6

0.045

-0.004

0.029

0.066

0.184

0.223

0.292

0.325

0.293

5.8

0.057

0.016

0.017

0.056

0.173

0.210

0.277

0.310

0.281

6.0

0.069

0.028

+0.006

0.047

0.162

0.196

0.183

0.261

0.295

0.270

0.301

6.2

0.081

0.039

-0.006

0.039

0.151

0.181

0.171

0.245

0.279

0.259

0.288

6.4

0.092

0.051

0.017

0.031

0.141

0.166

0.159

0.228

0.263

0.249

0.275

6.6

0.104

0.061

0.027

0.024

0.132

0.150

0.147

0.212

0.247

0.240

0.262

6.8

0.114

0.072

0.037

0.017

0.123

0.134

0.135

0.196

0.232

0.248

7.0

0.125

0.081

0.046

0.011

0.115

0.119

0.123

0.181

0.217

0.224

0.233

0.248

7.2

0.134

0.091

0.055

+0.004

0.108

0.103

0.111

0.166

0.203

0.217

0.218

0.235

7.4

0.143

0.099

0.062

-0.002

0.101

0.088

0.099

0.152

0.189

0.210

0.203

0.221

7.6

0.152

0.107

0.070

0.008

0.094

0.073

0.087

0.138

0.175

0.204

0.187

0.208

7.8

0.160

0.114

0.077

0.014

0.088

0.060

0.074

0.125

0.162

0.197

0.170

0.193

8.0

0.167

0.121

0.083

0.020

0.082

0.046

0.062

0.112

0.150

0.155

0.178

8.2

0.174

0.127

0.090

0.026

0.075

0.034

0.049

0.099

0.137

0.139

0.163

8.4

0.180

0.134

0.096

0.032

0.069

0.021

0.026

0.087

0.125

0.124

0.148

8.6

0.187

0.140

0.102

0.038

0.063

+0.010

0.023

0.075

0.113

0.109

0.133

8.8

0.193

0.146

0.108

0.044

0.057

-0.002

+0.010

0.063

0.101

0.095

0.117

9.0

-0.199

-0.152

-0.114

-0.050

0.051

-0.012

-0.003

0.051

0.089

0.082

0.103

* Unstable in this region of pH.
t Decomposes in this region of pH.

684 THE DETERMINATION OF HYDROGEN IONS

TABLE M
SYMBOLS AND CONVENIENT FORMULAS

For notation see definitions in text as a notation is introduced
(A) Read: The activity of A.
[A] Read: The concentration of A in moles per liter, unless otherwise

specified.

= Read: Is approximately or essentially equal to.
= Read: Is equal to.
= Read: Is identical with.
> Read: Is greater than.
< Read: Is less than.
f Symbol of integration.
S Read: The sum of all terms following.
A Read: The increment of.
II Read: Liquid junction potential is here considered to be eliminated

or otherwise allowed for.
| Read: There is a potential difference here.

J Read: There is a junction potential here and the junction is a flow-
ing junction.

In Read: Logarithm to the base e.
log Read: Logarithm to the base 10.
log x = 0.43429 In x
In x = 2.3026 log x
d Read: The infinitesimal increment of or differential of.

d(a^) d v

-^— ' = arln a —

dx d x

pH s log ; — — (formally). For the experimental meaning see Chapter

XXIII.

pK s log — (formally). For experimental meaning compare with pH.

JEV

Internet Archive Audio

Featured

Top

Images

Featured

Top

Software

Featured

Top

Books

Featured

Top

Video

Featured

Top

Mobile Apps

Browser Extensions

Archive-It Subscription

Save Page Now

Full text of "The determination of hydrogen ions; an elementary treatise on the hydrogen electrode, indicator and supplementary methods, with an indexed bibliography on applications"

See other formats