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A TEXT-BOOK OP ELECTRO-CHEMISTRY

^Jrt^^

A TEXT-BOOK OF

ELECTKO-CHEMISTRY

MAX LE BLANC

PROFESSOR IK THE UNIVBRSITT OF LBIPZIO

TBANSLATED FROM THE FOURTH ENLARGED GERMAN

EDITION

WILLIS R. WHITNEY, Ph.D.

BIRBOTOB or THB BB8BARCH LABO&ATORT OF THB
OBBBBAL BLECTBIC COMPAMT

AND

JOHN W. BROWN, Ph.D.

BIBBCTOB or THB BB8BABCH AHD BATTBBT LABOBATOBT
or THB NATIOHAL GABBON OOMPABT

THE MACMILLAN COMPANY

UOVDOS: THE MACMILLAN CO., Ltd.

1910
All right* ruennd

CUvv^ ^Uc<f, JC>, 3

c^^

^ COTYEXOBT, 1907,

bt thb macmillan company.

Set up ftad dectrotjrped. Publiihed March, 1907. Reprinled
March, 19x0.

» ••

KARVAR9 COLLEGE UDRARY

GIFT OF

V/ILLI9 A. &OUGl!TON

J. B. Cnshinff Oo. —Berwick dt Bmlth Oo.
Norwood, Maaa., U.8.A.

HIS TEACHER

PBOFESSOR WILHELM OSTWALD

THIS BOOK

IB 6BATEFULLT DEDICATED

BT THE AUTHOR

EXTRACT FROM THE AUTHOR^S PREFACE TO

THE FIRST EDITION

Thb present work was nearly completed in connection with the
course of lectures given by me during the winter of 1894-1895. It
is meant, first of all, for students of science; for such persons as,
having completed their studies, are already in practice; and, finally,
for whoever is interested in electro-chemistry. I have endeavored
to write as clearly and simply as possible, but those who have but
slight previous knowledge must study the book carefully in order
to obtain the greatest benefit from it In modem electro-chemistry
there are certain methods of conception which any one studying the
subject must make his own, and this cannot be done without work.

M. LE BLANC.
Lmrzio, September, 1896.

vii

AUTHOR'S PREFACE TO THE FOURTH EDITION

DuBiNO the three years which have passed since the appearance
of the third edition of this book^ an abundance of work has appeared
in the domain of electro-chemistry. The difficully of including
all of the essentials of the science without unduly increasing the
size of the book is continually increasing. I have given my best
effort to overcome it.

Up to the present there has appeared an English translation of
the first edition, an Italian translation of the second edition, and
a French translation of the third edition of this book.

Shortly after the appearance of this, the fourth (German edition,
an English translation of it will be published.

For assistance in reading the proofs, I am this time indebted to
G. Just, Ph.D., and A. Kdnig, Dipl. Ing. I am also indebted to
Professor Abegg for valuable suggestions.

M. LE BLANa

KASL8KUHB, BADUT,

August, 1906.

yiii

TRANSLATORS* PREFACE

Thk present work is a translation of the fourth Gterman edition,
and is essentially a revision and enlargement of that of the first
German edition prepared hy one of the present translators. Although
in its preparation the earlier translation has been freely used, the
changes and additions made by Professor Le Blanc, as well as
minor additions introduced by tJie present translators, have either
necessitated or rendered advisable the rewriting of a large part of
the book. The additions made by the translators have been in-
closed in brackets.

Special attention has been given to the following: —

The Notation. A consistent system of notation has been used
throughout the book. An outline of it will be found in the Appendix.

The Nomenclature. We have endeavored to make the nomen-
clature conform to that of the best recent text-books of electricity
and chemistry.

The lUtutrationa. Of the 62 illustrations, 25 are new ones intro-
duced by the translators, and 21 have been redrawn.

Special credit is due Mrs. J. W. Brown for aid in preparing the
manuscript and in reading the proofs.

W. R. WHITNEY,
J. W. BfiOWlff.

CONTENTS

CHAPTER I

THB FOHM8 OF BNBROT AND THEIR mASUBBBCElTT.
THB FXTRDABSBNTAIf PBINdPUaS HELATINO TO
BLBCTRICAL BETEROT

Energy and its forms 1

Measurement of mechanical, heat, and electrical energy .... 1

Electric currents and their proi>erties 6

Electromotiye force, current, and resistance 7

Electrical equiyalent of heat 16

Electric furnace and its industrial importance 18

Dark or silent electrical discharge 28

Electrical capacity 24

Positiye and negative electric!^. The electrometer 26

Electrical measurements 27

CHAPTER n
DEVBLOPMEITT OF ELECTRO-CHEBnSTRT UP TO

Eariiest records of electrical phenomena 81

Work of Oalvani 82

WorkofVolta. The Voltaic pile 88

Electrolytic decomposition of water 86

Measurements of the potentials of a Voltaic pile 87

Migration of acid and alkali and the discorery of the alkali metals . 88

Rise and fall of the electro-chemical theory of Berselius .... 40

Laws of electro-chemical change 42

Electro-chemical nomenclature . .44

Development of the present theory of electrolysis. The Grotthus theory . 44

Conductance of solutions and the constitution of ions .... 46

Replacement of the Grotthus theory by the Clausius theory ... 47

Relation between chemical and electrical energy I 49

zii CONTENTS

CHAPTER ni

THB THSOBT OF BLBCTBOLTTIC DISSOCIATION

The lawB and theories lelating to osmotic preeBore G2

Abnormality of acids, bases, and salts. Electrolytic dissociation . 57

Calculation of the degree of dissociation 58

Dissimilarity between gaseous and electrolytic dissociation. The ions • 59

Ionization aocozding to the material conception of electricity . • • (K)

CHAPTER IV

THB mOBATION OF IONS

The migration of ions 02

CHAPTER V

THB CONDnCTANOB OF BLECTROLTTB8

Specific and equiyalent conductance 85

General regularities 89

Application of the mass-action law to gaseous and to electrolytic disso-
ciation 95

Determination of the electrical conductance of electrolytes. The method

ofKohlrausch 98

Method of Nemst and Haagn 104

Calculation of the dissociation constant from electrical conductance . . 105

Relation between dissociation constants and chemical constitution . Ill

Velocity of migration of individual ions 116

The absolute velocities of the ions 119

Electrolytic frictional resistance 128

The limited applicability of the Ostwald dilution law. Empirical rules . 124

The conductiyity and degree of dissociation of water 128

Supersaturated solutions 129

Temperature coefficient 180

Heat of dissociation 188

Influence of pressure 185

Mixed solutions. Isohydric solutions. Application of electrical conductiyity

to chemical analysis 186

Regularity of ionization. Reactivity of electrolytes 141

Solvents other than water. Relation between the dissociating power and

the dielectric constant of solvents 142

The internal friction and conductance of organic solvents • . . .151

The electrical conductance of salts in the fused and solid states . . . 158

CONTENTS xiii

rAGB

Unipolar condaotioii • • • 164

Technioal impoxtanoe of electrical condootiTi^ 166

CHAPTEB VI

BLBCTBICAIi EZTDOSMOSn MIGRATION OF SUSPENDBD
PARTICLES AND OF COLIiOIDS. BLECTRO-STBNOLT-
818

Electrical endosmoee. Migration of suspended particles and of colloids.

Electrowitenolysis 167

CHAPTER Vn

ELBCTROMOTIVB FORCB

The determination of electromotive force 161

Beyersible and irreversible cells 164

Relation between chemical and electrical energy H 166

Electrolytic solntion pressure 176

Calculation of the electromotiye force existing at the surface of reTersible

electrodes 181

Concentration cells 184

Different concentration of the substances which axe electromotiyely

active 184

Different concentrations of the ions 107

Concentration double-cells 211

Use of the electrometer as an indicator in titration 216

Liquid cells 217

General consideration of concentration and liquid cells .... 224

Thermoelectric cells — the electromotive series 228

Chemical cells 231

Determination of single potential-differences 234

Influence of negative ions upon the potential-difference, Metal — metal

salt solution 240

Cells in which the electromotively active substances are not elements . 250
Formation of potential-difference at the electrodes. Spontaneous evolution

of oxygen or hydrogen. The process of current production . 263

Electromotive force and chemical equilibrium 267

Velocity of ionization. Passivity. Catalytic influence .... 276

(General theory of the course of the electro-chemical reactions • . . 281

Elements possessing double natures 284

xiv CONTENTS

CHAPTER Vin
BLBCTROL7SI8 AND PO£

FAAB

Method of meararing polarization 286

Deoomposition valaes of the electromotive force. The hydrogen-oxygen

cell. Primary and secondary decomposition of water . . 988

Importance of the decomposition voltage in making electrolytic separations

and in preparing new compounds 800

Electrolysis with an alternating current 816

Electrolysis without electrodes 817

Decomposition voltage and solubility 818

CHAPTER IX

SUPPLEMENT. STORAGE CELLS OB ACCUMXTLATORS

Supplement. Storage cells or accumulators 821

APPENDIX

NOTATION
Notation • • • • • 887

A TEXT-BOOK OF ELECTRO-CHEMISTRY

CHAPTER I

THB FORBCa OF ENERGT AND THBIR MBA8XTRBBCBNT.
THB FXntDAMHNTAIi PBINCIPLB8 RBLATINa TO BLBC-

Energy and its Ponns. — A clear conception of the funda-
mental principles relating to the forms of energy, especially of
electrical energy, is essential to the successful study of electro-
chemistry. For this reason, before beginning the study of electro-
chemistry proper, these principles will be considered briefly.

Energy plays a most important part in human affairs. When
food or coal is bought, it is the energy content that chiefly concerns
the buyer. Similarly when a current of electricity is delivered to
the consumer, it is the quantity of electrical energy so deliyered
that is of greatest importance and that determines the price to
be paid.

Energy may be subdivided into five distinct kinds or /omw of

energy; namely: —

Meohanioal bnxbgt,

Hkat energy,

Eleotbical energy,

Chemical energy, and

Badiant energy.

These forms of energy are mutually transmutable.

The Xeasnrement of Mechanical, Heat, and Electrical Energy.

— The units used in the measurement of mechanical energy are
grouped into two systems; namely, the Meter-Elilogram-Hour
(M. K. H.) System and the Centimeter-Gram-Second (C. G. 8.) Sys-
tem. In the former, the technical, system, the unit of mechanical
energy or work is that quantity of energy or work which is required to
raise a kilogram weight one meter in height. In the centimeter-gram*

2 A TEXT-BOOK OF ELECTRO-CHEMISTRY

second system, which is used in all exact scientific work, the unit of
mechanical energy, the erg, is that quantity of energy or work which
is required to displace a unit of force through a unit distance. The
unit of force, the dyne, is defined to be that force which is required
to produce an acceleration of one centimeter per second in a mass of
one gram. The relations between these units are represented by the
following equations : —

Force (F) in dynes = Mass (M) in grams x Acceleration (A) in
centimeters per second.

Mechanical energy (EJ) in ergs = Work ( W) in ergs = Force (F)
in dynes x Distance (d) in centimeters.

In scientific work, it is very important to distinguish clearly
between mass and weight. Mass is an unchangeable property of
matter, while weight, since it is the force with which a quantify of
matter is drawn toward the earth's center, is a property of matter
which varies according to the location on the earth's surface. The
unit of mass, called the gram-mass, is defined to be equal to the
mass of one cubic centimeter of water at four degrees,^ the tempera-
ture of its maximum density. That mass of any other substance
which, under the influence of a given force, receives the same accel-
eration as does one cubic centimeter of water, under the influence of
the same force, may also be taken as a unit of mass. The unit of
weight, called the gram-weight, is defined to be that force with which
a gram-mass is attracted toward the earth's center. Since this
attractive force, at a latitude of 45 degrees and at sea level, pro-
duces an acceleration of 980.6 centimeters per second in a gram-mass
when falling freely, it is equal to 980.6 dynes.

The relations which exist between the technical unit, the meter-
kilogram, and the scientific units, the gram-centimeter, the erg, and
the joule, are given by the following equations : —

1 M. Egm. = 10* cm. gm. » 10* x 980.6 ergs s 9.806 joules.

With these units defined, it is now possible to measure and to
compare various quantities of mechanical energy, or work.

The unit of heat energy, called the calorie, is that quantity of heat
which is required to raise one gram of water from 15^ to 16^ t

Having now defined the units for two of the energy forms, it is
possible, with the aid of the law of the conservation of energy, to
determine the relation between these units. By direct experiment, a

1 As a matter of fact, however, the unit of mass is ooe thousandth part of the
mass of a certain piece of platinom kept at Paris, iHilch is very nearly one thousand
times as great as the ahove theoretical unit.

FORMS OF ENERGY AND THEIR MEASUREMENT

known quantity of mechanical energy has been completely tnuuh
formed into heat energy, showing the following relation between the
nnits of mechanical and those of heat energy : —

.1890 X IV ergs or 42720 cm. gms. « 1 calorie.

This relation between the erg or joule and the calorie is called the
mechanical equivcUerU of heat.

In an analogous manner, the relations between the units of all the
other forms of energy could be found if units for these forms of energy
were known. Since, however, besides mechanical and heat energy,
only electrical energy has, at present, well-defined units, there
remains to be considered an electrical-heat, and an electrical-
mechanical, equivalent.

Accepting the transmutability of the energy forms without ques-
tioning the conditions under which such transmutation takes place,
the case of transference of energy between two systems in contact
with each other and containing unequal quantities of the same
form of energy will now be studied. This study will be carried out
with two gaseous systems possessing different quantities of volume
energy, a kind of mechanical energy which may be expressed in
terms of the mechanical units already defined.

Let us first consider the system represented by Figure 1, consist-
ing of a gas reservoir O closed by a weightless and frictionless pis-
ton j9, and placed in the vacuum F.
The gas contained in the reservoir
is now said to possess a definite vol-
ume energy, since it possesses the
power of doing a definite quantity
of work by expanding against a
pressure. If, when the gas sup-
I>orts a 100-gram weight upon the
piston, the latter is in the position
a, and if, upon heating the gas,
the piston and weight are raised to
the position &, 60 centimeters above
a, a weight of 100 grams is raised

60 centimeters at the expense of the volume energy of the gas.
The work done may be expressed as follows : —

ir» F(100 gms.) X d (50 cms.) s 6000 gm. cms.
If, now, the piston has a cross section of 100 square centimeters,

Fxo. 1

A TEXT-BOOK OF ELECTRO-CHEMISTRY

Fio. 2

each square centimeter of it exerts a pressure of one gram on the gas.
The gas is, then, under a pressure of one gram per square centi-
meter. The volume increase, when the piston rises from a to 6,
is 5000 cubic centimeters. Hence the product of the pressure, in
grams per square centimeter, and the volume, in cubic centimeters,
is 5000, a value identical with the number of gram-centimeters of
work done during the expansion. The work done may therefore be
expressed as follows : —

Work =s Pressure (1 gm.) x Volume (5000 cu. cm.) sa 5000 gm. cm.

Let us next consider the horizontal vessel represented in Figure 2,
which is provided with a movable piston p, on one side of which is

hydrogen and on the other
nitrogen. If, now, the
two gases exert equal
pressure upon the piston, '
it remains motionless and
no transference of energy
from one gas to the other
takes place, although the
energy possessed by the
nitrogen is much greater than that possessed by the hydrogen.
This difference in the energy of the two gases can be made as great
as desired by increasing the volume of the nitrogen and decreasing
that of the hydrogen, without causing the piston to move. Hence
it is evident that the quantity of energy possessed by the two gases
does not determine whether or not a transference of energy will
take place between them. If, however, we decrease the volume, and
thus increase the density and consequently the pressure of one of
the gases, the piston is at once set in motion, resulting in an expan-
sion of the gas under the greatest pressure and a corresponding com-
pression of the other. During this change, the gas undergoing
expansion loses a definite quantity of volume energy, while that
undergoing compression gains the same quantity. When the piston
has again come to rest, the same pressure is exerted upon the
piston by each of the two gases. The rekUive pressures, then, and
not the relative voluTnes of the two gases, determine whether or not a
transference of energy wiU take place between the two gases.

It has already been shown that the volume energy of a gas may
be represented as the product of two factors according to the
equation,

FORMS OF £N£R6Y AND TH£IR MEASUREMENT

The factor p, as shown above, determines the equilibrium of a
gaseous system and for this reason is called the intensUy factor. The
other factor v is defined by the equation,

E^ Volume Energy
^ jj *^ Intensity Factor*

It determines the quantity of volume energy for any given value
of the intensity factor j9, and is called ^A€ capacity factor.

A similar resolution of several of the other forms of energy into
two such factors has been made, which has greatly facilitated the
understanding of energy phenomena. In each case, the following
general equations represent the relation between the energy E^ its
intensity factor/ and its capacity or quantity factory^

E^fiXfe

The

^ — y< ^K Jc*

The intensity and capacity factors of electrical energy E^ are
the electromotive force f and the quantity of electricity q. The
relation between electrical energy and its factor is, then, represented
by the equation,

CaSCV

ZnSQ4

i^AMW

^, = F X Q.

This will be made clearer in the following pages.

Bleotrio Currents and their Properties. — On account of our
limited sense of perception of electrical phenomena, we cannot
comprehend them to the extent possible in the case of the
phenomena of mechanical en-
ergy. In order to comprehend
and control them the actions and
effects of electrical energy must
be studied, for even the idea of
a unit of work or of a unit of
length, such as the meter, could
not l^ comprehended if the ac-
tion of a unit of work or the
length represented by the meter
had not been observed.

Consider a vessel divided into
two parts by means of a porous

plate, e. g., of unglazed porcelain, as shown in Figpire S. If
into one part of the vessel is poured a solution of copper sulfate,
and into the other a solution of zinc sulfate, and a rod of copper is
placed in the copper sulfate solution and a rod of zinc in the zinc

FiaS

« A TEXT-BOOK OF ELECTRO-CHEMISTRY

-sulfate solution, we have an arrangement called a galyanic cell. If
now the zinc and copper rods, the two poles of the cell, be connected
by means of a wire, the latter becomes heated. If a magnetic needle
be placed near the wire, the needle is turned from its natural
position. Finally, if the wire be cut, its two ends fastened to
pieces of platinum foil, and these pieces of foil be dipped into a
solution of copper sulfate in such a manner that they are not in
contact with each other, it is observed that metallic copper deposits
upon one of the pieces of platinum.

From these observations, we must conclude that something has
taken place in the wire, for the wire always produces these three
effects when connecting the zinc and copper poles of the cell and
never produces them when disconnected from them. Whenever a
wire produces these effects, a current of electricity is said to be passing
orjlotoing through it.

It is conceivable that a wire might be found which, when con-
necting the poles of a galvanic cell, would affect the magnetic
needle but not become heated, which, therefore, would not produce all
of the three effects stated above to be characteristic of a wire conduct-
ing an electric current. This was formerly supposed by many to be
true, but, as a matter of fact, such is not the case. From long
experience, it is known that whenever a wire produces one of these
three effects it always produces the other two, together with a
number of other effects which are not of interest at this point.
That some of these effects may be made inappreciably small does
not contradict the above statement.

These properties of the electric current which serve to detect its
presence being known, it is now possible by means of suitable
arrangements to study the other properties of the electric current.
Considering again the galvanic cell, if ^the wire is left in its former
position with the exception that the end which was joined to the
zinc rod is now joined to the copper rod, and the other end is now
joined to the zinc rod, the same effects of the electric current are
again observed with the simple difference that the magnetic needle
is deflected in the opposite direction, and that the metallic copper is
deposited upon the other piece of platinum. Therefore we may
properly speak of tJie direction of an electric current.

Naturally, the next thing to be determined is whether the deflec-
tion of the magnetic needle or the amount of copper deposited upon
the platinum in a given time remains constant or varies, and, in the
latter case, to determine upon what the variation depends. If, to
this end, the connecting wire be lengthened, it is observed that the

FORMS OF ENERGY AND THEIR MEASUREMENT

1U8 /"~"

■W^

-'V^V

■wv»-

late of the deposition of copper is decreased \ while if the wire is
shortened, the rate is increased. We must conclude from these facts
that the electric current has a strength depending upon circumstances.
This giyes us the conception of current-length of an electric current.

The current-strength varies inyersely as the length of the connect-
ing wire. Therefore the wire hinders or opposes to a certain extent
the passage of the electric current, and is said to possess a certain
resistimce.

It has now been observed that the greater the resistance of the wire,
the less thQ current. The question now arises whether or not it is pos-
sible to change the current-strength without changing the resistance.
Experiment has shown
that it is possible to thus
change the current,
instead of using one gal-
vanic cell, two are used,
the zinc rod of one cell
being connected with the
copper rod of the other,
as shown in Figure 4, it
is observed that a much

greater current is ob- ^^ ^

tained, although the re-
sistance of the second cell has been added to that of the wire ; that
is to say, the electric current starting say at *a must pass through
the wire ac and also through the cell 11 before it reaches the
pole b. The second cell acts as if it had increased the pressure or
force by which the electric current is driven through the wire.
Consequently, we come to speak of the electriccU pressure, or etectro-
motive force w of the current.

It is assumed that the terms current, resistance, and electromotive
force are no longer meaningless concepts, but that they possess a real
significance to the reader. We may, therefore, proceed to the con-
sideration of the units in which these quantities are expressed. This
consideration will be of a much simpler nature than that by which
the units were first established.

Eleetromotive Force, Current, and Sesistanoe. — The electromotive
force of a galvanic cell such as has been used in the previous discus-
sion (called the Daniell cell, from its discoverer), when the concen-
tration of the copper sulfate is equal to the concentration of the zinc
sulfate, is defined to be 1.10 units, called volts. The resistance of a
column of mercury^ 106.3 centimeters in length and one square milli-

8 A TEXT-BOOK OF ELECTRO-CHEMISTRY

meter in cross section, at 0° t, is defined to be one unit, called an ohm.
Finally, a current which deposits 0.3294 milligram of copper in a
second is defined to be one unit, called an amptre.^ These units
may be tabulated, briefly, as follows : —

Unit of E. M. F. = Volt « E. M. F. of the Daniell cell -t- 1.10.
Unit of current s Ampere as Current which deposits 0.33 mg. of

copper per second.
Unit of resistance ss Ohm = Resistance of a mercury column, 106.3

cm. X 1 sq. mm.

Why these particular values have been chosen as units need not be
discussed here, for this question belongs more to the history of
electrical science.

It has already been observed that the current depends upon the
electromotive force, on the one hand, and upon the resistance on the
other. The assumption was made by Ohm that the current is
directly proportional to the electromotive force and inversely pro-
portional to the resistance. This assmnption, which is also expressed
by the equation,

Current (o) = g^^^^^^o^^^ ^o^ {^) ^

Resistance (b)

has been found by experiment to be universally true. In this equa-
tion, f is a ratio factor, depending on the units in which the current,
electromotive force, and resistance are expressed. However, the
units defined above are so related that if , in a circuit whose resist-
ance is one ohm, an electromotive force of one volt exists, the cur-
rent flowing through the circuit is one ampere. Consequently the
above factor in this case is equal to unity. Hence the equation,

With the above units and their mutual relation known, it is now
possible to consider how an unknown electromotive force or an un-
known resistance may be determined. It is evident that the current
in amperes may be determined by simply finding the number of
milligrams of copper deposited by the current in one second and
dividing by the number of milligrams of copper deposited in the

1 These terms, volt, ohm, ampere, coultmb, farad (the last two terms will
be explained later), have been derived from the names of the following pioneen
of electrical science : Volta, Ohm, Ampere, Coulomb, and Faraday.

FORMS OF ENERGY AND THEIR MEASUREMENT 9

same time by a current of one ampere, namely, by 0.3294. This is
also expressed by the equation,

c (in amperes) -- milligrams of copper deposited per seoond

The resistance of the circuit may now be determined by connect-
ing it to the poles of a Daniell cell and measuring the current pro-
duced by it in the manner just outlined. If the current is found to
be 0.001 ampere, then, since the electromotiye force of the Daniell
cell is equal to 1.10 yolts, the resistance may be calculated by means
of Ohm's law as follows :

Then^ by substitution of numerical for literal values^

1.10 volts

0.001 ampere

= 1100 ohms.

Mnally, an unknown electromotive force may be determined by
introducing it in the above circuit in place of the Daniell cell, the
resistance of the circuit remaining unchanged, and again measuring
the current produced in the circuit. If, in this case, the current is
found to be equal to 0.01 ampere, then, since the resistance of the
circuit is known to be 1100 ohms, the electromotive force may be
calculated as follows : —

O.J.

or V = CB.

Then by substitution of numerical for literal values, -»

F =s 0.01 ampere x 1100 ohms =s 11 volts.

In order to obtain a still clearer conception of the electric current,
let us consider its analogy to a stream of water. The electromotive
force or electrical pressure corresponds to the pressure of the water,
the electrical resistance offered by the conductor of electricity to the
frictional resistance offered by the conductor of water, and the
strength of the electric current to that of the current of water.
When a certain current of water is spoken of, it is meant that, in a
unit of time, a certain quantity of water passes through a cross

A TEXT-BOOK OF ELECTRO-CHEMISTRY

section of the conductor. A unit for water currents has not been
established for scientific use, but such a current as would cause one
cubic meter of water to pass through a cross section in one second
might, for example, be considered to be such a unit.

Just as we speak of the quantity of water in a water current, so
we may also speak of the quantity of electricity in the electric
current, without necessarily imagining the electricity to be of a
material nature. Accordingly, when a current of electricity of one
ampere is flowing in a conductor, it is proper to say that a unit
quantity of electricity passes through a cross section of the conduc-
tor in one second. This unit of quantity of electricity is called the
coulomb. The total quantity of electricity which passes through a
cross section of a conductor is, then, equal to the product of the
current by the time during which the current passes. This is ex-
pressed by the following equation : —

Quantity of electricity, in coulombs =s

Current, in amperes, x Time, in seconds.

In electrical science, it is usual to distinguish between electro-
motive force and potential or voltage (potential-difference or
voltage-difference). The term dectromoHve force is applied to the
potential-fall in a cell, which remains a constant value as long as
the cell remains constant. It may be compared with the original,
constant pressure which forces a quantity of water through a pipe.
The term potentialf or voltage^ is applied to the variable electrical
pressure which is found at different points along a conductor. The
distinction between these two terms will be made clearer in the
following pages.
In most courses in physics, the following experiment is per-
formed: Water,
under a certain
pressure, is driven
through a narrow,
horizontal tube of
uniform bore, upon
which are a num-
ber of upright
manometer tubes,
as shown in Fig-

'^•' The height of

the water in each of the upright tubes is a measure of the pressure

FORMS OF ENERGT AND THEIR MEASUREMENT 11

with which the water is being driven through the horizontal tube
at that point. Considering the tube from a to b, it is seen that the
pressure of the water decreases in a regular manner from p^ to p'^,
and that with the latter pressure the water leaves the tube. Cor-
responding to the decrease in pressure along the tube ab, there is a
decrease in the quantity of work which can be obtained when a
given quantity of water flows through the tube^ as will be evident
from the following discussion : —

The quantity of work which can be obtained from a given quan-
tity of water Q., leaving the reservoir at the point a or c, under
a pressure p^ per square centimeter^ is equal to Q^p^ But the
quantity of work which can be obtained from the same quantity of
water leaving the tube ab at b, under a pressure p*^ per square
centimeter, is equal to Q^p ». Hence the quantity of water Q^, in
moving through the tube from atob, has decreased its power to do
work from Q^p^ to Q^p'^ and the quantity of energy Q^p^ — QwP* wy
or Q^{Pw — P*w) l^&Sy therefore, been consumed in overcoming the
resistance which the tube offers to the passage of the water. This
quantity of energy has been changed into heat, which has been
absorbed by the surroundings and consequently lost. From this it
is evident how much depends upon the size of the conducting tube ;
for the greater the size of the tube the less is the resistance which it
offers to the passage of a given quantity of water, and consequently
the greater the quantity of available work at its exit.

Similar relations are found in the case of the electric current, as
will at once be shown. Consider the wire AB^ shown in Figure 6,
which represents a com-
plete electric circuit in T
the form of a straight
line. Just as the pres-
sure of the water at
different points along
the conducting tube was
measured by means of
upright manometer j
tubes, so the tension or ' ' ^^ ^»

r--.

! ^-v

**.

iJ^

potential of the electric-

ity along the conducting ^la, 6

wire can be measured by

an electrometer, an instrument which will be described later on.

In this manner the potential at the point A (which is identical with

the electromotive force of the circuit) is found to be v^ and at the

12 A TEXT-BOOK OF ELECTEO-CHEMISTRY

point JB to be zero, when B is connected to the earth by a conductor.
Furthermore, just as in the case of the water flowing through the
horizontal tube, the quantity of work which can be obtained at the
point A from a quantity of electricity q, at a potential or under an
electrical pressure f, is equal to fq. Similarly, the quantity of work
which can be obtained at the point B from the same quantity of
electricity at a potential, or under an electrical pressure Fo, is equal
to FqQ, or zero, since Fq is equal to zero. Hence the quantity of
electricity q, in flowing through the wire from A to B, has de-
creased its power of doing work from fq to FoQ, or to zero, and
therefore the entire electrical energy fq has been changed into
heat in overcoming the resistance which the wire offers to the pas-
sage of the electricity. The heat has disappeared into the sur-
roundings. The same is true of every electrical circuit in which no
work is done.

If now work is caused to be done, as, for example, in the decom-
position of a solution, at some point in the circuit almost the entire

electrical energy can be
^r *— *•. transformed into useful

I ****! work ; and, moreover, it

{ i* is entirely immaterial at

{ J I what point of the circuit

J I \ the work is done. Only

] I \ a small part of the en-

J { «p^ ^^EJf depending upon

I J r -^^^ the material and seo-

l ■' @ ^"^T^ > ^o tional area of the cir-

Fio.7 the surroundings. A cir-

cuit in which the elec-
tric energy is nearly completely transformed into work is repre-
sented in Figure 7, where the wire circuit ACB is cut to admit the
electrolytic cell at the point G. Along the resulting circuit ^ to B
the electrometer gives the fall in potential as represented in the
figure by the dotted line, showing that the fall takes place almost
enti|*ely where the work is being done in decomposing the solution.
The fall in potential in the same circuit when but one half of the
total electrical energy fq is transformed into work is represented in
Figure 8.

It is evident, then, that, in an electric circuit, electrical energy may
be entirely transformed into heat, or into varying proportions of heat
and work, depending upon the nature and arrangement of the circuit.

FORMS OF ENERGY AND THEIR MEASUREMENT 13

In an entirely analogous manner, the energy possessed by the
water, in the case already considered, may be almost entirely trans-
formed into heat as has
been shown, or it may be P^'*''**^

i-w-

almost entirely trans-
formed into work, for,
if the tube be closed at
the point b, the pres-
sure at that point at
once rises, as shown in
Figure 9, from p'^ to p^
and the maximum quan-
tity of energy, p^Q^
may then be obtained
at b and transformed
into work as desired. The current of water differs from the cur-
rent of electricity in that the former may leave its conductor while
still in possession of a certain amount of kinetic energy. This
property is not possessed by the latter current.

t06flEllll

FlO. 8

P P

' ' 1

Tia, 9

The fall of potential throughout any galvanic circuit may be pre-
sented by the method just employed. If no work is done in the cir-
cuit and if the resistance of the circuit is uniform throughout, the
potential falls regularly from its highest value at one end to its low-
est value, zero, at the other, as represented in Figure 6. If, however,
work is done at some point in the circuit requiring a certain quantity
of electrical energy and consequently a certain potential, the poten-
tial falls by a definite amount at the point where the work is done.
Supposing this faU in potential to be equal to f, then the remaining
potential v — f' decreases regularly throughout the rest of the circuit

"-..

14 A TEXT-BOOK OF ELECTBO-CHEMISTBY

as representod in Figure 7. If, finally, the circuit does not possess
the same resistanoe in every part, the faU in potential in each part is

propartianat to its resist-
T\f once. Consider, for in-

I I ^^ stance, the circuit rep-

^ j \^ resented in Figure 10,

where the resistance of
AB is twice as great as
that of BG and four
times as great as that
^ . of CD.

— -^-*^ As shown in the fig-

* ■ ■ ^ ^''^■^-1 F^ ure, the fall in potential

ABC jD along AB is twice as

_ tosfrtte great as that along BO,

and four times as great
as that along CD. This relation between the fall in potential in a
conductor and its resistance follows of necessity from Ohm's law,
which holds for the whole circuit as it does for each part, as will
now be shown. In applying the equation which expresses Ohm's
law, —

to any part of a circuit, the value of f is the difference of potential
between the two ends of that part, and the value of b is the resistance
of the part Hence in the case represented by Figure 10 the
following equations are true, since the current is the same through-
out the circuit, whatever the arrangement of the resistances of the
parts, as in the case of a current of water flowing through a series
of tubes of varying diameters : —

F — Fo F — Fi Fj — F, Fj— Fj

O ^ ^ -f- f- y

B R| Bf Bg

where F — Fos=(F — Fi)-h (fi — f,) + (f, — f,) and bssBi + Bj-Hb^

It follows from the equations that the potential-difference between
the single points must be proportional to the corresponding resist-
ances. Whether the resistance in the circuit is that of a metallic,
or of a liquid, conductor, such as a salt solution, or that of a com-
bination of both kinds of conductors, this statement is still true.

If, in a galvanic cell, the poles be connected by a wire, the total
resistance of the circuit consists of that of the wire, called the ex-

FORMS OF ENERGY AND THEIR MEASUREMENT 15

temsd resistanoey and that of the liquid, or liquids, of the cell (for
instance in case of the Daniell cell, that of the zLqc sulfate and
copper sulfate solutions), called the internal resistance. If, now,
the external resistance of a Daniell cell is 1000 ohms, aud the internal
resistance is 100 ohms, while the electromotive force of the cell is
1.10 volts, it follows from the above discussion that the potential-
fall in the external part of the circuit, the wire, is 1.00 volt and in
the internal part of the circuit, the solution, is 0.10 volt. It is evi-
dent that there is a difference between the electromotive force of a
cell and the potential-fall in the external part of its circuit, being in
the Daniell cell, just considered, 1.10 and 1.00 volts, respectively. If
p denotes the electromotive force of the cell, f^ and B], the potential-
fall and the resistance in the internal circuit, Vj and Bj, the potential-
fall and the resistance in the external circuit, then the following
relation exists between these quantities : —

then Z=Sl±S=5i±5«.

F, Fj Bs

From this relation it follows that the greater the external resistance
B„ the more nearly the fraction ^"^"^ approaches the value one, and

hence the more nearly the potential-fall in the external circuit f^
approaches the electromotive force of the cell f. If the external
resistance is made infinitely great by breaking the external circuit,
these two quantities, f, and f, become identical ; for on the open cir-
cuit there can never be a fall in potential, since this can only take
place when current flows, transforming electrical energy into heat or
into heat and work. Except when the external resistance is made
infinite by breaking the circuit, the potential-fall in the external cir-
cuit is always less than the electromotive force of the cell, but
approaches the latter as the external resistance approaches infinity
or the internal resistance approaches zero.

The Electrical Equivalent of Heat — From its analogy to the
expression for the mechanical energy of water p^Q^ it has
been assumed that the expression fq represents electrical energy,
it being the product of the quantity of electricity by its '^ pres-
sure'' or potential. If the correctness of this assumption be
questioned, it is easily possible to prove it to be correct by
direct experiment, and, at the same time, to calculate the electrical
equivalent of heat Let us consider, first, a circuit in which there

16 A TEXT«BOOK OF ELECTRO-CHEMISTRY

exists an electromotive force f, expressed in volts, or, in other
words, a circuit in which there is a fall of potential from f to 0. It
may here be mentioned that the beginner is inclined to &11 into
error through the former expression by assuming that the value of
F remains constant throughout the circuit, which, as seen from the
latter expression, is not at all the case. The resistance of the cir-
cuit is so chosen that in one second, the quantity of electricity g, ex-
pressed in coulombs, passes through a cross section of the conductor.
Since the quantity of electricity passing through a cross section in
one second is equal to the current, expressed in amperes, this is
equivalent to saying that a current of q amperes is flowing through
the conductor. If now the current performs no work in the circuit,
the entire quantity of electrical energy is transformed into heat.
Hence the quantity of heat generated in one second when the entire
circuit is placed in a calorimeter is equivalent to the quantity of
electrical energy which disappears in the same time, or is equivalent
to the product fq, under the assumption that this product correctly
represents the electrical energy.

Let us consider, next, a circuit in which an electromotive force ^ f
exists, causing a current of two amperes to flow through it. The
quantity of heat which would be generated in one second in a calo-
rimeter containing this circuit should be the same as in the former

case, since

^fx2qsfq.

Similarly, under the above assumption, whenever the electromotive
force and current in any circuit have such values that their product
is equal to fq, the same quantity of heat should be generated in a
given time in a calorimeter containing the circuit, for the same quan-
tity of electrical energy would in each case disappear. Experiment
has shown that this is actually the case. Moreover, if the resistance
of the circuit is such that, with an electromotive force of 2 f volts,
the same current, q amperes, is produced, then, since the product

2 F X Q = 2 FQ,

twice as much heat should be generated in one second as in the for-
mer cases, and so forth. Experiment has proven this also to be true.
Therefore the product fq does represent correctly the quantity of
electrical energy.

The calculation of the electrical equivalent of heat is now very
simple. The unit of electrical energy is naturally the product of
one volt by one coulomb, or one volt-coulomb. It is only necessary

FORMS OF ENERGY AND THEIR MEASUREMENT 17

to measure the heat generated when one coulomb of electricity is
forced through a circuit by an electromotive force of one volt^ or
expressed differently, when one coulomb of electricity undergoes a
fall in potential of one volt. The resistance of the circuit does no;t
enter into consideration, because the quantity of energy is indepen-
dent of the time and because the resistance only determines the time
required for the fall to take place. If this quantity of heat is x

calories, - is the electrical equivalent of heat, and represents the

number of units of electrical energy which are equivalent to one unit
of heat energy.

The dectriccU equivalent of heat has been found to be : —

1 volt-coulomb = 0.2387 calorie,
or 4. 189 volt-coulombs = 1 calorie.

The mechanical equivalent of electricity is easily calculated from
the mechanical and the electrical equivalents of heat.

Since 42720 gram-centimeters = 1 calorie,

then 1 vollrcoulomb = 10198 gram-centimeters,

which is the mechanical equivalent of electricity.

The quantity of electrical energy which is available when a quan-
tity of electricity q is forced through a wire by an electromotive
force F is equal to fq. If this energy is completely transformed

into heat, then

FQ = *; X Q, (1)

when Q is the total quantity of heat generated and A; is a factor
which depends on the ratio existing between the units in which the
two forms of energy are expressed. If the corresponding current is
represented by c, then

Fo = fe X g, (2)

where q is the quantity of heat generated in a unit of time. But'
according to Ohm's law

c=A:'x -, (3)

or F =5 A;'bc ; (4)

then by substitution of this value of f in the equation (2),

we get cMd = & . g; or if ^= A;",

c^ = fc" . q. (5)

18 A TEXT-BOOK OF ELECTRO-CHEMISTRY

The last equation may be expressed in words as follows : The heat
energy generated in the whole or in a pari of a circuit is proportional
to the resistance involved and to the square of the current. This law
was discovered by Joule in 1841 and is known as JouU^s law. Its
experimental verification is a further proof of the validity of Ohm's
law. If the quantities c, b, and Q are expressed in amperes, ohms,
and calories, respectively, then the number of calories generated in
one second is given by the equation, —

0.2387 X amperes' x ohms =

The following facts may also be of interest to the readers: —

1 jonle =s 10^ ergs = 1 voltconlomb.

A certain number of joules, then, denotes a certain quantity of
energy independent of the time. If the quantity of energy supplied
to a machine in a given time is divided by this time, expressed in
seconds, the quotient is the quantity of energy supplied in one
second and is called the power of the machine. The unit of
power,

1 volt-ampere =s 1 watt » 1 joule per aeoond.

The following equations give the relations between the electrical
units of power: —

Watts = p^ = Volt^ulombs ^ ypn^n,
Seconds Seconds

The power multiplied by the time in seconds gives again the en-
ergy supplied during this time. Hence the equations^

1 watt-second = 1 joule
and 1 watt-hour = 3600 joules.

In technical work the watt-hour or kilo-watt-hour is generally used
for the measurement of power instead of joule or kilo-joule, and the
ampere-hour instead of the coulomb, for the measurement of quantity
of electricity. It may be mentioned that 1 ampere-hour equals 3600
coulombs.

A table showing the relation between the energy units most fror
quently used may be found at the end of the book.

The Electrical Furnace and its Industrial Importance. — An exact
knowledge of the relation between electrical energy and heat which
has just been considered is of great importance both in pure science
and in technical work. If it is desired to obtain very high tempera-

FORMS OF ENERGY AND THEIR MEASUREMENT 19

tures, from^ say, 1500^ to 3000^ and higher, as, for instance, in the
manufactare of calcium carbide from calcium oxide and charcoal
according to the equation,

CaO + 3 C = CaC, + CO,

it often happens that electrical heating is the only method of heat-
ing by which the required temperature can be reached, or by which
commercially favorable conditions can be obtained. The apparatus
in which such processes are allowed to take place is called an '^ elec-
tric furnace."

One method of heating, which will be considered in detail, con-
sists in leading two insulated ends of a circuit through two opposite
sides of the furnace and connecting them inside the furnace by
means of a rod of material of great resistance, such as carbon. The
resistance of this rod should be much greater than that of the ends
of the circuit leading into the furnace ; since the greater the ratio
of the internal to the external resistance, the better the utilization of
the electrical energy in the furnace. By means of this arrangement
it is possible, in a very small space, to convert practically the entire
electrical energy supplied to the furnace into heat which is imparted
to the reaction mixture packed around the rod. The high tempera-
ture attainable is only limited by the inertness and stability of the
material of the high resistant conductor. The utilization of the
heat is excellent, since the heating is done from the interior. In
order to illustrate the thermal effect of the electric current, the
following numerical example is given.

Let us consider that an electromotive force of 100 volts is avail-
able and that the resistance of the circuit outside of the furnace is
0.001 of an ohm. If now the circuit be completed by means of an
inner furnace resistance of 0.999 ohm, then, since the total resist-
ance of the circuit is equal to 0.10 ohm, according to Ohm's law,

o.r.

or c = MJ^=:1000 amperes.

0.10 ohm ^

Since the potential-fall in the two parts of the circuit is propor-
tional to the respective resistances, then there will be a potential
fall of one volt along the circuit outside, and of 99 volts along the
circuit inside of the furnace. Hence 99 per cent of the available
electrical energy is transformed into heat in the furnace. The

20 A TEXT-BOOK OF ELECTRO-CHEMISTRY

number of calories of heat generated per second is easily found by
either of the following two methods : —

Method A.

1 watt-second = 1 joule = 0.2387 calorie

Wattrseconds » Volts x Amperes » 99 x 1000 = 99,000.

Then the heat generated in
calories per second « 99,000 x 0.2387 s 23,631.

Method B.

Amperes' x Ohms x Seconds &= calories X 0.2387.
or 1 ampere -ohm-second = 0.2387 calorie.

Number of ampere'-ohm-seconds = 1000* x 0.099 = 99,000.
Hence number of calories per second=99,000 x 0.2387 =23,631.

If the quantity of heat is too great, less electrical energy can be
taken from the current source by increasing the resistance inside of
the furnace. At the same time, the electrical energy is thus better
utilized, since the utilization increases with the value of the ratio of
the internal to the external resistance. The quantity of heat re-
quired in any given case naturally depends upon
the heat of reaction, the heat capacity of the sub-
stances, and the loss of heat by conduction and
radiation. For commercial work electric furnaces
are now built with a capacity of 1000 kilowatts and
over, to be operated with a voltage of 50 volts and
a current of 20,000, or more, amperes.

The internal resistance is very often replaced by
Fio. 11 an electric arc, especially if it is desired to concen-

trate the heating on a small surface. The calculation of the heat
effect thus obtained is similar to the calculation in the example just
considered. It requires only that the potential difference between
the two poles and the current be
known. Even in the case of the elec-
tric arc, it cannot be assumed that the
temx>erature is higher than 3500^ t,
since at that temperature the carbon
itself begins to vaporize. The glow-
ing gas of the arc, can, however, be ^'
brought to a considerably higher temperature.
Models of the electrical resistance furnace of Borchers and of the

FORMS OF ENERGY AND THEIR MEASUREMENT 21

electric arc furnace of H^roolt are shown in Figures 12 and 11,
respectively. These furnaces are on the market in a great variety
of forms.

Since in technical work the economy of a process is of first
importance, electro-chemical industry has developed mostly in the
direction of such processes as may be carried out in the electric
furnace. These processes are carried out to advantage when elec-
trical energy may be had at a price of about one quarter of a cent per
kilowatt-hour and under. Thus during the last ten or twenty years
enormous works have been established in the United States of North
America (especially at the Niagara Falls), in France, in Switzer-
land, and in Norway, which daily transform many millions of
meter-kilograms into chemical energy by means of the electric cur-
rent. In order to give the reader an idea of the magnitude and
commercial importance of these works, their products and the im-
portance of them will be briefly considered.

Most of the processes carried out in electric furnaces involve the
reduction of oxides by carbon. Borchers was the first to state that
in the electric furnace all oxides could be reduced by carboy at a
sufficiently high temperature. As a result of this reduction with
carbon, pure metal is not necessarily formed, for carbon compounds
of the metal may instead be formed.

This is the case in the preparation of calcium carbide, which is
made on a very large scale to be used in turn for the preparation of
acetylene gas. Calcium carbide is of great interest also from
another point of view. Under certain circumstances it is capable of
uniting with atmospheric nitrogen to form calcium cyanamide ac-
cording to the equation,

CaC, + Nj = CaCNj + C,

and the latter compound when treated with steam under pressure is
decomposed with the formation of ammonia. This decomposition
is represented by the equation,

CaCN, -f 3 HjO =CaCO, -f- 2 NH,.

On the other hand, when calcium cyanamide is leached with hot
water and the calcium hydroxide formed is filtered off, the finely
crystallizing substance, dicyandiamide, is obtained upon cooling.
The reaction is as follows : —

2 CaCN, -h 4 H,0= 2 Ca(OH), + (CN,H,),.

By fusion with soda, dicyandiamide is transformed into sodium

22 A TEXT-BOOK OF ELECTRO-CHEMISTRY

cyanide and ammonia together with small quantities of tricyan-
triamide (CNsHs),. Even the latter compound can also be trans-
formed into sodium cyanide and ammonia.

The reactions just described are of great importance because they
furnish a means of transforming atmospheric nitrogen into a form
which can be utilized. In view of the threatened exhaustion of the
great saltpeter deposits, this importance is not to be undervalued.

A further advance in the domain of nitrogen fixation has been

made by so conducting ^ the processes that calcium cyanamide is

obtained, although not quantitatively, from calcium carbonate,

carbon, and atmospheric nitrogen, without the necessity of forming

calcium carbide as an intermediate product The following reaction

is involved : —

CaO + 2C+N8«CaCN, + CO.

The conglomerate, containing the calcium cyanamide, gives on
analysis from 12 to 14 per cent of nitrogen. By experiment it has
been shown to be a good fertilizer, capable of being used on the soil
in its original form.

Besides calcium carbide, silicon carbide (carborundum), valued
especially as an abrasive substance, is prepared on a large scale in
this way. The following reaction is involved : —

SiO, + 3C=:SiC+2CO.

Various alloys are prepared in the electric furnace by the reduc-
tion of certain minerals. For instance, when chrome-iron ore
(FeO-CrsOa) is heated with sufficient carbon an iron-chromium alloy
results, containing over sixty percentage of chromium. In a similar
manner an iron-titanium alloy, containing a proportion of titanium
varying with the conditions of preparation, may be prepared from
Ilminite (FeO-TiO,).

These alloys are used in the production of steel, etc., in order to
obtain a definite chromium or titanium content.

Electrical heating is also used to advantage in the production of
phosphorus by heating mixtures of the natural phosphates (chiefly
calcium phosphate) with carbon and quartz or kaolin. The follow-
ing reaction takes place : —

Ca3(P04),H-3SiO, + 5C = 2P + 3CaSiO, + 5CO.

The phosphorus which distills off from the mixture is collected
under water.

Recently, carbon bisulfide has been prepared from pieces of sul-
fur and carbon in an electric furnace.

FORMS OF ENERGY AND THEIR MEASUREMENT 23

Finally^ it may be mentioned that the preparation of the nitrogen
oxides by the action of the electric arc upon air has recently
received increased attention.^ The air is forced past an electric arc
formed by an alternating current, .becoming highly heated and
forming a small quantity of the nitrogen oxides. Before these
oxides can decompose to any considerable extent, they are rapidly
cooled to ordinary temperatures.

In all of these processes, the number of which might easily be
increased, the electric current exerts only a heating effect. The
electric furnace is, however, also used in processes in which the
current is a direct one and exerts both an electro-thermic and an
electrolytic action, as, for example, in the process for the prepara-
tion of metallic aluminium. In this case, the current furnishes the
heat required to maintain the fusion and also decomposes the alu-
minium compounds dissolved in it with the separation of metallic
aluminium at the cathode.

Dark or Silent Electrical Discharge. — The mutual discharge of
two oppositely charged bodies, when they are separated by air or any
other dielectric, takes place in various ways according as the poten-
tial-difference, the distance, and the form of the bodies is varied.
It can take place in the form of a dark or so-called silent discharge
accompanied by faintly visible streamers of light. Such a discharge
differs from the familiar electric arc in that in the former case the
passage of electricity takes place only through the gas separating
the two electrodes, while in the latter case it takes place chiefly
through the vapors formed from the electrodes. If, in the latter
case, a constant potential-difference is maintained, the conductance
of the electrode vapors increases greatly both the current intensity
and the quantity of electrical energy which in the imit of time is
transformed into heat.

If the potential-difference between the two electrodes is increased
successively, the non-luminous discharge through gases becomes
finally an electric arc. Under the usual circumstances, as soon as
this transformation takes place, the current suddenly increases to a
high value while the potential-difference sinks considerably. It is,
in general, not possible to utilize the high potential-difference
obtainable by very powerful machines, since the current would in-
crease to such an extent as to cause even the most non-volatile
electrodes to volatilize. Nevertheless under certain conditions all

1 For farther particulars see J. Brode, ** Oxydation des Stickstoffs in der
HockspannuDgB flamme. HabilitaUonsBChiilt, Karlsrahe'* (1906), W. Knapp,
publisher, Halle, Saxony.

24 A TEXT-BOOK OF ELECTEO-CHEMISTEY

possible transition phenomena between discharge through gases and
through the electrio arc can be produced, as, for instance, when the
electric current is transmitted chiefly by means of the electrode
vapor near the electrode, and undergoing a gradual transition into
purely a discharge through gases at greater distances.^ It would
be more correct to characterize the electric arc (which, in the case of
the preparation of the nitrogen-oxygen compounds as just described,
appears as a quietly burning flame) as a case of discharge through
gases. In the case of alternating currents, even with those of high
frequency, the discharge is naturally discontinuous. It is in fact
possible that every discharge is discontinuous. This is certainly
true of spark discharges, which may be considered to be electric
arcs of exceedingly short duration. During such discharges the
current rises to enormous values. That, in this case, the vapor of
the electrodes plays a part in the conduction of the electricity, is
shown by spectroscopic observations, and also by the fact that if
sparks are allowed to pass between electrodes of the noble metals
under water, colloidal solutions are formed.

As already indicated, silent discharges (and also spark dis-
charges) may exert a chemical influence on gases. Thus, to a cer-
tain extent, hydrogen and nitrogen are made to combine to form
ammonia, hydrogen and cyanogen to form hydrocyanic acid, carbon
monoxide and water to form formic acid, and oxygen to be trans-
formed into ozone. In one respect this last technically important
reaction is very remarkable. While in all the other applications of
the alternating current which have been mentioned, only the quan-
tity of heat or the temperature attainable entered into consideration,
in this case it appears that the form of the current must be consid-
ered. According to the investigations of Warburg,' a close rela-
tionship exists between the nature of the light at the points of the
conductors and the yield of ozena It is very probable that the for-
mation of ozone should be attributed to photo- or cathodo^hemical
action. It is also interesting to note that Warburg found that, for
the form of discharge used by him, the direct excels the alternating
current.

When the ozone has reached a certain concentration, it ceases to
be formed.

Electrical Capacity. — It may be well at this point to explain the
term electrical capacity, although it has more to do with static eleo-

1 See also O. Lehmann, ** Elektrische Lichterscheinmigen und Entladangen,**
W. Knapp, Halle, Saxony (181)8).

« Drude'B Anndlen, 12, 988 (1904) ; 17, 1 (1906).

FORMS OF ENERGY AND THEIR MEASUREMENT 26

tricity than with our present subject. It is to be especially noted
that this so-called electrical capacity is quite distinct from the ca-
pacity factor of electrical energy, or the quantity of electricity. By
electrical capacity is meant the capacity of a body for taking up
or holding electricity. This capacity of a body is independent of
its material content, but dependent on its size, form, temperature,
and surroundings. If two bodies of unequal electrical capacities be
charged with the same quantity of electricity, the potential of the
two charges will be unequal, and, further, it will be higher on the
body of least capacity. If these two bodies be charged with such
quantities of electricity that the two charges are at the same poten-
tial, the two quantities of electricity will be unequal, and the larger
quantity will be on the body of greatest capacity. The electrical
capacity is also defined by the following equation : —

The unit of capacity is called the farad, and is defined to be the
electrical capacity of a body upon which a charge of electricity of
one coulomb possesses a potential of one volt. The above equation
may therefore be written as follows : —

- . ^ , Q, in coulombs

AC., in farads = -^ — : rr — •

F, in volts

PoiitiYe and Vegative Electricity. The Electrometer. — Thus far
we have considered the electric current as analogous to the water
current. This analogy is especially useful to beginners, as it serves
to facilitate the comprehension of electrical phenomena. It is, how-
ever, not a perfect one, and care must be taken to prevent misguid-
ances ; for an electric current is not as simple as a current of water.

If a solution of copper chloride be introduced into a circuit as
previously described, it is observed that, while copper is separating
at one of the pieces of platinum, chlorine is separating at the other.
If now, from these facts, it is conceived that the copper is trans-
ported through the solution to one electrode, then it must also be con-
ceived that the chlorine is transported in the opposite direction to the
other electrode. From this movement of ponderable matter in two
opposite directions by means of the electric current, it must be
assumed that the electric current, unlike the water current, simul-
taneously possesses two opposite directions. But we know from the
science of static electricity that we have to distinguish between two

26 A TEXT-BOOK OF ELECTRO-CHEMISTBY

kinds of electricity; called respectivelj positive and negative eleo-
tricity. Hence it may well be concluded that the electric current
consists of simultaneous motions of positive electricity with copper
particles in one direction and of negative with chlorine particles in
the other. This conclusion is supported by the electrometric experi-
ments to be described later.

The conditions in the case of electrical energy differ, then, some-
what from those in the case of mechanical energy, as will now be
shown. The product, volume by pressure, has been shown to repre-
sent a quantity of mechanical energy. The capacity factor, the vol-
ume, is always a positive quantity, since but one kind of volume is
known. The product, quantity of electricity by electromotive force,
has also been shown to represent a quantity of electrical energy.
In this case, the capacity factor, the quantity of electricity q, may
be either positive or negative. For these two kinds of capacity fac-
tors, -f- Q and — Q, we have the following laws: Whenever a quantUy
+ Q combines with an equivalent quantity — Q, a zero quaniity always
results. Whenever a quantity of positive electricity is produced^ there is
alioays produced at the same time an equivalent quantity of negative
electricity; and when these two quantities of electricity are brought
together again, they completely neutralize each other.

In the study of electrical phenomena, it is necessary to become
accustomed to abstract thinking. It cannot be expected that a quan-
tity of electricity can be made as tangible to us as a quantity of
matter. Upon closer consideration it will be seen, moreover, that if
the term m,aUeT is intelligible there is no reason why the term elec-
tricity or quantity of electricity should be unintelligible. Let us
£rst understand clearly what is understood by the term matter. We
speak of matter when we recognize a certain number of properties in
a given place. One of these properties is the occupying of space or
the presence of a certain quantity of volume energy. If, for instance,
the quantity of matter be compressed, its volume is diminished and
the work done is the equivalent of this compression. Similarly we
speak of a quantity of electricity when we recognize a certain num-
ber of definite properties in a given place. These properties are not,
however, the same as those which characterize the presence of
matter. A quantity of electricity does not fill space or possess vol-
ume energy, and hence cannot be grasped by the hand.^ The ques-

1 It should be noted, however, that Helmholtz and others have attributed an
atomic strocture to electricity, assuming the existence of positive and negative
elementary particles. According to this view we must assume the existence
of two new, univalent, and nearly maasless elements, namely, positive and nega-
tive electrons

FORMS OF ENERGY AND THEIR MEASUREMENT 27

tion then often arises : What is the nature of electricity and what is
meant by quantity of electricity ? The question. What is the nature
of matter ? however, is but seldom raised. The two questions are
equally idle, for the terms matter and electricity are nothing more
than expressions or collective names for certain groups of definite
properties.

Mechanical work may be transformed into electrical energy by
rubbing a stick of sealing wax with a woolen cloth. In this case
both the sealing wax and the cloth become electrified, the one with
positive, and the other with negative electricity. It is a well-known
law of nature that whenever electrical energy is produced, it always
appears simultaneously in two separate places, although these places
may lie exceedingly near to each other.

It is usual to speak of a quantity of electricity, q, as passing
through a circuit in the direction in which copper particles are car-
ried during electrolysis, and we too have followed the custom.
According to the conceptions of the present, however, when a quan-
tity of positive electricity passes in one direction during electrolysis, a
certain quantity of negative electricity passes in the opposite direction.
These quantities are carried on the positive and negative ions, respec-
tively. While the quantities of the two kinds of electricity flowing
may not be equal, they must always be so related to each other that
in all parts of an electrolytic conductor their sum shall be the same.
In metallic conduction it is assumed that the electricity which flows
is negative (negative electrons). However, since positive electricity
flowing in one direction through a metallic circuit produces the same
effects as an equal quantity of negative electricity would produce in
flowing in the opposite direction, we are justified for the sake of
simplicity in speaking of the whole quantity of electricity of an
electric current as flowing in the direction of the migration of copper
particles. It should, however, be borne in mind that this method of
expression is not strictly correct.

Electrical Measurements. — In measurements of any kind it is
necessary to establish a zero or starting point. For the intensity
factor of heat energy, the temperature, the absolute zero is taken at
273 degrees below the centigrade zero (— 273"^). For the intensity
factor of volume energy, the pressure, the absolute zero is taken
as the pressure existing in a vacuum. For the intensity factor of
kinetic energy, the velocity, there is no absolute zero point known.
Only relative velocities can be measured. For all ordinary meas-
urements the velocity of the earth is considered to be zero, and
when, for instance, a body is said to possess a velocity {7, it is really

A TEXT-BOOK OF ELECTRO-CHEMISTRY

meant that this is the difference between its absolute velocity and
the absolute velocity of the earth. Similarly, in the case of the
intensity factor of electrical energy, the potential, there is no
absolute zero point upon which measurement may be based. As
in the case of velocity, an arbitrary zero point has been adopted.
Accordingly, zero potential is taken as the potential which exists at
the surface of the earth. If it is desired to bring the potential of
any point of an electric circuit to the potential zero, it is only
necessary to connect this point with the earth by a good conductor,
and thus, in a way, make this point a part of the earth's surface.

Electrical potentials are measured by means of electrometers, of
which there are many forms, most of which need not be considered
here. The principle is the same whatever the form (excepting
galvanic electrometers), and may be understood from a description
of one of the simplest forms, known as the gold-leaf electrometer,
shown in Figure 13.

If the metal rod c be connected with the earth, the strips of gold
leaf a and b are brought to zero potential and hang in parallel posi-
tions. If now, after disconnecting the
electrometer from the earth, it be
brought into contact with a point whose
potential is to be measured, positive or
negative electricity passes from this
point to the strips of gold leaf, which
immediately s^arate as shown by the
dotted line in the figure. This is due
to the electrostatic repulsion of the
like kinds of electricity upon them.
The greater the potential at the point
the greater the quantity of electricity
which will pass to the gold leaves and
the farther apart they will separate.
Consequently, the position of the gold
leaves is a measure of the potential of
the point. By calibrating the elec-
trometer, and constructing a suitable
scale, unknown potentials may be measured directly in volts by
means of it.

There remains to be considered a peculiar property of electrical
energy, namely, the additivity of the intensity factor, the potential.
If we have two sources of such energy, as, for instance, two Daniell
cells having the same electromotive force, 1.10 volts, and connect

Fia. 13

FORMS OF ENERGY AND THEIR MEASUREMENT 29

the source of negative electricitj of each, its negative pole, with the
source of positive electricity of the other^ its positive pole, the result-
ing combination has an electromotive force equal to the sum of the
forces of the two cells, or 2.20 volts. If, on the other hand, like
poles are connected, no current flows through the circuit. These two
combinations are represented in Figures 14 and 15.

-VN/^

AAA-

Fig. 14

A very different relation is found, for instance, in the case of the
intensity factor of heat energy, the temperature. It is not possible
in a similar manner to add two temperatures. If we have two
pieces of metal, each having .a temperature of 0^ at one end and
of 100° at the other, they cannot be so combined as to produce a
temperature of 200°.

-V\A

AA/*^

Fio.15

With electrical energy, when a potential-difference exists between
two points, this difference is not altered through a change involving
simply an increase in the absolute potential of those points. It is
because of this fact that it is possible to produce an electromotive
force of any desired magnitude. If the negative pole of a Daniell
cell be connected with the earth, at the positive pole there is a
potential of 4- 1.10 volts. If now to this positive pole, the nega-
tive pole of a second Daniell cell be connected, then at the positive

80 A TEXT-BOOK OF ELECTRO-CHEMISTRY

pole of the second cell there will be a potential of + 2.20 volts, and
so on. Cells thus connected are said to be arranged in series or in
tandem.

Another arrangement, useful for certain purposes, consists in con-
necting like poles of different cells into groups and then connecting
these groups with each other. Although, in this way, no increase in
electromotive force over that of a single cell is obtained, the internal
resistance of the battery thus formed is less than that of the single
cell. These cells are said to be arranged in parallel.

Having considered the fundamental principles relating to the
electric current, we may now turn our attention to the subject of
electro-chemistry itself. As an introduction to this branch of elec-
trical science the history of electricity is briefly presented in the
following chapter.

CHAPTER II
DEVELOPMBNT OF ELECTRO-CHEBSISTRT UP TO THB

Earliest Eeoords of Eleotrioal Phenomona. — A little more than
two thousand years ago, the first electrical phenomena of which we
have record was observed by Thales. He observed that under cer-
tain conditions amber (^Xeicrpoy) possessed the power of attracting
light bodies, such as pieces of paper, feathers, etc. Later, it was
found that this property was not confined to amber alone, and then
it became known as '^ ^XcxrpoK-like," which later was contracted to
the word dectrioaL The phenomena of atmospheric electricity,
such as lightning, St. Elmo's fire, aurora borealis, etc., have been
known from the earliest times, but their recognition as electrical
phenomena is of comparatively recent date.

Up to the beginning of the seventeenth century our knowledge of
electricity was extremely scanty and imperfect. At that time, how-
ever, it was somewhat increased by the work of William Gilbert.
He showed that a great many substances, other than those previously
studied, became electrified upon being rubbed, but that none of the
metals possess this property. He was the first to declare the neces-
sity of rubbing the material in order to produce electricity.

From this time on an increased interest was taken in electrical
phenomena, resulting in the discovery of means for the production
of greater electrical effects than were possible through the rubbing of
such substances as amber, and in the discovery, by Dufay, in 1733,
of the existence of two opposite kinds of electricity. Dufay called
the electricity which remains on the glass, vitreous, and that which
remains on the resin, resinous electricity.

At the end of the eighteenth century five different sources of
electricity were known. The usual, and up to the time of Franklin
the only, source of electricity was friction. Franklin discovered
that the atmosphere was a second source. A third source was found
by Wilke, who observed that electricity was produced when fused
substances solidify. This he named '' electricitas spontanea." The
warming of tourmaline became the fourth source. The fifth and

82 A TEXT-BOOK OF ELECTRO-CHEMISTRY

last source was found in the living animal organism, when the power
of certain fish, such as the gymnotus, torpedo, and silurus, to pro-
duce electrical shocks was recognized.

The Work of Oalvani. — The great electrical discovery of the
eighteenth century, the one which attracted the attention of the best
investigators of that time, and which has proved to be the discovery
of a much more productive source of electricity than was previously
known, we owe primarily to the wife of Aloisius Galvani, Professor
of Medicine in the University of Bologna. She observed that the
freshly prepared hind legs of a frog which were touching a scalpel,
moved as if alive while sparks were passing from an electric machine
near by. She called Oalvani's attention to the phenomenon, and in
a short time he was deeply involved in a study of it, considering it
a good proof of his pet theory that the animal organism, in general,
was in possession of electricity.

In carrying on his experiments he was accustomed to place the
preparations of frogs' legs upon an iron railing in the open air. He
often watched the contractions taking place in them there, and con.-
ceived that it might be due to atmospheric electricity. He observed,
further, that when lightning was discharged, or storm clouds ap-
proached, contraction in the frogs' legs was most often produced.

Repeating this experiment during a series of calm, clear days, and
observing no effect upon the frogs' legs, he twisted the wire which
was hooked through the spine of the frog about the iron railing
from which the preparation was hanging, thinking thus more easily
to discharge any atmospheric electricity which might have accumu-
lated in the preparation. He observed muscular contractions which
he then concluded were at least not entirely produced by atmos-
pheric electricity. Later experiments carried on in a room showed
him conclusively that these contractions in the frog preparations
have nothing to do with atmospheric electricity, and that they can,
under certain circumstances, be made to take place in any place
at any time.

The breadth of influence of this simple discovery is almost without
parallel. It was recognized that the contractions of the frogs' legs
were produced by electricity. The question then arose as to the
source of this electricity.

Galvani declared that the electricity existed in the preparation,
which he compared to a Leyden jar. The muscles, and nerves,
according to him, correspond to the two coatings of the Leyden jar,
and the wire to the discharging rod. He believed, further, that
every animal organism was a source of electricity, to a greater or

DEVELOPMENT OF ELECTRO-CHEMISTRY 83

less degree, as in the case of the electric eel and certain other fishes,
and he hoped through this discovery to be able to penetrate further
into the mysteries of life itself.

The Work of Volta. The Voltaic Pile. — For a time, Galvani's
opinions were very generally accepted by physicists, many of whom
had repeated the above-mentioned experiments. Even Volta, who
was a professor in the XJniyersity of Pavia, and who already had
achieved marked distinction, at first was inclined to accept these
views. Later, however, he observed that the effects produced were
very marked when the back of the frog or the nerve was connected
with the leg, or muscle, by a wire the ends of which were of dif-
ferent metals, while the effect was very weak or entirely wanting,
when a wire of a single metal was used. Upon further investigation
hefownd that whenever two metals and a liquid are combined to make
a circuity an electric current ta produced. This showed clearly that
the explanation given by Galvani was untenable.

From these experiments Volta concluded that the source of the
electricity was either at the point of contact of the two different
metals of the circuit, or at the point of contact of the two metals
with the liquid. In the case of Galvani's experiments this liquid
was the moisture of the preparation. Volta considered the frog's
legs, themselves, to be nothing more than a delicate electroscope,
indicating the presence of an electric current in the circuit. He
finally concluded that the principal source of the electricity was at
the point of contact of the two metals, and not at the points of con-
tact of metal and liquid. This conclusion has been commonly
accepted until within very recent years.

As a sequence of his experiments, it should be mentioned that
Volta distinguished, for the first time, between two classes of
electrical conductors. In the first class, he included the metals,
carbon, and certain other good conducting substances, such as the
metallic sulfides ; and in the second class, all conducting solutions.
This distinction is, in the main, still recognized. According to the
prevailing ideas of the present time, conductors of the first class
may be defined to be such as conduct the electric current without a
movement of ponderable matter, and conductors of the second class,
such as conduct the electric current only by means of a movement of
ponderable matter. The effect of temperature upon the two classes
of conductors is remarkable, in that in general, those of the first
class conduct electricity less readily, and those of the second class
more readily, with increasing temperature. It has also been found
to be a fact, which is in agreement with the electro-magnetic theory

84 A TEXT-BOOK OF ELECTRO-CHEMISTRY

of light, that metallic conductors are, even in very thin layers,
opaque, while other conductors in thin layers are always more or less
transparent to ordinary light. This behavior towards heat and
light is a convenient means of distinguishing between the two classes
of conductors in such doubtful cases as are met among the oxides.

For conductors of the first class, Volta soon established the con-
tact electromotive series, which is a table of conductors so arranged
that if any two of them be connected with each other and also with
a conductor of the second class (a liquid thus completing a circuit)
an electric current will flow from the conductor higher in the table
or series through the liquid to the other. Moreover, the current is
greater, the farther apart the two chosen metals stand in the series.

[In the following table is given such a contact-series: —

Zing

Lead

Tin

Iron

Copper

Platinum]

After the establishment of the order of contact electromotive
forces, Ritter made the discovery, entirely unappreciated at the
time, that this order is the same as the order in which metals pre-
cipitate one another from solutions of their salts. A reference to
the above contact-series will make this clearer. Metallic zinc when
placed in a solution of a lead salt dissolves and causes the separation
from the solution of metallic lead. Similarly, metallic lead causes
the separation of metallic tin, and so on down the series. Moreover,
any metal causes the separation of all the other metals of the series
which are situated below it, from solutions of their salts. ITie
identity of the order of Hie contact electromotive forces of the raetcds and
the order of their precipitating powers shows a relation between electricity
and chemistry. The discovery of this relation may be considered to
mark the beginning of scientific electro-chemistry.

A little later, Volta stated his Law of Contact Electromotive Force,
This law states that the same potential always exists between two
given metals, whether they are in contact with each other directly,
or only through a series of other metals. [The following table gives
the metals in the order of the contact electromotive force series,
together with the potential-difference between adjacent metals : —

DEVELOPMENT OF ELECTBO-CHEMISTBY 86

^TAT^ POTKHTXAL-D.

n YOXAB

Zino

0.210

Lead

0.060

Tin

. 0.818

Iron

0.146

Copper

0.288

Flatinnm 0.976

According to the above law, whether zinc be connected with plati-
num directly or through the series of metals, lead, tin, iron, copper,
etc, the difference of potential between them will be 0.976 volt.] It
also follows from the above law, that it is impossible to obtain an
electric current from a circuit made up entirely of metals ; for in
such a circuit the sum of all the potential-differences is equal to
zero. [This is at once evident from the following diagram : —

The sum of the potential-differences at the points of contact of dis-
similar metals urging an electric current in one direction (0.21 +
.069 + 0.313 + 0.146+0.238) is exactly equal to the potential-differ-
ence (0.976) urging an electric current in the opposite direction.]

The law of contact electromotive force, according to Volta, does
not apply to conductors of the second class. Since he believed that
only slight potential-differences were produced at the points of con-
tact of the metals with the conducting liquid, he reasoned that the
two metals could be connected with a liquid with scarcely any
change in potential from one metal to the other through the liquid.
[Accordingly, if the circuit shown in Fig. 16 be broken at a, and the
two ends dipped in a conducting liquid, a current would flow through
the circuit so produced under a potential-difference of nearly 0.976
volt]

As long as investigators were mainly devoted to the study of fric-
tional electricity, scarcely any attention was given to the relations

A TEXT-BOOK OF ELECTRO-CHEMISTRY

between electrical and chemical processes. This was in a large de-
gree due to the fact that the quantities of electricity which were
produced by the friction method were too small to bring about any
considerable chemical effects. A few facts bearing upon the, rela-
tion between these two energy forms were known as early as the
middle of the eighteenth century. It was known that, by means of
electric sparks, metals could be ^^ revived " or obtained from their
oxides ; that air, other gases, and water were affected by the passage
of electric sparks had also been observed. The chemical effect of
the electric current was first studied on a large scale after Volta had
constructed the apparatus commonly known as the Voltaic pile. [A
diagram of this appai-atus is shown in Fig. 17.]

It consists of pairs of plates of dissimilar metals, as, for instance,
silver and zinc, separated from each other by pieces of absorbent

material like blotting paper or
flannel cloth, moistened with a
liquid conductor such as a salt
solution. The strength of the
pile depends upon the metals
chosen, and upon the number of
metallic pairs used in its con-
struction. [Referring to Fig.
17, the greatest potential-differ-
ence is obtained between the
poles a and &, decreasing as,
instead of the pole a, the poles
a', a", etc., are taken.] At the
^^ beginning of the present cen-
tury almost every one who was
in a position to do so built a
Voltaic pile, and consequently the scientific papers of that period
were filled with descriptions of experiments in which the pile was
used.

The Electrolytic Decomposition of Water. — It is worthy of notice
that Volta himself says nothing of the chemical actions which may
be produced with his apparatus, although it is evident from his ex-
periments that he must have observed the electrical decomposition
of water. This indicates that he did not appreciate the significance
of this phenomenon. The discovery that water could be decom-
posed by means of the Voltaic pile thus became the work of others.

In the year 1800 Nicholson and Carlisle showed that on conduct-
ing an electric current through water, by dipping the two terminals

Fio. 17

DEVELOPMENT OF ELECTRO-CHEMISTRY 87

of a voltaic pile into it, at one of the terminals hydrogen, and at
the other oxygen, was produced. The fact was also not overlooked
that the water about the terminal at which hydrogen was produced
became alkaline, and that about the other terminal became acid.

Measurement of the Potentials of a Voltaic Pile. — It is surprising
that, as early as 1802, thorough measurements of potentials of the
Voltaic pile, which are still accepted as correct, were made by Er-
mann. Some of the results have already been considered in the
introduction, and others will now be considered.

Ermann inserted a silver tube, filled with water, into the circuit.
The ends of the tube were closed with pieces of glass through which
the terminal wires of a battery were passed, making contact with
the water inside of the tube. By connecting an electroscope to any
desired point of the silver tube, the presence of electricity through-
out the tube was shown.

Ermann also established the important fact that the column of
water between the two ends of the battery terminal wires actuaXly
contains electricity during the galvanic action. The fall in potential
when the column of liquid forms a part of the circuit still takes
place according to the principles discussed on pages 11 to 13. In
this case, a sudden fall in potential takes place at the poles due to
the work performed there.

When wires are placed between the two ends of the battery wires
in the tube as shown in Figure 18, Ermann observed that gas was
evolved at each wire end ; and that in every case an end at which
hydrogen appeared was adjacent to one at which oxygen appeared.
This is indicated in Figure 18.

Fio. IS

The electric current was conducted partly by the water and partly by
the wires.^ In this case also, the fall of electroscopic potential took
place as in the cases already considered.

1 If the water has become good-condDCting by dissolying oxygen salts, or if
the platinum wire is too short, no evolution of gas takes place at the ends of the
wire, and the wire takes no part in the conduction of the electric current The
evolution of gas and the conduction of the electric current by the wire takes
place appreciably only when the potential-difference between the ends of the

S8 A TEXT-BOOK OF ELECTRO-CHEMISTRY

By connecting the circuit with the earth, it is possible to have
-either positive or negative electricity alone in the column of water
and the wires. It is also possible to cause one part of the circuit to
exhibit positive, while the rest exhibits negative, electricity.

The Migration of Acid and Alkali, and the Discovery of the Alkali
Metals. — It was very difficult for the early investigators to compre-
hend the formation of hydrogen and alkali at one of the points where
the wires from a Voltaic pile came into contact with water, and of
oxygen and acid at the other. It was a question with them whether
or not the acid and alkali were actually created by the action of elec-
tricity on water. Such a question was not absurd, for at that time,
the law of the conservation of matter was not at all generally recog-
nized. It was one which required an experimental answer. The
task of answering this question was undertaken first by Simon, and
then a few years later by Davy, who showed, by a series of very care-
ful experiments, that pure water is decomposed into hydrogen and
oxygen by the electric current, without the formation of acid and
alkali, and that the formation of the latter, in earlier experiments,
was due to the presence of impurities in the water. He perf ormed,
furthermore, experiments of the greatest importance upon the migra-
tion of acids and bases to the two poles, respectively, for which a
satisfactory explanation was not found until the establishment of the
accepted theories of the present time. This experiment is briefly
described at this point because the phenomena involved should be
known. It will be more thoroughly understood after the modern
theories have been studied. The reader is advised then to attempt
to discover the explanation of this experiment, as thereby he will
recognize more fully the advantages of modern conceptions.

If two platinum wires are connected to the poles of a voltaic pile,
and the free end of one of them is placed in a vessel filled with pure
water, and the free end of the other in one containing a solution of

wire and of the liquid layer parallel to the wire reaches about the value 1.7 volts
(the decomposition voltage of water). This process, which is of great industrial
importance, cannot be completely understood until the study of polarization
(Chapter VIII) is taken up. For a further discussion see Danneel, Ztschr.
mektrochem., 9, 266 (1903).

When higher current densities are used, the fractional part of the current
which flows through the wire becomes greater and greater. This fact has recently
received a practical application in the fusion of metals under water by means of
large currents of electricity. The water is heated but slightly by the electric
current because only a very small part of the current passes through it. More-
over the heating of the water by the glowing metal is reduced to a minimum by
the existence of the Leidenfrost's phenomenon.

DEVELOPMENT OF ELECTRO-CHEMISTET

-AAr

AAt'

FzQ. 19

X>ota8siam sulfate, the two yessels being connected by means of a tube
filled mtb water as shown in Figure 19, acid is formed at the wire
which is connected with the positive pole of the pile and alkali is
formed at the other wire.

The same result is obtained if three vessels, connected in this
manner, and filled, respectively, with water, potassium sulfate solu-
tion, and water are used
with the two platinum
electrodes dipping into the
end vessels. The positive
pole appears to possess an
attraction for the acid, and
the negative pole for the
base, resulting in the de-
composition of the salt.

Davy desired to study the motion of the acid and base towards the
positive and negative poles, respectively. He proposed to follow this
motion by means of litmus paper, and found to his astonishment, that
the first appearance of acid or alkali was not in the water at the point
where it came into contact with the salt solution, but at the elec-
trodes, whence it gradually diffused throughout the water. If acid
and alkali could thus be made to pass through pure water in going
to the poles, without affecting the litmus on the way, Davy ques-
tioned whether it was not also possible that they might pass through
substances for which they had a great chemical affinity without acting
upon them. He found that an interposed concentrated acid solution
did not in any way hinder the passage of alkali to its pole, nor did a
concentrated alkali solution hinder the passage of acid. There was
found, however, in the interposed acid and alkali solutions some of
the corresponding salt. This seemed to indicate that the chemical
affinity had caused some of the passing compound to be retained.
If, further, barium chloride be used to intercept the passage of, sul-
furic acid, barium sulfate is formed, and only after a long time
does sulfuric acid reach its pole. Here, thought Davy, the chemical
affinity has completely overcome the electrical attraction.

A little later Davy crowned his experimental work with the dis-
covery of the alkali metals by the separation of them from their fused
hydrates by means of the electric current. He thus laid the founda-
tion for the present day commercial preparation of metallic sodium,
as, for instance, by the so-called Castner process.

This process consists, principally, in passing an electric current
through sodium hydrate which has been heated but slightly above its

40 A TEXT-BOOK OF ELECTRO-CHEMISTRY

point of fusion. The metallic sodium which separates at the cathode
is kept from moving away toward the anode by means of a gauze of
iron wire of fine mesh. At the anode both oxygen and water are
formed. The former is evolved from the fusion to a great extent,
while the latter dissolves in the fusion and finally reaches and reacts
with the metallic sodium at the cathode, forming there hydrogen
and sodium hydroxide. In this way one half of the metallic sodium
set free by the current is reconverted into the hydroxide, so that the
yield of sodium by this method never exceeds fifty per cent. If
the temperature is too high, the metallic sodium also dissolves in the
fusion and becomes oxidized at the anode. The yield of metallic
sodium finally becomes zero.^ The following equations represent the
process under normal conditions. By the action of the electric cur-
rent,

2NaOH = 2Na + 2 0H;

at the cathode,

2Na + 2HaO = 2NaOH + H,; and

at the anode,

40H=Os + 2H,0.

The Bite and Fall of the Eleotro-ohemical Theory of Berseliiui. — At
the time of Davy's great work, Berzelius was just beginning his scien-
tific investigations. In one of the first of these, carried out jointly
with Hisinger, he studied the action of the electric current upon solu-
tions of various inorganic substances, resulting chiefly in the estab-
lishment of the first electro-chemical theory. This theory dominated
the science of chemistry for many decades. According to it, each
chemical atom, when in contact with another, possesses, like a ms^et,
an electro-positive and an electro-negative pole. Moreover, one of
these poles is usually much stronger than the other. Consequently
an atom behaves as if it possessed but one pole, either electro-positive
or electro-negative according as the positive or negative pole, respec-
tively, predominates in strength. The magnitude and sign of this
resultant polarity upon the atoms of a given element determines its
chemical behavior. If, for instance, the atoms of an element are
electro-positive, it will react with elements whose atoms are electro-
negative, and conversely. During this reaction, the two kinds of
electricities neutralize each other more or less completely, according
to the degree of inequality existing between the positive and neg&-

1 For a further discussion see the article by Leblanc and Brode, ** The Elec-
trolysis of Fused Sodium and Potassiom Hydroxides," Ztschr, Elektrochem.y
8, 697 (1902).

DEVELOPMENT OF ELECTRO-CHEMISTRY 41

tive charges npon the reacting atoms. If complete neutralization
does not take place, the resulting compound itself is electro-positive
or electro-negative according as. the electro-positive are greater or
less than the electro-negative charges upon the component atoms.
Compounds which thus possess a resultant polarity may then enter
into further combinations with each other in such a way as to
form a complex compound which is more nearly, or quite, neutral.
Thus th^ theory explains not only the formation of simple com-
pounds from their elements, but also the formation of complex com-
pounds, such as double salts, from their component simple compounds.

The essential elements of the electro-chemical theory may, perhaps,
be more easily comprehended from a consideration of a concrete
example. Adopting the table of atomic weights used at that time,
the oxide of potassium would be represented by the symbol KO.
According to the electro-chemical theory, the charge of positive elec-
tricity on the potassium atom is greater than that of negative elec-
tricity on the oxygen atom, and, consequently, the compound KO
still possesses a certain excess charge of positive electricity. Sulfur
combines with oxygen, forming the compound SOj. In this case a
negative sulfur atom combines with three negative oxygen atoms,
forming the negative compound SOs* Berzelius explained the ener-
getic action between these two negative substances, by assuming
that the sulfur atoms possess a comparatively great positive charge
as well as the predominating negative charge, and that the. negative
charge of the oxygen neutralizes the former. Since the molecules
of potassium oxide are positively charged and those of sulfur trioxide
negatively charged, these two kinds of molecules may combine
chemically with a partial or complete neutralization of their charges,
forming KO • SOs. It was supposed that the latter compound still
retained a slight positive charge. An entirely similar explanation
applies to the formation of aluminium sulfate, Al^Os • (S03)s) ex-
cept that it was supposed that this salt retains a slight negative
charge. Assuming the sulfates of potassium and aluminium to be
thus oppositely charged, it follows from the theory that it should be
possible to cause them to combine with each other. Xhis explains
the formation of the double salt, KO • SOj — AI2O8 • (803)8.

According to the above theory, chemical and electrical processes
are closely related, and all compounds have a dualistic nature, being
formed of an electro-positive and an electro-negative component.
This theory is therefore known as t?ie electrochemical or dualistic
theory. It was applied throughout the domain of inorganic chemis-
try, which at that time was practically the entire science of chemistry,

42 A TEXT-.BOOK OF ELECTRO-CHEMISTRT

and although it contamed many arbitraty assumptions, it performed
a great service to science because of its systematizing influence.

The Laws of Sleetn^ehemical Cihaiige. — For several decades after
the establishment of the dualistic theory, no considerable advance
was made in electro-chemistry. This lack of progress was soon
counterbalanced by the important discoveries which were made by
Faraday about the year 1835. He was the first to show that, whether
electricity is produced by means of friction or by means of a voltaic
pile, it is capable of producing the same effects. This fact convinced
him that there exists but one kind of positive and one of negative
electricity. He next attempted to discover a relation between the
quantity of electricity flowing through a circuit and the magnitude
of the chemical and magnetic effects which it could produce. His
results may be expressed as follows : —

The magnitude of the chemical and of the magnetic effects produced
in a circuit by an electric current is proportionai to the qvantity of
electricity which passes through the circuit.

A further discovery was made by Faraday by comparing the
quantities of different substances in solution which are decomposed
by the same quantity of electricity. This comparison may be made
in a very simple manner by connecting into one circuit a series of
solutions of different substances so that the same quantity of elec-
tricity passes through each solution. The chemical decomposition
produced by the electric current in each solution may then be deter-
mined by analysis. The results obtained may be summarized as
follows : —

The quantities of the differeiU substances which separate at the eleo-
trodes throughout the circuit are directly proportional to their equivalent
weights^ and are independent of the concentration and the temperature
of the solutions, the size of the electrodes^ and all other ctrcum-
stances.

The above statement, expressing the relation between the quantity
of electricity flowing through a conductor of the second class and
the quantity of chemical decomposition which is produced by it, is
known as the law of electro-chemical change, or Faraday's law.

If a solution of an acid, of a mercurous salt, and of a mercuric
salt be connected into a circuit by means of platinum electrodes, and
the chemical decomposition at the negative electrode be measured
in each case, it is found that for every gram of hydrogen liberated
in the first solution, two hundred grams of mercury are set free in
the second, and one hundred grams in the third. These quantities
are identical with the equivalent weights of these elements. The

DEVELOPMENT OF ELECTRO-CHEMISTRY 48

quantities of mercury separated are to each other as 2 : 1, or inyersely
proportional to the yalences of mercury in the two solutions.

The fact just illustrated, that the quantity of an element deposited
by a given quantity of electricity increases the lower its valence in
the solution used, is of commercial importance. For instance, the
same quantity of electricity deposits twice as much copper from a
cuprous chloride (in a sodium chloride solution) as from a cupric
chloride solution. Therefore, in obtaining copper by the electrolytic
process, the former solution is preferred if other circumstances permit.

The above laws discovered by Faraday, both that relating to the
proportionality between the quantity of electricity and the quantity
of chemical change which it may produce, and that relating to the
deposition of equivalent weights of different substances by the same
quantity of electricity, have been proven to hold with great exact-
ness. At the present time, there is no reason for doubting their
validity in any case. They hold not only for all solvents, but for
fusions as well.

The quantity of electricity which, according to most recent meas-
urements, is necessary to deposit exactly one equivalent weight of
any conducting substance is equal to 96,540 coulombs.^ This num-
ber, which will be denoted by q, represents the electrochemical unit
of electricity, and is called the dectro^JiemiccU constant. The quan-
tity of electricity, q, will then decompose 169.97 grams of silver
nitrate with the deposition on the negative pole of 107.93 grams of
metallic silver. It follows from these values that the quantity of
silver deposited by one coulomb of electricity, or in other words by
a one-ampere current in one second, is equal to

^^ = 0.0011180 gram.'
96,540 ^

It is evident from these figures that in the case of conductors of the
second class, large quantUies of electricity move with very small quanr
titles of matter. In this connection it is interesting to note that,
while one hundred coulombs of electricity deposit but 0.111 gram
of silver, or but a little more than 0.001 gram of hydrogen, it is
sufficient to charge the earth's surface to a potential of more than
100,000 volts.

1 This Talne is that adopted by the International Congress for Applied Chem-
iBtry held in 1903. It wiU be used throughout the book. According to the
measurements of Richards and Heimrod (Ztschr. phys, Chem.^ 41, 302, 1002),
the value of this constant is 96,680 coulombs.

* The table at the end of the book contains the values for many other
metals, etc.

44 A TEXT-BOOK OF ELECTRO-CHEMISTRY

The law of electrcxihemical change, when first published by Farar
day, met with great opposition; due principally to the imperfect
conception at that time of the fundamental principles relating to
electrical energy and to faulty understanding of the law. Even
Faraday himself did not have a clear idea of them. The quantity
of electricity, for instance, was not distinguished from the quantity
of electrical energy. Now the law refers to quantity of electricity,
but not at all to quantity of electrical energy; for it states that
when a given quantity of electricity passes through any solution, it
always produces the decomposition of the same number of chemical
equivalents of the solute or solutes. It states nothing in regard to
the quantity of electrical energy necessary to effect this decomposition.
Among those who did not understand correctly the meaning of the
law was Berzelius. He understood the law to state that equal quan-
tities of energy were required to effect the decomposition of equal
chemical equivalents of different substances. This made the law
seem absurd, for the chemical affinity or cohesion between the
particles separated by the electric current in the case of substances
differing widely from one another cannot be the same. The factors
of an energy are still often mistaken for the energy itself.

Eleotro-chemical Homenclature. — Besides discovering the law of
electro-chemical change, Faraday also devised the system of electro-
chemical nomenclature. To explain the phenomena observed during
the passage of electricity through a solution, he assumed that the
movement of electricity was associated with a movement of particles
of ponderable matter. These particles he called ions. Those ions
which move in the direction of the positive electricity he called
cations^ and those which move in the opposite direction, anions.
Substances which conduct electricity with an associated movement
of ions, or conductors of the second class, Faraday called eUctrolytesy
and to the conduction of electricity by an electrolyte he gave the
name electrolysis. The name electrode he gave to the surface of con-
tact between conductors of the first and second classes of the circuit.
That surface to which the cations move received the name cathodey
and that to which the anions move, the name anode. These terms
will be used throughout the remainder of the book.

Development of the Present Theory of ElectrolyBUi. The Orotthns
Theory. — Those who first recognized the decomposition of water by
an electric current, as already indicated, sought an explanation for
the simultaneous appearance of hydrogen at one electrode and of
oxygen at the other. It was not imtil 1805, however, that a com-
prehensive theory for this phenomenon was put forward. During

DEVELOPMENT OF ELECTRO-CHEMISTRY

that year such a theory was published by Orotthus. According to
this theory^ the electric current charges one electrode positively and
the other negatively^ and these charged electrodes then exert an
electrical influence upon the water molecules. Under this influence
the water molecules (then represented by HO) acquire a polarity,
the hydrogen atom becoming charged with positive, and the oxygen
atom with negative, electricity. The positive electrode then attracts
the negatively charged oxygen atom ; and the negative electrode, the
positively charged hydrogen atom, causing the water molecules to
arrange themselves in the order represented by the row a in Figure
20. If now the electromotive force applied to the electrodes, and
the consequent charge of electricity upon the electrodes, is great
enough, the attraction exerted on the atoms 1 and 1' nearest the
electrodes causes the decomposition of their respective water mole-
cules. Each of the attracted atoms then moves to the electrode

w^—

«^ ^B^^l^F^ ^B^*^^^^ ^■^^■^^ ^B^^^^ ^B^^^^ ^^^^^^

Fio. 20

attracting it, where its charge is neutralized by the charge on the
electrode, and it assumes the form of electrically neutral gas. The
oxygen and hydrogen atoms 2 and 2' which are thus left free in
the solution, according to the theory, combiue with the hydrogen
and oxygen atoms 3 and 3' respectively, of the adjacent water
molecules, forming new molecules of water. The action continues
with the other water molecules between the electrodes, resulting in
a row of new water molecules, arranged as represented in the row h
in the above figure. Under the attractive forces of the charges on
the two electrodes, these new molecules are then orientated like
those represented in row a, and the process proceeds as before.
This explanation satisfied the scientific world for many decades.
The Conductance of Solutions and the Constitution of Ions. — Soon
after Grotthus advanced his theory, the question whether the water
or the dissolved substance conducted the electric current, and the
question as to what constitutes the positive and the negative ions,
were exhaustively studied. The opinion was for a long time divided.

46 A TEXT-BOOK OF ELECTRO-CHEMISTRY

In general, it was usual to avoid the former question by simply stat-
ing facts without involving any particular conception of the process
of electrolysis. For instance, it was a common mode of expression
to speak of ''water which by the addition of sulfuric acid has become
a good conductor," i.e. merely a statement of experimental obser-
vation. The question regarding the constitution of anions and
cations of various dissolved substances also was the subject of con-
siderable disagreement. The opinion advanced by Berzelius was the
first to be universally accepted. According to this opinion, in the
case of sodium sulfate, NaO • SOj, NaO is the positive ion, or cation,
while SOs is the negative ion, or anion. These ions move to the
cathode and anode respectively, where they combine with water
forming alkali and acid. Sometime later the view was expressed
that the ions of this salt are Ka and SO4 instead of those given
above.

Both of the questions considered in the preceding paragraph
were answered by an experiment performed by Daniell. The answer
can, however, be considered as decisive only in the light of the con-
ceptions then accepted. Daniell electrolyzed a solution of sodium
sulfate and one of sulfuric acid simultaneously in the same circuity
and found that the quantities of hydrogen and oxygen liberated
from each solution were the same. He found, further, that the
quantities of acid and alkali formed at the electrodes in the salt
solution were equivalent to the above quantities of hydrogen and
oxygen. The results of the experiments show the conception of
Berzelius regarding the ions of sodium sulfate to be untenable.
According to his conception, it would require twice as much electric-
ity to form the above quantities of acid and base and also to set
free the above quantities of hydrogen and oxygen in the salt solu-
tion as it would to set free the same quantities of hydrogen and
oxygen in the acid solution. Since both solutions are in the same
circuit, it is evident that this is in contradiction to the law of electro-
chemical change (Faraday's law). In agreement with this law,
Daniell explained his experiment by assuming that Na is the positive
and SO4 the negative ion, and that these ions give up their electric
charges at the electrodes and then react with water, producing alkali
and hydrogen, and acid and oxygen [according to the following
equations : —

2 Na + 2 HO = 2NaO + H, (at the cathode);
2 SO4+ 2 HO =: 2 HSO4+ 0, (at the anode)].

It follows from this theory that the quantities of acid and alkali

DEVELOPMENT OF ELECTRO-CHEMISTRY 47

formed in the salt solution must be equivalent both to the quantities
of hydrogen and oxygen set free in the same solution and those set
free in the acid solution. The requirements of the theory agree
then exactly with the results obtained by experiment. It also
follows from this theory that the salt alone must have conducted the
electricity through the solution; for if the water conducted a part of
the electricity^ besides the hydrogen set free as a result of the above
secondary and purely chemical reaction, there would be a quantity
of these two gases set free corresponding to the quantity of electric-
ity conducted by the water. In this case the quantities of acid and
alkali formed must always be less than the equivalent of the quan-
tities of oxygen and hydrogen set free. This is contradicted by the
experimental results already mentioned.

Later experiments made by Hittorf and Kohlrausch confirmed the
explanation of the phenomena of electrolysis given by Daniell. Ac-
cordingly, the metals and radicals behaving like metals, such as H',
Na , K-, Ag-, Hg, Hg *, Fe *, Fe ' ', NH/, NHsCCH,)', etc., are
considered to form positive ions, while all remaining atoms or groups,
of conducting substances in solution, such as OH', NO,', 01', Br', I',
Fe(CN)e' ' ', Fe(CN),' ' ",* etc., are considered to form negative ions.
It is seen here that there are isomeric ions of different valences
among both the negative and the positive ions. For instance
Fe(CN)e"' is the negative ion of potassium ferricyanide, and
Fe(ON)j"", its tetravalent isomer, is the corresponding ion of
potassium f errocyanide. It is by means of such ions as those given
above, formed almost entirely from the dissolved substance, that
electricity is conducted through a solution. The electrical conductance
of a solution is, tlierefore, a property of tJie diaaolved substance, the
solute, and not of the solvent, ^

Seplaoement of the Grotthus Theory by the Clausini Theory. —
As science gradually developed, the imperfection of the theory ad-
vanced by Orotthus became more and more apparent. According
to this theory the splitting of the molecules, which is necessary for
the conduction of electricity, cannot take place until the electro-
motive force is sufficiently great to overcome the affinity or cohesion
between the two components of the given compound. As a matter
of fact, however, it was found that, under suitable conditions of ex-
periment, it is possible to cause an electric current to pass through
a solution even when the electromotive force of the current is ex-
tremely small. For example, such an electric current will pass

1 As recommended by Ostwald, a dot is used to denote a positive charge and
a prime to denote a negative charge.

48 A TEXT-BOOK OF ELECTRO-CHEMISTRY

through a solution of silver nitrate between silver electrodes, causing
silver to dissolve from one electrode and to deposit upon the other.
The entire action thus consists merely in the transfer of silver from
one electrode to the other. It follows from what has just been said
that Ohm's law holds for all differences of potential, from the small-
est upward, in the case of electrolytic conduction.

In order to show still more clearly the incompatibility of the
Grotthus theory and experimentally determined facts, let us consider
the following illustration : If to each point in a horizontal row of
points, a small sphere is held with a certain force X, then a move-
ment of the entire row of spheres in a horizontal direction, such
that each sphere moves to the position of the sphere in front of it,
can only take place by the application of a force sufficiently great
to overcome the force X. Even with the application of such force,
a continuous " current " of spheres can only be maintained when the
spheres moving away are continually replaced by others. The
analogy between this "current" of spheres and the current of
molecules assumed by the Grotthus theory is at once apparent.

Clausius was the first to direct attention to the disagreement of
the Grotthus theory or conception of electrolysis with facts. Basing
his conclusions upon the experimental results already mentioned, he
declared " every assumption to be inadmissible which requires the
natural condition of a solution of an electrolyte to be one of equi-
librium in which every positive ion is firmly combined with its nega-
tive ion, and which, at the same time, requires the action of a
definite force in order to change this condition of equilibrium into
another differing from it only in that some of the positive ions have
combined with other negative ions than those with which they were
formerly combined. Every such assumption is in contradiction to
Ohm's law."

It is a necessary conclusion from the above statement of Clausius
that the individual ions must exist uncombined and free to move in
the solution. Clausius himself was prevented from drawing this
conclusion by the prevailing theories of his time. He chose rather
to follow a middle path by assuming that the positive and negative
particles of a molecule of a dissolved electrolyte were not firmly
combined with each other, but were in a state of vibration, and that
often this vibration became vigorous enough to cause the positive
part of one molecule to come into the sphere of influence of the
negative part of another molecule, with which it then, for a time,
vibrates. The positive and negative particles, thus left momentarily
free, soon come into the sphere of influence of oppositely charged

DEVELOPMENT OF ELECTRO-CHEMISTRY 49

parts of other molecules with which they, also, for a time, vibrate.
Thus there takes place in a solution a constant exchange between
the positive and negative parts of the molecules of the dissolved
electrolytes. When now an electric current flows through the solu-
tion, an electrical force is exerted in the direction of the current,
and the vibration and exchange between the positive and negative
parts of the molecules no longer take place with entire irregularity
as before, but take place in such a manner that the vibrations
become more vigorous and the exchanges more frequent in the
direction of the action of the electrical force. If a cross section of
the solution be taken perpendicular to the direction of the electrical
force, then evidently more positive particles would move through it
in the direction of the current of positive electricity or positive
direction, than in the direction of the current of negative electricity
or negative direction, per unit of time, and similarly more n^ative
particles would move through it in the direction of the current of
n^ative electricity than in the opposite direction. There is, then,
a resultant motion of the positive parts of the molecules in the
positive and of the negative parts in the negative direction through
the cross section. It is by means of this movement of the two
oppositely charged parts of the molecules of the dissolved electrolyte
that the electric current passes through a solution.

From this discussion it is evident that, whereas Grotthus assumed
that the electric current decomposed the dissolved molecules of the
electrolyte, Clausius assumed that the electric current merely guides
and hastens the charged parts of the molecules toward the oppo-
sitely charged electrodes, respectively, during their momentary
periods of freedom. The latter theory was generally accepted
almost up to the present time.

At about the same time that Clausius advanced his theory^
Hittorf began work upon the migration of the ions, and a little
later Kohlrausch commenced experiments upon the electrical con-
ductance of solutions. The work of these investigators greatly
increased the knowledge of the process of the electrolysis. Making
use of their work, Arrhenius in 1887 replaced the theory of vibrating
ions of Clausius by the theory of free ions.

Relation between Chemical and Electrical Energy L — When Volta
stated that electricity was produced at the point of contact between
two metals (see page 33), the law of the conservation of energy had
not been advanced, and therefore he did not know that the energy
of the electric current could only be produced at the expense of
some other form of energy. He considered perpetual motion to be

60 A TEXT-BOOK OF ELECTRO-CHEMISTRY

possible, and believed also that an arrangement might be devised
which would neither wear out nor require attention, and whichy
moreover, would be capable of furnishing an unlimited quantity of
electrical energy. Since the middle of the last century, when the
law of the conservation of energy was discovered, these views of
Volta of necessity have suffered a change. The chemical reactions
which take place between metal and liquid, which earlier were
considered insignificant phenomena of the electric current, are
now recognized as the source of the electric current. They furnish
the energy necessary for its production.

It is remarkable that the source of the electromotive force of the
current was assumed to be at the point of contact of the two dis-
similar metals. Without the best of reasons, it is clearly inadmis-
sible to consider that the reactions which take place about the
electrodes are the source of the electric current and, at the same
time, to consider that the source of the electromotive force is situ-
ated at another point. It would be quite as reasonable to assume
that when a quantity of heat is generated at a given point in a cir-
cuit, the rise in temperature corresponding to it takes place at a
different point. The simplest assumption is that the source of both
electrical energy and electromotive force is at the same point. This
assumption is justified as long as it is not shown to be untenable.
As a matter of fact, with it, it is possible to explain perfectly the
existing relations. At the present time, the electromotive force of a
cell is considered to be made up of the sum of the two potential-
differences occurring at the surfaces of contact between the two
electrodes and the liquid.

After the establishment of the law of the conservation of energy,
and after it was recognized that the processes which go on in a
galvanic cell give rise to the electrical energy, the question whether
or not the chemical energy involved in these processes, as measured
by the heat which they generate, is completely transformed into
electrical energy, still remained to be answered.

The Daniell cell (see Figure 3) may be represented by the follow-
ing scheme : —

Zn — ZnS04 solution — CUSO4 solution — Cu.

When the cell is in operation, zinc goes into solution and copper
separates out Now the heat generated by the reaction involved is
known from thermochemical measurements. When equivalent
weights of the substances enter the reaction, it amounts to 25,050

DEVELOPMENT OF ELECTRO-CHEMISTRY 61

calories. Hence the thermochemical equation^ inTolving two equiva-
lents of the substances in question, is as follows : —

CUSO4+ Zn = ZnS04+ Cu + 2 x 26,060 calories.

If now instead of heat this reaction produces electrical energy, the
quantity of the latter produced would be the electrical equivalent of
26,060 calories. The quantity of electrical energy actually pro-
duced by the cell can be easily calculated as follows : The quan-
tity of electricity which flows through the circuit when pne
equivalent of copper is deposited is equal to 96,640, or q, coulombs,
since it follows from Faraday's law that, whenever one equivalent
of any substance is dissolved or deposited electrically, this quantity
of electricity always passes through the circuit. The electromotive
force of the cell in volts can be measured and the electrical-heat
equivalent is known,

1 voltKK)ulomb = 0.2387 calorie.

The electrical energy produced by the cell, expressed in calories, is,
therefore,

0.2387 X 96640 x f calories.

The chemical energy of the reactions involved is 26,060 calories.
If the chemical energy is completely transformed into electrical
energy, we have the following equation : —

0.2387 x 96640 X F » 26060 ;
or F 3= 1.087 volts.

Since this value of the electromotive force of the Daniell cell is very
nearly identical with the value of the electromotive force found by
experiment, it may be concluded that the chemical energy is com-
pletely transformed into electrical energy.

Later experiments carried out with other cells gave results not in
agreement with this conclusion. The question was finally answered
by the theoretical and experimental investigations of Willard Gibbs,
F. Braun, and H. von Helmholtz. These investigators showed that
there is usually a difference between the chemical energy consumed
in a cell and the quantity of electrical energy given out by it. This
difference is made evident by an evolution or an absorption of heat
by the celL

CHAPTER III

THB THEORY OF BLECTBOLTTIC DISSOCIATION

The theory advanced by Arrhenius in 1887^ gave a great impulse
to electro-chemical research. By means of it, the relation between
well-known facts which formerly seemed to have nothing in com-
mon became at once evident. It has also been an invaluable aid in
making further discoveries. So fundamentally important has this
theory become, that it is considered to be the foundation of the
electro-chemical science of to-day. Its development, and then the
present status of electro^ihemistry in light of the new conception,
will therefore be considered in detail.

In 1887 van't Hoff published an article in the first volume of the
Zeitschrifi filr physikcUiacTie Chemie entitled^ ^' The Rdle of Osmotic
pressure in the Analogy between Solutions and Grases." In this arti-
cle he showed, both theoretically and experimentally, that the gas
laws of constant pressure-volume product (Boyle) and of partial
pressures (Gay-Lussac) apply also to dilute solutes. He also stated
the following very important generalization of Avogadro's principle :

The same number of gaseous or of solute molecules are contained in
a given volume of any gas or of any solution, respectively, when, at the
same temperature, the gaseous pressure and the osmotic pressure ha/ve
the same value.

The Laws and Theories relating to Osmotic Pressure. — The mean-
ing of the term osmotic pressure may be made clear by a description of
an experiment. Consider an apparatus, such as is shown in Figure
21, consisting of a vessel A filled with water and an upright tube
B, open above and closed by a semipermeable membrane m below,
which contains a quantity of an aqueous solution as, for example, of
sugar. The lower end of the upright tube is then submerged in the
water contained in A until the water and sugar solution are at the
same level a.

The semipermeable membrane is of such a nature as to permit the
free passage through it of water but not of sugar moleculea Many
skins and precipitates possess such a semipermeable nature. A pre-

1 2kachr.phy8. Cfhem., 1, 631 (1887).

THEOBT OF ELECTROLYTIC DISSOCIATION

cipitated semiperroeable membrane may be prepared by closing the

lower end of the upright tube with a piece of parchment paper or a

piece of unglazed porcelain, and placing in the

tube a solution of potassium ferrocyanide and

in the vessel A a solution of copper sulfate.

The two solutions then penetrate the pores of

the parchment or unglazed porcelain from

opposite sides, and, meeting within, form a

precipitate of copper ferrocyanide in the pores.

After washing free from the salts used in its

preparation, the membrane is ready for use.

With the apparatus thus completed and
ready for action, it is observed that the sur-
face of the liquid in the upright tube steadily
rises, due to the influx of water through the
membrane into the sugar solution. In order to
prevent the water from entering the upright
tube in this way, a definite pressure must be
exerted downward on the surface of the sugar
solution in B. That pressure which is just sufficient to hold the
level of the liquid in the tul^ at its original position a is equal
to the osmotic pressure of the sugar solution. In the figure, the
hydrostatic pressure of the liquid column ab is equal to the osmotic
pressure. This osmotic pressure exerted by the molecules, of solute
is analogous to the pressure exerted by gaseous molecules.

The general equation expressing the laws of constant pressure-
volume product (Boyle) and of partial pressures (Qay-Lussac) and
the principle of equimolecular volume (Avogadro) for all gases is

Fio.21

pv = nBT,

where p is the pressure exerted by a gas upon a surface of one square
centimeter, v its volume, n the number of mols (molecular weights
expressed in grams), B a constant, and T the absolute temperature.

The expression ^ has a constant value for one mol of a perfect gas,

independent of its nature or concentration. This constant value is
represented by R, and is called the gas constant. It represents ex-
perimentally determined facts, although the theoretical concept, the
mol, is involved indirectly. Whenever the molecular volume of any
gas in cubic centimeters is multiplied by its corresponding pressure
in grams per square centimeters, and the resulting product divided

64 A TEXT-BOOK OF ELECTK0-CHEM18TRY

by the absolute temperature, the value of B is obtained, namely,
84800 = 0.8316 x 10^ ergs =0.0821 liter-atm. = 1.985 calories.

An equation, identical in form with the above general gas equa-
tion, applies to solutes. A consideration of an experiment performed
by Pfeffer will make this evident. He found that the osmotic pres-
sure P exerted upon an area of one square centimeter by a one per
cent sugar solution at 6.8** t or 279.8** T is equal to 50.5 centi-
meters of mercury or 50.5 x 13.59 grams. Since 100 cubic centi-
meters of the solution contained very nearly one gram of sugar, and
since one mol of sugar is 342 grams, the volume of solution V con-
taining one mol of sugar is 34,200 cubic centimeters. Consequently
for this sugar solution

PF^50.5x 13^59 X34200^g3^ ^^ ^^^
T 279.8 ^ ^^ '

This value, within the limits of experimental error, is identical with
the value of the constant iZ, obtained from the analogous expression

^* It is evident, from this identity of the numerical value of ---

and ^, ihai the osmotic pressure exerted by the dissolved sugar mole-
cules is eqiLal to the gas pressure which the same molecules would exert
if the sugar existed as a gas in the same volume and at the same
temperature.

Having considered the phenomenon of osmotic pressure and the
laws which it obeys, it is unnecessary as far as the phenomenon it-
self is concerned to form special conceptions concerning its mechan-
ism. Since, however, osmotic pressure figures prominently in the
discussions in the following pages, and since many new conceptions
are most clearly understood by means of their analogy with it, the
following hypothetical discussion of the cause of osmotic pressure is
given : —

If a sugar solution be placed in a glass tube which is sealed at the
bottom, no evidence of osmotic pressure is observable. At the sur-
face of the solution there exists a pressure, called the internal pres-
sure, directed inward at right angles to the surface, amounting to over
a thousand atmospheres.^ In the case of a one per cent sugar solution
there is a pressure, the osmotic pressure, amounting to only about one

^ Experimentally determined facts, which cannot be described here, have neces-
sitated the recognition of saoh a pressure. Ostwald, Allgem. Chem.^ Vol. II,
page 688, second edition.

THEORY OF ELECTROLYTIC DISSOCLA.TION

atmosphere, directed against this enormous internal pressure. This
is due to the dissolved sugar molecules, which act in the water just
as they would if they were in the gaseous state and confined in the
same volume. Even with very concentrated solutions the internal
pressure is still hundreds of atmospheres greater than the osmotic
pressure. It is because of this that the vessel containing a solution
is not broken by the osmotic pressure which is exerted in the out-
ward direction by the dissolved substance. As it is, only the weight
of the solution itself exerts a pressure upon the walls of the con-
taining vessel.

By the employment of a semipermeable membrane, however, evi-
dence of the phenomenon of osmotic pressure may at once be ob-
served. As already noted, when the upright tube in Figure 21 is
closed at its lower end with such a membrane, partly filled with a
sugar solution, and then set in position as described, water enters
through the membrane unless opposed by a pressure in the opposite
direction equal to, or greater than, the osmotic pressure of the solu-
tion. The solution is bounded by its surface of contact with air and
with the walls of the tube and by the porous membrane with which
the solution forms no continuous surface, since it is permeable to
water. At all the surfaces the internal pressure P^^ is exerted in-
ward, and the osmotic pressure of the dissolved sugar P outward,
while at the membrane, since there is no liquid surface, only the os-
motic pressure P is exerted. Because of this, osmotic pressure is
sometimes defined to be the pressure exerted on the
membrane by the dissolved substance. Besides the
pressure which would be exerted if the tube con-
tained pure water, the solution, then, exerts os-
motic pressure which tends to expand it. This
expansion can take place, however, only when, by
means of a semipermeable membrane, water can
enter the solution. It is for this reason that evi-
dence of osmotic pressure is observed only when a
semipermeable membrane is used.

The rising of the solution in the tube due to
pressure exerted by the dissolved substance may
perhaps be more easily comprehended by calling
to mind the action of a suction pump.

[If water is placed in the tube and outer vessel as
shown in Figure 22, it will assume the same level
if the downward pressure a and a' are equal. If, however, the
downward pressure a is diminished by raising the piston p, water

E-

«._

. .. .

Sr'

Fio. 22

66 A TEXT-BOOK OF ELECTRO-CHEMISTRY

will flow through the membrane and rise in the tube as in the case
of the suction pump. The same movement of water would evi-
dently take place if^ instead of decreasing the downward pressure
a upon the surface of the water in the tube, an upward pressure a'^
against the surface is allowed to act. As already shown, such an up-
ward pressure may be produced b^ dissolving in the water some
substance, as, for example, sugar. Hence it is that the osmotic pres-
sure, which is this upward pressure, causes the liquid to rise in the
tube.]*

The far-reaching analogy which exists between the behavior of
gases and of dilute solutes was first pointed out by van't Hoff. He
was also able to deduce, from the laws of osmotic pressure, analogous
laws applying to phenomena, which, apparently, were not related to
osmotic pressure, such as, for instance, the lowering of the vapor
pressure or of the freezing point of a solvent by dissolving a sub-
stance in it. The laws followed by these phenomena had already
been empirically established, principally by Eaoult They may be
expressed as follows : —

The lowering of the vapor pressure or of the freezing point of a solvent
caused by a dissolved substance is directly proportional to its concentra-
tion. The lowering, in each case, for a given solvent is the same for
equimolar solutions of aU substances. Equimolar solutions contain,
in the same quantity of solvent, such quantities of dissolved sub-
stances, respectively, as are proportional to their molecular weights.
These laws made possible a considerable increase in the knowledge
of the constitution of matter, especially in regard to the molecular
weights of solutes, or substances in solution. Previously, molecular
weights could be determined only in the case of those substances
which could be volatilized without undergoing chemical change.

The laws of constant pressure-volume product (Boyle-Mariotte)
and of partial pressures (Gay-Lussac) are laws of a limiting condi-
tion, holding strictly only for gases at extreme dilution. Therefore,
from the analogy which exists between gaseous and osmotic pres-
sures, it would be expected that deviations from the simple laws of
solutions would be found in the case of concentrated solutions.
Such has indeed been found to be the case when, as has been the cus-
tom, the volume involved was taken equal to that of the solution.
Recently, however, very surprising results have been obtained by
Morse and Erazer' in their experimental work on osmotic pressure.

1 For a more exact definition of osmotic preasuie, see Flanck, Ztschr. phys.
CAem., 48, 584 (1008).

* ZtBchr. Elektrochem.^ 11, 621 (1906).

THEORY OF ELECTROLYTIC DISSOCIATION 57

They found that, even for concentrated solutions (oyer 30 %), the
following statement holds : —

The o&notic pressure exerted by cane sugar in water solution is equal
to that whidi it would exert at the same temperature if it existed as a
perfect gas expanded in the volume occupied by the pure solvent.

Calculating in a similar manner, it has also been found that the
freezing-point lowering is normal eyen for concentrated solutions.
We may well be impatient to see whether or not this relation, which
is without analogy in the gaseous state, obtains generally.

Abnormality erf Acids, Bases, and Salts. Blectrolytie Dissooia-
tion. — One great difficulty presented itself, and cast a dark shadow
upon the otherwise bright theory of solutions. Almost all acids, bases,
and salts which are soluble in water produce in water solutions a
much greater osmotic pressure, vapor-pressure lowering, and freezing-
point lowering than that calculated on the assumption that the mo-
lecular weights derived from a study of their vapor densities and
chemical properties are correct. Corresponding to the abnormality
of these properties, the values of the molecular weights of these sub-
stances calculated from these properties are, of course, abnormally
low.

Not very long before, the molecular theory of gases had been in a
similar position, because of the deviations of the vapor densities of
a number of substances from the requirements of the theory. It was
only with considerable hesitancy that the explanation of these ab-
normal values on the assumption of a dissociation of the molecules
of the gases was then accepted, although at the present time the cor-
rectness of this assumption is never doubted. Certainly, it was nat-
ural in the light of the close analogy known to exist between the
gaseous and the dissolved state, to assume that in solution a similar
dissociation takes place. From thermodynamical considerations,
the physicist Planck concluded that such a dissociation does take
place.* This conclusion was not, however, shared by chemists. In-
deed, such a supposition seemed absurd, for it required that sub-
stances like potassium chloride, in which the atoms were considered
to be held together by the strongest chemical affinity, should spontar
neously decompose and exist in water solution as potassium and
chlorine, in spite of the fact that metallic potassium reacts very en-
ergetically with water. Moreover, the supposition seemed to be con-
tradicted by the law of the conservation of energy ; for it apparently
implied that substances which combine energetically with the gen-
eration of much heat may separate again spontaneously.

1 Ztsehr. pkys. Chem., 1, 577 (1887).

68 A TEXT-BOOK OF ELECTEO-CHEMISTRY

Before such a radical change could be made in the conceptions of
the constitution, in water solution, of these important classes of
compounds, it was necessary to remove the apparent contradictions
of the new conception to laws of well-proven validity, and also to
present strong evidence of its correctness. This was done by
Arrhenius.

In an early investigation of the electrical conductance of electro-
lytes, Arrhenius had already recognized two kinds of solute molecules,
namely, active molecules which caused the electrical conductance,
and the inactive molecules. He also expressed the opinion that at
extreme dilution all the inactive would be transformed into active
molecules. He recognized an " activity coefficient '^ of a solution
which is defined by the equation,

Number of activt. molecules ^ ^^^^.^^ coefficient.
Total number of molecules

At infinite dilution the value of this coefficient would, then, be unity.
For all other dilutions, it would be less than unity and would express
the ratio of the equivalent conductance at a given dilution to the
limiting value of the equivalent conductance, or the equivalent
conductance at infinite dilution. He had not then shown in what
respect the active molecules differ from the inactive. As soon as
the above-mentioned works of van't Hoff appeared, Arrhenius was
able, by comparing the freezing-point lowering produced by electro-
lytes with the electrical conductance of their solutions, to adduce
remarkable and convincing evidence of the correctness of the theory
of electrolytic dissociation.

Calculation of the Degree of Dissociation. — As already stated,
there is a class of compounds, such as sodium chloride, for example,
which give an abnormally large lowering of the freezing point.
Thus while one mol of sugar dissolved in ten liters of water lowers
the freezing point by about 0.186°, one mol of sodium chloride (con-
sidered as NaCl), dissolved in the same volume, lowers it by^ nearly
twice that value. It is evident that, if van't Hoff's principle be
accepted as applying to this case, and the sodium chloride be con-
sidered as dissociated in solution into a sodium and a chlorine part,
the extent of this dissociation may be calculated from a knowledge
of the deviation of the freezing-point lowering of the salt from the
freezing-point lowering of an undissociated substance.

T ^. Abnormal freezing- point lowering .

Normal freezing-point lowering

THEORY OF ELECTROLYTIC DISSOCIATION 69

where the abnormal value is the value actually determined^ and the
normal value that which would be obtained if the salt was entirely
undissociated.

Then i = 1 — a + nos,

where x represents the degree of dissociation and n the number of
parts into which one molecule dissociates. For the salt NaCly n is
equal to 2, and for MgOl, 3^ and so on.

The degree of dissociation x is then given by the equation,

n — 1

Arrhenius calculated the degree of dissociation, or, as he called it,
the affinity constant, for a great many substances from the known
values of their freezing-point lowering, and found that the results so
obtained agreed with the dissociation values which he obtained from
measurements of the electrical conductance. It follows from this,
thai only those substances in wcUer solution conduct the electric current
which are to some degree dissociated^ and that the greater the degree of
dissociation the more readily does the substance conduct the electric
current. It is a logical conclusion from these statements that the
conductance of a solution is due entirely to dissociated parts of the
molecules. Arrhenius ascribed electrical charges to these dissociated
parts and called them ions.

Even at that time Arrhenius called attention to the fact that many
other physical and chemical phenomena were very clearly explained
upon the assumption of the existence of free ions in solution.

Dissimilarity between Oaseous and Electrolytic Dissociation. The
Ions. — It is evident that there is an important difference between
dissociation in the dissolved and that in the vapor state, as, for
instance, in the case of ammonium chloride vapor. In the former
ease only are the parts of molecules resulting from dissociation
charged with electricity. The question at once arises as to the
source of these charges of electricity which appear suddenly when
an electrolyte is dissolved in water. They seem to be produced
from nothing. It is not difficult to give a satisfactory answer to this
question, as will be evident from the following theoretical discussion.
Consider, for example, equivalent quantities of the elementary sub-
stances, sodium and iodine. They possess definite quantities of
chemical and internal energy. If now they be allowed to react
with each other to form sodium iodide, they lose a portion of their
chemical or internal energy in the form of heat. The rest of the

60 A TEXT-BOOK OF ELECTRO-CHEMISTRY

energy originally possessed by the sodium and iodine remain asso-
ciated with the salt) sodium iodide, until some further change is
allowed to take place. If the salt be dissolved in water, it dissoci-
ates to a large extent, and the chemical or internal energy is again
decreased, this time with the appearance of the equivalent quantity
of electrical energy in the form of equivalent positive and negative
charges on the sodium and iodine ions, respectively. It is evident
from this discussion that the sodium and iodine ions differ from the
elementary substances, sodium and iodine, in that they possess elec-
trical energy, and also in that their energy content is less. They
may be transformed into the corresponding elementary substances
again by supplying electrical energy to them by means of an electric
current under suitable conditions. When the ions have taken up
the requisite quantity of energy, a transformation of electrical into
chemical energy takes place, and the sodium and iodine separate at
the electrodes as elementary substances.

We may now inquire into the cause of this transformation of
chemical into electrical energy when sodium iodide is dissolyed in
water, and also question the possibility of positively and negatively
charged particles existing together in a solution without neutralizing
each other. This inquiry and this question is briefly answered by
an assumption of the theory of electrolytic dissociation. This
assumption states that the solvent possesses the power of causing this
transformation ofene^yy and of preventing the mutual neutralization of
the ions. It may be questioned further whether the assumption of
electrically charged particles is of value to science. Experience up
to the present time answers this question emphatically in the affir-
mative.

Ionization aocording to the Katerial Conception of Bleotrioity. —
According to the material conception of electricity indicated in the
note at the bottom of page 26, an ion may be considered to be a com-
pound of positive or negative electrons with the element in question.
These two new elements, or electrons, are represented by the sym-
bols, ® and 0. The formation of an ion is, then, entirely analogous
to the formation of a compound from two ordinary elements. For
instance, in the formation of ions from sodium iodide, the sodium
atoms combine with positive and the iodide atoms with negative
electrons according to the reaction,

Nal+ © + e =Na® +1© =N"a* + I'.
This conception is very comprehensive, for, according to it, the law

THEORY OF ELECTROLYTIC DISSOCIATION 61

of electro-chemical change (Faraday's law^ see page 42) appears as
a consequence of the laws of definite and multiple proportion.

Althoagh the theory of electrolytic dissociation was not spared
great opposition in its early years, it has successfully advanced until
at the present time by far the greater number of investigators accept
it and recognize its value. As a matter of fact, it possesses the ad-
Tantages to be expected of a good theory. It correlates a large number
of apparently unrelated facts and serves as a good guide for new in-
vestigations. At present there is no other theory dealing with the
same subject that even approaches this one in usefulness, and for
this reason it will be applied throughout the book. However^ U
should be borne in mind that it is a theory and not a dogma that is in-
volvedf the condvsums from which must be impartiaUy tested by eooperi-
mentaUy determined facts.

CHAPTER IV

THB MIGRATION OF IONS

AoooBDiKG to the dissociation theory, electrolytes exist in aqaeons
solution partly in the form of ions, each of which possesses a definite
electrical charge. For example, in a solution of hydrochloric acid
there are hydrogen ions, H*, charged with a definite quantity of posi-
tive, and chlorine ions, Gl', charged with an equivalent quantity of
negative, electricity. Calling to mind the law of electro-chemical
change, or Faraday's law, it may be stated, first, that the conduction
of electricity through a solution takes place only by means of a
movement of those ponderable particles which are charged with
electricity (in the above case, the hydrogen and chlorine ions) ; and
second, that chemically equivalent quantities of these particles are
charged with equal quantities of electricity.

A galvanic, or, what is the same thing, an electric, current may be
produced in an electrolyte by dipping into it two electrodes which
are connected with the positive and negative -poles, respectively, of a
source of electricity. In consequence of the potential-difference thus
produced between the two electrodes, the positive and negative ions
move in opposite directions toward their respective electrodes, and
an electric current is said to flow through the solution. In all cases
the passage of the electric current is accompanied by a decomposition
of the electrolyte, even though, in case of a very feeble current, it
may not be evident. With hydrochloric acid, electrically neutral
hydrogen and chlorine gases separate at the cathode and anode,
respectively. An electric current can also be produced in a solution
by induction without the use of electrodes. In this case no transfor-
mation from the ionic to the electrically neutral state takes place.

When an electric current is conducted through a solution, a certain

number of positive ions pass through a cross section of the solution

between the electrodes in one direction, and simultaneously a certain

number of negative ions pass through it in the opposite direction.

It was formerly believed that when the two ions possessed the same

valency, the same number of positive and negative ions pass through

a cross -section in a given time. This belief owed its existence

THE MIGRATION OF IONS 68

undotibtedlj to the fact that the quantities of the constituents of
the electrolyte which separate at the two electrodes are equivalent
to each other. It is now known, however, that sddom or never do
equal numbers of the two kinds of ions pass throtigh a cross section
of the solution in the same time. The phenomena of electrical con-
duction and decomposition are not as closely related as was formerly
believed. Their relation was discovered by Hittorf ^ by a careful
study of the changes in the concentration of an electrolyte which
take place about the electrodes, during the passage of an electric
current.

It will now be explained how a knowledge of the relative numbers
of the two kinds of ions passing a cross section in a given time, or,
what is the same thing, a knowledge of the relative velocities of
migration of the two kinds of ions, can be obtained from a study of
the concentration changes just mentioned.

As already stated, whenever a current of electricity passes through
a solution of an electrolyte, such as of hydrochloric acid, a move-
ment of ions, and a decomposition at the electrodes, takes place. It
follows also that, in a solution of such an electrolyte, there are always
the same number of negative and positive ions ; for if a negative ion
separates on the positive electrode as an electrically neutral sub-
stance without the simultaneous separation of a positive ion at the
negative electrode, the solution afterwards contains more positive
than negative ions and hence contains an excess of positive electric-
ity. This excess of positive electricity is large, since the electrical
charge upon an ion is very great. If still another negative ion is to
be separated alone at the electrode, a greater quantity of work would
be required than before, because the positively charged solution
would now have a greater attraction for the negative ion and there-
fore would resist its separation more strongly than before. On the
other hand, the separation of a positive ion at the other electrode
would require very little work because of the repellent force of the
positive electricity of the solution. Since this electrostatic force,
compared to the other forces involved, is very great, the decomposi-
tion of the electrolyte must take place in such a manner that the
positive and negative ions always leave the solution at such rates
that the solution itself remains electrically neutraL

The necessity of the separation of equivalent quantities of the
two kinds of ions at the electrodes has now been demonstrated. It
is known from electrical science that the current, or the quantity of

1 Pogg. Ann,, 88, 98, 108, 106 (1853 and 1869). A reprint of this work may
be found in Ostwald's Klasaiker d. exakL Wiss.^ Nos. 21 and 23.

64 A TEXT-BOOK OF ELECTRO-CHEMISTRY

electricity passing through a cross section of the solution of the elec-
trolyte per unit of time, is the same at all points of the circuit It
is eyident also that the total quantity of electricity in motion is
equal to the sum of the positiye and negative electricities flowing in
the circuity but it does not follow that the ratio of the positive
to the negative electricity must remain the same throughout the
circuit. Indeed, without contradicting the teachings of electrical
science, it may even be assumed that in a given circuit the total
quantity of electricity 1, is made up of \ positive and ^ negative at
one point, of \ positive and | negative electricity at another, and so
on. Since the motion of one kind of electricity in one direction pro-
duces the same effects as the motion of the other kind in the oppo-
site direction, it is justifiable to consider the total quantity of elec-
tricity in motion as flowing in one direction, although, in reality, any
portion of the total quantity may be flowing in one direction while
the rest of it is flowing in the other. It is evident from these state-
ments that there is no necessity for assuming equal velocities for
the different ions. This would only be the case when there is^ a
motion of equal quantities of positive and negative electricities at
the same rate in opposite directions.

As a matter of fact, seldom or never, when an electric current is
flowing through a solution of an electrolyte, do equivalent quantities
of positive and negative ions pass through a cross section of the
solution in a given time. This is due to the fact that the mobili-
ties of the two kinds of ions are never the same. Thus the
mobility of the chlorine ion is far less than that of the hydrogen ion.
Corresponding to this difference in mobility, when the two ions are
subjected to the action of forces of the same magnitude, as is the
case in the electrolysis of a solution of hydrochloric acid, the hydro-
gen ion moves about five times as fast as the chlorine ion. It must,
however, be remembered that the number of positive ions is always
equal to the number of negative ions not only in the whole solution,
but also, in general, in every part of the solution.

It will be seen later on that it is possible to correlate a large num-
ber of facts concerning electrolysis by the assumption that the differ-
ent ions migrate with different velocities.

The motion or migration of the two kinds of ions may be made
more comprehensible by a comparison with the movements of two
columns of cavalrymen which are passing each other. Suppose one
column proceeding at a walk, the other at a gallop, and imagine a
ditch in the way which both columns are crossing at the same time.
If the second column moves five times as rapidly as the first, then

THE MIGRATION OF IONS 66

five horsemen of the former column cross the ditch in one direction
in a certain time, while' one of the latter column crosses it in the other
in the same time. In all six horsemen pass the ditch. If each
horseman carries 100 grams of powder, then, during this time, 600
grams of x>owder is transported across the ditch, 500 grams, or | of
it, in one direction and 100 grams, or ^ of it, in the other. In this
illustration the two columns of cavalrymen represent the two kinds
of x>articles or ions, and the 100-gram portions of powder, the elec-
trical charge which each particle or ion carries. The case may now
be considered in which the cavalrymen and portions of powder are
replaced by ions and electric charges.

If a current of electricity be passed through a solution of hy-
drochloric acid between platinum electrodes, as already stated, the
hydrogen ions migrate in one direction with five times the velocity
with which the chlorine ions migrate in the opposite direction.
Hence when the quantity of electricity 6 passes through the solution,
the quantity 5, or f of it, is carried by the hydrogen ions, and the
quantity 1, or \ of it, by the chlorine ions. [This will be more
evident from a consideration of the following diagrams, in which

»i

+-f + ++-|-+4{-|-+++-l-!+-f-H-4-l"f4

^ ■ —

j Middle {

Aiied«S«e^ I iMdon L Otihod* $Mlio«

FlO.23

the hydrogen ions are represented by the symbol +, and the chlo*
rine ions by the symbol — , and the directions in which the ions
move when an electric current is passing are indicated by arrows.
In Figure 23 a line of twenty-one pairs of hydrogen and chlorine
ions are represented between the two electrodes, five of which are
situated between the two porous diaphragms D and D, which are
permeable to the ions and merely serve to prevent the stirring of
the solution by convection currents. This represents the condition
of the solution before an electric current has passed. If now a
quantity of electricity is passed through the solution sufficient to
separate at the two electrodes six ions of chlorine and six of hy-
drogen, and if the hydrogen ions move five times as fast as the
chlorine ions, the condition of the solution at the end of the elec-
trolysis is represented by Figure 24.

Here it is seen that five hydrogen ions have passed from the anode

A TEXT-BOOK OF ELECTRO-CHEMISTRY

section into the middle section, and the same number from the
middle section into the cathode section, and that in the same way
one chlorine ion has passed in the opposite direction from the
cathode section and one has appeared in the anode section. Since
each ion carries the same quantity of electricity, it is evident that
^ of the total quantity is carried through the middle section by
the hydrogen ions, and ^ by the chlorine ions. The number of
ions in the middle section has remained constant and need not be
further considered. From the anode section six chlorine ions
(shown in the vertical column) have given up their charges to the
anode and assumed the state of gaseous chlorine, while from the
cathode section six hydrogen ions (vertical column) have similarly
given up their charges and assumed the state of gaseous hydrogen.
The particles of the inert gases are represented by dots on the elec-
trode surface. The anode section has then received by migration to it
one chlorine ion, and has lost by migration from it five hydrogen ions
and by separation at the anode six chlorine ions. The concentration
in the anode section has then decreased from eight pairs of ions
to three pairs. From a similar consideration it may be shown that

I 4-

1 iiltll"*"

! Middi*

Aiioda S«ct*ofi

+ + + + + + -h

-I-
+

Fig. 2i

the concentration in the cathode section has decreased from eight
pairs of ions to seven pairs. Therefore the loss in concentration in
the anode section is to the loss in the cathode section as five is to
one. But this is also the ratio of the velocity of the hydrogen to
that of the chlorine ion. Hence the following relation exists be-
tween the losses in concentration in the two sections and the corre-
sponding velocities of the two ions :

Loss in the anode section _ Velocity of the cation 1

Velocity of the anion J

Loss in the cathode section

Only at the surfaces where the current passes to or from the elec-
trode does the migi*ation of a single kind of ion take place. At these
surfaces the conducnon of the current consists in the passage of a
given quantity of negative electricity directly to the anode, while
simultaneously an equivalent quantity of positive electricity passes

THE MIGRATION OF IONS

directly to the cathode. This explains the fact that the quantity of
the substances which separate at the electrodes, while dependent
upon the quantity of etedrieity which passes, is independent of the
vdocity of migration of the ions and all other drcumstances, and
explains also the fact that changes occur in the concentration of the
solutions about the electrodes during electrolysis.

The mechanism of electrolysis being thus illustrated^ an actual
problem will now be explained. Consider the vessel shown in Fig-
ure 25, which is divided into three equal parts by means of porous

FiQ. 26

plates permeable to ions, to be filled with a solution containing 30
equivalents of hydrochloric acid. In each compartment of the ves-
sel there are, then, 10 equivalents of the acid. If now 96,540 cou-
lombs of electricity are passed through the solution, 1 equivalent
of hydrogen will separate at the cathode, and 1 of chlorine at the
anode. This quantity of these gases may be considered to be
removed from the solution. Since the same quantity of electricity
passes through every cross section of a circuit, %,540 coulombs pass
through the cross sections of the solution, I and 11.

If it is assumed that both ions migrate with the same velocity,
then ^ of an equivalent of hydrogen ions, carrying 48,270 coulombs,
passes from the anode, through the middle, and to the cathode
section, and simultaneously ^ of an equivalent of chlorine ions, also
carrying 48,270 coulombs, passes the section in the reverse order.
The gain or loss in concentration in the three sections, due to the
electrolysis, may now be found. The cathode section has lost 1
equivalent of hydrogen ions by separation as a gas at the cathode,
and ^ of an equivalent of chlorine ions by migration to the anode,
and has gained ^ of an equivalent of hydrogen ions by migration
from the anode. It has therefore suffered a final loss of ^ an equiv-
alent of hydrochloric acid, and therefore contains, after the elec-
trolysis, 9^ equivalents of the acid. Similarly it may be shown that

A TEXT-BOOK OF ELECTRO-CHEMISTRY

the concentration of the solution in the anode section has decreased
to 9^ equivalents. The middle section has not suffered a change in
concentration, since equal quantities of the two ions have migrated
to and from it. [The following summary may serve to make the
above concentration changes more comprehensible : —

Original concentration in each section = 10 equiv. HCl^
Quantity of electricity passed = 96,540 coulombs.

Akodb Sbotioh

MiDDU SscrnoK

Cathodx Sxotioh

Eq.H*

Eq.Cr

Eq.H-

Eq. Cr

Eq. H-

Kq.a'

Loss by separation
Loss by migration
Gain by migration

1
i

Total loss

Final cone. H* Q'

n ]

It follows, then, that when the velocity of migration of the two ions
is the same, the solution in both the anode and the cathode section
will suffer the same change in concentration.

The hydrogen ions, however, really migrate about five times as
fast as the chlorine ions. The above consideration will now be
altered as required for this case. Accordingly, ^ of an equivalent
of hydrogen passes from the anode, through the middle, to
the cathode section, carrying with it f of 96,540 coulombs of
electricity, while ^ of an equivalent passes through the sections
in the opposite direction, carrying ^ of 96,540 coulombs. As be-
fore, in total, 1 equivalent of ions passes through the middle
section, carrying 96,540 coulombs of electricity. The concentration
of the solution in this section remains constant, while that of
the solution in the anode and cathode sections changes. The solu-
tion in the cathode section has lost by separation at the cathode in
gaseous state 1 equivalent of hydrogen ions, and by migration to
the anode section, ^ of an equivalent of chlorine ions, and has gained
f of an equivalent of hydrogen ions by migration from the anode
section. Consequently the concentration in the cathode section has
been decreased by ^ of an equivalent of hydrochloric acid, and is,
therefore, after the electrolysis, equal to 9f equivalents. The solu-
tion in the anode section has lost, by separation at the anode, 1
equivalent of chlorine ions, and by migration to the cathode section.

THE MIGRATION OF IONS

f of an equivalent of hydrogen ions, and has gained^ by migration
from the cathode^ ^ of an equivalent of chlorine ions. It has then
suffered a loss of f of an equivalent both of hydrogen and of chlor-
ine ions, and hence its concentration has fallen to 9^ equivalents of
hydrochloric acid.

[The foregoing may be restated briefly as follows : —

Original concentration in each section sa 10 equivalents H' GF.
Concentration in middle section remains constant.

AjroDK BsonoK

Cathodb Saonoir

•

£q. H'

Bq. Cr

£q. H'

Eq. or

Loss by separation
Loss by migration
Gain by migration

1
«

Total loss

Final concentration H' CI'

To summarize, after 96,540 coulombs of electricity have passed
through the solution, it is found that that part of it contained in
the cathode section has suffered a change in concentration from 10
to 9^ equivalents, or a loss of ^ of an equivalent of hydrochloric
acid, and that part contained in the anode section a change from
10 to 9^ equivalents, or a loss of f of an equivalent of hydrochloric
acid. Here, as was found in the diagrammatic illustration of the
electrolysis of hydrochloric acid, the loss in the cathode section is to
the loss in the anode section as the velocity of the anion is to the
velocity of the cation.] In this case of hydrochloric acid this ratio
is 1 : 5. This may also be expressed as follows : —

Loss in the cathode section _ Velocity of anion (C10 _,l ^^ H^l^
Loss in the anode section Velocity of cation (H*) 5

It was in the manner just indicated that Hittorf was able to
determine the relative velocities of migration of the different ions
from the changes taking place in the concentration of the solution
near the electrodes. His conclusions, although at first opposed, are
now generally accepted.

From a superficial consideration of the theory of the independent
migrations of the ions, it seems evident that if one ion migrates
with a greater velocity than the other, an accumulation of anions

70 A TEXT-BOOK OF ELECTRO-CHEMISTRY

around one electrode and of cations around the other must result
during electrolysis. That this is not the case has, however, already
been demonstrated. A further question which naturally presents
itself is: How can 1 equivalent of chlorine separate at the anode,
when only ^ of an equivalent is brought into the anode section
by migration ? This is answered by assuming that there is always
a large excess of ions in the immediate vicinity of the elec-
trode, so that in any given time more ions may separate on the
electrode than reach it by migration. This action is assisted by or-
dinary liquid diffusion.

The ratio of the migration velocities of any two ions may be
determined in a very simple manner by the method indicated in the
above illustrative problem. It is only necessary to divide the solu-
tion of known concentration into three parts, as shown in Figure 25,
and, after nie passage of a known quantity of electricity through it,
to determine the concentration changes which have taken place in
each part. The concentration of the middle portion must remain
constant. If this is not the case, it shows that the portions of so-
lution about the electrodes have diffused into this section, thus
destroying the value of the determination. Such a change in the
concentration of the middle portion often takes place when the elec-
trolysis is too long continued.

In general, the quantity of the substance migrated or transferred,
and not the quantities '^osf about the electrodes, is used in calcu-
lations. If one equivalent of the anion and one of the cation is
separated at the electrodes, and if the fraction of an equivalent n. of
the anion is transferred from the cathode to the anode section, then
the fraction 1 — n« of the cation must have migrated from the anode
to the cathode section. These experimentally determiuable quanti-
ties, 7i« and 1 — n« (or n<,), are called the transference numbers of the
anion and cation, respectively, and their ratio is equal to the ratio of
the velocities of migration of the ions. This is expressed by the
equation

n^ _ Velocity of the anion (u,) _ Loss at the anode (L^)
1 — n. ~ Velocity of the cation (u,) Loss at the cathode (L^)

From this equation it follows that

n. = — 5i-., and 1 -n.=;— Hs—.

Uc+U. IJ. + U.

Thus it is evident that n« and 1 — n. are equal to the ratios of the
migration velocity of the anion and cation, respectively, to the sum

THE MIGRATION OF IONS 71

of the two migration velocities. Because of this relation n« is also
called the relative migration velocity of the anioni and 1 — n. that of
the cation.

T7p to the present, only univalent ions have been taken into
consideration. However, the transference numbers of di- or polyva-
lent ions may be determined in an analogous manner. If we con-
sider, for instance, a divalent ion which is associated with two

CI'
oppositely charged univalent ions, as in the case of Ba " "^ , then

^ — 2— represents the ratio of the migration velocity of both chlorine

ions to that of the barium ion.

Although the relative migration velocities, and therefore also the
ratio of the migration velocities, can thus be determined, the abso-
lute value of each velocity cannot be found by this method. (See
the chapter on the conductance of electrolytes.)

For the sake of clearness it should be remarked at this point that,
by the term mohUity or migration velocity is meant the velocity with
which one equivalent of an ion moves when acted upon by a unit
force. Since, when acted upon by any other force, the velocity
varies with that force, the ratio of the velocities of the ions pro-
duced by any given force is equal to the ratio of the migration
velocities. This subject will be further considered in the section
on the absolute migration velocities of ions.

In carrying out a determination of the relative migration veloci-
ties of the ions, naturally the quantity of the ions separated at the
electrodes as electrically neutral substances must be taken into
account. An example taken from Hittorfs work will now be con-
sidered, in order to show how the calculation of results is most eas-
ily made.

A four per cent solution of silver nitrate was electrolyzed at 18.4^
for a considerable time, and the quantity of silver deposited and the
change in concentration about the cathode determined : —

Quantity of silver deposited and thus removed from

the solution about the cathode . . = 0.3208 gram.

Quantity of silver contained in a volume V of the

solution about the cathode before electrolysis = 1.4751 grams.
Quantity of silver contained in the same volume

about the cathode after electrolysis . . = 1.3060 grams.
Loss of silver in the volume Fof the solution about

the cathode = 0.1691 gram.

If no silver had come into this portion of the solution about the

72 A TEXT-BOOK OF ELECTRO-CHEMISTRY

cathode by migration, its loss would have been 0.3208 of a gram of
silver, the quantity deposited on the cathode, instead of 0.1691 of a
gram, the value found. Hence the quantity of silver which migrated
to the cathode portion is given by the equation,

0.3208 - 0.1671 = 0.1617 gram.

If as much silver had migrated to the cathode region as had been
removed from it by deposition on the cathode, namely, 0.3208 of a
gram, then since

transference number = q^^itity of the ion migrated

quantity of the ion separated

transference number of Ag"= '^^^^ = 1, and

^ 0.3208 '

transfer, number "SOJ = 1 — transfer, number Ag* s 0.

This would show that, in this case, the NO^' ions did not share in
the migration or in the conduction of the electric current. In Hit-
torfs experiment, then,

transference number Ag* = '^^^^ = 0.473, and

^ 0.3208 '

transference number NO,' = 1 — 0.473 = 0.627.

As a check on the accuracy of the determination, the change in
the concentration of the silver about the anode could be measured.
It should be found that the solution about the anode has lost by
migration the same quantity which that about the cathode has
gained. In the above experiment, for example, it should be found
that the loss in silver in the solution about the anode, due to migrar
tion away from it, is equal to 0.1617 of a gram, which is identical
with the gain in concentration about the cathode also due to migra-
tion.

If very exact results are desired, it is advisable to remove suffi-
ciently large portions of anode and cathode solutions, analyse them,
and from the results so obtained, to calculate the quantities of the
ions which have been transferred.

When the anion can be more easily determined than the cation,
its concentration changes may be measured at the anode, or the
cathode, or at both the anode and the cathode, quite as well as the
concentration change of the cation. This may be illustrated by
the determination of the transference numbers of cadmium and chlo-
rine ions. In this case the anode consists of amalgamated cadmium,

THE MIGRATION OF IONS 78

vhich reacts vith the chlorine liberated at its stuface, fcffiiiiDg
thereby cadminm chloride. Hence the quantity of chlorine sepa-
rated may be obtained by determiDing the loss in weight of the
anode during electrolysis. The concentration of the chlorine about
the anode before and after the pass^e of the electric corrent is
determined, and the quantity of chlorine separated at the anode
dedacted from the latter value. The difFerence obtained by snb-
tiaeting from the original concentration the difference between the
final concentration and the quantity of separated chlorine is the
" loss " suffered by the anode portion. From the total quantity of
chlorine separated and from the loss suffered by the anode portion,
the quantity of chlorine which migrated is easily calculated, since it
is equal to the quantity of chlorine separated diminished by the loss
about the anode.

There are a great many forms of apparatus which have been used
for the measurement of transference numbers. In order to ^ve an
idea of the essential features of such
an apparatus, that used by Nemst
and Loeb' for the determination of
the transference numbers of the sil-
ver salts is here described. It is
shown in Figure 26. In form it re-
sembles a Gay-Lassac burette.

The two electrodes are of silver.
When a current of electricity is
passed through the solution, a quan-
tity of silver deposits upon the cath-
ode 0, which is a measure of the
quantity of electricity passed, and
the same quantity of silver dissolves
from the anode A. In order to avoid
the disturbance caused by the falling
of the silver from the cathode, the
latter is placed iu a side tube, of the
same diameter as the main tube, be-
ing introduced as shown In the figure.
The cathode consiBta of a cylindrical Via. iM

piece of silver foil attached to a

silver wire. The anode A, consisting of a silver wire twisted into

a spiral at its lower end and encased by a glass tube throughout its

straight portion, is placed in the main tube as shown. The openings

> ZuthT. phyt. Chem., S, M8 (1886).

74 A TEXT-BOOK OF ELECTRO-CHEMISTRY

at a and c are closed by cork stoppers through which small pieces
of glass tubes are passed. The piece of tubing in a simply allows
the passage of the anode wire, while that in c has a piece of plati-
num wire fused into its side, upon which the cathode hangs. Both
tubes may then be closed by means of pieces of rubber tubing and
pinchcocks. With this arrangement it is possible to remove por-
tions of the solution from the apparatus, without disturbing the
electrodes, by merely blowing at the tube which passes through c.

In carrying out an experiment by means of this apparatus, the
electrodes together with the corks, without, however, the piece of
rubber tubing, are weighed. When the apparatus is again assembled
as shown in the figure, with the rubber tube at a closed with pinch-
cocks, and the end of the tube B placed in the solution to be inves-
tigated, it is filled to a point above the level of the upper side of
the side tube by sucking at the rubber tube at c. The apparatus
usually holds from forty to sixty cubic centimeters. With the exit
tube B closed with a rubber cap, the whole apparatus is placed in
an upright position in a thermostat. After the solution in the
apparatus has reached the temperature of the thermostat, the elec-
tric current is conducted through the solution. Immediately at the
end of the electrolysis, the exit is opened and, by blowing at the
tube c, the desired quantity of the solution about the anode (from
6 to d) is forced out through the tube B into a tared flask, weighed
and analyzed. The quantity of solution remaining in the apparatus
is found by weighing the apparatus and liquid together, and then
subtracting from this weight the weight of the apparatus alone. If
no considerable mixing of the solution by diffusion or convection
currents has occurred during the electrolysis, the portion of the
solution about the anode which has undergone a change in concen-
tration is mostly removed with the first few cubic centimeters.
The remainder is thoroughly washed out by the unchanged solution
which follows it through the tube B. The following portion of solu-
tion, from d to e, should then be unchanged in concentration, while
the concentration of the solution remaining in the apparatus is
changed, since it is from the region about the cathode. A test of
the accuracy of the experiment is found in the unaltered condition
of the middle portion of the solution d e, and also in the fact that
the solution about the cathode loses as much silver as that about
the anode gains.

In order to guard against a mixing of the solution, many investi-
gators have used diaphragms. It is now known that, while porous
porcelain membranes may be used without thereby incurring error,

THE MIGRATION OF IONS 76

other membranes, such as animal membranes, influence the yalue of
the transference number. In the case of the latter class, concentra-
tion changes take place directly at the two surfaces of the membrane,
just as they would if, in place of the membrane or diaphragm, a layer
of a solvent, in which the transference numbers of the electrolyte
are not the same as they are in the solution, is introduced into the
circuit.

At the beginning of his work, Hittorf questioned himself as to
the constancy of transference numbers, and further, if they are not
constant, as to the circumstances upon which their variation depends.
Upon further consideration, he recognized three influences which
must be taken into account, namely, that of the current, that of the
concentration of the solution, and that of the temperature. He
found that the velocities of migration were independent of the
current and therefore of the electrical force acting upon the ions,
but dependent upon the concentration of the solution.

As solutions of greater and greater dilutions were examined, he
found that a point was finally reached beyond which further dilu-
tions caused no appreciable change in the relative velocities of
migration. This behavior is easily explained. In the concentrated
solutions there are a large number of undissociated molecules, which
offer a resistance to the motion of the ions among them which
depends upon the nature of the molecules and of the ions. As the
dilution becomes greater, this influence gradually disappears, due to
an increase in dissociation and to an increase in the distance between
the molecules, and a consequent decrease in the resistance offered
by them to the motion of the ions. This statement may be applied
to mixtures of electrolytes. In this case also the transference num-
bers of individual ions remain unchanged for moderate concentra-
tions.

Very exact measurements of the influence of concentration on
the transference number have recently been carried out by A. A.
Noyes,^ which show that for all the electrolytes investigated, namely,

KCl HNOs Kj^04

NaCl AgNOa CUSO4

HCl Ba(N03),

the transference nxmibers remain constant within one per cent
between the concentrations 0.02 and 0.1 normal. Deviations were
only observed in the case of LiCl, GdS04, and the halogen salts of
the divalent metals. These deviations may, as will be made evident

^ Technology Quatierly, 17, No. 4, December, 1904.

76 A TEXT-BOOK OF ELECTRO-CHEMISTRY

later, be explained on the assumption of the formation of doable
molecules.

Hittorf did not discover any effect produced by such moderate
changes in temperature as were involved in his work. Recently,
however, Kohlrausch^ has found that in the case of electrolytes
with monatomic univalent ions the transference numbers approach
the value 0.50 with increasing temperature. It should be stated
here that at the same time the difference in mobility of the two ions
does not decrease, but actually increases. A numerical example
will make these statements clear. Consider that, at the tempera-
tore Xy the migration velocity of the positive ion is 100, and that of
the negative ion is 50 ; while at a higher temperature y the velocities
have become 115 and 60 respectively. The transference number of
the positive ion has increased from 0.333 to 0.343. It is evident
that the value 0.50 for the transference numbers of the two ions is
being approached. At the same time, however, the difference be*
tween the single velocities,

100 — 50 as 50, at the temperature x,
and 115 — 60 = 55, at the temperature y,

has increased with rising temperature. Such a simple relation
between the temperature and the velocity of migration of the ions is
not found in the case of other classes of electrolytes.

The values of the transference numbers obtained with the solvent
water do not apply to other solvents. For example, while potas-
sium chloride, bromide, and iodide dissolved in water solution all
give the value of the transference number n« = 0.51, when dissolved
in phenol they all give the value of n« = 0.19. With this change in
the value of the transference numbers, there is a corresponding
change in concentration at the boimdaiy surface between the two
solvents in which the same electrolyte is dissolved when an electric
current passes.*

Still another advance was made possible by Hittorf s study of the
concentration changes at the electrodes, namely, the discovery of
the composition of the ions resulting from the dissociation of com-
pounds. Silver cyanide, for example, dissolves in potassium cyanide,

1 SitnmgBber. d. k5iiigl. Pr. Akademie d. Wise. Fhysik. Mathem. Kl., 90, 672
(1902).

s Nemst and Riesenfeld, Drud. Ann., 6, 600 and 609 (1902). For transfer-
ence nnmbeiB in mixed solyents see Jones and Basset, Chem. Oentrbht 1905, 1,
71. A oollection of references to the literature is given by Walden, Ztachr.
phyi, Chem,, 46, 108 (1902).

THE MIGRATION OF IONS 77

forming a compound which in the solid state has the composition
represented by the formula AgCN • KCN. From this fact alone,
however, it is not possible to state what ions this compound forms
upon dissociation in aqueous solution. Now Hittorf passed an
electric current through such a solution and found that silver was
deposited upon the cathode. He determined further the concen-
tration of potassium and of silver about the cathode before and after
the electrolysis, and found that, including the silver deposit, an in-
crease in the potassium concentration above that of the silver had
taken place, corresponding to the quantity of electricity passed
through the solution. These results contradict the assumption that
both the silver and potassium are present in solution as positive
ioDS. Hittorf interpreted the results in the following manner:
The potassium forms positive ions, while the silver and the cyanide
radical unite and form negative ions. In solution, then, this salt
would be represented by the formula K'Ag(CN)t'. Leaving out of
account the quantity of separated substance, the positive and nega-
tive ions must always be present in equivalent amounts, which
evidently requires that before the electrolysis has taken place the
solution contain equivalent quantities of potassium and silver.
The potassium separated at the cathode immediately reacts with
water, forming potassium hydroxide, thus explaining the presence of
an extra quantity of potassium about the cathode corresponding
to the quantity of electricity passed through the solution. The
separation of silver is then a secondary reaction, caused by the
action of the separated potassium, and resulting in the appearance
of a double quantity of GN' ions in the place of decomposed

Ag(CNV ions.

In a similar manner Hittorf investigated the constitution of other
double salts in aqueous solution. He found that they dissociate as
shown in the following table : —

Symbol or Solid Salt lom xk Aqueous SoLunow

Na,PtCl« 2Na>PtCle"

NaAuCl4 Na + AuC^'

K4Fe(CN), 4 K> Fe(CN)e""

K,Fe(CN)e 3 K* -f Fe(CN)e'"

It is even more simple to determine whether a given metal exists
in the positive or in the negative ion by a study of the concentra^
tion changes which take place about the anode during electrolysis.
Since at this electrode no deposition of a metal takes place, then, if
the anion is not decomposed at the electrode, the solution about it

78 A TEXT-BOOK OF ELECTRO-CHEMISTRY

will become more concentrated in respect to this ion. If the metal
in question is a part of the anion, the solution about the anode will,
eridently, become more concentrated in respect to it also. On the
other hand, if it forms the cation, it will migrate away from the
anode, thus decreasing its concentration in the solution about this
electrode. Strictly speaking, when a metal does form a part of an
anion, a certain quantity of the metal, even though it be an ex-
tremely small part, exists in solution in the form of cations. It
can happen, moreover, that the concentration of the solution about
the anode does not undergo a change in respect to the metal during
electrolysis. This is the case when the change in concentration due
to the migration of some of the metal as a part of the anion is
exactly compensated by the migration of the rest of it as the cation
in the opposite direction.

The constitution of salts which form more than two ions in
aqueous solution may also be determined by means of transference
numbers.^ For example, barium chloride may dissociate in two
stages according to the following equations : —

BaCl,;[tBaCr-|-Cl';
BaCr^tBa'-f Cr.

If it is assumed, accordingly, that, in moderately concentrated solu-
tions, the intermediate complex ion BaCl' exists, which on further
dilution breaks down, then the transference numbers, which are ob-
tained from a series of solutions of different concentrations, will differ
considerably from one another. With increasing dUution, the value
of the transference numbers should decrease, since then the quantity
of chlorine carried along with the barium in the ion BaCl' to the
cathode is decreased, and since this carrying along of chlorine tends
to increase the transference number of the barium and to decrease
that of the chlorine. As a matter of fact, however, it was found that
the transference numbers varied in the opposite direction from that
expected on the above assumption. Therefore it is concluded that in
moderately concentrated solutions, one or more mols of undissociated
BaCls combine with CI', forming such complex ions as BaCl^' or
BaCl 4", which on further dilution break down again. Whether or
not the dissociation in stages also takes place is not known.

It has been suggested by Kemst' that it would be possible to
obtain light on the question of hydrated ions by means of migra-
tion experiments. For instance, if the positive ion migrates with a

1 A. A. Noyes, Ztschr. phys. Ohem., 86, 68 (1001).
* Jahrb. d. ElektrochemU, 7, 70 (1901).

THE MIGRATION OF IONS 79

certain number of water molecules while the negative ion migrates
with a different number, then during the electrolysis water is trans-
ferred from one electrode to the other, causing a corresponding change
in concentration of an indifferent, non-conducting dissolved sub-
stance, the so-called indicator. As is evident, this method gives only
the difference of the quantities of water carried by the two ions.
The preliminary results obtained thus far indicate that the anions of
strong mineral acids are hydrated.

Exact experiments with a solution of silver nitrate in aqueous
methyl alcohol have recently been made by Lobry de Bruyn.^ He
was unable to detect a change in the concentration of the water or
alcohol, and consequently was unable to show either the formation of
ion-hydrates or of ion-alcoholates. Morgan and Kanolt,' however,
found that during the electrolysis of a solution of silver nitrate in
water and pyridine a decrease in the concentration of the pyridine
took place about the anode. From this it would be concluded that
the pyridine combines with the silver ions.

The interpretation of his results given by Hittorf when first
published met with great opposition, but are now accepted as cor-
rect. They are also now confirmed by the independent results ob-
tained by determinations of the freezing-point lowering of solutions.

It is very interesting to note that there are substances, the so-called
amphoteric electrolytes,^ which may dissociate in different ways.
Lead hydroxide, Pb(OH)t, for example,,may dissociate as follows: —

PbCOH), = PbOH' -h OH ' ;
Pb(OH), = Pb" -1-2 OH';
Pb(OH), « H" -f. PbO(OH) ';
or finally, Pb(OH), = 2 H* + PbO, .

In pure water all of these ions exist together in greater or less
quantities according to the respective degrees of dissociation. If the
first two modes of dissociation predominate, the solution reacts alkar
line; if the latter two, it reacts acid. If a strong acid be added to
the solution, nearly all of the OH ions combine with the H ions of the
acid, forming undissociated water. The re^stablishment of the equi-
librium then requires the further dissociation of the undissociated or
solid hydroxide into Pb" and 2 OH'. As before, the OH ions are
removed by the action of the added acid and the end condition is

1 Jahrb. d. Elektrochemie, 10, 260 (1004).
■ « Ztschr, phys. Chem., 48, 866 (1904).
* Bredig, Ztschr. ElektroGhem., 6, 88 (1809) ; ZUehr. anorg. Chem., 84, 202
(1908) ; Walker, Ztschr. phya. Chem., 49, 82 (1904).

80 A TEXT-BOOK OF ELECTRO-CHEMISTRY

reached that in acid solution divalent lead ions are present almost
exclusively. These ions may combine partially with the anions of
the acid to form an undissociated salt, or they may form some such
complex ions as exist in the case of barium chloride.

If a strong base be added to the solution, the OH ions remove the
H ions which were present, and we see at once that in an alkaline
solution of lead hydroxide the PbOs ions will predominate.

The hydroxides of other metals dissociate similarly. Hydroxides
of the alkalies dissociate exclusively into positive metal ions and
OH ions.

From what has been said it is evident that the metal in solutions
of such amphoteric electrolytes must migrate as cations to the cathode
in acid solution and as anions to the anode in alkaline solution.

Lead salts have been found to behave in this way. To be sure, the
fact must also be taken into consideration that colloids may migrate
with or against the electric current (see chapter on electrical
endosmose). Hence the presence of a metallic oxide as an anion in
an alkaline solution is not conclusively shown by a migration experi-
ment alone.

From a theoretical standpoint all ions which are possible in a
given solution must be present. However, only those whose existence
may be detected will receive consideration here. It is objectionable
to deal with ions which cannot be detected.

There is a special class of amphoteric electrolytes which form
ions which possess a double nature, being at the same time acid
and basic. GlycocoU furnishes an example of such an ion. It dis-
sociates according to the equilibrium equation,

HOHaNCHaCOOH z^ BtNCH^COO' + H* + OH'.

The ion undefined is charged both positively and negatively, and
hence is electrically neutral, taking no part in migration and in the
conduction of the electric current.

Another experiment concerning the electrolysis of mixtures of
electrolytes which was performed by Hittorf may well be men-
tioned here. He found, in his study of solutions of potassium chlo-
ride and of potassium iodide, that the chlorine and iodine ions
migrate with very nearly the same velocity. With our present
knowledge, it may be predicted with great certainty that during the
electrolysis of a mixture of these salts, the ratio of the concentra-
tions of the chlorine to that of the iodine will not change, since the
chlorine and iodine ions take part equally in the conduction of the

THE MIGRATION OF IONS 81

electric current Such was actually found to be the case. At that
time, the fact that when such a solution of these two salts was elec-
trolyzed iodine alone separates at the anode, caused much trouble,
since the phenomenon of electrical conduction was not distinguished
from that of electrolytic decomposition. It was concluded that pos-
sibly the iodine alone, belonging to a more easily decomposed com-
pound, conducted the current. The fact that iodine alone separates
at the anode has nothing to do with the phenomenon of conduction.
In the chapter on polarization this subject will be again considered.

Recently, the question as to whether the lines of current, or the
ions migrating from one electrode to another, may be diverted from
their paths by electro-magnetic action, has received attention,^ negar
tive results being obtained.

Up to the present but few transference experiments have been car-
ried out with fused electrolytes.'

It is natural that the important phenomenon of migration should
play an important part in commercial processes. In the electrolysis
of concentrated solutions of potassium chloride on a large scale in a
vessel divided into two parts by means of a porous diaphragm, alkali
is produced at the cathode and chlorine at the anode. The latter is
evolved and collected, while the alkali accumulates in the cathode
section. Consequently the alkali thus formed takes part in the con-
duction, by the migration of hydroxyl with the chlorine ions to-
ward the anode, thus decreasing the yield of alkali. This decrease
becomes greater the greater its concentration in the cathode section.
For this reason in the works the concentration of alkali is not
allowed to exceed six or eight per cent. It should especially be
remarked that, with an increase in temperature, not only is the con-
ductivity of the solution increased, but also the yield in alkali is
increased, since the transference numbers of electrolytes having
univalent ions thereby approach the value 0.5.

It seemed surprising, at first, that the alkali yield in the electroly-
sis of a potassium chloride solution is about ten per cent higher
than that in the electrolysis of a sodium chloride solution under the
same conditions. A consideration of the transference numbers in
the two cases, however, explains the phenomenon. The transfer-
ence number of OH' at 18** in 1/1 normal solution of potassium
hydroxide is 0.74, while in a 1 /I normal solution of sodium hydrox-
ide it is 0.826. Thus, in the former solution fewer OH ions migrate
toward the anode when a given quantity of alkali is formed at the

1 Heilbnin, Drud. Ann., 16, 988 (1904).

> Lorenz and Fausti, Ztgehr. Slekirochem,j 10, 690 (1904).

82 A TEXT-BOOK OF ELECTRO-CHEMISTRY

cathode than in the latter solution, since the migration velocity of
the potassium ion is greater than that of the sodium ion. The
yield may also be increased by conducting a stream of carbon diox-
ide through the alkali at the cathode. The rapid ion OH' is
thereby replaced by the slower ion CO,". To be sure, it must in
this case also be recognized that the product obtained, the carbon-
ate, is of less value than the hydroxide.

If a current of the solution is made to flow, with the velocity with
which the hydroxide ions migrate, from the anode to the cathode,
the loss in alkali is decreased. In the production of alkali, it is only
necessary to have a conveniently formed apparatus, without a dia-
phragm, through which a salt solution may be allowed to flow from
the anode to the cathode, in order to obtain a quantitative yield.
Since, however, the migration velocity of the OH ions is consider-
able, it would be expected that only a dilute solution of alkali could
be obtained when the electric current is well utilized. Nevertheless,
it is possible to obtain a fifteen per cent solution of alkali with a
ninety per cent utilization of the electric current, in this way. The
chief cause of this good yield must be sought in another direction.
It is found in the stream of concentrated salt solution which is
allowed to flow into the apparatus at the anode. The OH ions,
migrating toward the anode, then pass from layers of solution which
are dilute in respect to the CI ions to those which are concentrated,
and, consequently, take part less and less in the conduction of the
electric current. The progress of the OH ions toward the anode is,
in this way, checked more and more as the anode is neared. The
so-called bell process is based upon these principles.^

A yield of alkali which is almost quantitative may also be ob-
tained by the electrolysis of chloride solutions, using a mercury
cathode. In this way the formation of OH ions is prevented, since
under the influence of the electric current an alkali amalgam is
formed. Care must, of course, be taken to constantly replace the
amalgam with pure mercury. The former is transferred to a second
vessel containing water, where it is decomposed, forming alkali and
mercury. This so-called mercury process is carried out in various
modified forms.' It possesses the advantage that by means of it
very concentrated lye, which is free from salt and which can be used
directly in the industries, is produced. The lye obtained by the

1 Adolph, Zt8chr. Elektrochem., 7, 681 (1901) ; Steiner, Ztachr, Elektrochem,^
10, 317 (1904).

> F. Glaser, Ztschr, Elektrochem., 8, 622 (1902); Kettembeil-Carrier, Ztschr.
Elektrochem., 10, 661 (1908) ; Le Blanc-Cantoni, Ztschr, Elektrochem., 11, 009

0905).

THE MIGRATION OF IONS 88

heU or diaphragm processes must be concentrated by evaporation
and purified by removing the salts before being used.

In many cases it is possible to avoid the damaging effects of mi-
gration in a more rational manner. In the dye works, a solution of
chromic acid in sulfuric acid is generally used as an oxidizing
agent. During the oxidation, the chromic acid is transformed into
chromium sulfate. The chromic acid can then be regenerated,
electrolytically, by placing the chromium sulfate solution in the
anode section of an electrolytic cell, which is provided with a dia>
phragm, and sulfuric acid in the cathode section, and passing an
electric current through the cell. During the electrolysis, SO4 ions
migrate from the cathode section into the anode section, thereby
enriching the sulfuric acid in the latter section at the expense of the
acid in the cathode section. In such a process it is necessary to
precipitate the excess of sulfuric acid in the chromic acid solution
irom time to time with lime, and to replace, with concentrated sul-
furic acid, the diluted and impure acid of the cathode section. This
may, however, be avoided by first placing the chromic acid solution
in the cathode section, in place of the pure sulfuric acid, and passing
an electric current long enough to sufficiently oxidize the correspond-
ing liquid in the anode section. This anode liquid is used directly
in the works, whereby chromium oxide is again formed, and is then
allowed to flow into the cathode section, where it is again electro-
lyzed. The solution used in the previous electrolysis in the cathode
section, is, this time, used in the anode section. Before the second
electrolysis, the cathode solution is richer in sulfuric acid than the
anode solution, but during it this excess migrates to the latter solu-
tion. A cyclical procesd is thus carried out, in which the chromic
acid solution is alternately placed in the anode and cathode sections,
thus preventing the accumulation of an excess of sulfuric acid in it;
and making it possible to maintain the solution at a given concen-
tration during its regeneration by electrolysis. By means of such a
process, a solution of chromic acid in sulfuric acid may be used as an
oxygen carrier as long as desired without loss of either chromic or
sulfuric acid.^

A table of the transference numbers of the ions of the most im-
portant and best-investigated electrolytes is given on the next
page. The values have been taken from Kohlrausch and Holbom's
^'Das Leitvermogen der Elektrolyte," and from the recent works of
Noyes,* Jahn,' and Tower.*

1 Le Blanc, Ztschr, Elektrochem,, 7, • Ztschr, Phy$. Ckem,, 87, 673 (1901).
290 (1900). *J, Am. Chem. Soc., 96, 1089 (1904).

* Ztichr. Phy$, Chem., 86, 03 (1901).

A TEXT-BOOK OF ELECTRO-CHElflSTRT

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CHAPTER V

THB CONDUCTANCE OF BLBCTROLTTBS .

Spedfio and Equivalent Conductance. — The oonception of resist-
ance in the case of conductors of the first class has already been
discussed. The resistance of such conductors is dependent upon the
nature of the material of which they are formed, their form, and
their temperature. If, for a cylinder one centimeter in length and
one square centimeter in cross section, of a certain substance,

B, the resistance = - ,

then for any cylindrical piece of the same substance at the same
temperature,

K 8

when I represents the length of the cylinder in centimeters and s

its cross section in square centimeters. The factor - represents

the 9peciflc resistance of the substance. It depends only on the
temperature.

The unit of resistance is the ohm. It is the resistance of a con-
ductor in which a current of one ampere flows when a difference of
potential of one volt exists between the ends of the conductor. A
substance which in the form of a cylinder one centimeter in length
and one square centimeter in cross section possesses a resistance of

one ohm represents a unit of resistance. For it - = 1. In practice,

however, the unit of resistance is represented by the resistance of a
column of mercury, 106.3 centimeters in height and one square
millimeter in cross section, at the temperature of melting ice. The
mass of this column of mercury must be 14.4521 grams.

Formerly, the unit of resistance was defined to be the resistance
of a column of mercury, one meter in length and one square milli-
meter in cross section at 0"* t This unit is known as the Siemens or
mercury unit. It is related to the new unit as 1 : 1.063, and there-

86 A TEXT-BOOK OF ELECTRO-CHEMISTRY

fore, in order to calculate the resistance in ohms from a resistance
expressed in Siemens units, or conversely, the following equation
may be used: —

Resistance in ohms s Resistance in Siemens units -f- 1.063.

In the following pages, the ohm is used as the unit of resistance.

The greater the resistance, the less the conductance ; and, con-
versely, the greater the conductance, the less the resistance. Hence,
the resistance b and the conductance k are reciprocal quantities, or

The word condtictance is used mainly with reference to solutions,
and in the following pages will be used only with such a reference.
Just as in the case of conductors of the first class, the ujiit of
specific conductance, which may be expressed in reciprocal ohms,
could be represented by the conductance of a cylinder of a liquid,
one centimeter in height and one square centimeter in cross section,
which possesses a resistance of one ohm. For such a liquid k = 1.
Furthermore, the same law which expresses the variation of the
resistance of a conductor at constant temperature with a variation
of its dimensions applies also to conductors of the second class.
That is,

B ~ Z

where k is the conductance, k the specific conductance, or conduc-
tivity, B the resistance, s the cross section, and I the length of the
liquid conductor. This method of expressing conductance has not,
however, been found suitable for obtaining numerical relationships
between solutions. Since electro-chemistry deals chiefly with solu-
tions, it has been found advisable to adopt a special method of
expressing their conductances. In the case of solutions, the con-
ductance depends almost entirely upon the solute, or the dissolved
substance, and in comparing their conductances, it has been found
advantageous to refer the conductances to a certain quantity of
solute, namely, one equivalent weight, rather than to any particular
volume of solution. The conductance of a solution containing one
equivalent of the solute, when placed between parallel electrodes
one centimeter apart, is called its equivalent candudUmce e*

K C« represents the equivalent concentration of a solution, i.e. the
concentration expressed in equivalents of the solute per cubic centi-
meter of solution, then

CONDUCTANCE OF ELECTROLYTES

where ly^ represents the equivalent dilution of the solution, or in
other words, the Yolume in cubic centimeters which contains one
equivalent of the solute. Accordingly,

The relation between the equivalent conductance s and the spe-
cific conductance k is reached as follows : [Consider a vessel, such
as is shown in Figure 27, constructed of two non-corrodible metallic
plates A, and (7, serving as electrodes, which are held at a distance
of one centimeter from each other by the nonconducting material
which forms the ends and bottom of the vessel.]

One cubic centimeter of a solution containing one equivalent of a
solute is placed in this vessel, reaching to the level a. The cross
section of the solution, perpendicular to the
direction of the electric current between the
two electrodes, is then one square centimeter.
The equivalent concentration of this solution
is unity, and hence its dilution is also unity.
Since its volume is one cubic centimeter and
it is placed between electrodes one centi-
meter apart, its conductance is directly the JL,
specific conductance or conductivity, and
since it contains one equivalent weight of
dissolved substance placed between elec-
trodes one centimeter apart, its conductance
is also the equivalent conductance. These
facts concerning this solution may also be
expressed by the following equations : —

C\ s=s 1, D', = 1, and k =:k ==£•

If, however, the volume of the above solution be increased to one
thousand cubic centimeters by the addition of water, thereby reach-
ing the new level &, the cross section of this solution is one thou-
sand times as great as that of the original solution, or one thousand
square centimeters. But the conductance of a quantity of this solu-
tion having a cross section of one square centimeter is the specific
conductance, or the conductivity of the solution. Hence the actual
conductance of this solution is one thousand times as great as the
specific conductance, or conductivity. The solution still contains
one equivalent of the dissolved substance between the electrodes,
and therefore the actual conductance is still identical with the

Fixs. 97

A TEXT-BOOK OF ELECTRO-CHEMISTRY

equivalent conductancei this time at the dilution, 1000. It may
be said, in general, that whenever one equivalent of a substance in
aqueous solution, of any concentration or dilution, is placed in such
a vessel, its actual conductance is equal to the equivalent conduc-
tance at the concentration in question. It follows from what has
been stated, that in the above case the equivalent conductance of
the solution is also one thousand times as great as its conductivity.
These relations are expressed by the following equations : —

K = s=1000K=:D:K = i-

The specific conductance, or conductivity, of a solution changes
nearly in proportion to the concentration, while the equivalent con-
ductance generally increases rapidly at first, then more slowly, and
finally remains constant, with decreasing concentration. This will be
evident from a study of the table of equivalent conductances of salts,
acids, and bases in aqueous solution at different concentrations,
given here. This table contains among other results the most recent
ones obtained by Kohlrausch.

EQUIVALENT CONDUCTANCES AT IS** t

•qolTft-
lent

KGl

NaCl

KNOs

AgNO.

iCaBO«

|H^04

HCl

GH«0OOH

KOH

NHs

eqnlTA-
lent

ooDcen-
tntioni

diIaUoii>

0.0001

120.07

106.10

126.60

116.01

109.96

^^^

107

^^^

(66)

10000

0.0002

128.77

107.82

126.18

114.66

107.90

—

5000

0.0006

128.11

107.18

124.44

118.88

1WJ56

(808)

—

88.0

2000

0.001

127.84

100.49

128.66

118.14

98.56

861

(877)

(284)

28.0

1000

0.003

126.81

106J$6

122.60

112.07

91.94

851

876

80.2

(288)

20.6

600

0.006

124.41

108.78

130.47

110.06

80.98

880

878

20.0

280

18.2

200

0.01

122.48

101.96

118.19

107.80

71.74

806

870

14.8

228

9.6

100

0.02

119.90

99.62

116.21

—

02.40

286

867

10.4

225

7.1

0.06

116.76

95.71

109.86

99.60

61.16

256

860

6.48

219

4.6

0.1

112.06

92.02

104.79

94.88

48.85

226

851

4.60

218

8.8

0.2

107.90

87.78

98.74

—

87.66

214

842

8.24

206

2.80

0.6

102.41

80.94

89.24

77.6

—

206

827

2.01

197

1.85

98.37

74.86

80.46

67.6

26.77

198

801

iJSi

184

0.89

92.6

64.8

09.4

—

188.0

254

0.80

160.8

0.682

0.6

88.8

66.6

(61.8)

—

166.8

215.0

0.64

140.6

0.864

0.88

*^"

42.7

""■

185.0

152.2

0.286

106.8

0.202

0.2

1 Equivalent concentration, C. = ^^^^'^^"^'^

Liters

^ Equivalent dilution, D« =

Liters

Equivalents

CONDUCTANCE OF ELECTROLYTES

General Similarities. — The first clear conceptions concerning the
conductance of electrolytes resulted from the epoch-making work of
Kohlrausch. The work of discovery was then rapidly pushed for-
ward by Arrhenius, Ostwald, and others. It was found that, with-
out exception, the equivalent conductance of different electrolytes
increases with increasing dilution, reaching in many cases a maxi-
mum value which does not change upon further dilution. The fol-
lowing statement, called Kohlrausch's principle,^ has been found to
hold for solutions which have been diluted until the maximum
equivalent conductance has been reached : —

The equivalent conductance of a binary electrolyte is equal to the sum
of two values, one oftoMch depends upon the cation, and the other upon
the anion.

This principle expresses the fact that the conductance of an elec-
trolyte is equal to the sum of the conductances of its ions. Because
of this fact the conductance of an electrolyte is called an additive
property. The principle is evident from a study of the following
table,' in which the equivalent conductances, at great dilutions of
several series of salts, are given. For example, in the first horizontal
row are given the values for KCl, NaCl, TlCl, and LiCl, and the
differences between these values ; while in the first column are given
the equivalent conductances of KGl, KNOa, KF, and ECsHsO^, and also
the differences between these values. The differences in each case
are printed in small type.

dlff.<-
NOg

dlff.«
P

diff.-

CjHiOi

dlff.

Nft

dlff.

129.1

n.o

108.1

S2.2

180.3

82.2

8.6

—

8.6

—

8.7

—

126.5

M.9

104.6

22.0

126.6

82.1

16.0

—

16.S

—

12.2

— .

110.6

21.1

80.4

25.0

114.4

—

10.5

—

12.6

—

100.0

28.8

76.8

—

98.1

8.6

94.5

If now the differences in the rows and in the columns be consid-
ered, it is seen that they are nearly constant for any given row or
column. Such a relation is possible only when the values of the con-
ductances are made up of two independent constants. A great many
other properties of dUtUe solutions of electrolytes are known which
may similarly be considered as the average of the properties of the

1 Wied. Ann,, 6, 1 (1870), and 26, 213 (1886).

2 Temperature = 18^ t ; equivalent dilution =10^ com.

90 A TEXT-BOOK OF ELECTRO-CHEMISTRr

ions constituting the electrolyte. Such properties are called additive
properties. As further examples of such properties of solutions,
may be mentioned the color and the index of refraction.

It will be seen that the dissociation theory offers a ready explana-
tion for the above experimentally found regularities. The conduc-
tion of electricity through a solution consists in the motion of single
ions. If, when a solution containing x ions is placed in an electric
circuit, 100 ions pass through a cross section of the solution in a
given time, then, if the number of ions be increased to 2x, other
conditions remaining constant, 200 ions will pass through a cross
section in the same time. In other words, when the number of ions
in a given solution is doubledf (he conductance of the solution is also
doubled.

As has already been indicated, the equivalent conductance of a
binary electrolyte can be measured directly by placing a solution
containing one equivalent of it in a vessel, such as is shown in
Figure 27, two of whose walls (exactly one centimeter apart) serve
as electrodes. Other dimensions of the vessel than the distance
between the wall-electrodes need not be fixed. The actual conduc-
tance measured is then the equivalent conductance. As long as one
equivalent of the electrolyte is in solution between the electrodes,
this is always the case, whatever the volume of the solution may be.
When the electrolyte is completely dissociated, its solution contains
one equivalent of anions and one of cations. Its equivalent conduc-
tance, then, remains constant, whatever the dilution, since the same
number of ions is always present, and since it is by means of these
ions alone that the conduction takes place. The conductance of the
electrolyte is independent of the size of the electrodes, providing a
change in size is not accompanied by either an increase or a decrease
in the number of ions in the solution. Hence it is possible to
extend the wall-electrodes to any desired size, without thereby affect-
ing the conductance of a given solution placed between them, and
thus to measure the equivalent conductance directly at such great
dilutions that its value finally remains practically constant. From
what has been said it is easy to understand why the equivalent con-
ductance of a concentrated solution is less than that of a dilute
solution. In the former case, since more molecules remain undissoci-
ate than in the latter case, it follows that fewer ions per equivalent
of electrolyte are present to conduct the electric current. Hence it
may be stated —

With increasing dilution the degree of dissociation^ and consequently
also the equivalent conductance, of an electrolyte increases, until complete

CONDUCTANCE OF ELECTROLYTES 91

dissodcUion and the corresponding, or maximum, value of the equivcUent
coiiducUmce is reached.

The requirement of the dissociation theory that upon dilution the
equivalent conductance should increase, reaching a maximum con-
stant value at great dilutionsi is in complete agreement with facts.
According to the Clausius theory, however, the conductivity depends
upon the frequency of the changes which take place between the
positive and negative parts of the molecules. It is, therefore, a
natural conclusion from this theory that the more concentrated the
solution, the more often will these changes take place, and, conse-
quently, the greater will be the equivalent conductance. This, how-
ever, is in direct contradiction to facts. The superiority of the
dissociation theory over the Clausius theory is, in this case, at once
evident.

The conductance of a solution depends not only upon the number
of ions which exists between the two electrodes, but also upon the
sum of their velocities of migration. Since dilute equivalent solu-
tions of neutral salts, strong acids, and strong bases are practically
completely dissociated, they contain the same number of ions, and
consequently their equivalent conductances are to each other as the
sums of the migration velocities of their respective ions. Since an
ion is free to move independently of other ions present in the solu-
tion, it possesses an independent and constant velocity of migration.
It follows then that the equivalent conductance may be expressed
in terms of the sum of the migration velocities of the ions involved
and a constant which depends upon the units chosen, as follows : —

5=s constant x (tt. + u^,),

where u« and Ug represent the migration velocities of one equiva-
lent of positive and negative ions, respectively (see page 70). This
is an expression of the Law of Kohirausch.

The sum of the migration velocities may therefore be obtained
from the maximum value of the equivalent conductance. The rela-
tion between the single migration velocities, or the relative migra-
tion velocity, is known from Hittorf s work. Therefore the single
values may be calculated.

K =s const (u. -I- Ue) ;

nj^=s const. X xj^

or u.= -^;

const.

92 A TEXT-BOOK OF ELECTRO-CHEMISTRY

and (1 — n.)5 =s const, x u«,

const.

If the migration velocities are expressed in the same units as the
conductances, then the constant becomes unity. The above equations
may be written as follows : —

u« = njSa «^d Ue = (1 — n«)jj^

When the value of the velocity of migration of a given ion is
once determined, that of the others may be calculated either from
transference numbers or relative migration velocities, or from the
maximum values of the equivalent conductances, whenever these
are known. Kohlrausch has calculated and compared many of these
migration velocities and found that the two methods of determina-
tion give the same results. This agreement of results obtained
from two sources is a strong confirmation of the correctness of
the present conceptions of electrolysis.

The following illustrative example will make the method of calcu-
lation clearer.

The maximum value of the equivalent conductance £», or the
value at infinite dilution, of potassium chloride was found by a
method of extrapolation to be 129.9. The transference numbers in a
very dilute solution of the salt were found to be —

n«« 0.603 and l — n„ = 0.497;

but Ua = »«a«i Uc a« 1 — nj^y

or u« = 0.503 X 129.9, u^ = 0.697 x 129.9 ;

u« = 65.3, Ue = 64.6.

The corresponding equivalent conductance of sodium chloride was
found to be 108.9. The value of Uo, or the migration velocity of
chlorine, was found in the preceding paragraph to be 65.3. Henc^
since

fiao = Ua + Uc

Ue = 108.8 - 65.3 = 43.6 for sodium.

The transference numbers in a sodium chloride solution were found
to be —

n. = 0.604, l-n.=: 0.396;

but n.=-^22_;

p. + ^c

or, since u. s 655, u. = -^^ - 65.3 « 42.8 for sodium.

CONDUCTANCE OF ELECTROLYTES

These two values for the migration velocity of sodium agree satis-
factorily with each other.

The following values of the migration velocity, at infinite dilution,
at 18*^ ty are taken from those collected by Kohlrausch : ^ —

CATIONS

ANIONS

OATIOir

OATIOHS

▲KIOH

AXIOMS

818.

iBa

55.10

174.

CHO,

46.7

64.87

ISr

51.54

46.64

C,H,0,

85.0

43.55

(Ca

51.46

65.44

CsHgO,

81.0

88.44

iMg

45.04

67.68

C4H7O1

27.6

67.6

iZn

46.57

66.40

CfH.O,

25.7

68.2

JCd

47.85

8CN

56.68

CeHiid

24.8

NH4

64.4

iCa

47.16

CiOt

55.08

i (COO)t

62.6

66.00

JPb

61.10

BrOt

46.2

i804

68.14

54.02

10.

88.87

iCr04

72.0

NOg

61.78

JCO.

60.0

CIO4

64.7

IO4

47.7

Mn04

58.4

Further values are given in the section on the migration velocity
of individual ions (see page 116). The corresponding values for
other temperatures may be calculated with the aid of the tempera-
ture coefficient given later in this chapter.

The conductance at great dilution is expressed by the equation,

K. = u. + u..
In this case the dissociation is complete. If, on the other hand, at
any other dilution D only a part of the molecules is dissociated, then
the conductance is less. For example, if at this dilution but one half
of the total number of molecules are dissociated, the conductance is
but one half its value at infinite dilution. This is expressed by the
equation,

1 Sitznngsber. d. K. Pr. Akad. d. Wiss. Physik. Math. EL, 574 and 582 (1002),
and also in the number dated July 28, 1004. (Abstracted in Ztschr. phys. Chem.j
SI, 744, 1005).

The Talne for H* has been confirmed by the recent work of Goodwin and
Haskell, Proc. Am. Acad, of Arts and Sci., Vol. 40, No. 7 (September, 1004).

The yalue for COt" has been taken from the investigation of BOttger, Ztschr.
phys. Chem.y 46, 504 (1003).

An attempt to explain the strikhigly great mobility of H' and OH' has been
given by Danneel, Ztschr. Slektrochem., 11, 240 (1005).

94 A TEXT-BOOK OF ELECTRO-CHEMISTRY

In deriving this equation, it was tacitly assumed that the elec-
trolytic friction, or the friction offered by other dissolved particles or
by the molecules of the solvent itself, to the movement of the ions
is, in dilute solutions, independent of the concentration. This
assumption being borne in mind, the equation may be generalized to
apply to monovalent or polyvalent ions as follows : —

Here s^ represents the equivalent conductance of the electrolyte,
or the conductance when one equivalent of it is dissolved in D cubic
centimeters of the solvent, and x the per cent of the equivalent
which is dissociated into ions, i,e. the degree of dissociation. By
combining the equations —

fi^ = u. + u. and 5i, = a? (u« + u.),

where s^ represents the maximum value of the equivalent conduc-
tance or its value at infinite dilution, the value of a?, or the degree of
dissociation, can be calculated.

X S5S •

The degree of dissociation of a substance in solution is equal to the
ratio of its equivalent conductance in thai solution to its equivalent
conductance in a solution of infinite volume.

As has already been seen (see page 68), Arrhenius had come to
this conclusion and had also found that the values of the degree of
dissociation obtained from measurements of the freezing-point lower-
ing of solutions agree satisfactorily with those calculated from the
electrical conductance. The extent of this agreement is well shown
in the carefully prepared article of A. A. Noyes.* According to this
article, the values obtained by the two methods do not differ by
more than two or three per cent between the concentrations 0.005
and 0.25 normal in the case of the salts, — NaCl, KCl, NajSO*, K^O^,
and BaClj. It should also be mentioned in this connection that the
experimentally determined values of the electromotive force of con-
centration cells (see the chapter on electromotive force) do not differ
more than about one per cent from the values calculated with the aid
of the dissociation values obtained from conductivity measurements.

The determination of the degree of dissociation of different sub-
stances has become a very important work.

Ostwald found that the order in which acids accelerate or catalyze

1 Technology Quarterly, Vt, No. 4, December, 1904.

CONDUCTANCE OF ELECTROLYTES 95

the saponification of methyl acetate, or invert cane sugar, is also the
order in which they compete for a base. The latter can be deter-
mined by either thermochemical or volume-chemical measurements.
Thus a measure of the '^ strength '^ or " affinity " of an acid (or base)
was obtained.

Arrhenius sought to discover the existence of a relation between
electrical conductance and chemical activity, and found that, in
reality, the two properties are closely related. As in the case of the
equivalent conductance, the chemical activity or strength of an acid
increases with the dilution and finally reaches a limiting value.
Consider, for instance, two equivalent solutions of different acids.
If the degree of dissociation is different in the two cases, then the
chemical activities or strengths of the two acids will also be different.
On diluting the two solutions the dissociation of each acid increases
with a ratio of its own imtil, at great dilutions, it is complete. At
such dilutions the two acids possess equal chemical activities or
strengths. The relative strengtJis of acids and bases change, there-
fore, with the concentration. This was shown by Ostwald before the
rise of the theory of electrolytic dissociation.

Application of the Mass-action Law to Gaaeons and to Electrolytic
Dissociation. — Accepting the dissociation theory, and the applicsr
bility of the gas laws to dissolved substances, as established by van't
Hoff, a disaociation or afflnUy constant, which is independent of the
dilution, may be calculated. This was first shown by Ostwald.^

According to the law of mass action, at constant temperature the
following principle holds for a gas which dissociates into two
components : —

The product of the a/stive masses of the two components^ divided by
the active mxiss of the undissociated part, is a constant.

By the active mass of a substance is meant the number of mols
of it which are contained in the unit volume. It is, therefore, iden-
tical with the molar concentration. In the case of gases, partial
pressures, which are proportional to the active masses, may be sub-
stituted for the active mass in the above statement. Consider, for
example, the dissociation of ammonium chloride, at a high and
constant temperature, into hydrochloric acid and ammonia according

to the equation : —

NH4CI 5^ NH, + HCL

Then according to the law of mass action,

P^H. X j>'hci ^ P^ ^ 3^
Pnh^O! Pnh«ci

^ Ztsehr. phys. Chem,,%, 270 (1888).

96 A TEXT-BOOK OF ELECTRO-CHEMISTRY

where p^^n^ p^acif c^cl Pmb«oi represent the partial pressures of ammo-
nia, hydrochloric acid, and undissociated ammonium chloride, respec-
tively, and E4 a constant characteristic of the equilibrium existing
between these substances at the temperature in question but inde-
pendent of the values of the single partial pressures. Thus, at the
constant temperature, the gaseous mixture may be compressed or
expanded, or an excess of any one of the constituents may be added,
without changing the value of the constant or the form of the above
equation. It is therefore evident that, whenever these three gases
are brought together in whatever proportions at this constant tem-
perature, such a rearrangement takes place in their individual con-
centrations, or partial pressures, that the above equation is still
satisfied with the same value of the constant Thus if ammonia gas
be added to a given volume of the dissociated ammonium chloride, the
partial pressure of the ammonia in the mixture is thereby increased.
In this case, if the partial pressures of the hydrochloric acid and of
the undissociated ammonium chloride did not undergo a change, the
constant E^ would necessarily increase. Since, however, the con-
stant E4 does not increase, either the numerator of the fraction

Ptruici

must decrease in value, the denominator increase, or both changes
must take place simultaneously. The latter happens. A part of
the ammonia combines with an equivalent quantity of hydrochloric
acid to form undissociated ammonium chloride. This reaction pro*
gresses until again the mass action equation is satisfied. In this
case, when equilibrium is again established, the values of |>'hbi ^^^
P^Bci ^^y of course, no longer equal.

Since, according to the theory established by van't Hoff, the
behavior of solutes in dilute solutions is analogous to that of gases
under small pressures, it may naturally be assumed that relations
entirely similar to those applying in the case of the dissociation of
ammonium chloride also hold for electrolytes which dissociate into
two ions. For example, acetic acid in dilute aqueous solutions dis-
sociates according to the equation,

CHjCOOH :;!: ch.coo' + k

Hence, according to the mass-action law, it would be expected that,
at constant temperature, the following equation would hold : —

'■▲• ^HA«

= -8-*.

CONDUCTANCE OF ELECTROLYTES 97

In this equation Ch^ C^y and Ghao represent the active or
molar masses of hydrogen ions, acetate ions, and undissociated
acetic acid, respectively, and K^ a constant, called the dissodaJtUm
consUaUy which is characteristic of the equilibrium between these
three substances and independent of the individual concentration of
each substance and of other substances which may also be present
in the solution. The dissociation constant is characteristic of the
compound and its determination is therefore of great importance.

In order to show the existence of this relation between the disso-
ciated and undissociated parts of an electrolyte in dilute solution, it
is, of course, necessary to have a method of finding, accurately, the
concentrations of the ions and of the undissociated molecules. For
this purpose the determination of the electrical conductance is most
satisfactory, and it is in consequence of this fact that conductivity
measurements are of such great value.

This method of testing the applicability of the law of mass action
to electrolytes in dilute aqueous solution will now be considered.
A mol of a binary electrolyte is dissolved in D cubic centimeters of
water, in which it dissociates according to the equation,

A 5t A + B'.

The mass-action equation for this case is, then,—

If o^s the degree of dissociation of the electrolyte or that frac-
tion of the mol which is broken up into the ions A'
andB',

andl— a;a=sthe fraction of the mol remaining in the undissociated

state AB,

then -=: s concentration, or active mass, of each of the ions A

and B',

and— —ss concentration, or active mass, of the undissociated part,

AB.

By substitution of these values in the above mass-action equation,
the f oUowing is obtained : —

1 — 05 ^

98 A TEXT-BOOK OF ELECTBO-CHEMISTBY

^' ^ -IT

It is evident that, in order to determine the dissociation constant^
it is onlj necessary to know the dilution D and the degree of disso-
ciation X of the solute. The former being already known, the latter
is determined from measurements of the equivalent conductance of
the solution at the two dilutions, D and infinity. As has already
been stated, the dissociation is equal to the ratio of the former to the
latter conductance, or, otherwise expressed,

ft.
This Talue of x may be substituted in the equation,

with the following results : —

S.(B.-ft^)i) *

Before proceeding further to the proof of this formula, it is advis-
able to become acquainted with the methods used for the determina-
tion of the conductance of solutions.

Determination of the Eleotrioal CSondnetance of Eleotrolytes. The
Method of Kohlranich. — By an application of Ohm's law^

Os= — 9

the resistance of metallic conductors, or conductors of the first class^
may be measured in a very simple manner ; but this is not the case
with solutions t)f electrolytes, or conductors of the second class. The
gradual fall of potential f which exists in that portion of the circuit
occupied by a solution is, in most cases, scarcely to be determined
accurately, because potential-differences which exist at the electrodes
and the solution are made variable by the nature of the chemical
decomposition or <^ polarization " taking place there. Many methods,
of more or less value, have been devised for overcoming this diffi-

CONDUCTANCE OF ELECTROLYTES 99

culty.^ Of these methods only that one will be described in detail
whioh is used almost exclusively at the present time for the deter-
mination of the electrical conductance of electrolytes^ namely, the
Kohlrausch method.

This method depends ux>on the use of an alternating current of
high frequency, and of non-corrodible electrodes, which are platin-
ized in order to increase their surfaces. By this method the dis-
turbing influence of the chemical changes at the electrodes, or the
<< polarization,'' is practically removed; for the polarization effect
produced by the current when flowing in one direction for a very
small fraction of a second is practically neutralized by the effect
produced when the current is reversed for the same small interval of
time. The disturbing influence being thus removed, the resistance
of the solution may be determined exactly as in the case of the
conductors of the first class.

[The apparatus employed is essentially a Wheatstone bridge.
Therefore, the principle of a Wheatstone bridge will be discussed
before considering the form actually used in the determination of the
conductance of solutions. A simple form of such a bridge is shown
in Figure 28, in which the different parts are named. The direct

current from the galvanic cell actuates the induction coil, thus
causing an alternating current of high frequency to flow through the
divided circuit consisting of the two branches AC and ac^ respec-
tively, which are uniform wires of different resistances extending
between the metal bars Aa and Co.

Let us now consider the relation between the fall in potential,
the resistance, and the flow of the electric current in the different
parts of the circuit during the momentary passage of electricity
from Aa to Cc, assuming the potential at ^a to be ten units and at
Cc zero. Then along each of the two wires AC and ac there is a

1 Ostwaid, Lehrhuch der Allg. Chemie, VoL II, 1, 622.

100 A TEXT-BOOK OP ELECTRO-CHEMISTRY

fall of potential of ten units. This would also be true of any other
wire, whatever its resistance, extending between the bars Aa and
Cc. Since the two wires, although of widely different resistances,
are each of uniform cross section, the fall of potential along them
will be uniforni. Thus along each tenth part of the distance
between Aa and Oc on each wire there will be a fall in potential of
one unit, as shown by the numerical values in the figure. These
values, then, represent the potentials of the different points along
the wires.

If now the point B, on the wire AOy at which the potential is
seven units, be connected with the point 6, on the wire cic, at which
the potential is also seven units, it is clear that no electric current
will flow through the connecting wire Bbf since there is no potential-
difference between the ends of the wire. If, however, the point B
is connected with the point 6^ at which the potential is nine units,
instead of with b, a current will flow through the wire from V to
B, since a potential-difference exists between the ends of the wire.
Finally, if the point B is connected with the point b'\ at which the
potential is five units, instead of with V, there will again be a
difference of potential of two units between the ends of the connect-
ing wire, and, therefore, an electric current will flow through it. In
this case the direction of the current is the reverse of that in the
previous case. It may then be stated that whenever a connecting
wire extends between equipotential points of the branches of a
divided circuit no current flows through it. In all other cases
a current does flow through the wire. As a means of detecting
whether or not an alternating current is flowing in the connecting
wire a telephone receiver is introduced into its circuit as shown in
the figure. When a current flows (as for instance when B and b'
are connected) a humming sound is heard in the telephone. If now
the end of the wire at V is moved along the wire to b and then to
V\ the humming sound diminishes, going through a sharp minimum
when the point b is reached, and rising again as the point b" is
approached. By listening at the telephone it is then possible to
tell when the wire connects equipotential points.

It is at once evident from the figure that when the wire connects
equipotential points, as, for example, B and 6, the following relation
exists between the fall in potential in the different parts of the two
branches of the divided circuit, otherwise known as the arms of the
Wheatstone bridge : —

FaU in ^4j5: Fall in BC= Fall in a6 : Fallin 6c.

CONDUCTANCE OF ELECTROLYTES

101

Becallmg to mind the fact that the falls in potential in the differ*
ent parts of a circuit are directly proportional to the respectiyei
resistances of the parts, in this case it follows that

Besistance AB : Resistance BC = Resistance ab : Resistance be.

If now the ratio of any two of these resistances, such as, for
example, the ratio of the resistance of a& to that of be, and the
actual yalue of either of the two resistances, AB or BC, are known,
then the fourth, or the unknown resistance, may be calculated from
the above proportion.

In this manner xmknown resistances may be determined by means
of the Wheatstone bridge.

When the resistance of an electrolyte is to be determined
the Wheatstone bridge is arranged as shown in Figure 29.^ The

similarity between this figure and the one directly preceding it is
at once evident In this figure the two branches of the divided
circuit are abc and aABc, respectively. The former branch includes a
resistance box, by means of which various known resistances can be
introduced into the circuit, and the conductivity cell containing the
solution to be investigated. The resistances in the resistance box
and in the conductivity cell are so great that those of the connecting
wires in this branch may be neglected. The branch dbc consists of a
platinum wire of uniform resistance, which is either stretched over a
meter scale or wound on a drum, which is marked off in millimeter
lengths. One end of the connecting wire Cb is made fast at any
point C between the resistance box and the conductivity cell, while
the other end b is connected with the platinum wire by means of a
sliding contact The position of this sliding contact may be read
off on the meter or drum scale to tenths of a millimeter. In series

^ Osfcwald, Ztschr. phys. Chem., 8, 661 (1888).

102 A TEXT-BOOK OF ELECTKO-CHEMISTRT

with the connecting wire is a telephone teceiyer (naturally a galva-
Dometei cannot be used), which serves to determine when the
sliding contact is in such a position that no current flows througli
the wire, i.e. when the wire connects equipotential points. The
four arms of the Wheatstone bridge are then ab, be, oAC, and CBc.
Hence when the sliding contact is in the position giving a minimum
tone in the telephone receiver, the following relations obtain: —
Reaiatance of ab _ Resistance in box
•c Besistance in cell

If the platinum wire is of uniform resistaDce, we have^

Resistance of ab _ Diatance ab

Resistance of be Distance be
Therefore,

Resistance in cell = Bosiatance in box X P!"'"'"^ ^,
Distance ab

or, K, = B, X ^■

The absolute value of the resistance of the platinum wire evidentlj
does not come into consideration, since only
the ratio of the resistances of the two parts
of it is required.]

A vessel, such as is shown in Figure 30,*
can in most cases be used for the determina-
tion of the conductance of an electrolyte.

The area of the electrodes and the distance
between them can be varied as desired. In
general, it is advantageous to platinize them,
using a solution containing about three per
cent of commercial platinic chloride and
about 0.025 per cent of lead acetate.

If the distance in centimeters between the

two electrodes is represented by I, and their

Fia.30 uea in square centimeters by a, then the

value of the specific conductance k is given by the following

equations: —

1 a& >

1 For other tomu of oondootivltf oelk, see Ootwald-Lather's Fhvt(k.-eSem.
Metrungen, page Ml.

CONDUCTANCE OF ELECTROLYTES 108

rion the specific conductance s, and the equivalent dilution of
the solution D in cubic centimeters, the value of the equivalent
conductance can be calculated in the manner described on page 86|
with the aid of the equation,

fi = K X 2),

providing the cross section of the vessel and the areas of the eleo-
trodes are practically the same. In order to avoid this proviso and
to obviate the necessity of measuring the space between the elec-
trodes, it is usual to determine the so-called '' ceU constant '' of the
conductance cell. The cell constant is equal to the resistance found
in the cell when it contains between the electrodes a solution of a
specific conductance, or conductivity, of unity. In this cell, since
the conductivity of the solution is unity,

R, =* — X » =^-fic>
8

where b, is the measured resistance, k a constant depending upon
the form of the cell and the position of the electrodes in reference
to the cell walls, and Kc the cell constant. When the surfaces of
the electrodes are equal to the cross section of the cell, the value of k
becomes unity.

It is not at all necessary, however, to have a solution whose
specific conductance is unity in order to obtain the value of the cell
constant. It can be obtained with the aid of any liquid of known
conductance. Thus, if the specific conductance of the liquid is s,
and its resistance when in the cell whose constant is to be deter-
mined is B, then the value of the cell constant Kc is given by the
equation.

When the cell constant is known, the specific and equivalent con-
ductances of any liquid may be obtained with the use of the
equations,

K as — ^ or g = Z> — J.

where b. is the resistance of the liquid as measured directly on the
Wheatstone bridge. If the conductance of the liquid used to
obtain the cell constant is expressed in ohms, then the specific or
the equivalent conductance, calculated according to the above equa-
tions, is also expressed in ohms, even though the resistance in the
resistance box used both to obtain the cell constant and to obtain the
unknown conductance is expressed in other units.

104

A TEXT-BOOK OF ELECTRO-CHEMISTRY

In determining the cell constant, a 0.02 normal solution of potas-
sium chloride is often used as the liquid of known conductance.
According to the most recent measurements, its specific conductance^
or conductivity, at 18° and at 25° is

Km, = 0.002399, and k«p = 0.002773,

while its corresponding equivalent conductance is

fii8o = 119.96, and fijBo = 138.67.

The value of the equivalent conductance is a large one. The re-
sistance of one equivalent of potassium chloride in this solution,
when placed between electrodes one centimeter apart, is accordingly

1199 ^^ 1387 ^^^^' respectively.

The equivalent conductances of all binary electrolytes, at infinite
dilution, are of the same order of magnitude, varying between 60
and 500, as may be seen from the table on page 93. On the other
hand, the value of the equivalent conductance, at other dilutions,
may be exceedingly small for some electrolytes. This will be evi-
dent from a glance at the table on page 88.

Hethod of Hemst and Haagn.^ — This method of determining con-
ductance permits an easy measurement of the internal resistance of
a cell even while a current is passing through it. It is characterized
by the use of two condensers, in place of two of the resistances
employed in the Wheatstone bridge. The arrangement of the
apparatus is shown in Figure 31.

Fig. 31

The condenser G^ is used to prevent closing the circuit of the cell
C| the internal resistance of which is t(x~ be measured. Under these

^ Ztschr, EUktrochenL, 2, 408 (1896) ; Ztsihr.phys. Chem,, 9S, 97 (1897).

CONDUCTANCE OF ELECTROLYTES 106

drcnmstances the cell produces no current. After the known re-
fiistanoe b has been varied until a minimum tone is heard in the
telephone receiver^ the value of the unknown resistance b^ of the cell
G may be calculated from the equation,

B. : B = Cj : Oi,

where Gs and Gi represent the respective capacities of the two lower
condensers. The ratio GjiGi must be determined independently.
This can be done by means of an ordinary Wheatstone bridge.

In order to obtain the internal resistance of a cell while producing
an electric current, the cell is short-circuited through a known re-
sistance as indicated in the figure by the dotted line. It must be
clearly understood that the real internal resistance b^ of the cell is
not obtained by direct measurement, but is obtained from the meas-
ured resistance b^' and from the resistance of the dotted shunt cir-
cuit, according to the equation : —

B*'< B. B."

The value of b^'' may be obtained with suf&cient exactness from the
equation,

Calculation of the Dissooiation Constant from Electrical Conduo-
tanoa. — It has already been shown that the dissociation constant
may be calculated by tiie aid of the equation.

In order to obtain the value of the constant, it is therefore neces-
sary to know both the value of the equivalent conductance at dilu-
tion Z>, or ^, and that at dilution infinity, or 2«* ^^ method of
obtaining the value of £^ has already been considered. In some
cases the value of £^ may be obtained by the same method, it being
placed equal to the maximum value of the equivalent conductance
found upon diluting the solution. This method is applicable only
to electrolytes which dissociate to a large degree in solutions of
ordinary dilutions. It is not applicable to other electrolytes, be-
cause, at the extreme dilutions at which the value of £ could be con-
sidered equal to 2^, it is impossible to determine the conductance of
the solution. This is the case with practically all organic acids and
bases, where a knowledge of the value of the dissociation constant is

106 A TEXT-BOOK OF ELECTRO-CHEMISTRY

of special importance. Fortunately, howeyer, the alkali salts of all
acids and the halogen salts of practically all bases are largely dissoci-
ated in moderately dilute solutions, and nearly completely dissociated
in solutions the conductance of which can still be determined. Thus
the Talue of j^ for these salt solutions may be determined by direct
experiment. But this value has been shown to be equal to the sum
of the migration velocities of anion and cation : —

[In the case of the alkali salt of a slightly dissociated acid HA, s»
may be determined directly, and Ue is a known value. The value of
u. for the anion A' is thereby determined. But the value of u^ for
the cation H', is a known value. Hence the value of ^^ for the acid
HA may at once be obtained by adding together the known migra-
tion velocities of its ions. Thus

j^ (for HA) = u, (for H) + u„ (for A').

In a similar manner the equivalent conductance at infinite dilution
for a slightly dissociated base, BOH, may be obtained. For its
halogen salt, ^ can be determined directly, and u. for the halogen
ion is known. Hence the value of u^. for the cation B* is known.
From this value and the known value of Ua for the anion OH' the
equivalent conductance of the base BOH at infinite dilution may
be obtained by the aid of the equation,

K^ (for BOH) = Vc (for B') + u^ (for OH').

In the above explanation of the indirect method of determining
the value of the equivalent conductance of a slightly dissociated acid
or base at infinite dilution, the individual migration velocities of the
ions were involved. This is not at all necessary in making actual
calculations, as will be made evident from a reconsideration of the
above acid HA. The value of fi^, for example, of hydrochloric acid,
of sodium chloride, and of the sodium salt of the acid HA may be
obtained from direct measurements on very dilute solutions. Hencei
the three equations,

K, (for HCl) = Ue (for H') + u« (for CI');
fi^ (for NaCl) == u^ (for Na) 4- u. (for CI');
fi. (for NaA) = u« (for Na*) + xj^ (for A').

Combining these equations,

fi« (HCl)-fi, (NaCl) + K. (NaA) = u, (H-)+u. (A');
fi« (HCl)-fi. (NaCl) + fi. (NaA) = fi. (HA).

CONDUCTANCE OF ELECTROLYTES

107

The latter equation, in which migration velocities do not appear, may
be used for the calculation of the value of ^ for the acid in ques-
tion.] As is evident, it is only necessary to add to the difference of
the values of s« ^^^ hydrochloric acid and sodium chloride, the value
of s^ for the sodium salts of any slightly dissociated acid, to obtain
the equivalent conductance of the latter acid at infinite dilution.
The values of j^ for hydrochloric acid and sodium chloride accord-
ing to most recent measurements, and their differences, are given in
the following table : —

TufpaBATirsB

&» vobHCI

Sao rO* ^^^

DirmmoB

18^
26 *»

383.4
427.1

108.9
126.6

274.6
800.6

From the values of the equivalent conductance at the dilution D
and at the dilution infinity, obtained as above described, the dissoci-
ation constants have been calculated for a large number of slightly
dissociated acids and bases at different dilutions. It was found that
the constants are independent of the concentration. The results
obtained for acetic acid are given in the following table: —

Bqvitalbmt OovancTBATioir

DiBSOOIATION GOIVSTANT X 10>.

0.00180

0.00179

0.00182

0.00179

0.90179
0.00180
0.00180
0.00177

The value of the dissociation constant may serve in many cases
as a trustworthy aid in the identification of a compound.^

Since a consideration of the significance of this constant belongs
to the subject of chemical statics, it will not be discussed further
here. It may be well to state, however, that the order of magni-
tudes of these constants for different compounds is also the order of
their degrees of dissociation in solutions of the same equivalent
concentration. A direct proportionality does not exist between the
constants and the degrees of dissociation, for, as the dilution is in-
creased, the latter approaches a constant value. Nevertheless, some

^Scudder, J. Phy. Chem., 7, 269 (1903).

108 A TEXT-BOOK OF ELECTRO-CHEMISTRY

conclusions from the existence of such constants, which were em-
pirically established by Ostwald before the dissociation theory was
proposed, will be considered.

1. With increasing value of D in the equation,

the left-hand side finally becomes infinite. Since j^ and j^ are
always finite quantities, this can only be true when

Hie equivcUent conductance approaches its value aJt infinite dilution
<u the dilution is increased.

2. In the case of slightly dissociated, and consequently poorly
conducting, binary electrolytes, where j^j, is very small in compari-
son with 2», the expression (^ — ^j^ changes but slightly with the
dilution and may theief ore be considered as a constant Hence the
equation,

fe- =: Constant.

The equivalent conductance increases vnth increasing dilution in pro-
portion to the square root of the dilution; or the square of the equiva-
lent conductance increases in proportion to the dilution,

3. If the mass-action equation for the dissociation be written in
its original form as follows : —

(1-«)D-^"

then for substances which dissociate but slightly, the value of 1 — o^
may be considered as unity without serious error and the equation
assumes the form,

In the case of slightly dissociated electrclytesy the dissodaiion constant
varies directly as the square of the percentage dissociation and inversely
as the dilution,

4. According to the derivation given in No. 2, the following equa-
tions hold for two or more slightly dissociated electrolytes : —

^^^ = Constant,
and a£^'=: Constant, eta

CONDUCTANCE OF ELECTROLYTES 109

These two equations may be combined, resulting in the equation^

3= Constant.

If now the dilution of one of the electrolytes (Z)') is equal to that
of the other (D"), then the equation becomes

^S|f^ = Constant. (a)

From the equations derived in No. 3, it may be shown in a similar
manner that the following equation holds : —

In the above equations, "^j^ ^\ ^*> <^d s''j^ a?", and K^^^ represent
the equivalent conductances at dilution D, the degrees of dissocia-
tion, and the dissociation constants of the two electrolytes respeo-
tively. It has been shown that

Hence for the above electrolytes we have the equation,

If now the value of s'^ is equal to that of s''^, such as is the
case with many acids because of the very great migration velocity of
the ion which they have in common (the hydrogen ion), this equa-
tion becomes

Combining equations (&) and (c), the following equation results : —

The 9quareB of the equivaJerU conductances of different electrolytes at
the same dUvtion are to each other as the corresponding dissociation
constants.

6. In the equation —

110 A TEXT-BOOK OF ELECTRO-CHEMISTRY

the value of j^ may, in the case of electrolytes which dissociate to
a large degree, be considered as remaining practically constant with
increasing dilution, and as s. is in itself constant, the equation
becomes

(S.-fii>P

= Constant.

The difference between tA6 equivalent conductance at a given dUutian
and that at the dUuHon infinity multiplied by the former dihaicn gives a
constant value.

6. In the case of electrolytes which dissociate to a large extent,
the value of the percentage dissociation x may be considered as
approximately equal to unity. The equation

may then be written in the simple form,

^-:^-ir^or(i-«)D=l-.

I%e undisaodated portion of an electrolyte multiplied by the dUutkm
i$ equal to the reciprocal of the diseociation constant.

According to this statement, it is evident that if the undissociated
portion at an equivalent dilution of 50,000 cubic centimeters amounts
to one per cent, it will amount to only one half per cent at a dilur
tion of 100,000 cubic centimeters.

7. According to the derivation of Ko. 5, the following equations
hold for any two electrolytes which are largely dissociated : —

(fi'. -aVP' = Constant,
and • (s". -^"jrW ' = Constant.

These equations combined give the following:^

^ ■ " ^t^W s- Constant

When the dilution of one electrolyte D' is equal to that of the
other 2>", this equation becomes —

^''^'f -= Constant («)

In a similar manner, from the derivation of Ko. 6 the following
equation may be obtained : —

CONDUCTANCE OF ELECTROLYTES 111

1-x' IC

i-«"""jr'

(6)

The latter equation may be expressed in words as follows : —

The undiMockOed portiona of different electrolytes at the same equiva-
lent dUutUm are inversely proportioned to their dissociation constants.

When the equivalent conductances of the two electrolytes at
infinite dilution are nearly the same, equations (a) and (b) may be
combined, giving the approximate equation^

7%e differences between the equivalent conductance at a given dilution
a(nd that at infinite dilution of two electrolytes are inversely propor-
tional to their dissociation constants.

8. Finally, the following regularities for all electrolytes may be
deduced. If two electrolytes are dissociated to the same extent^
then the left side of the equation,

1 — 05 '

is the same for both, and, consequently, the same is true of the
right side.
Hence the equation,

or D" JTrf •

The equivalent dilutions at which different electrolytes possess the
same degree of dissociation (and also often nearly the same equivalent
conductance are in a constant ratio to each other, which is equal to
the inverse ratio of the respective dissociation constants.

The foregoing approximations may often be used with advantage.

Belation between Dissociation Constants and Chemical Constitu-
tion. Some very interesting relations have been found between the
magnitudes of the dissociation constants and the chemical constitu-
tion of acids, as may be illustrated by a few examples. The con-
stants (Ka' 1(f) for acetic acid and the three chloracetic acids, at 25"*,
are as follows : —

Acetic acid (CH3COOH) .... 0.00180

Monochloracetic acid . . (CH,C1C00H) ..... 0.155

Dichloracetic acid . . . (CHCl^COOH) .... 5.14

Trichloracetic acid . . (CClaCOOH) .... 121.

112 A TEXT-BOOK OF ELECTRO-CHEMISTRY

Thus the replacement of the hydrogen by chlorine causes a very
large increase in the value of the constant. That this increase is
not the same for the successive replacements by chlorine is evident
from the following table : —

BBPLAOUnXT

Ikokbass nr Cokrakt

Fint

Second

Third

n^rJlfL' or 86 fold.
0.00180

^'}\ , or 38.2 fold.
0.166

3^^^ , or 23.5 fold.
5.14

It may be concluded from this that the introduction of chlorine
into acetic acid produces an effect somewhat different from that
which it produces when introduced into chloracetic acid. This is
not surprising, since a chlorine atom is already present in the latter
compound. An increase in the value of the dissociation constant
indicates an increase in the degree of dissociation, and also an
increase in the intensity of its acid character. The replacement
of hydrogen by chlorine produces an effect in this direction. The
introduction of such other so-called negative radicals as Br, ON,
SCN, OH, etc., also increases the acid character of the original com-
pound in a similar manner.

The a and /9 substituted derivatives of acids possess very different
dissociation constants, thus showing the marked constitution prop-
erty of this constant. The same applies to the isomeric derivatives
of benzene, for example : —

Benzoic acid CeHsCOOH 0.006

o-Hydroxybenzoic acid . . o-CeH4(OH)COOH . . . 0.102

m-Hydroxybenzoic acid . . irt-C«H4(0H)C00H . . . 0.0087

j?-Hydroxybenzoic acid . . jp.C«H4(0H)C00H . . . 0.00286

These examples show that a knowledge of the dissociation con-
stant is of aid in the determination of the chemical constitution of
compounds. By the introduction of an hydroxyl group into benzoic
acid in the ortho position, the constant for the acid is increased
seventeen fold. When the same group is, instead, substituted in
the meta position, the change from the benzoic acid value is slight,
but still positive, while an entrance into the para position even
causes a considerable reduction of the constant. Consequently, it
might be assumed that if a series of acids be formed by introducing

CONDUCTANCE OF ELECTROLYTES 118

hydioxyl groups into oriho-oxybenzoic acid, their dissociation con-
stants would vary in a similar manner. That this is the case is
evident from a consideration of the following table : —

o^xybenzoic (salicylic) acid CeH4(0H)C00H . .
HydroxysalicyUc acid . . C«Hj(OH),COOH (2, 3)
HydroxysaUcylic acid . . CeH,(OH),COOH (2, 6)
Besorcylic acid .... CeHs(OH),COOH (2, 4)
Resorcylic acid .... C»H8(0H),C00H (2, 6)

0.102
0.114
0.108
0.052
6.0

In the acid (2, 3) and also in the acid (2, 6) the new hydroxyl
group is in the meta position in relation to the carboxyl group.
Consequently, only a very slight increase in the dissociation constant
is to be expected. This agrees with experimental observation.

In the acid (2, 4) the new hydroxyl group occupies the para posi-
tion, and, as in the case of hydroxybenzoic acids, a new constant, less
than the original one, results. Finally, when the second hydroxyl
group occupies the remaining ortho position, as in the acid (2, 6), a
corresponding great increase in the constant is found, the increase
being about fifty fold.

Interesting relations have been found in the case of the dissooisr
tion in stages of dibasic organic acids. From the fact that the mass-
action equation for the dissociation of binary electrolytes holds also
for weak dibasic acids, it follow that the dissociation takes place at
first according to the equation,

HJR^H- + HR'. (a)

Only in the case of strong acids does a further dissociation aocording
to the equation

HR':;J:H +R" (6)

take place. In such cases the equation

derived for binary electrolytes, naturally does not apply. Dif-
ferent dibasic or polybasic acids are strildngly characterized by the
way in which they dissociate. While in the case of some acids
the dissociation of the second hydrogen, according to equation (6),
takes place only after that of the first hydrogen, according to equa-
tion (a), is nearly complete, in the case of other acids the dissociation
I

114 A TEXT-BOOK OF ELECTRO-CHEMISTRY

of the second hydrogen takes place to some extent when bat fif iy per
cent of the first hydrogen is dissociated. This difference is evident
in the titration of acids with indicators. Solfurous acid, for example,
when titrated, using litmus as an indicator, gives no sharp end point,
the dissociation of the second hydrogen being too slight. However,
succinic acid, which in respect to the first hydrogen ion is far less
dissociated than sulfurous acid, may be easily titrated with the use
of this indicator.

Between the dissociation constant for the dissociation of the first
hydrogen atom (dissociation constant of the free acid) and the corre-
sponding constant for that of the second hydrogen atom there exists
the following relation : —

1. I7ie first hydrogen atom i8 dissociated to the ffreater, and the sec-
ond to the lesser extent, the nearer the two carboxyl groups are to each
other. The reverse is also true.

This statement was first made by Smith,^ who based it upon his
own work and also that of Ostwald and Koyes.

As an illustration of this principle, the following quotation from
Ostwald is given, in which it is assumed that the electrical charge of
the acid ion is localized on the hydroxyl oxygen of the carboxyl
group : —

'<In the case of the dissociation of the first hydrogen atom of
dibasic organic acids, the one carboxyl group exerts a negative influ-
ence upon, and tends tc increase the degree of the dissociation of, the
other carboxyl group. This tendency is the stronger, the nearer the
two carboxyl groups are to each other. If the first stage of the dis-
sociation takes place according to the equation

HjE^tH+HR'

then the second stage, HB' H*::;: + B''

will in general take place far more difficultly than the first stage,
since th& negatively charged ion HR' in dissociating must take up
an extra negative charge to form the ion R", and since the two
negative charges repel one another. Secondly, the ease with which
the second stage of the dissociation will take place depends upon
the distance between the charges. Thus the nearer the charges on
a bivalent ion are to each other, the less is the tendency of the
hydrogen atom to split off, and conversely."

The behavior of fumaric and maleic acids is in complete agree-

^ Ztschr.phys. Chem,, 85, 144 (1898).

CONDUCTANCE OF ELECTROLYTES

115

ment with the above principle and hypothesis. This will be evi-
dent from a study of the following formnlsB and tables : —

MaleU Add

H-C-COOH

Fumaric Acid

H-C-COOH

HOOC-C-H

MoIm DiLunoK

% DUBOOIATION

K^xW

% DiBSOOIATIOH

E^xlO*

128

68.8

1.16

29.8

0.095

256

78.8

1.14

89.0

0.097

512

87.1

1.15

50.8

0.099

1024

92.8

1.17

63.9

0.110

2048

98.2

^—

78.5

0.140

The per cent dissociation is calculated on the assumption that the
acids dissociate as if they were monobasic.

The carboxyl groups in the fumaric acid molecule are farther
apart than those in the maleic acid molecule. Corresponding to
this, the dissociation constant is much less in the former than in the
latter case. On the other hand, the dissociation of the second hy-
drogen takes place appreciably in the case of maleic acid only after
a nearly complete dissociation of the first hydrogen atom, while in
the case of fumaric acid it takes place when but about fifty per cent
of the first hydrogen atom is ionized. This is indicated in the above
tables by the increase in the value of the constant. The acid salts
show an analogous behavior in respect to the dissociation of the
second hydrogen atom. At a molar dilution of 64, the dissociation
of this atom is 0.39 per cent in the case of the acid salt of maleic,
and 0.85 per cent in that of fumaric, acid.

The effect of substituted groups in organic dibasic acids upon the
dissociation of the^ second hydrogen atom is expressed in the
following statement : —

2 a. The degree of dissociation of the second hydrogen atom of dU
substituted acids is less than that of the original acidy except in the
case of hydroxy! substituted acids, in which it is increased.

Thus the dissociation of the second hydrogen atoms of methyl-
and ethyl-succinic acids is less, and of the hydroxysuccinic acids,
malic and tartaric acids, is greater, than that of succinic acid itself.

The relation between the dissociation constants of the first and
second hydrogen acids of analogous substituted dibasic acids may
be expressed as follows : —

2 b. The dissociaiion constant (10' ^ of ^e second hydrogen atom

116 A TEXT-BOOK OF ELECTRO-CHEMISTRY

of a mbstUtUed acid is the anuxUeTf the greater the constant (K^^ of
the first hydrogen atom. In other wordsy the substituted groups affect
the dissociation of the two hydrogen atoms oppositely.

While, for example, the vaJue of K*4 for methyl- and ethyl-succinio
acids is greater, the value of JT''^ for these acids is less than the
corresponding constant K4 iot succinic acid.

A knowledge of the dissociation constant of the second hydrogen
atom would undoubtedly, in many cases, be of an importance equal
to that of the first hydrogen, in the study of the constitution of
dissolved substances.^

Finally, it should be mentioned that with the aid of- the dissocia-
tion constants of weak acids the degree of hydrolysis of their alkali
salts may easily be calculated.'

Velocity of Migration of Individual Ions. — From conductance
measurements not only have the dissociation constants of a large
number of organic acids and bases been determined, but also the
relative velocities of migration of the organic cations and anions.
It has already been stated that the sodium and potassium salts of
acids and the chlorides and nitrates of bases are dissociated to such
a degree that the equivalent conductance at infinite dilution ^
is experimentally determinable. By subtraction of the known
velocity of migration of the sodium, potassium, nitrate, or chlorine
ion, as the case may be, from this value of £», the velocity of
the migration of the other ion of the compound is obtained (see
page 106).

Through a stoichiometrical comparison of the numbers represent-
ing the migration velocities of the individual ions, certain relations
have been discovered, some of which will be mentioned. These are
taken from the comprehensive work of Bredig.*

The migration velocity of ions of elementary substances is a
periodic function of the atomic weight. It increases with increas-
ing atomic weight in any series of related elements. In these cases,
the rule applies that considerable differences occur with the first two
or three members of each series. Moreover, similar or related ele-
ments whose atomic weights are greater than thirty-five migrate
with nearly the same velocity. These statements are illustrated by
the following results obtained at 18^ t See also the values given
on page 93.

^ For farther relationships between the chemical constitation and the affinity
constants, see Wegscheider, Wien. MonaMefte^ 88, 287 (1002).
< Walker, Ztschr, phys. Chem., 82, 137 (1000).
* ZUchr. phys. Chem,, 18, 191 (1894).

CONDUCTANCE OF ELECTROLYTES

117

EumsHT

Atomic Wsmht

u«

SiiUsirT

Atomio Wbioht

Lithium

88.4

Fluorine

46.6

Sodium

43.6

Chlorine

66.4

Potassium

64.7

Bromine

67 6

Rubidium

67.6

Iodine

127

66.4

Caesium

188

68.2

Por complex ions the following principles have been established.
'Isomeric ions migrate with the same velocity, as is evident from
the following values :* —

Ibomsbio Aviom

Ibohxuo Catiorb

Butyric
Isobutyrio
I Cinnamic
( Atropic

80.7
80.9
27.8
27.1

( Propyl ammonium
(Isopropyl ammonium
j Chinolin methylium
1 Isochinolin methylium

40.1
40.0
86.6
86.6

Similar changes in the composition of analogous ions produce
changes in the same direction in the respective migration velocities.
The magnitude of these changes does not remain constant for suc-
cessive changes in the composition, but decreases with decreasing
migration velocity. In other words, as the number of atoms are in-
creased in an ion, or as an ion becomes more complicated in its
structure, its migration velocity decreases, tending towards the gen-
eral minimum value for univalent anions and cations, namely, about
seventeen to twenty reciprocal Siemens units. A glance at the fol-
lowing values will make this more evident : —

loa

Btmbol

V»IX)OITT

DiFRUKoi pxs Clla

Ammonium
Dimethyl ammonium
Diethyl ammonium
Dipropyl ammonium
Dibutyl ammonium
Diamyl ammonium

NH4

NHsCCHs),

NH,(C2H5)3

NH^CsHt).

NH,(C4H9)s

NHa(C5Hn),

70.4
60.1
86.1
80.4
26.9
24.2

2(10.2)

2(7.0)

2(2.9)

2(1.8)

2(1.4)

In analogous series of anions and cations of the same valence,
the migration velocity is diminished : —

^ These values have been taken directly from the article by Bredig, and are
expressed in reciprocal Siemens units. Temperature = 26^ (

118

A TEXT-BOOK OF ELECTRO-CHEMISTRY

a. By the addition of hydrogen, carbon, nitrogen, chlorine, and
bromine.

h. By the replacement of hydrogen by chlorine, bromine, iodine,
etc.

In general, the more complicated the ion, the lower is its migra-
tion velocity. Accordingly, a polymeric ion moves more slowly
than a simple one.

The effect of added atoms or atom-groups on the migration velocity
of an ion is often obscured by the effect of the constitutional dif-
ferences. Thus metameric ions, although of the same composition,
migrate with different velocities because of their different constitu-
tions. In general, in the case of such organic cations, the migration
velocity increases with the degree of symmetry, as, for example, in
passing from the primary form to the secondary, the secondary to
the tertiary, etc. This is illustrated by the values for the cations of
the series of bases given in the following table : —

FOBM

lOH

Symbol

Vblooxtt

Primary

XyUdine

C,H„N

80.0

Secondaiy

Ethyl aniline

CgUuN

30.6

Tertiary

r DimeUiyl aniline
I Collidine

CgHisN
CgHuN

38.8
34.8

Qoatemary

r Fecoline ethylinm
I Latidine methylium

CiHuN
C«HuN

36.1
36.2

Thus the effect of added atoms or atom-groups on the additivity,
particularly in the case of cations, is often destroyed by the opposing
influences of such constitutional differences. Indeed, the direction
of the additive change may even be reversed through over compen-
sation by the constitutional changes, as in the following case: —

Ion

Symbol

Vklocitt

Triethyl ammonlam
Metbyl-triethyl ammonium

(CjHOssN-H
(C,Hs)8 = N-CH,

82.6
34.4

In spite of the fact that the latter ion contains one OH, group
more than does the former, no retardation, but, on the contrary, an
acceleration, of the migration velocity takes place.

CONDUCTANCE OF ELECTROLYTES

11*9

In the case of the migration velocity of polyvalent ions of organic
acidsy Wegscheider ^ has called attention to the following note-
worthy legularities : —

The ratio of the migration velocities of bivalent and univalent ions
containing the same number of atoms is approximately equal to a
constant value (1.78). The same also holds true for the ratio of the
migration velocities of bivalent and univalent ions when the latter
contain one atom more than the former. In this case the same acid
is formed from the bivalent and from the corresponding univalent
ion and the value of the ratio is 1.81. The same relationship holds
approximately for inorganic acids, as follows : —

BlYALBM^ Ion

u«

UniVALurr Ion

v'a

Va-rV'm

HPO/'
HA8O4"

56.0
54.6

H,P04'
HsAsOa'

38.5
81.7

1.64
1.72

These relations are also of interest theoretically. It is a natural
assumption that the resistance encountered by a moving ion is in-
dependent of the number of electrical charges carried by the ion.
Furthermore, since the force driving the ion is, in the same electrical
field, proportional to the electrical charges on the ion, it would be
expected that the migration velocity of an ion would be doubled if
to its first charge another be added. However, as has been seen,
observation is not entirely in agreement with this conclusion.
Hence we must conclude that the resistance opposing the movement
of an ion is influenced by the extra charge upon the ion. To ex-
plain this, it may be conceived that the volume, and consequently
the frictional resistance, of the ion is increased by the mutual repel-
lent action of the two charges of the same kind.

As the valence becomes higher and higher, the effect of the extra
charge on the ion becomes less and less. In the case of ferro- and
ferri-cyanide ions it is practically zero. Their migration velocities
are 89.6 and 90.3, respectively.

Absolute Velocities of the Ions. — By the procedure given by
Kohlrausch, it is possible to calculate the velocity in centimeters per

second ( — - ) with which the individual ions are driven through an
\ sec /

aqueous solution under the influence of a given potential gradient, or

potential fall, per centimeter. For the sake of simplicity let us con-

iSitzangsber. d. E. Ak. d. Wiss. Wien. Math.-naturw. Kl., 61, 11 b, May,
1002. Units = SiemeuB; temperature = 25^

120 A TEXT-BOOK OF ELECTRO-CHEMISTRY

sider two platinum electrodes^ one centimeter apart^ with one equiya-
lent of negative and one of positive ions between them. Let the fall
in potential from one electrode to the other be one volt. If, under
these circumstances, exactly 0.001 ^ (q=s 96,540) coulombs of elec-
tricity pass through a cross section of the solution in one second,
and if the positive and negative ions migrate with the same velocity,
then each ion travels through a distance of 0.0005 centimeter dur-
ing this time, or possesses the velocity 0.0005. Since 0.001 q
coidombs pass though the cross section, 0.001 of an equivalent of
an ion separates at each electrode. Moreover, 0.001 of an equivalent
of ions must pass through every cross section of the solution, of which
quantity 0.0005 of an equivsdent are positive, going toward the
cathode, and 0.0005 negative, going toward the anode. Therefore
0.0005 of an equivalent of ions is brought up to each electrode. In
other words, the ions, which at the beginning of the electrolysis
were 0.0005 of a centimeter from the electrode to which they were
to migrate, would just reach the electrode in one second. This gives
the desired absolute velocity of the ions. In the case under con-
sideration, the sum of the distances traversed by the positive and
the negative ions in one second is equal to 0.001 of a centimeter.

The quantity of electricity which has passed through the solution
in one second (i.e. the current o in the amperes) divided by q, or
96,540, gives, under the conditions mentioned, the velocity of the
ions in centimeters per second, or, otherwise expressed,

Q^.^^ = Velocity of the ions in centimeters per second. (a)
Thus in the above case,

Q^i^^^ = 0.001 centimeter per second.

The relation between the current, fall in potential between the
electrodes, resistance, and conductance is as follows : —

Potential-fall

Resistance '
1

Current s=

and Conductances:^ . ^

Resistance

Combining these equations, the following is obtained : —

Current = Potential-fall x Conductance.

Since the potential-fall is one volt, it follows that —

Current s= Conductance (express in reciprocal ohms).

CONDUCTANCE OF ELECTROLYTES

121

But theie is one equivalent of the electrolyte between the two elec-
trodes. Therefore, in this case, the conductance. measured is the
equivalent conductance, and the above equation becomes —

Current = Equivalent conductance.

By substituting this value of the current in equation (a), the follow-
ing is obtained : —

Equivalent conductance
96540

= Total velocity of the ions. (6)

If the two ions do not move with the same velocity^ they share the

above total velocity in proportion to their individual migration

velocities.

A numerical example will make this discussion clearer. The

equivalent conductance of an infinitely dilute solution of potassium

chloride at 18^ ^ is equal to 130.0 reciprocal ohms. Hence, according

to equation &, —

130
Total velocity of K' -h CI' = ^^ ' , or 0.001346 cm. per second.

But for potassium chloride, — = rr^«
'^ ' u« 65.4

Hence the two ions K' and Gl' share the total velocity in the ratio
64.6 : 65.4. Accordingly, for the potential gradient of one volt per
centimeter,

Velocity of K' = 0.000669 cm. per second,
and Velocity of CI' = 0.000677 cm. per second,

in a solution of infinite dilution.

The absolute migration velocities Ue« and v^ of a number of
ions at infinite dilution in water solution at 18^ <, calculated from
the most recent values of the migration velocities expressed in units
of conductance (see page 93), are given in the following table: —

Gatioitb

_ sec

Veixkjttt

cm.

A mom

-- see.

VSLOOITT

cm.

NH*-

Na'

Li-

0.OOO669
0.000667
0.000460
0.000846
0.000669
0.003294

CI'
N0»'
CIO,'
OH'

0.000677
0.000640
0.000670
0.001802

122

A TEXT-BOOK OF ELECTRO-CHEMISTRT

The migration velocities of ions is less in solutions in which the
dissociation is incomplete. According to the above discussion, the
sum of the migration velocities of positive and negative ions, in
such solutions^ is given by the expression^

96640'

when Sx) represents the equivalent conductance of the electrolyte in
question at the dilution Z>. Since, in such cases, only a portion of
the electrolyte takes part in the migration, the absolute migration
velocity obtained upon the assumption that the entire equivalent of
ions migrates is too small. For the individual ions, in sufficiently
dilute solutions, the following equations hold : —

u. = «(Ua),, and Ue =» (Uc)..

Here, u^ and n^ represent the migration velocities of the anion and
cation respectively, in a solution in which the degree of dissociation
is equal to x.

It is of interest to note, that it is possible to verify the above cal-
culated values of the absolute migration velocities of the ions by
direct experiments. Such experiments have been carefully carried
out by Whetham, Masson, and later by Abegg and Steele,^ following
the method given by Lodge. The results obtained are in remark-
able agreement with the calculated values. In a preliminary experi-
ment. Lodge measured roughly the migration velocity of hydrogen
ions in the following manner: He brought an acid solution into
contact with a solution of sodium chloride made red with alkaline
phenolphthalein and solidified in gelatine as shown in the accom-
panying diagram [Figure 32]. An electric current was then passed

Fio. 32

from the acid solution through the salt solution, in such a direction
that the hydrogen ions entered the colored gelatine at a. As these
ions slowly penetrated this solution of sodium chloride in jelly they

^ Zt8chr.phy$. Chem., 11, 220 (1803); ZUchr. phys. Cfhem,, 99, 601 (1890);
Ztschr. JElektrochemie, 7, 618 (1901); Ztschr, phys. Chem., 40| 699 and 737
(1902).

CONDUCTANCE OF ELECTROLYTES 123

destroyed the red color of the indicator. Hence, by measuring the
rate of progress of this decoloration, t.e. the time required for the
moving boundary between the colored and colorless parts of the so-
lution to reach b (a known distance from a). Lodge obtained the
actual velocity of the hydrogen ions. He did not, however, correctly
interpret his results.

Whetham improved the method used by Lodge, and determined the
migration velocities of complex copper ions in ammoniacal solution
of chlorine, and of bichromate (CrsOj") ions. He placed two dilute
solutions of the same specific conductance, one of which was color-
less and the other colored (such as, for example, solutions of potas-
sium carbonate and potassium bichromate) in an upright tube, the
one of least density above the other. If this is carefully done, a
sharp boundary may be obtained between colored and colorless solu-
tions, and, when an electric current is passed through the solution in
such a direction that the colored ions are migrated into the color-
less solution, their velocity may be obtained by measuring the rate of
movement of this boundary. The fall in potential per centimeter, or
the potential gradient, must be measured at the same time, for the
velocity of the ions varies directly with it.

It has been shown by Abegg and Steele that the method employed
by Whetham is also applicable to solutions, which, although color-
less, refract a beam of light to different degrees, thus making it pos-
sible to follow the movement of the botmdary between the two
solutions. They determined the migration velocity of various ions
at different dilutions of the electrolyte used, and found that the
results obtained agree well with the requirements of the theory.
As the dilution increases, the migration velocity increases and
approaches the values calculated for infinite dilution.

In a way these experiments on the migration velocities are a con-
tinuation and extension of those performed by Davy and described
on page 38. Davy was, however, prevented from attaining the
real object of them by erroneous assumptions regarding ions.

In this connection it may be mentioned that Whitney and Blake ^
found that negative colloidal suspensions of gold, platinum, ferrio-
ferrocyanide, and a suspension of microscopic quartz particles,
possess an initial velocity of migration of 0.0004 to 0.0005 centi-
meter per second, i,e. nearly equal to that of CIO3' ions.

Eleotrolytio Frictlonal Besistance. — Having calculated the abso-
lute migration velocities of the ions, the frictional resistance, or the

1 J. Am. Chem. Soc., 86, 1839 (1904).

124 A TEXT-BOOK OF ELECTRO-CHEMISTRY

force required to drive them through a solution,^ is easily obtained.
The mechanical energy or work expended is given by the equa-
tion,

E^otW^ss Force x Distance.

If the force required to drive one equivalent of a given kind of
ions through a solution with a unit velocity of one centimeter per
second is F, then the force required to drive the same quantity with
a velocity U centimeters per second is equal to FU. By substitu-
tion of these values in the above equation^ we obtain

^m or W^ = FV X U.

The electrical energy E^ or electrical work, is represented by the
equatioui

£« or TF^ = Volts X Coulombs = Volts x Amperes x Seconds.

By substitution of the numerical values in this equation, the
following is obtained : —

E.otW.^ly. 96540 Cr= 984616 CTkgm. cm.

By placing the mechanical work equal to the electrical work, —

FU X r= 984616 U;
984614

F=:

If one equivalent of ions be represented by Eq^ then for one gram

of the ions,

jw^ 984616

" UxEq

The value of this force for hydrogen ions in a solution in which
complete dissociation has taken place has, for example, been calcu-
lated to be equal to 299 x 10^ kilograms. This enormous value of
the force is in agreement with the results of other calculations, and
may be accounted for by the extreme state of division of the gram
of hydrogen ions. According to the calculations made by Planck,
one atomic weight in grams of an elementary substance consists of
0.617 X 10** atoms. One atom of hydrogen, then, weighs 1.63 x 10~**
grams, and is charged with 16.66 x 10'"^ coulombs of electricity.
This charge may be considered as an elementary quantity of elec-
tricity.

1 WUd. Ann. 50, 886 (1808).

CONDUCTANCE OF ELECTROLYTES 125

The limited Applicability of the Ostwald Dilution Law. Empirical
Bnles. — It is evident from a consideration of its derivation that the
equation.

fi«(fi-fiooi>)-^

= iC

which is an expression of Ostwald's Dilution Law, is applicable only
in the case of binary electrolytes. From the fact that slightly dis-
sociated acids of other types, such as the di- and tri-basic acids, be-
have on dilution according to the requirements of the above equation,
it follows that, at first, only one hydrogen atom separates as a posi-
tive ion, leaving the others combined in the univalent negative ion,
as represented in the equation,

HsA:^H>H,A'.

On c<nitinued dilution, the other hydrogen atoms begin to separate
appreciably in the form of ions, and simultaneously the negative
ions from which they separate increase their valences. This is evi-
dent from the equation,

H^'^H +HA".

Experiments have not been made to determine dissociation con-
stants for tertiary electrolytes ; moreover, as will be seen from the
following discussion, they probably would not be very successful.

It has been found that the above dissociation equation does not
hold for highly dissociated binary electrolytes, such as the neutral
salts, the mineral acids, and the inorganic bases. Consequently the
relations formerly deduced for highly dissociated electrolytes from
the dissociation equation can only be considered as mere approxima-
tions. ^Regarding the cause of this inapplicability of the equation
opinions still differ widely.*

The following empirical equation holds well over a wide range of
temperature, for salts which dissociate into monovalent or into
monovalent and polyvalent ions, at concentrations between the
values 0.001 and 0.2 normal: —

^(V~^) = Constant,
{Cxy

where C represents the concentration of the solution, x the degree of
dissociation, and n a numerical value which varies from 1.43 to 1.56.

* See, for example, Jahrbueh d, ElelOrochemie^ 8, 102 (1908), and A. A.
Noyes, Technology QtMrterly, 17, No. 4 (December, 1004).

126

A TEXT-BOOK OF ELECTRO-CHEMISTRY

For salts which dissociate into monovalent or into monovalent
and polyvalent ions, the following simpler equations hold between
the concentrations 0.0005 and 1 normal : —

1 — as = Constant x C^'
1 — X = Constant x (Cx)^'

Hence the undisaociated part of a edit, aa determined by oonduO'
tivity meaeuremente, is praportional to the cube root of the total conoenr
tration of the saU, or to the cube root of Ue ion concentration.

An empirical rule, expressing the change of equivalent conduc-
tance of neutral salts with the dilution, has been discovered by Ost-
wald. By means of this rule, it is possible to calculate the basicity
of an acid, and also the value of its equivalent conductance at
infinite dilution. It is of great service in the case of salts which
undergo hydrolysis to a large extent at moderately high dilutions.^
Ostwald found that the equivalent conductance of the sodium salts
of all monobasic acids increases ten units,' of all dibasic acids
twenty units, and of all tribasic acids thirty units, between the
equivalent dilutions 32,000 and 1,024,000 cubic centimeters. If the
increase in equivalent conductance between these two dilutions be
represented by A, and the basicity of the acid by B, then the rule is
expressed by the equation,

10
The following yalaes for A and — haye been obtained : —

BoDnm 8AI.T or

▲

Nicotinio acid

Chinoline acid

Pyridine tricarbonic acid

Pyridine tetracarbonic acid ....
Pyridine pentacarbonic acid ....

10.4
19.8
81.0
40.4
60.1

1.04 (approx. 1)
1.08 (approx 2)
3.10 (approx 8)
4.04 (approx 4)
6.01 (approx 6)

On the other hand, from the value of this difference A of an acid
of known basicity, an indication may be obtained of the presence or
absence of hydrolysis. In the case of a salt of a very weak acid, as,
for example, potassium cyanide, as the dilution increases the cyanide
ions combine to a certain extent with the hydrogen ions of the water

1 Ztsehr,phy8. Chem., 1, 109 and 629 (1887) ; 8, 901 (1888).
> The values used on pages 126 and 127 are expressed in reciprocal Siemens
units.

CONDUCTANCE OF ELECTROLYTES

127

(see next section), forming undissociated hydrocyanic acid. The
cyanide ions which thus disappear are replaced by hydroxyl ions
from the water. This reaction between the salt and water, or the
hydrolysis, is represented by the equation,

K* + CN' + H- + OH' (from water) ^ HON + K* + OH'.

The final result, then, of the dilution is that the number of hy-
droxyl ions, instead of that of the cyanide ions, has been increased.
Since the migration Telocity of hydroxyl ions is far greater than
that of cyanide ions, the equivalent conductance of potassium cya-
nide increases more rapidly with increasing dilution than would be
the case in the absence of hydrolysis, and, consequently, the value
of the above difference A is abnormally great. An analogous pro-
cess takes place in the case of a salt of a strong acid and a weak
base, with the exception that, instead of an undissociated acid and
hydroxyl ions, an undissociated base and rapidly migrating hydro-
gen ions are formed.

Finally, for neutral salts which dissociate to a large degree the
following relation has been found to exist : —

fi. = (v. XV, xiO + fc„

when ^2) is nearly equal to fi^. In these equations, v. and v^. rep-
resent the valency of the anion and cation, respectively, and IT is a
constant for all electrolytes which is dependent on the dilution.
Having determined the value of the constant at different dilutions
once for all for a single electrolyte of known equivalent conductance
at infinite dilution, it is possible to calculate the latter equivalent
conductance for any other electrolyte from a knowledge of the va-
lences of its ions and its equivalent conductance, at any dilution for
which the constant is known. If the product v. x v^ X iSTis repre-
sented by Pp, when D is the equivalent dilution of the solution in
cubic centimeters, then

v«xVe

Pm»

Pu^

PiXfiOH

^02,000

i'l,OS4,000

(60)

128 A TEXT-BOOK OF ELECTRO-CHEMISTRY

In the preceding table are given the values found by Bredig for
Pj, for different values of the product of the valencies of the ions
and for different dilutions at 25" t.

The following relation, which was first noted by Bodlander and
Storbeck,^ can often be conveniently used : —

when a^^ represents the degree of dissociation of a salt which forms
univalent and^n-valent ions, and x^^i that of a salt which dissociates
only into univalent ions. This equation holds when salts of the
same base are compared at the same equivalent concentration.
Thus, if the salts potassium chloride and potassium ferrocyanide
be compared at the same dilution,

^4r«(CN% = ^Ka«

It may be mentioned, in conclusion, that the fact, already noticed,
that the migration velocities are dependent chiefly upon the number
of atoms contained in the ion, may be used in order to obtain the value
of the equivalent conductance of compound ions at infinite dilution.
If it is known, for example, that the anion of a certain acid contains
eighteen atoms, its equivalent conductance at infinite dilution may
be considered to be equal to that of another anion of the same num-
ber of atoms, without introducing any considerable error. The same
reasoning may be applied to the temperature coefficients of the con-
ductance of individual ions.

The] CondnctiYity and Degree of Dissoeiation of Water. — Thus far
it has been assumed that the observed conductance of aqueous solu-
tions is due entirely to the dissolved substance, or solute, and that the
water itself possesses no conductance. Strictly speaking, however, this
is not true, for the water dissociates, though to an extremely slight
degree, into hydrogen and hydroxyl ions which take part in the con-
ductance with whatever other ions there may be present. For all
ordinary measurements of the conductance of solutions, the conduc-
tance of the pure water is entirely inappreciable. On the other hand,
the impurities usually found in water, such as traces of salts, acids,
or bases, which are removed only with great difficulty, may cause a
considerable error in the conductance determinations in the case
of dilute solutions. When such solutions are being investigated,
it is necessary to determine the conductivity of the water used,
and to apply the value obtained as a correction in the final results.

For a number of years Kohlrausch expended a great deal of effort

1 Zt»cAr. anorg, CKem., 89, 201 (1904).

CONDUCTANCE OF ELECTROLYTES 129

in determining the actual conductance of pure water. For water
which was prepared and purified with the greatest care, he found
the following values for the specific conductance, or conductivity : * —

Tufpnu.Tuu (0

SpXOIFIO CONDUOTAITOK

0°
18**
60°

0.01 X 10-«
0.038 X 10-«
0.17 X 10-«

'' One millimeter of this water at 0^ possessed a resistance equal
to that of forty million kilometers of copper wire of the same sec-
tional area, or a length of wire capable of encircling the earth a
thousand times/'

For reasons not necessary to give here, it is probable that this
experimentally found value is very near the actual value of the con-
ductivity of pure water. Given this value, the degree of dissociation
of water can easily be calculated.

The above table states that the conductance of a centimeter cube
of this water at 18° is equal to 0.038 x 10~* reciprocal ohms. Con-
sequently the conductance of one liter of it between electrodes one
centimeter apart is lO' times greater than this value, or equal to
0.038 X 10~'. If there were present, in this quantity of the water,
one equivalent of hydrogen and one of hydroxyl ions, the conduc-
tance would have been equal to 492 reciprocal ohms, since, as has
already been explained, the conductance of oue equivalent of hydrogen
ions between electrodes one centimeter apart is equal to '318, and that
of the same quantity of hydroxyl ions, under the same conditions,
174 reciprocal ohms. If the conductance had been found to be equal
to 492 reciprocal ohms, the water would have been 1/1 normal in
respect to hydrogen and hydroxyl ions. It was, however, found to
be 0.038 X 10~* reciprocal ohms. Hence the concentration of these

ions in the water is equal to ^'^qo"^^"* ^^ **-^^ ^ ^^~^' normal, or,

otherwise expressed, one gram of hydrogen and seventeen grams of
hydroxyl ions are present in about thirteen million liters of water.

Supersatorated SolntionB. — The idea has been prevalent for a very
longtime, and has not even yet disappeared, that supersaturated
solutions must behave in a manner characteristically different from
saturated and unsaturated solutions. Conductivity measurements

1 Kohlrausch and HeydweiUer, Ztachr.phys, Chem., 14, 317 (1804).

180 A TEXT-BOOK OF ELECTRO-CHEMISTRY

have, however, shown that supersaturated solutions possess no
peculiar properties not manifested by other solutions. If, for exam-
ple, the conductivity of a solution of a salt, whose solubility increases
rapidly with rising temperature, be measured at a series of tempera-
tures varying from those at which the solution is supersaturated to
those at which it is unsaturated, it will be found that the change of
conductivity with the temperature is perfectly regular throughout.
If the results thus obtained be plotted on a codrdinate system, it will
be found that a regular curve results which gives no evidence of the
passage of the solution from the supersaturated to the saturated, and
finally to the unsaturated, state. If supersaturated solutions were
qualitatively different from ordinary solutions a sudden change in
the slope of the curve wotild have been observed at the saturation
temperature.

Temperature Coefficient — According to Kohlrausch, the change
in conductivity with the temperature is nearly linear, and may be
expressed, often between wide temperature limits, by the following
equation : —

In this equation k, and k^ are the conductivities at the temperatures
ts and ti respectively; (As,o) is the temperature coefficient, which
gives the change of conductance, expressed as a fraction of the
conductivity, ^ sA 2l given temperature, for a change in temperature
of one degree. Grenerally 18^ is chosen as the given temperature.
The above equation may then be written as follows : —

It has been found that, in the case of all well investigated elec-
trolytes which dissociate to a high degree into univalent ions, the
temperature coefficient is the greater the smaller the value of
the equivalent conductance. From this fact Kohlrausch deduced
the following principle;^ The temperature coefficient of univcUerU
ions is a function of their mobility. That is to say, the greater the
migration velocity the less is the temperature coefficient. It follows
from this that the ratio of the mobilities of any two ions approaches
unity as the temperature increases, which is in agreement with the

1 SitzongBber. der kOnigL Pr. Akad. der Wias. Physik. Bfathem. Kl., 96, 572
(1902).

CONDUCTANCE OF ELECTROLYTES

181

statement made on page 76 that the transference numbers approach
the value 0.5 with increasing temperature.^

The magnitude of the temperature coefficient at ordinary tem-
X>eratures is shown by the values for dilute solutions given in the
following table : —

DlLUTI SOLUTB

TmPEEATCftB OoBrviomrr

Salts

Adds

Bases

0.020 to 0.023
0.009 to 0.016
0.019 to 0.020

A temperature difference of one degree thus changes the value of
the conductivity by from one to two and a half per cent, from
which the importance of making conductivity measurements only at
constant temperatures is at once evident.

As the concentration of the solution is increased^ the temperature
coefficient at first decreases and then increases slightly.

With the aid of the expression,

U| = Ui^ (1 + a (< - 18) + )8 (« - 18f),

the migration velocity of an ion at temperatures not far from 18** ty
v„ can be calculated if the values a, )3, and n]9> be known for this
ion. A table of values of Vig, is given on page 93. In the follow-
ing table are given the values of a and /9 calculated by Kohlrausch'
from experimental data : —

lOlT

lOH

0.0164

-0.000083

0.0282

+ 0.000094

179

+ 08

10,

288

096

KOt

208

C,H,0,

286

101

206

iBa

289

106

aOf

207

iCu

240

107

216

JPb

244

114

217

246

116

220

iMg

266

182

NH4

223

}Zn

266

188

1S04

226

261

142

281

J CO,

269

166

JSr

281

1 Farther puticulars may be f omid in the recent comprehensive Investigation
of Jones and West, Am. Chem. </., 84, 867 (1906).
s aueung8ber.y 48, 1081 (1901).

132 A TEXT-BOOK OF ELECTRO-CHEMISTRY

It may further be mentioned that conductivity measurements
have recently been carried out at very high temperatures (to above

300^.^

If it be imagined that the ions in moving through a solution must
overcome a certain frictional resistance, the existence of a certain
parallelism between the change of the internal friction or viscosity
and that of electrical conductance of many solutions with the tem-
perature becomes comprehensible. There is not, however, a strict
proportionality between the two properties.

Finally, it is a noteworthy fact that, in corUrast to conductors of
the first dasSy the temperature coefficient of the conductance of electro-
lytes is nearly always positive. In other words, the conductivity of
an electrolyte nearly always increases with increasing temperature.
The conductance of a solution depends both upon the migration vdoc-
ity and the number of the ions contained in it. The migration velocity
itself depends upon the magnitude of the friction which the ions en-
counter in the water. Since the internal friction of the water dimin-
ishes with rising temperature, it may be assumed that the friction
of the ions also diminishes and, as a consequence, the conductance
increases. This must be the case especially with salt solutions,
since, owing to the high degree of dissociation, the increase in con-
ductance with rising temperature cannot be ascribed to any consid-
erable extent to a change in the degree of dissociation. According
to this conception of the temperature effect, a decrease in conduc-
tance with rising temperature can only take place when the effect of
the diminution in the number more than compensates the effect
of the increased mobility of the ions. In other words, with rising
temperature a decrease in dissociation of the electrolyte must in
this case take place. To many this conclusion may, at first sight,
seem unjustifiable, in view of the fact that from the kinetic gas
theory it would be expected that with rising temperature an increase
in dissociation would take place. According to the laws and princi-
ples of energetics however, this is not at all the case, but, on the
contrary, it may be predicted that in certain cases an increase in
temperature must be accompanied by a decrease in dissociation.
The principle of energetics applying to such changes may be stated
as follows: —

If one of the factors determining (he equilibrium of a system be
varied in one direction^ the equilibrium undergoes a change which,
if it took place of itself would be accompanied by a variation of this
factor in the opposite direction.

I A. A. Noyes and W. D. Coolidge, Ztschr. phys. Chem^ 46, 828 (1908).

CONDUCTANCE OF ELECTROLYTES 188

If the factor temperature be varied in a chemical system, the
above principle may be restated as follows: —

If a chemical system at equilibrium be Jieated, the equilibrium is dis-
pla/ced in that direction in which heat is absorbed.

Consider, for example, a saturated solution of a substance in con-
tact with the solid substance. If the solution be heated, according
to the principle of energetics, that change will take place which is
accompanied by an absorption of heat, i,e. by a cooling effect. Con-
sequently, if the substance dissolves (in a nearly saturated solution)
with an absorption of heat, more of it will go into solution; if with
an evolution of heat, some of it will precipitate out of solution.

In a similar manner, the principle may be applied to the change
of the dissociation of any electrolyte with the temperature. All
electrolytes which tend to become less dissociated with rising, tem-
perature, and consequently all electrolytes possessing negative
temperature coefficients of the conductance, must dissociate with an
evolution of heat, or, otherwise expressed, must possess a negative
heat of dissociation. By heat of dissociation is meant the heat
effect attending the union of ions to form an undissociated molecule,
and by positive and negative heats is meant respectively the heat
that is given off to or absorbed from the surroundings.

By means of direct determinations of the heat of dissociation, it
is possible to test the correctness of the above conclusions.

Heat of Dissociation. — According to the dissociation theory, the
process of neutralization of a strong base with a strong acid con-
sists solely in the combining of the hydrogen ions of the acid and
the hydroxyl ions of the base to form undissociated water molecules.
It has already been shown that the degree of dissociation of water
is very small. Consequently the product of the concentrations of
the hydrogen and the hydroxyl ions must be extremely small. Now
according to the law of mass action, whenever hydrogen and
hydroxyl ions are brought together, combination must take place as
required by the equation,

Cb,o

-jr».

Since, in an aqueous solution the concentration of the undissociated
water is very great compared with that of the hydrogen and hy-
droxyl ions, it may be considered a constant. The above equation
may then be written as follows,

Ch* X Cqh' ^ ■^^«

184 A TEXT-BOOK OF ELECTRO-CHEMISTRY

Since eyen in pure water sufficient hydrogen and hydroxyl ions
are always present to satisfy this equation, and as the value of
this product cannot be exceeded, it follows that all hydrogen and
hydroxyl ions brought into water must disappear. Now before
mixing an alkali with an acid solution, we have in one case metal
and hydroxyl ions and in the other acid and hydrogen ions, as may
be illustrated by sodium hydroxide and hydrochloric acid. In this
case the following ions are present in the two solutions, respec-
tively : —

Na and OH' ; H* and 01'.

After mixing the acid and alkali solutions, the ions of the metal
and of the acid radical are still present and free in the solution,
constituting a highly dissociated salt. They have taken no part in
the process of neutralization. In the case of sodium hydroxide and
hydrochloric acid, only sodium and chlorine ions are present after
mixing the two solutions, constituting sodium chloride in the dis-
solved state. Hence the real reaction which has taken place is
represented by the equation

H+OH' = HA

It is because of the fact that the ions of the metal and those of the
acid radical take no part in the process of neutralization that the
value of the heat of neutralization is the same for all highly disso-
ciated acids and bases, being in each case the heat of the union of
hydrogen and hydroxyl ions to form undissociated water. This
value for one equivalent of acid and base is 13,700 calories, at ordi-
nary temperatures. Hence the above equation may be written as

follows : —

H' + OH' = HjO -h 13700 calories,

where the ions are present in equivalent quantities.

The value 13,700 calories then really represents the heat of dissocia-
tion ofwaJter,

This value must not be confused with the heat evolved when
gaseous hydrogen reacts with gaseous oxygen to form water.

If a partially dissociated acid be neutralized with a highly disso-
ciated base, the heat of neutralization will be made up of the sum
of two heats of dissociation, namely, that of water and that of the
acid. Representing the heat of neutralization by JET., the degree of
dissociation of the acid by x^ and the heat of the dissociation of
the acid by H^ then

JET, « 13700 - (1 - a?) H^ calories.

CONDUCTANCE OF ELECTROLYTES 185

Hence it follows that

H^ =5 — - — Z — s calories.

1— JB

All dissociating acids which exhibit a greater heat of neutraliza-
tion than 13,700 calories have negative heats of dissociation. It has
actoallj been found by Arrhenius ^ and later by Euler that all acids
which possess a negative temperature coefficient of electrical con-
ductivity have also negative heats of dissociation. Such acids
therefore decrease in dissociation with rising temperature.

Inflnenoe of Pressnre. — The influence of pressure upon the con-
ductivity of electrolytes may be predicted from the same reasoning
which explains the influence of temperature. By means of a change
in pressure a change may be produced in the concentration of the
solution, the friction of the ions, and the dissociation of the elec-
trolyte. Eliminating the change in concentration, which may be
applied as a correction in the calculation of the flnal results, experi-
ment shows that, in general, the conductivity of dilute solutions of
highly dissociated electrolytes increases with increasing pressure.
This may be ascribed to a diminution in the friction of the ions
with the water. This is in agreement with the fact that the inter-
nal friction or viscosity of water decreases with increasing pressure.
Therefore, as in the case of the temperature effect, there exists here
also a parallelism between the change in conductivity and the change
in internal friction.

In the case of electrolytes which are but partly dissociated, the
effect of pressure upon the degree of dissociation must also be
taken into consideration. This may be obtained from the volume
change during dissociation, just as the effect of temperature change
was obtained from the heat evolved or absorbed during dissociation,
i.e. the heat of dissociation. If the formation of ions is accompa*
nied by a diminution in volume, then an increase in pressure is
accompanied by an increase in the degree of dissociation. This fol-
lows from the law stated on page 132 expressing the change in equi-
librium caused by a change in one of its factors, since an increase in
pressure is accompanied by a decrease in volume, and this change in
dissociation, taking place of itself, is accompanied by a decrease
in volume. As a matter of fact, the dissociation of many moder-
ately dissociated acids is accompanied by such a decrease in volume ;
and corresponding to this, the increase in volume during neutralizar
tion with a strong base is less for these acids than for acids which

1 ZUchr. phys. Chem., 4, 96 (1889) ; 9, 839 (1892).

186 A TEXT-BOOK OF ELECTRO-CHEMISTRY

are nearly completely dissociated. This is analogoas to the above
consideration of the heat of dissociation.

It is a necessary consequence from the investigations of Fanjung^
that the conductivity of such acids should increase with rising pres-
sure to a greater extent than that of highly dissociated electrolytes^
especially in the case of their sodium salts. This is in complete
agreement with the above explanations.

Mixed Solutions: Isohydric Solutions. Application of Electiieal
ConduotiTity to Chemical Analysis. — If the conductivities of two
solutions and of a mixture of equal volumes of the two solutions are
determined imder the same circumstances, it will not, in general, be
found that the latter value is equal to the average of the other two,
excepting in the case of completely dissociated solutions. On mix-
ing solutions of sodium chloride and potassium nitrate, for example^
some undissociated potassium chloride and sodium nitrate must
result, whereby the relations are complicated.

Solutions which, when mixed, do not mutually affect the indi-
vidual conductivities, have been called by Bender ^^corresponding
solutkms/' and by Arrhenius, who investigated acid solutions
chiefly, "iaohydric solutions^' Two solutions are now said to be
isohydric when the concentration of the common ion is the same in
each solution. No change in dissociation occurs, then, upon mixing
them. This will be evident from the following discussion : —

Consider, for example, one solution to be of acetic acid and the
other of salicylic acid. For the solution of acetic acid, according to
the law of mass action, we have the equation,

C/| X C/| C/< r^

—jn n — — -"^HAei

and for salicylic acid, the equation,

^ i X G i Oi __ -n"

"7? — 79 ^HM^

in which C7ha<» O^s^ Ot, and C", represent the concentrations, in the
respective solutions, of the undissociated acetic acid, the undisso-
ciated salicylic acid, each ion in the acetic acid solution, and each
ion in the salicylic acid solution. Since the solutions are isohydric,
and hence are of equal concentration in respect to hydrogen ions,

d = Of.

If now one liter of the acetic acid solution be mixed with four liters

1 Ztschr, phys. Chem., 14, 673 (1894).

CONDUCTANCE OF ELECTROLYTES 187

of the salicylic acid solution, the contraction in volame is negligible
for such dilute solutions, and the resulting concentrations of the
various constituents in the mixed solution are as follows : —

Hydrogen ions s= Ci or O^ (unchanged).

Acetate ions (CHaCOO') = i CI-

Undissociated molecules of acetic acid = \ Chao*
Salicylate ions (C«H«OCOO') = \ CV

Undissociated molecules of salicylic acid s ^ Chbh*

By substitution of these new values in the above equations we ob-
tain, for acetic acid in the mixture,

7i — ^HAa>

HAoy

or C,^ _j^

^HAe

and for the salicylic acid in the mixture^

Therefore upon mixing the two solutions no change in dissociation
shoidd take place, since the requirements for equilibrium between the
ions and the undissociated molecules in each case remain satisfied.
Finally, it is evident that this is still true whatever the volume of
the one solution may be which is mixed with a given volume of the
other ; and, further, that when two solutions are isohydric in reference
to a third solution, they are also isohydric in reference to each other.
From what has just been said, it may be concluded that solutions
of a chloride, or of a bromide, etc., of the same metal, or of nitrates
of closely related metals, of the same equivalent concentration, are
nearly isohydric, since they are dissociated to nearly the same extent.
Hence the conductivity of a mixture of such solutions is very nearly
equal to the average of the conductivities of the individual solutions.
Upon this fact may be based a method of quantitative chemical
analysis. If, for example, the conductivities of two solutions of
potassium chloride and potassium bromide of equal percentage con-

188 A TEXT-BOOK OF ELECTRO-CHEMISTRY

centration are s and K'y respectively, then the conductivily of a
mixture of these solutions ig" is given by the equation —

K" = mi + (l-m)K',

when m and 1 — m represents the quantity of potassium chloride and
of potassium bromide, respectively, contained in a unit quantity of
the mixture. When the value of z!' is determined, the value of m
is easily obtained from the above or the following equation: —

m = —. •

Since here only conductivity ratios are involved, it is evident that
the conductivity measurements may be expressed in any system of
units without changing the value of m. It is most convenient to ex-
press these values in terms of the conductivity of a simple solution.
The inaccuracy of m increases with the differences between s and s'.

In general, it is best to ascertain whether or not the conductivities
of any two solutions in question are in fact additive in a mixture of
them by means of measurements carried out with known mixtures ;
for two other factors now to be mentioned may exert a disturbing
influence. There may be a complex compound formed when the
two solutions are mixed, in which case the equations deduced above
no longer apply. The fact that the conductivity of the mixture is
not the average of the conductivities of the constituent solutions
may even serve to detect the presence of such complex compounds.
Secondly, the nature of the solvent may be changed by the mixing
of the two solutions, resulting in a change in the degree of dissocia-
tion and in the internal friction which the ions must overcome dur-
ing migration. For instance, potassium chloride is dissociated to a
greater extent when dissolved in pure water than when dissolved in
a mixture of water and acetic acid containing a considerable portion
of the latter liquid. (See later.) For the same reason, the addition
of considerable quantities of acetic acid or of any other substance
may change the conductivity of an electrolyte.^

Finally it should be remembered that, as a matter of fact, the
requirements of the law of mass action are not always realized.
The following empirical rule, which is of wide applicability when
no complex compounds are formed, is therefore of considerable
value. 7%e condiustivity and the freezing^int loioering of a mixture
of salts having one ion in common are those calculated under the assump-
tion thai the degree of ionization of each salt is that which it wouid

^See Ztschr. phys. Chem,, 40, 222 (1902).

CONDUCTANCE OF ELECTROLYTES 189

ham if it wets present alone cU stich an equivalent concentration that
the concentration of either of its Urns ia equal to the sum of the equiva-
lent concentrations of aU of the positive or negative ions present in the
mixture}

Assuming that a mixed solution of sodium chloride and sodium
sulfate is 0.1 normal in respect to the first salt, 0.2 normal in respect
to the second salt, and 0.18 normal in respect to the common positive
ion (or to the negative ions), then according to the above rule the
degree of dissociation of each of these salts in the mixture is the
same as it would be in pure water when its ion concentration is 0.18
normal.

In explaining this further, it is recalled that the following equa-
tion holds for a single salt dissolved in water (see page 126) : —

l-.aj=ir(a?0)t

Applying this equation to each of the salts in the above mixed
solution, we have,

1 - aji = Ki{xiCi + XiCi)h and 1 - 05, = K^XiCi + aj^C,)*-

The concentration of the common ion of the mixed solution,
Xid+XsCs, is here the concentration of the positive or negative ions
of each individual salt in the simple water solution. Since Ki and
K2 may be known from conductivity measurements in the case of
the individual salts, and since naturally the concentrations of the
two salts Ci and Ct are known, the values Xi and a^ may be found.
This may best be accomplished by repeated trials until a satisfactory
approximation is obtained. The equivalent conductance of the
mixture is then given by the equation,

fi/>=aaato(CiZ>) + iB8fifco(C',I>).

where (GiD) and (CfD) represent the fractions of an equivalent of
the two salts, respectively, which are present in a volume D of the
mixture. The sum of the two values is equal to unity. It follows
from this that the conductivity, or specific conductance, is given by
the equation,

If the empirical rule stated above is valid, then the value of the
conductivity of the mixed solution calculated from the above equa-
tion must agree with the experimentally determined values.
It should be added that conductivity measurements have been

1 A. A. Noyes, Techtiology Quarterly, 17, SOI (December, 1904).

140

A TEXT-BOOK OF ELECTRO-CHEMISTEY

used in chemical analysis in other cases, namely, in the deter-
mination of the solubility of salts which are but slightly soluble in
water, as carried out by HoUemann,^ Kohlrausch, and F. Rose.
The solubilities of such salts can be determined by ordinary chemical
methods only with great difficulty.

If the solution is so dilute that the electrolyte may be considered
to be completely dissociated, then

and

Sd, — Soo —

from which the value of !)«, the volume in cubic centimeters of the
saturated solution in which one equivalent of electrolyte is dissolved,
may be calculated : —

J) -feJ^.

The values of R^ and K^ the actual resistance of the solution in the
conductivity cell and the cell constant, are found by direct experi-
ment, while that of s^ is often obtained by calculation. The value
of i>« being known, the solubility is determined.
The following results have been obtained in this way : —

Salt

Tbmpk&atctbb

CONOKKTSATIOK OF SaTU-RATID BOLUTIOMS

Silver bromide . . .
Silver iodide ....

21.r
20.8*»

0.67 X 10-* C^ or 0.107 mg. per liter

0.0035 mg. per liter

In determining the solubility of many salts, as for example of the
carbonates of the alkali earths, hydrolysis must be taken into con-
sideration (see page 126). Since the hydrolysis may be driven
back by the addition of OH ions, the conductivity, not of a solution
of the salt in pure water, but rather of one in a dilute alkali solu-
tion, should be measured. The true value of the solubility can then
be calculated from the increase in conductivity of the alkali solu-
tion which takes place when the salt is dissolved in it.

Finally, it should be mentioned that Ktlster ^ has recently shown

1 Ztschr. phys. Chem., 18, 126 (1893).

s2i(scAr. phy9. Chem., 12, 234 (1893). See also Sitzongsber. d. k5nigL
Fr. Akademie d. Wiss. Physik. Mathem. Kl., 41, 1018 (1901) ; Ztschr, phys.
Cfhem,, 60, 366 (1906).

^Ztsehr. anorg. Chem., 85, 464 (1903); 4S, 226 (1904). This application
was suggested by Kohlrausch as early as 1886. See Wied. Ann., 96, 226 (1886).

CONDUCTANCE OF ELECTROLYTES 141

•

that oonductiyity measurements may often with advantage replace
indicators in the titration of acids and bases. If^ for example, 10
cubic centimeters of a 0.1 normal solution of HCl be diluted to
500 cubic centimeters and titrated with a 0.1 normal solution of
NaOH, then during the titration the rapidly migrating H ions
of the acid are gradually replaced by the slower Ka ions, and con-
sequently the conductivity of the acid solution gradually decreases.
After all H ions have been replaced and more NaOH is added, Na
and rapidly migrating OH ions are increased in the solution, and,
consequently, the conductivity of the solution being titrated is also
increased. Hence the end point of the titration is the point at which
the conductivity reaches its minimum value. In carrying out a
titration in this manner, care must be taken to insure good stirring
and constant temperature.

Beg^ularity of lonization. BeaetiTity of Electrolytes. — It follows
from what has already been said in regard to electrical con-
ductivity that different substances when dissolved in water or in
any other solvent often dissociate to very different degrees. The
question at once arises whether the ionization of different substances
follows any regular scheme. It may first be questioned whether
additive relations exist, or, in other words, whether for a given atom
or atom-group there always exists the same tendency or force tend-
ing to form ions. If this was actually the case, and if this ten-
dency always appeared in the same way, the following would be
observed: Given all the electrolytes with a certain negative ion
arranged in the order of magnitude of their dissociations, then this
order would not be changed if another negative ion was substituted
throughout the series." From a study of experimentally determined
facts, however, it is seen that this assumption is untenable. Thus it
is found that hydrochloric acid is always dissociated to a greater
extent than any metal chloride in a solution of the same normality ;
while acetic acid is always less dissociated than any metal acetate.
Moreover, zinc, cadmium, and mercury salts are notable exceptions
among salts. With the halogens these metals form electrolytes which
are but slightly dissociated, and with many organic anions they form
electrolytes which are largely dissociated. The degree of dissocia-
tion of the corresponding acids is in the reverse order. Up to the
present, furthermore, no other simple relation concerning the regu-
larity of ionization has been discovered.

It may, however, he stated that in general aU saUs dissolved in water
are highly dissociated, whUe acids and bases show very great variations
in this respect, some being highly and some bvt slightly dissociated.

142 A TEXT-BOOK OF ELECTRO-CHEBilSTRY

Solutions of substances not included in these classes generally
possess a small, yet by exact measurements detectable, conductiyity.

If a chemical process is capable of taking place between two
dissolved substances, it always takes place instantaneously if the
substances are dissociated to a moderate d^ree. The usual
reactions of analytical chemistry may be cited as examples. In
other cases in which the substances are either dissociated to an
extremely slight degree, or to a degree beyond our means of detec-
tion, the reactions usually, but not always, take place slowly at
ordinary temperatures. Thus in the preparation of organic com-
pounds, it is usually necessary to carry out the reactions involved
at a high temperature in order to obtain a satisfactory yield with-
out an undue expenditure of time. Nevertheless, it should not be
claimed that chemical reactions can take place only when the sub-
stances involved are ionized. Such a claim is decidedly too broad and
is not in harmony with facts ; for undissociated substances can react
with each other, and in some cases with a high velocity. This is shown
in an especially striking manner by the investigation of Kahlen-
berg,^ according to which, solutions of stannic chloride and of cop-
per oleate in benzene, which were nonconductors of the electric cur-
rent, when mixed immediately gave a precipitate of copper chloride
with the simultaneous formation of stannic oleate.

Solvents other than Water. Halation between the Disaoeiating
Power and the Dieleotrio Constant of Solvents. — Already a large
number of investigations have been carried out with solvents other
than water or with mixtures of various solvents. It would be
natural to expect that the conceptions which have been found ser-
viceable in the case of solutions in water could be applied directly
to solutions in other solvents, keeping in mind that, according to
the individual nature of any given solvent, the degree of dissocia-
tion, the migration velocity of the ions, and consequently the con-
ductivity of a solution of a given concentration would be different.
It is a noteworthy fact, however, that the behavior of non-aqueous
is much more complicated than that of aqueous solutions. This is
shown especially by the investigation of the conductivity of solu-
tions of various substances in liquid sulfur dioxide made by Walden
and Centnerszwer.' Neither the law of the independent migration
of the ions, nor the law that by increasing dilution the conductance
approaches a maximum value, nor, finally, the dilution law, was

1 J. phy». Chem., 6, 9 (1902).

* Ztschr, phys. Chem., 89, 613 (1902), and Walden, ZU(^r. phys, Chem., 43,
885 (1908).

CONDUCTANCE OF ELECTROLYTES

143

found to hold. Molecnlar weight determinations carried ont at
the same time by the boiling-point method gave normal values
for non-electrolyteS| and abnormally large values for electrolytes,
whereas abnormally small values would be expected. This indi-
cates that association has taken place to a considerable extent,
which in all probability takes place not only between molecules of
dissolved substance, but also between these molecules and those of
the solvent. Considering these circumstances, it is very fortunate
for the advance of the sciences of chemistry and electro-chem-
istry that such complications are generally, although not always,^
absent in the case of aqueous solutions. It is due to this fact tiiiat
it has been possible to deduce simple laws from a study of such
solutions.

Although for solvents other than water a single generalization
under which individual results may be brought is still lacking, it
is, nevertheless, important to consider some of the individual results
themselves. A summary of such results compiled by WaJden' is
therefore presented here.

The solvents which have been most frequently investigated
belong to the alcohol class and are given in the following table : —

SOLTXNT

Methyl alcohol,
Ethyl alcohol,
Propyl alcohol,
Isopropyl alcohol,
Isobutyl alcohol,

FORMUUL

CHtOH

CsHftOH

CsHtOH

C4H9OH

SoLTwrr

Trimethyl carbinol,
iBoamyl alcohol,
Glycerine,
Benzyl alcohol.

FOBMiriiA

(CH$)tCOH
CfHuOH
C8H5(OH)s
CeHsCHsOH

The conductivity of solutions of a large number of salts (includ-
ing others besides those of the alkalies), acids, and bases have been
determined. Li the case of methyl and of ethyl alcohol, the disso-
ciation constant of many salts were determined both by the boiling-
point and by the conductivity method, without, however, obtaining
anything like a satisfactory agreement. According to the results
obtained by the former method, the molecular weight of the salts
decreases with increasing dilution. It was not possible, however,
to obtain a dissociation constant independent of the dilution, either
in the case of these or of other alcohol solvents. It is a remarkable
fact that only in the case of solutions of trichloracetic acid has the
dilution law been found to hold.

1 W. Blitz, Ztschr.phya. Chem^ 40, 186 (1002).

* ZtMchr, phys. Chem., 46, 103 (1903). An eztenslTe list of references to the
literature of the subject is also given.

144 A TEXT-BOOK OF ELECTRO-CHEMISTRY

Of the acids, the following have been used as ionizing substances :

Acetic acid, Butyric acid,

Formic acid, Benzoic acid (fused),

Propionic acid, o-Nitrobenzoic acid (fused).

With the solvent formic acid^ the following values were obtained

at26^ —

S. (for KCl) = 60.8 ; fi. (for NaCl) = 47.5.

A considerable difference was found between the dissociation values
obtained by the freezing-point method and those obtained by the
couductivity method. The dilution law does not hold for these
solutions.

Some of the nitriles are excellent ionizers ; namely, the following
lower members : —

Aceto-nitrUe, Butyro-nitrile,

Propio-nitrile, Benzo-nitrile.

In aceto-nitrile, silver nitrate possesses an abnormally small molecu-
lar weight corresponding to electrolytic dissociation ; in benzo-nitrile
it possesses an abnormally large molecular weight, indicating the
existence of polymerization.

Of the ketone solvents, acetone is the most interesting. The
equivalent conductance of binary salts dissolved in it increases con-
siderably with increasing dilution, without, however, attaining a
maximum value. In this case also the dilution law does not hold.

Of the other groups of organic compounds which have been in-
vestigated, the following may be mentioned : —

Aldehydes, Nitrogen bases (pyridene),

Esters, Nitro-compounds,

Ethers, Hydro^^arbons.

It has already been shown that water possesses a conductivity of
its own. Do other pure solvents, organic and inorganic, also con-
duct the electric current ? It has been found that the conductivity
of most of the good ionizing solvents (SOsCli, SOs, NH,, AsCls), be
they organic or inorganic, is of the same order of magnitude as that
of water, varying between the limits,

K«*' = 1.10-^ to 6.10-'.

Nevertheless, some solvents have been found which possess high con-
ductivities, as will be evident from the following table : —

CONDUCTANCE OF ELECTROLYTES

145

BoLTm

Form-amidey
Acet-amide,
Acetyl acetone,
Foimic acid.

OoiCDU C T IVl T t

4.7. 10-* (26^

29.10-* (81*)

1.6.10-* (26*')

1.6 . 10-» (8.6«»)

BOLTSMT OOBUUOnVRT

Nitric acid (anhydron8),1626 • 10-«(a*)
Sulfuric acid (anhydrous),

1000 . 10-« (approx.) (26*)
Antimony trichloride, 11.7 • ia-«(80*)

These conductivities approach those of typical electrolytes.

There are other solvents which possess no conductivity even
when salts or acids are dissolved in them. Such solvents are PBrg,
SnC!l4, SbClfi, SiCli, and bromine.

It is interesting to note that the conductivity of pure organic
(also of liquid, i.e. fused, inorganic) substances has been shown to
be dependent on the constitution of the substance in question. The
first member of homologous series possesses the highest value,
which is decreased with each successive introduction of a GHrgroup.
Substances containing OH- or CO-groups give the highest values of s.

If we hold to the dissociation theory, we must assume that all
substances which conduct electricity electrolytically are ionized. In
regard to the nature of this ionization, we can only surmise.

It is a remarkable fact, finally, that iodine, IBr, ICl, and IG1|,
when dissolved in SOjCls conduct the electric current.

According to Thomson and Nemst ^ there exists a relation between
the dielectric constant and the dissociating power of a liquid. In
order to facilitate the understanding of this relation a few illustra-
tions relating to the dielectric constant Kd and its determination
will be given.

Besides the galvanic conductance, there is also a second constant
by which the electrical behavior of a body is characterized. This
constant is of great importance in the case of just those substances
which conduct electricity galvanically very little or not at all, i.e,
the soK^alled insulators or dielectrics. The dielectric constant, jE1>,
of a substance is proportional to the capacity of a condenser the
l^^/^'lnsi^lating layer, or dielectrum, of which is this substance. If the
V capacity of the condenser in air is represented by k (although usually
placed equal to unity) and its capacity in the medium in question
by kiy then the value of the dielectric constant is given by the
equation,

The dielectric constant may also be defined as the factor which
gives the decrease in the electrostatic attraction between two

1 ZUchr. phys. Chem^ 18, 631 (1894).

146 A TEXT-BOOK OF ELECTRO-CHEMISTRY

charged spheres when the latter, while maintained at a constant
distance from each other, are transferred from a space filled with
air to one filled with the non-conducting medium being investigated.

A method for the determination of this constant which is very
often used is that known as the Kemst Method.^ It will be briefly
considered.

Starting with the apparatus used in the Kohlrausch method for
the determination of electrical conductivity as shown in Figure 29
and replacing the two resistances, the known and the unknown, in
the Wheatstone bridge by two condensers, an apparatus is obtained
with which, as had already been shown by Palaz, the capacities of
the two condensers may easily be obtained in case the dielectrics are
good insulators. The minimum sound is heard in the telephone
only when the following relation obtains (see also page 104) : —

If the resistance JBi is made equal to the resistance i2^ the two
condensers placed in air and one of them ki varied in k known
manner until, at a value ki, a minimum tone is heard in the tele-
phone, then the capacities of the two condensers are equal. If now
the dilelectrum to be investigated be inserted in the condenser kf, and
the condenser ^ be again varied until the point of minimum tone
in the telephone is obtained at the value k!\ the dielectric constant
of the substance Kj, is given by the equation^

When there is bad insulation in the condenser, no minimum sound
is heard in the telephone, and the measurement of the dielectric
constant cannot be carried out directly by the above method. It
can, however, be determined if an auxiliary circuit be introduced,
giving the other condenser a suitable conductance. In this case,
a minimum tone is heard in the telephone when both the capacities
and the conductances of the two condensers are equaL By means
of this artifice, it is at once evident that it is possible, not only to
determine the dielectric constant of substances which conduct gal-
vanically, but also to determine at the same time the magnitude of
the galvanic conductance.

The principle first stated by Nemst, expressing the relation
between the dielectric constant and the dissociating power of a
solvent, may be stated as follows : —

1 ZtBChr, phya. Chem., 14, 620 (1894).

CONDUCTANCE OF ELECTROLYTES 147

Hie greater the dielectric capacity of a solvent, the greater is the
degree of electrolytic dissociation of substances dissolved in it, when the
conditions are otherwise the same.

The following consideration will make this principle clearer:
The positively and negatively charged ions would unite to form
electrically neutral molecules because of the electrostatic attraction
which exists between them, if it were not for the action of another
and opposing force the nature of which is as yet unknown. The
equilibrium between these two forces gives rise to the equilibrium
between the ions and the undissociated molecules, or determines the
degree of dissociation. When the dielectric constant is increased,
the electrostatic attraction between the ions is alone weakened, and
hence the degree of dissociation is increased.

As will at once be seen, the principle stated by Nemst is well
substantiated by the very recent measurements made by Walden.^
Since a number of other interesting relations are furnished by these
results, they will be considered somewhat in detail.

Walden determined the dissociating power of half a hundred sol-
vents by dissolving in them one and the same binary salt, tetraethyl
ammonium iodide, ^(Q^^^,^ measuring the value of £ over wide
limits of dilution and, by calculation, extrapolating for the value of s^.
In this manner he was able to calculate for the different solvents
the value of the dissociation, —

which, for equal dilutions, is a measure of the dissociating power.
He used the values so obtained in order to throw light on the in-
fluence of chemical constitution on the diesociating power of various
solvents, and found that the dissociating power is increased by the
introduction of —

a. Oxygen-containing radicals, such as the carboxyl, hydroxy!,
keto, and aldehyde groups ;

b. Nitrogen- and sulfur-containing radicals, such as the cyanide,
sulf ocyanate, isosulf ocyanate, nitro, and sulf o groups ; and

c. Oxygen in ring compounds, and amido groups in acid amides.
The values of x referred to a volume of 1000 liters is given in the

following table in the order of the relative dissociating power for
various groups combined with the methyl group.

1 Ztsehr, phys, Chem., M, 129 (1906).

3 For molecular weight determinationB for this salt in varions solvents see
Ztschr.phys. Chem.^ 56, 281 (1906).

148

A TEXT-BOOK OF ELECTRO-CHEMISTRY

ISAJOt

JLoetio acid . . .
Acetyl chloride . .
Acetone ....
Methyl isosulfocyaiiate
Acetaldehyde . .
Methyl alcohol . .
Methyl sulf ocyanate .
Methyl cyanide .
Nitro methane . .

FOBMULA

«(%)

CHs . COOH

CHi . COCl

CH, . COCHs

CHs • NCN

CHa . COH

CHs- OH

CHaSCN

CHg.CN

CHs . NOi

A study of the homologous series of organic compounds has
shown that, as the carbon content increases, the dissociating power
decreases with greater or less rapidity in much the same way as in
the case of the electrical conductance of the solvent.

We may now proceed further to the relation between the dis-
sociating power and other physical properties, especially that of
association. According to the assertions of some investigators a
proportionality should exist here, and, moreover, the value of ^
should depend on the degree of association. But if the association
factors of Ramsay and Shields be accepted, then it follows that both
of these assertions are untenable. The comparison of the dis-
sociating powers of various solvents with their dielectric constants
has, however, resulted in the discovery of an important general-
ization. It has been found that a direct parallelism exists between
the dissociating power and the dielectric constants of solvents, com-
pletely confirming the principle put forward by Nemst. This will
be at once evident from the results given in the table on the next page.

This table gives an interesting survey of the magnitude of j^ for
the various solvents. It will be seen that it varies from 8 to 225,
the value for water, 112, occupying a middle position. From this
fact it follows that it is inadmissible to draw a conclusion, as often
has been done, regarding the degree of dissociation from the value of
the equivalent conductance alone.

It is remarkable that in the case of several solvents the equivalent
conductance does not increase with increasing dilution, but, according
to the nature of the solvent and of the electrolyte, in one case it de-
creases regularly, while in another it varies in a periodic manner,
passing through one or more minima and maxima. These phe-
nomena are explained on the assumption of chemical interaction
between the solvent and the electrolyte.

In the case of the two solvents, acetonitrile and epichlorhydrine.

CONDUCTANCE OF ELECTROLYTES

149

SOLTXHT

Water, H^

1. Formamide, HCONH4 . . .

2. Glycolnitrile, H/X>HCN .
8. Ethylene cyanide, (CHgCN)

4. Nitrosodimethylene . . .

5. Gitracon acidanhydride . .

6. Nitromethane, CHgNQg . .

7. Fnrfarole

8. Lactonitrile

9. Acetonitrile, CHgCN . . .

10. Methyl tbiocyanat^ CHsSCN

11. Glycol, (CHaOH)a ....

12. Nitrobenzene, G^sNOa .

13. Methyl alcohol, GH«OH .

14. Gyanacetomethylester .

15. Propionitrile, GsH^GN . .

16. Ethyl thiocyanate, GsHfiSGN

17. Gyanacetoethylester .

18. Benzonitrile, GeHgGN

19. Epichlorhydrine

20. Ethyl acetone .

21. Ethyl alcohol . .

22. Acetaldehyde . .

23. Acetone

24. Methyl isothiocyanate

25. Ethyl isothiocyanate

26. Propionaldehyde . . .

27. Acetic acid anhydride

28. Benzaldehyde . .

29. Benzyl cyanide
80. Acetyl bromide .
31. Anisaldehyde . .
82. Acetyl chloride .

33. Salicylaldehyde

34. iBobntyric acid anhydride

35. Thioacetic acid <

86. Benzoyl acetic acid ester

87. Malonic acid dimethyl ester

88. Isovaleric aldehyde ....

39. Acetic acid •

40. Dimethyl sulfide, (GH8)3S

41. Ethyl mercaptan, GsH^SH

42. Aldoxime, GHsGHNOH . .

43. Tetranitromethane ....

44. Dimethyl sulfate

45. Diethyl sulfate

46. Asym. Diethyl sulfite,

GaHjSOg

47. Ethyl nitrate

48. Sym. Diethyl sulfite,

SO(OG2H6)2

49. Trimethyl borate

DiELBGTRIO
COIIBTANT

i8'»(«')

81.7

67.9

57.8^1.2

53.3

39.5

38.2-40.4

36.5-89.4

37.7

35.8-86.4

33.3-35.9

34.5

33.4-37.4

32.5-84.8 J

28.8

26.5-27.2

26.5-81.2

26.2-26.7

26.0

(26?)

25.1-2C.0J

21.7-27.4

28.6-21.1

20.7-21 .9 J

17.9-19.7

19.4-22.0

14.4-18.5

17.9

14.5-16.9-4

15.0-16.7

16.2

15.5

13.9 (19.2)

13.6

12.8-17.3

11.0-14.3

10.8

10.1-11.8

6.46

6.2

7.96

3.4
<2.2
46.5
301

38.6
19.4-17.7

16.0
8.0

LuimD
Valus of

112

71.5
35J$(eO°)

22.5
120

40
200

96
8

40
124

29U$
165

84.5

28.2

56.5

66.8

60
180(0*') 1
226

134(60*»)l
106
(1461

42.5

36
114

16.5
1721

421

771

>7
>25

211

43
43

26.4
138orl40

76
1881

Deorkb op
Dissociation
D^ Dm, D-
lUO 1000 8000

91
93
93
90

82
78
781

74
77
78
71
73
69
65
63
65
61
60

55
58
51
46

46
34

(Per cent) -
98 99

98
98
96

98
99
96

(89) (91)

93 94

92 93

91 93

89 91

90 92
89 91
89 —
88 90
88 90
84 87
84 87
83 86
83 87

80 84

81 85
83 87

78 82
(84 86)
74 80
771 —
66 —
751) 1451

79 84

73
74
73
76
72
55

78
79
78
81
79
61

- 661 7ai

- 681 741

- 501 561

- — 41

- (7) (9)

91
84

93
86

94 95

58(72) 67(78)

50 61
(9) (12)

TBMPXKATinW

COBFriOIBHT

^i (0*-26*)

0.044

0.0229-0.0219

0.025

0.0149-0.0144

0.041 -0.044

0.0132-0.0136

0.0242-0.0254

0.0303-0.0328

0.0103

0.0148

0.092 -0.096

0.0254-0.0245

0.0151-0.0159

0.0439-0.0437

0.0109-0.0112

0.0149-0.0144

0.0392

0.0227-0.0231

0.0168-O.0209

0.0172

0.0230-0.0224

0.0082-0.0068

0.0082-0.0090

0.0101-0.011

0.0124-0.0130

(0.0081-0.011)

0.0171-0.0177

0.0207-0.0224

0.028 -0.031

0.0096

0.063 -0.072

0.007 -0.0088

0.0467

0.018

0.0138

0.086 -0.097

0.0285

(0.0047-0X)12.3)

(0.057 -0.060)

0.0230^).0228
0.024 -0.026

0.0325-0.0327
0.0105-0.0220

0.0111-0.0133
0.0068

^Approzimftto.

150 A TEXT-BOOK OF ELECTRO-CHEMISTRY

in which a considerable number of electrolytes have been investi-
gated, it has been found that the law of the independent migration
of ions (Eohlrausch's law) is valid.

From a further consideration of the values of fi^ given in the
table it is evident that there also exists a certain relationship be-
tween them and the chemical constitution of the solvent. For
example, in homologous series the value decreases with increasing
carbon content. A relationship between the value of s, and the
physical properties of the solvent has not been found. On the
other hand, it has been found that the product of s^, the equiva-
lent conductance at 2B>'y and the temperature coefficient for the con-
ductance of very dilute salt solutions varies about the same value in
the case of solutions differing widely from each other. Otherwise

exnressed*

fi^ . A,K((y*-26*) = 1.30 (approx.),

where A,k(O^-26'0 = — • ^^^ •

The variation from the value 1.30 is considerable only in the case
of a few substances.

There is also a numerical relationship between the dielectric con-
stants and the dilutions in various solvents which give the same de-
gree of dissociation. The relation,

JTd Vd ^K^j^VD':^ ^"dV5" - = Constant,

where jBTp, jT^, K"j, represent the dielectric constants of the individual
solvents and 2>, 2>', D", the corresponding dilutions at which the value
of the degree of dissociation is the same.

From the table ^ on the next page it may be seen, further, that the
dielectric constant, and therefore also the dissociating power, is re-
lated to various other properties of the solvent.

As the value of the dielectric constant K^ decreases, it is seen
that the values of the latent heat of vaporization Hj„^ of the abso-
lute conductance of heat JS^, and of the critical pressure P^i, also
decrease, while the values of the van der Waal constant a and of the
molecular volume at the boiling point V^ increase. There is not,
however, a strict proportionality.

At this point it should be mentioned that Euler' has neticed that
the dielectric constants of solutions increase with their ion content.
It has, for instance, been shown that the dielectric constant for

1 Ztschr. phya, Chem., 46, 172 (1003).
> Ibid., 88, 619 (1899).

CONDUCTANCE OF ELECTROLYTES

161

water is increased by the addition of a salt to it. It is possible
that this fact, even if not alone, plays a part in the deviation of
strong eleetrolytes from the dilution law (see page 125), for naturally
the law can only hold as long as the nature of the solvent remains
unchanged.

III

Ki>

vap.

erft.

Water

81.7

536.5

5.77

18.0

200

0.154

Methyl alcohol ....

82.5

267.5

0.53

42.8

0.0405

Ethyl alcohol

21.7

205

15.22

62.3

62.8

0.0423

Propyl alcohol

12.3

164

16.32

81.8

50.2

0.0378

Formic acid

57.0

103.7

41.1

0.0648

Acetic acid

6.5

80.8

17.60

63.8

57.1

0.0472

Ammonia

320

4.01

20.2

115

.Ml.

Methyl amine

<10.5

—

7.40

—

Ethyl amine

6.17

—

0.44

—

i-Propyl amine ....

5.45

—

13.7

85.6
(Dormal)

■^

Solfur dioxide

02.5

6.61

43.0

—

Acetone

20.7

125.3

77.1

Methyl-ethyl ketone . . .

17.8

—

11.06

—

Formic methyl eeter . . .

8.87

116.1

11.38

62.7

50.25

m.^.

Formic ethyl ester . . .

8.27'

00.3

15.68

84.7

46.83

0.0378

Acetic ethyl ester . . .

5.85

86.7

20.47

106.0

38.00

0.0848

Benzene

2.26

03.5

18.36

06.2

47.0

0.0338

Toluene

2.31

83.6

24.08

118.3

41.6

0.0807

Ether

4.36

84.5

17.44

106.4

35.61

0.0803

Chloroform

4.05

68.5

14.71

84.5

55.0

0.0288

Tetrachlormethane . . .

2.18

46.35

10.20

103.7

45.0

0.0252

Tin tetrachloride ....

3.2

30.53

26.04

181.1

37.0

—

The Intemal Friction and Conductance of Organic Solvents. —

With the aid of his comprehensive series of measurements, which
have already been mentioned, and also of new determinations of
friction coefficients of a large number of organic solvents, Walden^
has been able to find the relation which exists between the internal
friction of a dilute solution of the '^ normal electrolyte" N(G9H«)4l
and the electrical conductance s,. He found, moreover, that the

1 Ztschr. phys. Chem,^ 66, 207 (1006).

162 A TEXT-BOOK OF ELECTRO-CHEMISTEY

internal friction of dilute solutions and of the solvent are practically
identical. Hence in the considerations which are to follow this one
value /will be used.

Walden found the following regularities : —

(a) Both the internal friction and the conductance are dependent
on the nature of the solvent.

(b) The smaller the friction, the greater is the value of ^y and
conversely. From this fact the relationship between the internal
friction and the migration velocity of the ions, ^(GsHf)/ and I', is
evident.

(c) The limiting value fi***^ is inversely proportional to the corre-
sponding friction coefficients at 25^ t, according to the equation,

or, in general, according to the equation,

fi'«-/'. = fi"«-r,= Const.

This constant varies about the value 0.700, between the limits 0.64
and 0.71.

With the u$e of one and the same electrolyte, it toas found that for aU
of the thirty solvents which were inve^gated the product of the internal
friction and the limiting value of the equivalent conductance u>as the
same, although Hie individual limiting values varied from about 8 to 226.

With the aid of the relation,

K":-/^,= 0.700;

it is possible to obtain the limiting value of the conductance of the
^' normal electrolyte '' in the solvent under consideration from the
value of the internal friction.

Finally, if the temperature coefficients of friction and of conduc-
tance be compared, a striking agreement is found, and considering
the sources of error involved, it may be said with great probability
that for one and the sam£ solvent the tv)o coefficients are identical.

From this result it would be expected that the above relation

between friction and conductance which holds at 26^ would also

hold at other temperatures. As a matter of fact it has been found

that at 0^

K^ -/^ = Const. = 0.700.

It therefore follows that

fit -r: =&*:•/: =0.700.

Hence the following general statement may be made : —

CONDUCTANCE OF ELECTROLYTES

153

WUh the use of one and the same electrolyte N(CsH5)4l the prod-
MCt of the internal friction and the limiting value of the equivalent
conductance is independent of the nature of tJie solvent and of the
temperature in the case of organic solvents.

In order to explain these interesting relations, we may assume^
as did Kohlrausch in the case of aqueous solutions, that the migrat-
ing ion is associated with a large number of molecules of the solvent,
and. consequently in its forward motion encounters a friction which
is identical with the internal friction of the solvent. It is then clear
that the temperature coefficient of the limiting value of the con-
ductance and that of the internal friction must become identical.

The Electrical Conductance of Salts in the Fused and Solid
States. — The substances which conduct the electric current freely
in the state of fusion are chiefly salts and bases, such as silver
chloride and caustic soda. Their conductance can be determined by
the method used by Poincar^, by using silver electrodes and adding
a trace of a silver salt with the same anion as that of the salt being
investigated in order to avoid polarization. By this method the
measurement can be carried out as in the case of conductors of
the first class. The order of magnitude of the equivalent conduc-
tance of fused salts is shown by the values^ expressed in reciprocal
ohms, contained in the following table : —

Salts

TSMPSBATUBB

Eqdiv. Conduotavcz

KNOt

360^

44.9

NaNOs

860°

68.0

AgNO,

860**

60.0

KCi

760«>

90.6

Naa

760**

186.3

In order to compare these values with those obtained for salts in
dUute aqueous solutions, it will be recalled that the equivalent
conductance of a fiftieth normal solution of potassium chloride at
18° is equal to 119.96 reciprocal ohms.

The results thus far obtained in the case of mixtures of fused
salts show that their conductance is approximately equal to the sum
of the conductances of the constituent salts.

Not only above the melting point, but also below it, many salts
conduct the electric current readily. Graetz has investigated the
conductance of salts about the melting point, and has found that no
considerable sudden change in the conductance occurs as the melting
point is passed. On the other hand, the temperature coefficient of

154 A TEXT-BOOK OF ELECTBO-CHEMISTBr

the conductance reaches a maximnm value in the yicinity of the
melting point.

It is a noteworthy fact that, at lower temperatures {l(f to 180**),
according to the investigation of Fritsch,^ the addition of a small
quantity of a salt to a large quantity of another salt is, in many cases,
accompanied by a great increase in the conductance of the latter salt.
This is a striking analogy to the behavior of liquid solutions, justify-
ing the assumption that the one salt exists in solid solution in the other.

The same phenomenon was observed by Nemst' in the case of
the solid oxides such as magnesium oxide, and it is upon this phe-
nomenon that the Nemst incandescent lamp is based. While the
conductance of the pure oxides increases but slowly with the tem-
perature and remains comparatively small, that of a mixture of the
oxides increases rapidly, attaining finally an enormous value. For
example, values have been observed which were about six times as
great as that of the best conducting sulfuric acid solution at 18^.

The fact that glasses also conduct the electric current electrolyti-
cally, or, in other words, through the migration of ions, was shown
to be very probable by the pretty experiment made by Warburg in
the year 1884. He used a piece of glass, one end of which was
dipped in sodium amalgam and the other into mercury, as the elec-
trolyte, through which he passed an electric current from the amal-
gam as anode to the mercury as cathode. After the electriciiy
had passed for some time he found a quantity of sodium equiva-
lent to it in the mercury. Since during the experiment the glass
remained clear and constant in weight, it must be concluded that
the electricity was conducted almost entirely by means of sodium
ions, or, in other words, the migration velocity of the anion, perhaps
SiOs", is extremely small.'

ITnipolar Conduction. — It was already observed by Ermann about
one hundred years ago that, when the two poles of a galvanic cell
are inserted into a well-dried piece of soap, no appreciable continu-
ous current passes through the circuit ; and, further, that when one
hand is brought into contact with the positive pole and the moist-
ened other hand is pressed upon the soap, an electric shock is
received. This latter phenomenon is not observed if, instead of
the positive, the negative pole is touched by the hand. From these

1 Wied. Ann., 60, 300 (1897).

3 Ztschr, Elektrochem., 6, 41 (1800); see also E. Bose, Drude^a Ann,, 9, 164
(1004).

* Farther particalaTB regarding the conductivity of fused salts may be found
in the book of Lorenz, Die Elektrolyse geaehmoUener ScOze, 1006, W. Knapp,
Halle, Saxony.

CONDUCTANCE OF ELECTROLYTES 166

facts, as well as from electroscopic experiments which hare been
made, it is to be concluded that, whereas the electric current may
flow unhindered from the negative electrode into the soap, it cannot
do so from the positive pole, but, upon attaching an auxiliary circuit,
such as that from hand to hand, it must flow exclusively through
this circuit The soap was called by Ermann a unipolar conductor.

The phenomenon of unipolar conduction was explained by Ohm
by assuming that electrolysis takes place in the soap the moment it
is connected with the poles of the cell, by which alkali is separated
at the negative, and the fatty acid at the positive, electrode. The
fatty acid is, however, a nonconductor, and therefore prevents more
or less completely the passage of electric current according to the
water content of the soap.

Similar observations may be made in the case of the electrolysis
of solutions whenever a poor conducting substance is formed at, and
adheres to, one of the electrodes. Very recently this has been util-
ized in a very interesting manner in transforming an alternating
into a direct current.

If aluminium be used as an anode in a solution of alkali phosphate,
or of alkali salts of the fatty acids, and any other metal as a cathode,
a poor conducting aluminium compound is formed on the surface of
the aluminium, which prevents the passage of an electric current,
even when a potential-difference of 200 volts is applied at the elec-
trodes. When now the two electrodes are connected with the termi-
nals of a circuit carrying an alternating current, only the current in
one direction is allowed to pass. The alternating is thus trans-
formed into direct current. This application of unipolar conduction
will, however, scarcely become of practical importance.

It appears doubtful that, in the case of the above aluminium cell,
the whole action can be explained by the fact that a relatively thick
layer of great resistance is formed at the anode. It is more probable
that a thin dielectrum of slight conductance is formed at the elec-
trode, thus forming a powerful 'acting condenser in the circuit.

Technical Importance of Electrical Conductivity. — A knowledge
of the conductivity of various solutions (and of fused salts) under the
most varied conditions is essential to the rational management of an
electrolytic industry, for it should always be the aim to work with
the best possible conducting solutions. Thus, if other circumstances
do not prevent it, a solution of potassium chloride is always to be
preferred to a solution of sodium chloride of the same molar con-
centration. Furthermore, it is always preferable to c^rry out an
electrolytic process at a high temperature, if the cost of heating

166 A TEXT-BOOK OF ELECTRO-CHEMISTRY

does not exceed the saving in electrical energy due to the increase
in conductivity. Since very often the concentration can be chosen
at will inside of wide limits without injury to the process, that con-
centration should, in such cases, be chosen which has the greatest
specific conductance. In this connection it should be remembered
that, in the case of electrolytes which are very soluble in water,
the specific conductance, or conductivity, in contrast with the
equivalent conductance, at first increases and then decreases with
increasing concentration. This is shown by the results for sulfuric
acid at 18°, given in the following table : —

PBBcnrrAGB CoxonrraATioii

SPBCinO OoVDITCr^HOB

0.6527

0.7171

0.7388

0.7248

0.6800

0.2167

Hence, whenever sulfuric acid is used as an electrolyte, as, for
example, in the case of the electrolytic regeneration of chromic
acid where only about 100 grams of chromic oxide as an acid
salt in sulfuric acid is contained in one liter of solution, the con-
ductance is increased by the addition of an electrolyte, which is
without injury to the process. In the above chromic acid process
sulfuric acid serves as such an electrolyte, enough being added to
increase the specific conductance of the mixed electrolytes to its
maximum value. Very often it is necessary for the electro-chemist
to make his own measurements, in order to find the best proportions
of electrolytes to use in a given case.

The investigation of the cause of benzene conflagrations^ has
shown that the practical application of electrical conductance to
poor conductors may give rise to great fire danger. The electro-
static charges generated by friction are prevented from being con-
ducted away rapidly enough by the poor conductance of the pure
benzene. This leads to the formation of electric sparks, which, of
course, may easily cause explosions. An addition to the benzene
of a small quantity of a magnesium salt of a fatty acid increases
the conductance sufficiently to prevent the formation of the sparks.

The conflagrations which suddenly break out during work with
other poor conducting organic liquids, such as acetone, ether, etc.,
may be explained in the same manner.

1 Just, Ztschr. Elektrochem.^ 10, 202 (1904).

CHAPTER VI

BLECTRICAIa XSNDOSMOSE. MIGRATION OF SUSPENDED
PARTICLES AND OF COLLOIDS. ELBCTRO-STENOLTSIS

As early as the year 1807 Beuss observed that, during the eleo-
trolysis of water contained in a vessel which was divided into an
anode and a cathode section by a capillary, or a system of capillaries
such as a porous diaphragm, the water was carried by the current from
the former to the latter section. In the case of the better conducting
solutions, this phenomenon, or electrical endosmo8ey is not very
pronounced.

Later on, Quincke and G. Wiedemann carried out further experi-
ments in this direction. The following statement was found by
Wiedemann to express the laws of electrical endosmose for a given
liquid : —

The quantity of a given liquid carried through a porous diaphragm
in a definite time varies directly with the current strength and is
independeiU of the area or thickness of the diaphragm.

In 1809 Beuss observed that suspended particles, such as clay,
etc., are migrated under the influence of a fall in potential. When
suspended in water, they are migrated toward the anode. Recently
such migrations in the case of the so-called colloidal solutions have
been closely studied. This has led to the recognition of two classes
of colloids, namely, positive and negative colloids. The positive
colloids, such as gold, platinum, cadmium, antimony, arsenic sulfide,
molybdinum blue, indigo, etc., migrate toward the anode, while the
negative colloids, such as ferric hydroxide, aluminium hydroxide,
chromium hydroxide, hemoglobin, methyl violet, etc., migrate
toward the cathode. The behavior of suspensions of nickel, zinc,
and copper oxide is more complicated. In these cases, the addition
of small quantities of foreign material, such as traces of alkali or
of acid, changes the direction of migration.

It is interesting to note that a difference between positive and
negative colloids also appears in the case of their precipitation. The
positive colloids are more easily precipitated by means of NaOH,
while the negative are more easily precipitated by HCl. The former

157

168 A TEXT-BOOK OF ELECTRO-CHEMISTRY

are also precipitated by the ^radium rays, which contain n^ative
electrons^ while the latter are not. Finally, if the two kinds of col-
loids are brought together, they precipitate each other. It is a
peculiar fact, however, that this precipitation does not take place if
the two colloids are not brought together in certain proportions.^

It is evident from the above experiments that the electric current
exerts a force in a certain direction, not only upon ions, but also upon
other movable bodies of matter. This may, in all cases, be explained
by the assumption of the presence of an electrical charge upon the
portion of matter in question. The probability that this assumption
is correct is greatly increased by the deductions of Helmholtz. He
reasoned that at the surfaces of contact of two dissimilar media, for
instance the contact surface of water and glass, an electrical charge
or double layer must form. The existence of such a double layer
seems comprehensible from the results of experiments on the for-
mation of contact or frictional electricity. If now a potential-fall is
produced in a liquid by the passage of an electric current through it,
then the positive part of the double layer is attracted by the negative,
and the negative part by the positive, pole. Thereby a displacement
of the two layers takes place, resulting, when the force of the current
is sufficiently great, in the migration phenomenon noted above. The
movable liquid layer, according as it is charged positively or nega-
tively, migrates toward the cathode or anode, respectively, and by
means of friction carries with it the neighboring liquid or in case
the migration takes place in capillaries, the entire liquid. The dis-
rupted double-layer gradually becomes neutral by conduction, form-
ing a new double-layer, and the process goes on again. By means of
a suitable pressure, moreover, as much liquid may be^ forced back
through the center of the tube as is brought up by the electric cur-
rent along the walls of the tube, thus establishing a stationary state.
Conversely, if by means of a powerful pressure the liquid be forced
through a capillary tube so that the charged liquid forming a part
of the double layer is forced along the wall of the tube together with
the current of liquid in the middle of the tube, an electric current
is produced. The arrangement is entirely analogous to the ordinary
electric machine, with only this difference, that whereas in the
former case a liquid rubs past a solid, in the electric machine a solid
rubs past a solid.

This explanation is naturally directly applicable to the migration
of suspended particles. These particles take the place of the glass
wall and, being movable, migrate, in the opposite direction from the

» Biltz, Sen, 87, 1095 (1904).

ELECTRICAL ENDOSMOSE 159

water, to the anode.^ The question arises as to what other properties
may be connected with this phenomenon. If now another liquid
be substituted for water, a change will be observed. When turpen-
tine, for example, is substituted, it migrates to the anode, while the
suspended particles migrate to the cathode. Goehn gives the fol-
lowing answer to the above question,' which he has confirmed by
many experiments : If ttjoo substances are brought into contact with
each othety thai one possessing the higher dielectric constant will become
positively charged. It has already been stated that water possesses a
very high dielectric constant This fact then furnishes a ready
explanation for the migration of water, in most cases, to the cathode.

The technical application of the phenomenon of electrical endos-
mose has recently been undertaken.^ If a vessel, the opposite sides
of which are formed of perforated pieces of metal serving as elec-
trodes, be fiUed with a quantity of wet turf, and an electric current
be passed through it, water bubbles out of the perforations in the
side forming the cathode. This is a striking lecture experiment. The
turf itself which becomes dried acts as a diaphragm, while the water is
carried to the cathode, where it flows off. In a similar manner it was
endeavored to extract the sap from sugar beets, and to accumulate it
about the cathode, preparatory to the crystallization of the sugar.
It is not at present known, however, whether or not the extensive
experiments have shown the process to be of commercial value.

In the electrical tanning process, electrical endosmose appears
also to play a leading rdle, by forcing the tanning liquids quickly
into the pores of the hides.

An observation of Braun is closely related to electrical endosmose.
He observed that when a salt solution separated into two portions
by capillaries is electrolyzed, a deposition of metal takes place in
the capillaries. This phenomenon is called dectrostenolysis. Capil-
laries, most suitable for demonstration purposes, may be prepared by
dipping the hot closed end of a glass tube into cold water. This
end is then pierced by numberless fine cracks. If now a solution
and one electrode be placed in this tube, and the tube be placed in a
beaker also containing solution and the other electrode, the desired
apparatus is obtained.

Electro-stenolysis has also been explained by Coehn.^ It has

1 Another theory has been advanced by BUlitzer, Ztschr, phyB, Chem.^ 46,
807 (1906).

s Wied. Ann., M, 217 (1806).

• German Patents 124609, 124610, 128086.

« ZUehr. Slektrochem,, 4, 601 (1898) ; Ztschr.phys. Chem.^ M, 661 (1898).

160 A TEXT-BOOK OF ELECTRO-CHEMISTRY

already been noted that with a sufficiently great potential-fall, a
displacement of the positive water layer takes place, leaving the
glass wall of the capillary negatively charged. If now positively
charged metal ions are present in solution, they will be attracted to
the wall of the capillary, and there discharged and deposited. To
be sure, this deposition will be very slight since very large electrical
charges are present on the ions. The metal layer deposited cannot
in general be increased by taking part in the conduction, because
one end then becomes an anode and loses as much metal as the
other end gains as cathode. Under these circumstances, only a dis-
placement of the layer in the direction of the cathode can take place.
In those cases, however, in which the weight of the layer can in-
crease by taking part in the conduction of electricity, tiie trace of
deposited metal increases and finally becomes visible.
Such cases are the following : —

1. When the deposited metal is not oxidized at the anode, as, for
example, the platinum salts.

2. When an insoluble compound is formed at the anode, especially
the peroxides.

3. When, in the case of salts in the lower state of oxidation, the
negative ion can react on the solution with the formation of a
higher oxidized salt as in the case of a cuprous chloride solution.
In this case the chlorine liberated oxidizes the salt to cupric chloride.

As a specially interesting result of the experiments substantiating
these statements, it may be mentioned that solutions of cobalt salts,
which are weakly acid through hydrolysis, show stenolysis regularly,
while in the case of nickel salts no deposition of metal is visible.
It was concluded from this fact, that of the two, only the cobalt
salts form peroxides by electrolysis. Utilizing this fact, not only
a simple and certain qualitative test for cobalt in nickel solutions,
but also a quantitative, although somewh^rt tedious, separation of
the two metals is possible.^

1 Zt9chr. anorg, CKem., 83, 9 (1908).

CHAPTER Vn

BLBCTROMOTIVB FORCB

HAYDra dealt in the preyious chapters especially with the one
factor of electrical energy, the quantity of electricity, the other
factor, the electromotiye force, will now be considered.

The Determination of Eleotromotiye Foroe. — As already indicated
in the introduction, the electromotive force of a cell may be deter-
mined by means of a delicate galvanometer through an application
of Ohm's law,

*«+B-i'

when B„ is made so great that B|. is inconsiderable in comparison
with it. In this case, the deflections of the needle of the galvanom-
eter caused by two different cells successively introduced into the
same circuit are to each other as the respective electromotive forces
of the cells. If one of the two cells be a normal cell, the electro-
motive force of the other cell is thus easily obtained directly in volts.
If the internal resistance has not been made negligible compared
with the external, the electromotive force may still be determined
by reading the galvanometer deflections caused by the two cells,
both connected in the same circuit, first in series and secondly iu
opposition to each other. In this case we have the equation^

Cl ». -f F,

» .

or F.= F^

Oi-C,

in which Oi and Of are the currents found in the two cases and
F. and F« are the electromotive forces, respectively, of the unknown
and of the normal cell.

In more general use than the above method is that devised by
Poggendorf and known as the campenmtion method. By this method,
the unknown electromotive force is exactly compensated by a known
M 161

162 A TEXT-BOOK OF ELECTRO-CHEMISTRY

electromotive force. A diagram of a convenient form of apparatos
for this method is shown in Figure 33.^

Normal C«ll

Fig. 83

In the above figure, the line AC represents the meter wire of a
Wheatstone bridge or of a drum, usually of about ten ohms resist-
ance. The other parts are named in the figure. When the storage
cell is in place, a current flows through the wire AC and there is a
definite and uniform fall in potential between the points A and G.
In order to obtain the value of this potential-fall, a carefully tested
normal cell and an electrometer, galvanometer, or any other instru-
ment which shows when no current is flowing in a circuit are con-
nected in an auxiliary circuit as shown in the diagram, and the
sliding contact B is moved until the electrometer indicates that no
current is flowing in this circuit. The potential-fall between the
points A and B is, then, equal to the known electromotive force of
the normal cell. Since the fall in potential is uniform along the
wire, the fall per millimeter of the wire may then be calculated.

The unknown electromotive force of any other cell may now be
determined by substituting it for the normal cell and again moving
the sliding contact until no current flows in the circuit. If the new
position of the sliding contact is B', then the xinknown electro-
motive force is equal to the known potential-fall from the point A
to the point B\

When the electromotive force of a cell is to be measured, that
which it possesses on an open circuit is, in general, the value
desired, for the value which would be obtained while the cell is in
action would be indefinite because of the change in the state of the
electrodes or of the electrolyte which takes place. In the case of
electrometric, and especially in the case of galvanometric, meas-
urements, the conditions under which no current flows in the

1 For a more detailed description, see Ostwald-Luther, Phy9iko<hemUche Jfea-
9ungen^ page 867. For a more sensitive potentiometer based on the same prin-
ciples, see J&ger, Die NormaleUmenU (WihL Knapp, Halle, Saxony, 1902).

ELECTROMOTIVE FORCE 168

circuit do not strictly prevail even when according to the electrom-
eter, or other instrument, they should be fulfilled. This is due
to the fact that every instrument consumes, at the expense of
the source being measured, a certain quantity of electricity for
its operation. It is necessary, therefore, to ascertain whether or
not this quantity of electricity is greater than allowable, or in other
words, whether or not the state of equilibrium actually measured is
appreciably different from that which it is desired to measure. As
a matter of fact, in the case of measurements made on gas and
similar cells, a considerable error is frequently introduced because
of failure to pay suf&cient attention to the sensitiveness of the
galvanometer or to the capacity of the electrometer.
The following normal cells are those most generally used : ^ —

1. The so-called HdmhoUz calomd cellf which consists of

Zn - ZnCl, solution (sp. gr. 1.409 at 16**) - HgCl - Hg.

This cell, when made in the prescribed manner, possesses an electro-
motive force of one volt at about 15^ U The change of the electro-
motive force is very small, being equal to + 0.00007 for a rise of one
degree.

2. The Clark ceU, which consists of

Zn — ZnS04 paste — Hg2S04 paste — Hg.

When made according to the specifications of the ^^ Physikalisch-
Technischen Keichsanstalt," it has an electromotive force of

1.4328 - 0.00119 (t - 15) - 0.00007 (t - 16)» volts,

where t is its temperature.

(3) The Weston or cadmium ceU, which consists of

Cd (better a 10 to 15% amalgam) — CdS04 paste — Hg^SOf paste— Hg.

This cell, when made in the prescribed manner, has an electro-
motive force of

1.0186 - 0.000038 (t - 20) volts,

and is preferable to the Clark cell, because its temperature coefficient
is nearly zero.

For exact measurements it is recommended that normal cells be
obtained from the '^ Technischen Reichsanstalt." The electro-

1 For further particulars, see Ostwald-Luther, FhygikO'Chemische Messungen,
page 361 ; Jftger, Zt9chr. EleJUrocliem., 8, 486 ; and Jager, Die Normalelemente
(Wihl. Knapp, Halle, Saxony, 1902); Holett, ZUchr. phy$. Chem.^ 48, 483
(1904).

164 A TEXT-BOOK OF ELECTRO-CHEMISTRY

motive f 0106 of these cells is obtained from measuiements of resist-
ance and current.

Beyersible and InreTenible Cells. — Any arrangement which, as a
result of a chemical reaction or of such physical processes as diffu-
sion, etc., is capable of producing electrical energy is called a gal-
yanic cell ; whether the reaction takes place between a liquid and a
solid or between two liquids does not come into consideration. All
cells, or, as they are also called, elements, may be divided into two
classes, namely, into those which are reverMle and those which are
irreversible. To the first class, for example, belongs the Daniell cell,
which consists of

Zn — ZnS04 solution — GUSO4 solution — Cu.

The meaning of the term reversible cell may be made clearer by
the following consideration : Let us consider, for example, a Daniell
cell, the electromotive force of which is exactiy compensated by
another, oppositely directed, electromotive force. If the latter be
now slightiy diminished, the cell at once becomes active, zinc goes
into solution, and copper separates out. On the other hand, if the
compensating electromotive force be, instead, slightly increased,
thus becoming slightly greater than that of the Daniell cell, copper
dissolves, and the zinc deposits out of solution. Hence, if the con-
dition of the cell is changed by a process like the former, this
change may be exactly compensated and the original condition of
the cell restored by a process like the latter, i.e. the cell is reversible.
Of a reversible cell it is theoretically true that the maximum elec-
trical energy which can be obtained through its action at constant
temperature exactly suffices to bring it back to its former condition.
This statement may also be taken as a definition of a reversible celL

As an example of an irreversible cell, that one discovered by
Yolta which consists of

Zinc — dilute sulfuric acid — silver

may be given. When this cell is in operation, zinc dissolves, and
hydrogen separates at the silver electrode and is lost. From this
fact alone it is evident that the original condition cannot be restored
by simply reversing the current On the contrary, in this case
silver goes into the solution, and hydrogen separates at the zinc
electrode.

It is characteristic of reversible cells that, when the current is not
too great, the electromotive force which they possess immediately
after being set into operation remains nearly constant as long as

ELECTROMOTIVE FORCE 166

the material necessary for the chemical reaction is present. On the
other handy the initial high electromotive force of an irreversible
cell falls considerably, and reaches a nearly constant minimum only
after some time. Hence the terms, non-polarizable and polarizablef
which are often applied to these two classes of cells. More definite
information relating to these phenomena will be given later, in the
chapter on polarization. It may, however, be stated here that a
metal which is not too positive, dipping into a solution which contains
a su£&cient number of its own ions (preferably a saturated solution
in contact with some of the solid salt), forms, for ordinary current
densities,^ a non-polarizable electrode. In the case of the Daniell
cell both electrodes, and consequently the whole cell, is non-
polarizable.

Since at the present state of science the actions which take place
in reversible cells may easily be comprehended, and even quantita-
tively followed, they may now be considered to advantage.

Sdation between Chemical and Electrical Energy H — The ques-
tion now arises : How may the quantity of electrical energy which
a cell is capable of producing be calculated from the chemical
energy expended, — or, more strictly speaking, — from the heat
effects of the reactions taking place in the cell, since the latter
still constitute our measure of the chemical energy? It has already
been mentioned in the introduction that the assumption originally
made by Helmholtz and William Thomson, that the quantities of
heat involved are completely transformed into electrical energy, is
untenable. It is only in certain rare cases that this simple relation
exists. About thirty years ago Gibbs, Braun, and Helmholtz suc-
ceeded, by calculation, in fixing the real relations.

The first law of energetics may be stated as follows : —

Energy can neither be created nor destroyed, and oonseqtienUy the
total quantity of energy is a constant.

This law says nothing about the possibility of transforming one
energy form into another, and, indeed, from it alone it appears as
if it would be possible to transform heat at constant temperature
into work. If this were true, it would no longer be necessary to
use expensive coal to furnish power to run our railroad trains, for
the inexhaustible heat energy of the surroundings could be used

^ Current density may be defined to be the current per square centimeter of
electrode sorface. While the total current is the same at both anode and
cathode, the current density at the two electrodes yaries according to the
respectiTO sizes of the electrodea It is therefore usual to dlstingoish an anode
and a cathode current density.

166 A TEXT-BOOK OF ELECTRO-CHEMISTRY

instead. As a matter of fact, it has not been found possible to
obtain such a form of perpetual motion, called perpetual motion of
the second kind. This experience has resulted in the formulation
of the second law of energetics, which excludes the unlimited trans-
formability of the forms of energy. It was expressed by Glausius
as follows : —

Heat cannot pass of itself from a lower to a higher temperature.

The following more general statement of the law by Nemst is,
however, to be preferred: —

" Every process which takes place of itself in any system, or, in other
words, witJiout receiving energy in any form from the surroundings, is
capable of furnishing a definite quantity of work"

Conversely, such a process can be made to take place in the
opposite direction only by the expenditure of work upon it. If no
spontaneous processes existed, then no work of any kind could be
performed. For example, at constant temperature, and excluding
other changes in state, a transformation of heat into work is im-
possible.

It should he home in mind that these two laws of energetics express
the conclusions of experience and not the deductions from theories.

The maximum external work which a spontaneous process is
capable of furnishing is of great interest, since this work is an im-
portant characteristic of the process. It is not worth the trouble to
investigate values other than the maximum value, because they are
indefinite and may vary even to zero.

From a closer consideration, it is evident that the maximum
quantity of work is obtained from a process when it is made to
take place reversibly, or, in other words, in such a manner that,
theoretically speaking, at every instant equilibrium exists in the
process.

A process may be carried out isothermally and reversibly in
several ways. The question then arises as to whether the values of
the maximum work obtained in these different ways are identical?
Kow they must be identical, for otherwise perpetual motion of the
second kind would result, and this, according to the second law of
energetics, is an impossibility. Therefore if the value of the maxi-
mum work of a process when carried out in one way, is known, its
value when the process is carried out in any other way is also known.
If, for example, the maximum osmotic work which a process is
capable of producing is known, then the maximum quantity of elec-
trical energy which may be obtained from it is also known. When,
further, the quantity of substance, and so the quantity of electricity.

ELECTROMOTIVE FORCE

167

involyed is known, the electromotive force may at once be calcolated
with the aid of Faraday's law as follows : —
Electromotive force x Quantity of electricity s Electrical energy.

Hence

Electromotive force =-7r -r- — ^-^s — ^.^ *

Quantity of electricity

From the above discussion, it is evident how important it is,
especially for the calculation of electromotive forces, to know the
maximum external work obtainable from an isothermal process.
Such knowledge will be applied later on in the book. The second
law of energetics may also be stated in the following form : —

The 8um of the quantities of work involved in the different parte of
an ieothermal, reversible, cyclical process is equal to zero.

It is also of great importance in electro-chemistry to know the
maximum quantity of work obtainable when a given quantity of
heat is lowered from one temperature to another ; for this, too, is a
spontaneous process. In order to find this quantity of work, it is
necessary to devise a process by means of which heat may be trans-
ferred reversibly from one temperature to another which is lower.
Such a process is easily found. As the machine or carrier of heat
from the one temperature to the other a perfect gas may be used. In
this case the calculation is especially simple. It is only necessary to
be able to determine the quantity of work ob-
tainable when a gas of a volume v and pressure p
changes isothermally to a volume v' and pressure
p\ This quantity of work is the same as that
obtainable when an << ideal '' solution of a volume
V and osmotic pressure P changes isothermally
to the values V and P respectively. As fre-
quent use of osmotic work will be made, the fol-
lowing derivation is of twofold interest

If in the apparatus shown in Figure 34 one
mol of a saturated vapor (in contact with its
liquid) of volume v and pressure p be allowed
to expand against the constant pressure p \mtil
the volume v^ is reached, the maximum work
obtainable is easily calculated. If it be imagined that the increase
in volume (y^ — v) is divided into infinitely small parts designated
by dv, then the work obtainable during each successive expansion of
dm is equal to pdv, and the total work.

Fio. 34

W=^pCdv.

168

A TEXT-BOOK OF ELECTRO-CHEMISTRY

Expresaed in woidsy the total work is equal to p times the sum of
these infinitely small volumes dv from the value v to that of v'. Con-
sequently

Attention is here called to page 4 of the introduction^ where it is
shown that the product pv, and therefore p(v' — v) or jw", represents

a quantity of work [and also to
Figure 35, which is a graphical
representation of the relation of
p, v' — V, and TT].

In the case now to be consid-
ered, the relations are not quite so
simple, since the pressure, instead
of remaining constant as in the
above case, continually changes
with the volume until it reaches
the value p\ We have not then
merely to add together the values of dv; the sum of the endless
number of infinitely small quantities of work pdv must be found,
where the value of p is no longer a constant but a function of v, or
in other words, where the value of p depends upon and varies with
the value of v. The quantity of work involved during the change
in volume and pressure of the perfect gas is given by the equation,

Fio. 36

Tr= r pdv.

The values of p and v are dependent upon each other in a definite
and known manner. For one mol of a gas, the following equation
holds (see page 63) : —

pv^RT'j

1> =

By substituting this value of p in the above equation and placing
the constants before the sign of summation (the integral sign), the
following equation is obtained : —

Jv V

There is here only one variable, and the integral is determinable.
From integral calculus it is known that

ELECTROMOTIVE FORCE

169

= In — . or =

1 , v[
0.4343 ^^v'

where In signifies the natural and log the ordinary logarithm;
consequently

Tr=J2rin- = jr-7rT5log-
V 0.4343 V

Since, according to the gas law of constant pressure-volume product
(Boyle-Mariotte),

!!!—£.

the above equation may also be written as follows : —

^=^^^f^=ori3^<-

It is evident, from the above equation, that the available work is
proportional to the absolute temperature of the gas, and further,
that it does not depend upon the absolute values of the pressure
or volume, but upon the relation between the respective values of
each. Accordingly, the quantity of available work is the same
whether the gas passes from a pressure of ten to a pressure of one
atmosphere, or from a pressure of one to a pressure of one tenth of
an atmosphere.

It may be recalled that when it is desired to express the work in

mean gram-calories, the value of 12 = 1.985,
gram-centimeters, the value of £ = 84800 (approx.), and in
joules, the value of ii = 8.32.

[The relation between the pressure and volume changes and the
maximum quantity of work obtain-
able during an isothermal expan-
sion of a gas is shown graphically
in Figure 36. The line ab is the
pressure-volume curve and the
area a&tn;' represents the work
done by the gas in expanding from
the volume v to v' at constant
temperature. In the above math-
ematical derivation of the equa-
tion representing the work, there-
fore, this area has been found by obtaining the sum of the infinitely
small areas pdv of which it is composed.]

Fio. 86

170

A TEXT-BOOK OF ELECTRO-CHEMISTRY

If one mol of a gas expands so that its pressure decreases to one
hundredth of its original value, or, what is the same, its volume
increases a hundred fold, the maximum quantity of work obtainable
from the process at 17* t or 290** T is given by the following equar
tions : —

™ 1.985x290, 100 ^^-^ , .

04343 — ^^ T"' ^' ^ gram-calories,

™ 84800x290 , 100 ^^ooka iA» 4^ 4.

or Tr = — — log -=-, or 113250 x 10* gram-centimeters.

If, instead of one mol, n mols of gas had been taken, the quantity of
work obtainable would have been n times as great.

It may be well to remark that this work which is obtained during
the isothermal expansion of a gas is not taken from the internal
energy of the gas itself, but from the heat energy of the surround-
ings. The gas serves only as a medium for the transformation of
heat into work.

It is now possible for us to consider the process for the reversible
transference of heat from one temperature to another, and to calcu-
late the quantities of work involved in the different parts of the
process.

Pabt 1. One mol of the gas is compressed reversibly at the tem-
perature T from a volume v* to the volume v. The work done upon
the gas is given by the equation

Fi=xJB!rin--

This quantity of work is converted into heat, which is absorbed
by the surroundings. Moreover, the quantity of heat thus set free

is, according to the first law of
energetics, equivalent to the work
done, or

Qi = i2!r In-.

[This quantity of heat and of work
is represented in Figure 37 by the
area o&v'u]
• Pabt 2. The gas is now brought
into surroundings of a tempera-
ture T+dT. The quantity of
heat thereby absorbed by the gas is negligibly small as compared
with Q, and, moreover, the same quantity is given off to the sur-

Fio. 87

ELECTROMOTIVE FORCE 171

Toondings in a later part of the process. Since the volume v of the
gas remains constant during the change in temperature, no exter-
nal work is done. [This change is represented by the line be in
Figure 37.]

Pabt 3. At the new temperature, the gas is expanded reversibly
from volume v to volmne v'. The work done by the gas is, then,

A quantity of heat equivalent to this work is absorbed from the
surroundings, —

a=J2!rin--H^rin-.

\_Wz and Qb ^^ represented by the area odv'v.']

Part 4. Finally, the gas is brought into surroundings of a tem-
perature T. After the same negligible quantity of heat as was
absorbed in part 2 has been given out to the surroundings, the
process has passed along the line da to a^ and the gas is in its origi-
nal condition. The process is now complete.

As a final result of the whole process, it is evident that the
quantity of work TT obtained is as follows : —

[Referring to the figure, W is seen to be equal to the area abed.']
An equivalent quantity of heat has therefore been transformed into
work, but at the same time the quantity of heat

BTln^

has disappeared at the temperature T+dT, and been recovered at
the temperature T. Here there are two different kinds of heat
transformations taking place simultaneously. A definite quantity
of heat Q' can only be transformed into work by a reversible-cyclical
process operating between the temperatures T+dT and T when
another definite quantity of heat Q passes from the higher to the
lower of these two temperatures. The following equation gives the
relation which exists between these two quantities of heat : —

The result of the above deduction is of general application.

172 A TEXT-BOOK OF ELECTRO-CHEMISTRY

Whenever a quantity of heat is transferred from a higher to a lower
temperature, and no other change in state takes place, only a frac-
tion of it can in any case be transformed into work. The relation
between this fraction and the rest of the heat when the maximum
quantity of work is obtained is given by the above equation.

Let us apply these considerations to the reversible galvanic ele-
ments. If the heat evolved by the reactions taking place within
such an element, having no internal resistance, be entirely changed
into electrical energy while the element is immersed in a calorimeter,
no heating effect would be observed. The reason is that just as
much energy as was produced would be consumed as electrical
energy (capable of transformation into work) in the external circuit.
As a matter of fact this simple relation very seldom exists, and
therefore a generation of heat in the calorimeter can usually be
observed.

Imagine a reversible cell of electromotive force f at the tempera-
ture T, and suppose the quantity of electricity, 96,540 coulombs, or
q, be passed through it, then the maximum electrical energy which
may be produced is vg. Let Q be the sum of the heats of the
corresponding reactions. The action of the cell is attended by
absorption of heat, the heat absorbed being fq — Q, according to
the first law of energy. Suppose the temperature increased by dT
and the amount of electricity q again sent through the cell, but in
the opposite direction, and under the new electromotive force,
F 4- cZf ; the amount of work thus consumed will be ^(f 4- dF). The
corresponding sum of the heat of reaction in this reversed process
has changed but little, and, neglecting this change, is Q + dQ. The
heat generated in the cell is in this case equal to the difference be-
tween the electrical energy used and the heat taken up in the chem-
ical processes, and is thus equal to fq + qdF -- (Q *f- dQ). If the
element be brought again to the temperature T, it is once more in
its original condition.

As the end result of the process, the work qdv has been per-
formed, and accordingly the equivalent amount of heat gdF pro-
duced. At the temperature T the heat f— q Q has been lost, but at
T+ dT the heat fq + qdr — (Q 4- dQ) has been obtained, which
with slight error may be simplified to qf + qdF — Q. As qdF is
derived from the work done, the amount of heat fq — Q has been
raised from the temperature Tto T+ dT. Conversely, in order to
change the quantity of heat qc^f into work, the amount of heat
QF — Q must fall from the temperature T+ dT to T, consequently
the following expressions are correct in accordance with i>age 171 : —

ELECTROMOTIVE FORCE 178

Qd»=(F9-Q)^; (1)

ws-Q = qT^i (2)

-1 + ^^' (3)

Since we can calculate Q from thermochemical data, or can deter-
mine it directly, we are able, with the help of the experimentally
determined temperature coefficient of the electromotive force, to
calculate the maximum electrical energy obtainable, or the electro-
motive force of the cell. In the thermochemical data the numbers
always apply to a gram equivalent or gram-molecule, the heat gener-
ated being considered positive.

If the temperature coefficient is positive, i.^. if the electromotive
force increases with rise of temperature, it follows from equation
(2) that FQ is greater than Q : the cell in activity tends to be-
come cooler, and so takes heat from the surroundings. If, on the
other hand, the temperature coefficient is negative, fq is less than Q,
and the cell becomes warmer. If finally the temperature coeffi-
cient is zero, the heat of reaction is simply and completely trans-
formed into electrical energy, and the cell itself exhibits no ther-
mal change. This latter condition is nearly realized in the Daniell
cell.

It is necessary to emphasize this fact that the heat of the chemical

reactions is not a strict measure of the available electrical energy of

a reversible element, although experience has shown that in many

dF
cases it enables us to estimate it approximately, since—— is very

often negligible as compared with Q, and therefore may be omitted
from equation (3).

The above formula of Helmholtz has been qualitatively proven
by Czapski and Gockel, and quantitatively by Jahn and others. Sev-
eral apparent contradictions, as later shown by Nemst, arose from
erroneously assumed values for the heat of formation of mercury
compounds.

For illustration, the values found by Jahn^ and Bugarszky*
are given in the table on the next page.

In the table, w denotes the electromotive force at 0%^ the

1 Wied. Ann,, M, 180 (1808).
^ZUchr. anorg. Chem'., 14, 146 (1897).

174

A TEXT-BOOK OF ELECTRO-CHEMISTRY

change in electromotive force per degree, 2 fq the electrical

energy given out by the cell when two equivalents of the substances

have reacted, and Hr the heat of reaction for the same quantities of

the reacting substances, expressed in calories. In the last two

columns are given the values of the heat effect in the cell, i.e. those

J—,
calculated from — and from the expression, Q — 2 fq, respectively.

Cbll

Cu-CuS04 + 100 HaO .

Zn-Zn804 + 100 H,0 J

Ag-AgCl ,

Zn-Znaa + 100 HaC J

Ag-AgBr .

Zn-ZnBra + 26 HiC J

Hg-HgCl + KCl, 0.01C«— 1

1 Cn, KNO,
Hg-HgaO + KOH, 0.01 C- '

FjATOO

1.0962

1.016

0.828

0.1483
t=18.6°

+0.000084
-0.000402
-0.000106

+0.000837

8 rq

60626
46907
88276

7666

60110

62046

39764

-8280

Hkat Epfxct IK Ckll

OAIjO.

-428

+ 6082

+ 1326

-11276

^— 2 F«

-416

+ 6189
+ 1488

-10846

As is evident, the agreement between the heat value of the cell
as observed in the calorimeter and that calculated from the differ-
ence between the electrical energy produced by the current and the
corresponding heat of reaction is satisfactory in each case. The
last set of measurements is particularly interesting, since the chemical
process which spontaneously gives rise to the electric current is
endothermic and the cell when in operation absorbs heat from the
surroundings. It furnishes a striking proof of the incorrectness of
the assumption that the heat of reaction is a measure of the work
obtainable from a cell.

The above equations have also been found to hold for cells of fused
electrolytes at high temperature.

It may be advisable to add that electrical energy may be measured
by inserting the cell in a circuit, the resistance of which is so great
that internal resistance of the cell is negligible in comparison.
The electrical energy being allowed to change into heat, the
amount of the latter generated in the unit of time is c'b, ac-
cording to Joule's law (page 18), where r represents the resist-
ance of the circuit, and c the current-strength. Knowing the resist-
ance B, and having measured the current-strength, the quantity of
electrical energy produced per unit time may be calculated. From
this the quantity of energy produced when 96,540 coulombs, or twice

ELECTROMOTIVE FORCE 175

that nombery pass through the circuit may be easily determined, the
choice between these numbers depending upon whether one or two
gram equivalents of the substances take part in the chemical reac-
tion. As the internal resistance of the cell itself is negligible com-
pared to the external, the electrical heat effect produced within the
cell is insignificant, and may be left out of consideration. The heat
generated in the cell, and measured in a calorimeter as previously
described, has nothing to do with the electrical heat effect, c'b,
which is the heat generated by the electric current and hence a
measure of the electrical energy furnished by the cell. It is, instead,
equal to the difference between the heat of the reactions which take
place in the cell and the electrical heat effect just mentioned.

The equation previously derived enables us to determine the
electromotive force of a cell from a knowledge of its temperature
coefficient and of the heat of reaction. The electromotive force of
reversible cells may be determined in another manner, as already
indicated on page 166. Before proceeding with the calculation, a
clear idea of the concept, electrolytic solution tensiouy which was intro-
duced by Nemst, is necessary.^ We will, however, follow Ostwald's
nomenclature and call it electrolytic solution pressure.

Bleotrolytic Solution Pressure. — The expression ^' vapor pressure
of a substance '' is one commonly understood. It signifies the tend-
ency of a substance to enter the gaseous state.
If, for example, we allow water at a certain tem-
perature to evaporate in a long cylindrical vessel,
as shown in Figure 38, in which there is a mov-
able air-tight piston, and if a pressure p^ is exerted
upon the piston less than the vapor pressure of the
water, the piston is moved upwards and more
water evaporates. Hence a condition of equilib-
rium is only established when a certain definite
pressure equal to |> is exerted upon the piston irio. as

from without. The latter will then remain station-
ary in whatever position it be placed as soon as equilibrium between
water and vapor obtains. If the pressure on the piston be slightly
increased, the piston will fall and all of the vapor will condense to
water ; if, on the other hand, it be slightly diminished, the piston
will rise and all of the water will vaporize. The pressure downward
on the piston at equilibrium represents the vapor pressure of water
at the temperature of the experiment.

The ^'solution pressure" of a substance, for example sugar, ia

^ Ztschr. phys. C?iem., 4, 129 (1889).

Water V*iM

176 A TEXT-BOOK OP ELECTRO-CHEMISTRY

spoken of just as is the vapor pressure, and thereby is meant its
tendency to pass into the dissolyed state. This pressure may be
measured in a manner similar to the measurement of vapor pres-
sure. A diagram of the apparatus is shown in Figure 39. At the

bottom of the vessel there is an excess of the
solid substance, over which is its saturated solution,
and a semipermeable piston, that is, one which
is permeable to the water but not to the dissolved
substance. Above the piston is pure water.
If the piston be weighted, the magnitude of the
load determines the direction in which the piston
will move. If the load be less than the pressure
derived from the dissolved particles, the '^ osmotic
pressure,'' the piston will rise and water penetrate
into the solution, which being thereby diluted, al-
lows more of the solid substance to be dissolved. If it be greater, the
piston sinks, and water passes from the solution. The latter becoming
supersaturated, some of the solid substance separates out again.
Under a certain weight the condition of equilibrium must exist and
the piston remain stationary at any part of the cylinder. Evidently
the relations are here exactly analogous to those of the vapor pres-
sure of water, and the magnitude of the solution pressure of the
substance at a given temperature is measured by the weight on the
piston when in a condition of equilibrium.

It may here be repeated that, as made evident through these con-
siderations, the vapor pressure of water being that pressure exerted
by the vapor in contact with water, that is, the <^ saturated"
vapor, so also the ^^ solution pressure " of a substance is the osmotic
pressure of the solution which is in equilibrium with the substance,
that is, the '' saturated " solution.

This conception may finally be applied to the passing of sub-
stances, chiefly in the case of elements, and especially metals, into
the ionic condition. Hydrogen and the metals are capable of form-
ing only positive ions ; chlorine, bromine, iodine, etc., on the con-
trary, form only negative ions. The magnitude of this ^^electro-
lytic solution pressure" may be conceived as determined in exactly
the same manner as the ordinary solution pressure. We imagine
the substance in contact with water saturated with the ions in ques-
tion, under a similar piston, which separates the saturated solution
from the water, and is impermeable for the ions. The equilibrium
with the osmotic pressure of the ions will be brought about by a
certain weight jof the piston, and no ions will enter the solution

ELECTROMOTIVE FORCE

177

Hi-

- +

from the substance nor pass out of solution. The weight of the
piston in equilibrium represents the value of the dedrolytic 9oltUion
presmirej which is usually represented by p^ and also expresses the
equally great and oppositely directed osmotic pressure of the ions.
This method is practically inapplicable, because in no case can
appreciable amounts of positive or negative ions alone come into
existence; this does not, however, affect the value of the conception.

In order to explain the production of a potential-difference
through the contact of a solid substance with a liquid, imagine a
metal dipped into pure water, and that a certain amoimt of metal
ions is produced owing to the electrolytic solution pressure. The
metal at the same time becomes negatively electrified, since both
kinds of electricity must be simultaneously produced whenever
electrical energy comes into existence. The solution is thus posi-
tively electrified and the metal negatively, and
there is formed a so-called double-layer Q^ Dop-
pelschicht'^ of electricities of opposite signs.
[This is represented in Figure 40, in which the
positive and negative ions are represented by
plus and minus signs, respectively.]

The ions sent into the solution with positive
charges and the negatively charged metal at-
tract each other; in other words, a potential-
difference is produced. The solution pressure
constantly tends to send more ions into solu-
tion, while the electrostatic attraction of the electrical double-layer
opposes this action, and evidently equilibrium is reached when the
opposing tendencies are equal. Since the ions have very high
charges of electricity, this condition of equilibrium occurs before
weighable quantities of the ions have passed into the water. In the
case of pure water the potential-difference, or strength of the elec-
trical double-layer, depends only upon the magnitude of the solution
pressure, but if the metal be in a solution of one of its salts, another
factor is introduced, due to the metal ions already present. The
osmotic pressure of these ions opposes the entrance of new ions of
the same kind. It may occur that this osmotic pressure is exactly
in equilibrium with the electrolytic solution pressure of the metal,
consequently the latter will yield no ions and will not become nega-
tively charged ; in short, under these circumstances there will be no
electrical double-layer produced. The nature of the negative ions
of the salt in solution has no influence.

If the osmotic pressure of the metal ions differs from the electri-

Fxo. 40

178 A TEXT BOOK OF ELECTRO-CHEMISTRY

cal solution pressure, two different cases may be distinguished
according as the former or the latter is the greater. In the second
case, ions pass from the metal into the solution as in pure water,
and an electrical double>layer results. This action would evidently
not be as great as in pure water, since so many ions cannot enter
the solution, owing to the fact that the electrolytic solution pressure
is opposed by the osmotic pressure of the ions already present.
The quantities here involved are shown by the calculation made by
KrUger.^ In the case of zinc which is dipped in a solution which is
of normal concentration in respect to Zn ions, 3.10~* grams per square
centimeter go into solution. In the other case ions separate from the
solution and are precipitated upon the metal, communicating their
positive electric charges to it. The metal thus becomes positively
electrified, the solution, which formerly contained equivalent amounts
of positive and negative ions, negatively electrified, and again the
electrical double-layer is produced, the attraction of which opposes
the previously superior osmotic pressure and adds itself to the solu-
tion pressure. This proceeds until the condition of equilibrium is
reached. Here also the quantity of ions which is precipitated is
unweighable. The strength of the electrical double-layer and the
electrostatic attraction due to it is evidentiy dependent upon the
osmotic pressure of the metal ions in the solution.

In all, three cases must then be distinguished : —

First, when ^ = -P|

where p is the electrolytic solution pressure and P the osmotic pres-
sure of the metal ions under consideration. Here equilibrium
exists and no potential-difference or electrical double-layer is formed
between solution and metal.

Second, when p > -P.

In this case, the metal possesses a negative and the solution a
positive charge of electricity. The electrostatic attraction opposes
the solution pressure.

Third, when p < P.

Here the metal possesses a positive and the solution a negative
charge. The electrostatic attraction is superposed on the solution
pressure.

On turning our attention to the actual experimental facts, it is
found, as will be seen later, that such base metals as the alkali
metals, zinc, cadmium, cobalt, nickel, and iron, are always nega-
tively charged when placed in solutions of their salts ; the solution

1 Ztachr. phys, Chem., 85, 18 (1900).

ELECTROMOTIVE FORCE

179

pressure in these cases is so great that^ owing to the limited solu-
bility of the salts^ the osmotic pressure of the metal ions can never
be raised to equilibrium with the solution pressure. On the other
hand, with the noble metals, silver, mercury, etc., the metal is
usually positively electrified in solutions of its salts. The solution
pressure of the metals is here slight, and it is only by employing
solutions containing very few of the ions in question, t.e. such as
have very low osmotic pressure due to these ions, that it is possible
to have the metal negatively charged in the solution.

With such substances as produce negative ions, e,g. chlorine, there
is complete analogy. If the osmotic pressure of the chlorine ions is
greater than the electrolytic solution pressure, ions pass into the
condition of ordinary chlorine, and the '^ chlorine electrode '' becomes
negatively charged. In the other case
the electrode becomes positively charged.
As a matter of fact, as far as we know,
all substances which produce negative
ions have high solution pressures.

So far the electrolytic solution pres-
sure of a substance has been referred to
as if it were a constant, but, just as with
the vapor pressure and ordinary solution
pressure, it is only constant under cer-
tain conditions, t.6. only when the tem-
perature and the concentration of the
electrode substance in question remains
unaltered.

It is well known that the vapor pres-
sure of water changes greatly with the
temperature; but that it is aifected by

the concentration or density of the water itself, and is higher the
greater this concentration, may be less commonly recognized. The
fact may be recalled that if two open vessels containing water at
different heights be allowed to stand in a confined space, the water
distills from the higher level to the lower. The water in each ves-
sel is under the pressure of the vapor above it, and these columns of
vapor differ in height by the difference between the levels of the
water surfaces. Consequently the system is not in equilibrium, the
tendency being for vapor to condense under the greater pressure and
be generated under the lower, which process continues until the sur-
faces of the water in the two vessels are at the same level, or that
in one of the vessels is exhausted.

Fig. 41

180 A TEXT-BOOK OF ELECTRO-CHEMISTRY

In the accompanying figure^ the pure water and any water eola-
tion are separated by a membrane permeable to the water only.
Under the conditions represented the liquids are in osmotic equi-
librium, but the vapor pressure pi at the surface of the solution is
less than that p of the water, and the equation pi -h w=p must
represent the existing condition, where to is the weight of the column
of vapor whose height is equal to the difference in level between the
two liquids. If this were not true, water would dutill from one sur-
face to the other, thereby destroying the existing condition of osmotic
equilibrium, and would also pass through the membrane in one
direction in order to reproduce the osmotic equilibrium, etc. In
short, a perpetual motion would result, by which an unlimited
amount of the heat of the surroundings cU constant temperature could
be transformed into work (through the distillation of water vapor).
This conflicts with the second law of energetics, and therefore is
impossible.

If the upper end of the tube be closed by a membrane, allowing
the passage of water vapor only, and a quantity of a gas insoluble
in the liquid be placed between this membrane and the surface of
the liquid, it will exert a certain pressure upon the latter, which
will consequently sink to a lower level. The conditions of the
equilibrium must again be that the vapor pressure pi' at the surface
of the solution, increased by the pressure of the column of water
vapor d* between the two levels, is equal to the vapor pressure of
the pure water p, or Pi +w' ^p. Evidently p has remained unal-
tered, d' is less than d, therefore pi is greater than pi] that is, at
the. '^compressed" surface, where the water is at the greater con-
centration, there is a higher vapor pressure than when the water is
under a lower external pressure. The increase in the vapor pres-
sure is evidently proportional to the pressure acting on the surface.'

Of the ordinary solution pressure it is also known that the con-
centration of the substances plays an important part This is
shown by Henry's law, in accordance with which the solubility of
a gas, and therefore its solution pressure, since the two are synony-
mous, is to a great extent dependent upon the pressure, in other
words, upon the concentration ; it is, in fact, nearly proportional to
the latter.

1 Ztsehr. phys. Ohem., S, 116 (1880).

s This conclusion was established by the work of Des Coodres and the aathor,
which preceded the appearance of the article of Schiller on the same sabject
(Wied, Ann,^ 5S, 396, 1894). The experiments in connection therewith were
nnaYoidably interrupted and never concluded.

ELECTROMOTIVE FORCE 181

Wliat has been said of vapor pressure and solution pressure applies
equally well to electrolytic solution pressure, and accordingly there
are cells possessing certain electromotiye forces dependent only
upon the different concentrations of the same ion-producing sub-
stances. It is true that usually but one condition of concentration
for solid substances is recognized, iand consequently only a single
definite electrolytic solution pressure. But even here the concentra-
tion will be varied, as will be later described.

As in the case of the solubility, so the electrolytic solution pres-
sure changes with a change in solvent. However, it has been shown
by Luther ^ that the rdoUiona hebween the solution pressures of various
metals are independent of the nature of the solvent, and, moreover,
always possess the same value.

The electrolytic solution pressure varies with the temperature.

Calculation of the Electromotiye Foroe existing at the Surface
of Beveriible Electrodes. — The potential-difference which appears
when a reversible electrode is placed in contact with a liquid may
easUy be calculated according to the procedure given by Nemst. At
the same time, the mathematical importance of the electrolytic solu-
tion pressure will be made evident.

Let us consider the following isothermal, reversible, cyclical pro-
cess, noting first, however, that only the pressure of the correspond-
ing ions come into consideration, e.g. in the case of a silver elec-
trode, only the silver ions need be considered. Let f represent the
desired potential-difference, and P the osmotic pressure of the univ-
alent ions corresponding to the metal of the electrode.

Pakt 1. The quantity of electricity 9 is passed from the elec-
trode into a solution of osmotic ion-pressure P, at a potential f.
The quantity of work thereby obtained from the system is given by
the equation

Part 2. The equivalent of ions of volume V which has been
formed in solution is now diluted reversibly to the volume V+dV,
and the following quantity of work is obtained : —

Tr"=PdF.

Quantities of work of the second order of magnitude have here been
neglected.
Past 3. Since, in the above part, the volume has been increased

1 Ztschr. Elektroehem.j S, 496 (1902). See also Bnmner, Ztschr. JSlektra-
eKem.y 11, 415 (1905).

182 A TEXT-BOOK OF ELECTRO-CHEMISTRY

to V+dV, the osmotic pressure of the ions under consideration has
been decreased to P — dP and the potential-difference at the surface
•of contact of this diluted solution and the electrode has been in-
creased to F + (2f. - Hence now when, under these new conditions,
one equivalent of the ions is separated out of solution, the quantity
of work consumed is as follows : —

TT'" = (f + dv)q.

The process is now complete and the quantities of work involved
in the different parts may be summarized. Bepresenting the work
done by the system by a plus, and that done upon the system by a
minus sign, then the sum must be equal to zero, or: —

F^ + PdF- (F + dF)9 = 0.
Hence Q^f s= Pd V.

Since, according to Boyle's law, at constant temperatnrei— >

/WF-FdP=:0,andr=^,

it follows that qidr » - rdP== - BT^,

or, after integration, f sa — -. In P + const.

Instead of the constant appearing in the last equation, the logarithm

of another constant p, multiplied by — , may be substituted. This

equation then becomes

9 Q 9 ^

When p = P, F = 0,

and the constant p receives a comprehensible significance and is
known as the electrolytic eoltUion pressure.

If the ion is not univalent, but polyvalent, then the electrical
work VF9 per gram-ion is involved where v is the valency of the
ion. The above equation then becomes

VQ P

The quantity - is called the ^' electrolytio gas constant,'' and its

9
value is 0.861 x 10"*,

when the value of f is desired in volts.

ELECTROMOTIVE FORCE 188

Hence the above equation may be written as follows: —

,=?:8«l^riog|volt8,
or, after multiplying by 2.3026,

,^aoooi?83j.i P 1^

V ^ P

Referring the above equation to a room temperature of 18^ f, then

r= 291^
and the following equation is obtained,

, 0.05771, P ,,

p log _ YoltS.

V ^ F

This is a fundamental equation in the theory of reversible cells.
In considering a cell composed of two metals and two solutions,
as, for instance, the Daniell cell,

Zn — ZnS04 solution — GUSO4 solution — Cu^

there are four places where potential-differences are produced : —

1. At the point of contact between the two metals,

2. At the point of contact between the two liquids,

3 and 4. At the points of contact of the two electrodes with the
respective solutions.

The potential-difference at the point of contact between the two
metals is so small that it may be usually left out of account This
is also often true of that existing between the two solutions. These
magnitudes will shortly be calculated. Considering only the poten-
tial-differences at the points of contact of the electrodes with the
liquids, the electromotive force of the cell at 18^ is expressed by the
following equation : —

,^005771, P ^0057711 p:.
V ^P V' ^P*

p represents the electrolytic solution pressure of the one substance,
the valence and osmotic pressure of whose ions are v and P;
while p', V\ and P are the corresponding values for the other sub-
stance. The minus sign is used because at one electrode ions enter
the solution, while at the other they pass from the solution; for
example, in the Daniell cell zinc ions are produced, and simultane-
ously an equal number of copper ions separate at the other electrode ;
for the same number of positive and negative ions must always

184 A TEXT-BOOK OF ELECTRO-CHEMISTRY

be present in the solution. The investigation of special cases will
nov be taken up.

CONCENTRATION CELLS

1. Different OonoentratioBi of the Bubitanoes whieh aie Beetro-
motlTely Aotive. — a. A cell formed of two differently concentrated
amalgams of the same metal, for example zinc, in a solution of one
of the salts of the metal, as zinc sulphate, possesses, according to
the preyious considerations, an electromotiye force at T^ expressed
by the equation, —

0.0001983 _ , p 0.0001983

Fas-

^, p 0.0001983 -»,_p'

riog-p 2 — riogp

where p and p' represent the electrolytic solution pressure of the
zinc in the concentrated and in the dilute amalgam, respectively, and
P the concentration of the zinc ions in the solution. Since the
latter concentration is the same throughout the solution^ the above
equation may be simplified to

0.0001983

Fs-

r log-, volts.

Dilute amalgams may be considered to be solutions in which the
mercury is the solvent and, in the above case, zinc the dissolved
substance. The zinc, like all dissolved substances, exerts a certain
osmotic pressure which, since the amalgams are not of the same con-
centration, is different at the two electrodes. Since these are pro-
portional to the concentrations, the electrolytic solution pressures of
the amalgams may be assumed to be proportional to the osmotic
pressures of the dissolved zinc.^ From this

,^aOOM^Tlog|volt8,

where C and Ci are the concentrations of the zinc in the amalgams.
That values of f calculated in this manner agree with those experi*

^ This ia eqaiyalent to aagoming that the dissolved substance is present in the
mercury as atoms, which will be demonstrated from a consideration of concen-
tration cells formed from gases. If it be assumed that a compound is formed
between the mercury and the substance dissolved in it of the type X-Hg., then
another term most be added to the above equation. Since this term is within
the limits of experimental error, the question of the formation of such a
compound remains unanswered. It must at least be concluded from the
experiments, either that the molecules of dissolved substance are monatomic,
or that they are combined singly with the solvent, mercury.

ELECTROMOTIVE FORCE 186

mentally determined may be seen from the following lesults obtained
by Q. Meyer:* —

Zinc Amalgam and Zinc Sulphate SaluHon

C Ci Ffonnd F calculated

11.6"

0.003366

0.00011305

0.0419 Yolt

0.0416 volt

18.0»

0.003366

0.00011305

0.0433 volt

0.0426 volt

12.4»

0.002280

0.0000608

0.0474 Tolt

0.0446 volt

60.0»

0.002280

0.0000608

0.0620 Tolt

0.0619 volt

Oadmium Amalgam, and Cadmxwm Iodide Solution

(

rfonikd

vealcnUted

16.3"

0.0017705

0.00006304

0.0433 70lt

0.0440 volt

60.r

0.0017705

0.00006304

0.0662 Yolt

0.0607 volt

13.0'

0.0006937

0.00007035

0.0260 volt

0.0262 volt

Copper Amalgam and Copper Sulphate Solution

Ffonnd

vealonlated

17.3»

0.0003874

0.00009687

0.01815 volt

0.0176 volt

20.8«

0.0004472

0.00016646

0.0124 volt

0.0125 volt

The electromotive force f of snch cells can be calculated in a
second way^ independent of the idea of electrolytic solution pressure.
The action of the cell consists in zinc passing from the more con-
centrated amalgam into the solution^ and at the same time from the
solution into the weaker amalgam. As a result of the whole action^
zinc is transferred from the concentrated to the dilute amalgam, or,
in other words, zinc at an osmotic pressure P, or the proportional
concentration C, changes to the osmotic pressure P^ or the concen-
tration Oi. The maximum amount of work thereby obtainable
osmotically is

^ 0.4343 ^""^Ci'

for a gram-atom, when the metal is assumed to be present in the
mercury in the form of atoms.

The value of the work obtained electrically from the same process
is 2 X 96540 x f, and since the two maximum quantities of work
must be equal,

1 ZUchr. phya. Chem,, 7, 447 (1891), and Ostwald, Mlgem. Chem.^ U, 1,
861. «

186 A TEXT-BOOK OF ELECTRO-CHEMISTRY

0.0001983 _ , C

or F =

2* log 77 volts.

This is the same fonnula obtained by the previous method, and will
also be used later in the calculation of f.

It was assumed that the metal is present in the mercury in the
atomic state, and since the experimentally determined values of f
agree with those calculated, this assumption may be considered
justified.

If the metals had dissolved in the mercury in complexes of two
atoms each, the work obtainable osmotically, through the trans-
ference of the same amount of metal as before, would have been

„ 1 RT , G

because the number of separate particles to be transferred is only
half as great. The work obtainable depends upon their number, but
not upon their weight. The corresponding electrical energy would be

2 X 96640 X f',

therefore

2x96640x,'-|^^log^,

and

2 2 ** Ci 2 '

or in such a case the electromotive force of the cell would be only
half as great as is actually found. The monatomic character of the
metal molecules in mercury solutions has also been proved from
measurements of the vapor-pressure lowering.

As shown by the equation, f depends only upon the relation
between the concentrations and upon the valence of the metal, and
is in other respects independent of the nature of the metal.

The amalgams have been considered simply as differently concen-
trated zinc electrodes; it might be asked if the mercury in them
does not also play the part of an electrode, and its electrolytic solu-
tion pressure come into consideration. In order to dispose of this
question at once, it may be stated that, in the case of electrodes
composed of two or more metals, three cases are recognized.^

Case 1. If the metals form a mechanicdL mixture^ the potential will
be that of the least noble metal. Such a mixture of metallic zinc

1 Herschkowitz, ZUchr. phy$. Chem^ 27, 123 (1898) ; Ogg, Ztsehr, phifs.
Chem,^ 27, 286 (1898) ; Haber, Ztsehr. JSlektrochem., 8, 641 (1902) ; Reindena^
Ztsehr. phys. Chem., 48, 226 (1902).

ELECTROMOTIVE FORCE 187

and metallic cadmium, for example, when used as the negative elec-
trode of a cell containing acid, sends practically only zinc ions into
the solution. The electromotive force is, therefore, at first that of
pure zinc.

If zinc ions be added to the solution, but little effect is produced.
Only a small quantity of cadmium dissolves. On the other hand, if
cadmium ions be added to the solution, a considerable secondary
reaction results. This proceeds until such a number of cadmium
ions have been deposited and replaced by zinc ions as will make the
potential-difference between the zinc and the zinc ions equal to that
between the cadmium and the cadmium ions. When this has occurred,
again practically only pure zinc goes into solution.

The above-mentioned equality of the potential-differences between
the metals and the solution is, under all circumstances, spontaneously
established, i.e. a local action takes place until it is established. Since
the individual potential-differences depend upon the relation between
the electrolytic solution pressure and the osmotic pressure of the
corresponding ions, evidently in the case of equi-valent metals, the
osmotic pressures of the corresponding ions must be related to each
other as the solution pressures, in order that equality of potential-
difference may be attained. In the case of great differences in the
solution pressures, as, for example, between zinc and cadmium,
the concentration of the cadmium ions must be extremely small as
compared with that of the zinc ions. Since, because of the extreme
smallness of the former concentration, it is greatly changed by the
addition of new quantities of cadmium ions, while the latter concen-
tration is but slightly changed by the addition of a far greater
quantity of zinc ions, it is evident that, if the potential-differences
must remain the same, practically only zinc ions will go into
solution.

In the case of a mixture of two equi-valent metals which possess
the same electrolytic solution pressure, equilibrium is only established
when the two corresponding ion concentrations are equal, i.e. when
the two metals dissolve to the same extent in the solution.

Case 2. If the metals form a solution (amalgam or alloy), the
latter is always more noble than the least noble component, and,
further, this is true to a greater extent, the greater the loss in free
energy accompanying the formation of the alloy. It may even
happen that the metallic solution is more noble than the noblest
component.

The solution or dissolving of such alloys takes place in a manner
analogous to that already outlined. In all cases, the potential-

188 A TEXT-BOOK OF ELECTRO-CHEMISTRY

differences between the alloy of the least noble metal and the ions
of this metal, and between the alloy of the more noble metal and
the ions of this metal, must be equal to each other. It is to be
noted, howeyer, that this potential-difference is not the same as that
which would exist between the pure metals and the same solution,
and, further, that because of the dependence of the electrolytic solu-
tion pressure upon the concentration of the metal in the alloy, it
changes with the composition of the alloy. If the solution pres-
sures of the two alloyed metals differ yery greatly, as is usually the
case, then the least noble metal is practically the only one which
dissolves in the solution.

Case 3. If, finally, the metals form a chemical compound with
each other, and if this compound can exist as- such in the solution,
which contains a definite quantity of the metal ions corresponding
to the constituent metal of the compound, as, for example, copper
and zinc ions in the case of a zinc-copper compound, then this com-
pound possesses its own electrolytic solution pressure. From this it
must be concluded that during the solution of the electrode, ions of
the same composition as the electrode are sent into the solution,
where they eventually are dissociated to a large extent into the
individual components. In this case, the potential-difference is
dependent upon the product of the concentrations of these individual
ions.

To avoid errors in the interpretation of the phenomena, it must be
borne in mind that only the composition of the layer of the electrode
which is in direct contact with the electrolyte is of influence upon
the electrolytic solution process. The composition of this layer, in
the case of a solid alloy, may change by the gradual solution of the
less noble metal alone. Since an appreciable diffusion cannot take
place, the more noble metal remains alone upon the surface of the
electrode. Hence it is that such an alloy exhibits, after a time, the
potential and other properties of the more noble metal.

Advantage is taken of the fact that the least noble metal dissolves
first, in the preparation of pure metal surfaces. When a metal con-
taining a quantity of a less noble metal is placed in a solution of
one of its salts, the latter metal goes into solution accompanied by
the deposition of some of the former metal from the solution. In
this manner, it is possible to free the entire mass of mercury from
the less noble metals dissolved in it

The same principles play a very important part in the commercial
purification of metals. For example, copper is purified by placing
the impure copper plate, as an anode, in an acid solution of copper

ELECTROMOTIVE FORCE 189

sulfate of a certain ooncentration, near a suitable cathode, upon
which the pure copper is to be deposited. When, now, an electric
current is passed through the cell thus formed, the less noble
metals contained in the impure copper plate dissolye first, but do
not, as will be shown in the chapter on electrolysis and polarization,
deposit upon the cathode. Thereafter the copper goes into solution.
When the impure anode plate is nearly consumed, what remains of it
is composed of copper, and the more noble metals, silver and gold.
The latter metals have, then, been concentrated partly in the remains
of the anode and partly in the anode mud which falls from the anode
during the electrolysis. Thus not only is the copper purified by
this process, but also the more noble metalii are so concentrated that
they may easily be obtained in the pure state.

The important practical question as to whether iron is better pro-
tected by a coating of a more, or of a less, noble metal, e.g, by a coat-
ing of copper or of zinc, can now be considered. As long as only
impenetrable coatings are to be considered, that one would naturally
be chosen which best resists the action of the atmosphere. Of the
two metals just mentioned, copper would be preferred. On the
other hand, if coatings which are penetrable, as are all coatings in
practice, are to be considered, then, since moisture is always present,
at the points of penetration there will be a mixture of two metals
in contact with a liquid. According to the principles already
studied, at these points the less noble of the two metals will be acted
on by the moisture. Hence if the iron is covered with zinc, as long
as the zinc remains it will dissolve and protect the more noble metal,
iron, while if the iron be covered with copper, it is not at all pro-
tected thereby, but, on the other hand, its corrosion is accelerated.

From the same point of view, the fact that aluminium cannot be
durably soldered may be explained. Since only the more noble
metals are suitable for soldering, in the case of such a metal as
aluminium a galvanic cell is formed at the soldered points which,
when in action, causes the aluminium to go over into the ionic state.
The aluminium thus dissolved finally becomes oxidized to aluminium
oxide, forming the observed fungus-like growth.

b. The combination,

Hg — Hg (-ous) salt solution — Amalgam of a noble metal,

can also be classed as a concentration cell. It is evident from the
discussion in the previous section that in this cell the mercury is
present in different concentrations at the two electrodes. Naturally
only those metals may be used to dilute the mercury whose solution

190

A TEXT-BOOK OP ELECTRO-CHEMISTRY

pressure is less than that of the mercury, as, for example, the so-
called noble metals, gold and platinum. A mercurous salt must be
used as the electrolyte. Murcuric salts are immediately reduced to
the mercurous state when brought into contact with metallic mei^
cury , according to the equation —

Hg+Hg = 2Hg.

The electromotire force of this mercury concentration cell may be
easily calculated, as was that of the previously described cell, either
with or without the use of the idea of electrolytic solution pressure.
It will be sufficient to apply the shorter method, since the electromo-
tiye force of such a cell has not yet been experimentally determined.
During the action of the cell, mercury dissolyes from the pure
mercury electrode, where the solution pressure is greater, and is
precipitated upon the amalgam electrode. The maximum work
ayailable osmotically will now be calculated and placed equal to the
maximum available electrical work.

Let us consider a system such as is shown in Figure 42, in which
the pure solvent, mercury, is separated from the solution of a metal

in mercury, the amalgam, by a
movable semipermeable piston.
Let P represent the osmotic pres-
sure of the solution, and V the
volume of it which contains one
mol of the dissolved metal. Now
let the semipermeable piston be
moved downward under the con-
stant pressure p, from the point a
to the point &, whereby the volume
Fof the pure solvent enters the
solution. If, for example, this
volume is one cubic meter, then
Fig. 42 one cubic meter of the solvent

passes through the piston into the
solution, and the piston is moved through the volume of one cubic
meter at the constant pressure p. Finally, let the volume of the
solution be so great that the introduction into it of the volume V
of the solvent causes no appreciable change in its concentration.
Since Fis the volume of the solution containing one mol of the dis-
solved substance, the maximum quantity of work which can thus be
obtained is as follows : —

W^PV.

ELEGTROMOTITE FORCE 191

But PV=- RT,

and consequently W„ = RT,

where W^ represents tbe maximum quantity of work obtainable

oamotically. In order to obtain the equivalent electrical energy of

work, the number of equivalents of mercury (n) contained in the

volume V must be dissolved at one electrode and deposited at

the other electrically. The electrical work is then given by the

equation,

IF. = nrg ;
tberefme hf^ = RT,

or F = .

The values of ^ T*, and 4 are known, and that of n, the number of
equivalents of mercury containing one mol of dissolved metal in the
amalgam, may be found. Hence the value of f is easily calculated.

This method serves also for determining the molecular weight of
the noble metals dissolved in the mercury ; n is the number of mola
of mercury containing one mol of the dissolved metal By measur-
ing F, n is obtained, and from the known concentration of the amal-
gam, the weight of the dissolved substance in n, which represents
the molecular weight, is calculable.

o. A second mercury concentration cell is the following : —
Mercury {p > p„) — Mercurous salt sol. — Mercury (p =pj),
where p and p^ represent the
pressure upon the mercury and
the atmospheric pressure respec-
tively. [It is shown in Figure
43,] In such a cell mercury passes
from the former electrode through
the electrolyte to the latter. Dea
Goudree' arranged this cell as
follows : A column of mercury of
height d formed one electrode;
the lower end of the tube con-
taining it, dosed by means of
parchment paper, was placed in
a salt solution. The paper was '^

impervious to the mercury as

such, but allowed the passage of

it in the form of ions. The surface of the second mercury electrode
> Wted. Ann.,*%, 298 (1802).

192 A TEXT-BOOK OF ELECTRO-CHEMISTRY

was at the level of the parchment membrane. The height of the
mercury column decreases by a definite amount when a mol of mer-
cury passes from the electrode under pressure p to the other under
the pressure p^. The maximum work thus obtainable may be cal-
culated, and placed equal to the electrical energy involved. The
work necessary for the transference of the ions through the solution
may be left out of account. If 200 grams thus leave the column of
mercury, which is of great height d, the effect is the same as though
200 grams of mercury had fallen the distance d. The maximum
available mechanical energy is 200 d gram-centimeters, where d is
expressed in centimeters. Therefore, since, according to page 17,
gram-centimeter units must be divided by 10,198 in order to obtain

electrical units,

200d

^ 10198 '

and the electromotive force has the value given in the following
equation : —

F ^^ volts.

96540x10198

In the following table, experimentally determined values are
compared with those calculated with the aid of the above equa-
tion : —

PBMAITBa VX CML

r OAXX)ULATU>

V rouiTB

118

7.2 X 10-< volte
0.3 xlO-« volte
28 X 10-« volte

7.4 X 10-» volte

10.6)? 10-« volte

21 X 10-« volte

Considering the difficulty of accurately measuring these small
values, the agreement must be considered satisfactory.

In this connection, it is of interest to inquire the value of the
electromotive force which would be obtained if the above experi-
ment be so changed that mercury columns of the same height but
situated at different levels in the solution are used as electrodes.
If the difference between the levels of the two electrodes is equal
to d centimeters, will the electromotive force be the same as in
the former experiment ? As before, by the passage of one mol of
mercury from the higher to the lower electrode, the following
maximum quantity of work can be obtained : —

W sa 200 d gram-centimeters.

ELECTROMOTIVE FORCE 198

Neyeriheless, in answer to this question, it may be stated that the
electromotive force of the latter must always be less than that of
the former cell, and that, moreoTer, under certain circumstances the
direction of the current may even be reversed. This is due to the
fact that the migration downward of the mercury ions necessitates
the corresponding migration upward of the negative ions, which latter
requires the expenditure of work. As long as the mass of negative
ions migrated upward is less than that of the positive ions migrated
downward, an electric current flows through the solution from the
lower electrode. When, however, the mass of the negative is the
greater, work may be obtained through the migration downward of
the negative ions and the corresponding migration upward of the
positive ions. In this case the direction of the electric current is
reversed, t.e. the current flows through the solution from the
lower to the higher electrode. It is evident that here the trans-
ference number, as well as the mass, of an ion plays an important
part, and, moreover, that a deficiency in mass of a given ion may be
compensated by a greater speed of migration.

Recent investigations carried out by R. R. Ramsay^ on the influ-
ence of gravity upon electrolytic phenomena have confirmed the
above conclusions. For example, in the case of a ten per cent solu-
tion of zinc sulfate, the current flows through the solution from the
lower to the upper zinc electrode. This would be expected, from the
fact that while 32.6 grams of zinc are migrated upward in a given
time, 57.7 grams of sulfate ions are migrated downward.

After this experience, the fact that when two pieces of the same
metal, in which respectively the metal exists in different modifica-
tions, or in which it possesses any differeMe in physical structure or
quality^ are dipped into a solution and then brought into contact, an
electric current is produced, is no longer particularly wonderful.
Thus iron which has been subjected to tension or pressure possesses
a greater electrolytic solution pressure than ordinary iron. The
recognition of this fact is of importance in so far as it furnishes
an explanation for the very active corrosion at certain places on iron
cables and boiler plates. It may be stated in general that iron which
has been subjected to an uneven strain, or which has not been uni-
formly treated, corrodes more readily than does iron which has been
treated uniformly ; and, further, that highly polished corrodes less
readily than unpolished or poorly polished iron.'

Since the transformation of an unstable form, or a form which is

1 Ztschr. phys. Chem., 41, 121 (1902).

' Jahrbuch der Elektrochemie, S, 224 (1902).

194 A TEXT-BOOK OF ELECTRO-CHEMISTRY

produced by the action of an eztemal force, into the form which Is
stable under ordinary conditions, is a process which takes place
spontaneously, and which is capable of producing work, the electric
current always flows in such a direction that the unstable may pass
over into the stable form.

tf. Finally, concentration cells may be produced from gases, or
aqueous solutions of different concentrations, as ion-producing sub-
stance. At the first glance it may seem im-
probable that gases or liquids, which pos-
sess no metallic conductance, can serve as
electrodes. [Nevertheless, by means of a
special arrangement, such as is represented
in Figure 44, this end is easily attained.] A
platinized platinum electrode (Pt) is passed
into a tube which is afterward closed, so
that its lower end extends into a liquidL
The tube is so filled with the gas under con-
sideration that the platinum plate is for the
greater part in the gas, the remaning por-
tion being in the liquid. The platinized
platinum absorbs a certain quantity of the
gas, and may then be considered as a gas
electrode. The only other part the platinum
plays in these cells is that of conductor of
the electricity. Because of its power of
dissolving the gases the platinum permits
the change from the gaseous to the ionic
state, and the reverse, without resistance. Such an electrode, e.g.
one of hydrogen, belongs to the reversible class, as has been experi-
mentally shown by Le Blanc' The quantity of work developed by
the passage of a certain quantity of gas into the ionic condition is
exactly the quantity necessary and sufficient to produce the reverse
action. Since this is true, the material of the metallic electrode can
have no effect upon the electromotive force, and, in fact, equal values
have been obtained with platinum and palladium electrodes.

By means of snch platinized platinum electrodes, reversible hydro-
gen, oxygen, chlorine, bromine, and iodine electrodes may be pre-
pared. By arranging a teversible cell of two such electrodes, using
as ion-producing material the same substance for each, but in differ-
ent concentrations, a concentration cell entirely analogous to that of
the amalgam results. The electrolyte to be used must evidently be
> ZUchr. i>Av«. Chem., IS, 333 (1S93).

ELECTROMOTIVE FORCE 195

one containiiig the same ions as the gas produces. If, for example^
hydrogen be the gas, an acid must be used ; if oxygen, the corre-
sponding ions of which are OH (or ions), a solution of a base
must form the electrolyte. This kind of a cell is independent of the
nature of the electrolyte, except for the above consideration defining
one of the ions.

In the calculation of the electromotive force of a gas cell, for
example one consisting of two hydrogen electrodes under the pres-
sures p and jpi, the process is the same as with the amalgam cell, ex-
cept that it must be borne in mind that the hydrogen molecule
contains two atoms. In the reversible change of one mol of hydro-
gen from the pressure p to p^ the maximum work is represented by

JBTln^.

The corresponding energy, when the process is considered as an
electrical one, is 2fq because one molecule of hydrogen produces
two univalent ions ; therefore

RT. p

F =-75— In^.

29 Pi

The factor 2 occurs here in the denominator, even though the equa-
tion applies in this case to univalent ions.

If the calculation be made in accordance with the osmotic process,
using solution pressures as on page 184, the equation is

RT, p
F =s In—,

9 ^1

p and Pi being the solution pressures of the gas corresponding to the
pressures p and pi respectively. Evidently the two must be equal,

BT, p RT. p

or -35— In — = In—,

29 Pi 9 ^1
and 5 In — == ^n — 5

« p*
therefore i_ = — 5 .

Pi ^i

That is, the squares of the solution pressures are in the same ratio
as the corresponding gas pressures. This result is not difficult to
understand. It may be recalled that p and Pj represent osmotic
pressures (page 177). If the osmotic pressure p exists in a solution

196 A TEXT-BOOK OF ELECTRO-CHEMISTRY

at the one gas electrode whose gas pressure is p, while at the other
the osmotic pressure is Pi and the gas pressure p^ there is no poten-
tial-difiference at the electrodes. There is a condition of equilibrium
between the gas molecules H, and the corresponding ions H'. When
such a condition exists that the undissociated portion H^ and the dis*
sociated portions H*+ H' are in equilibrium, the concentration of the
undissociated portion, divided by the product of the concentrations
of the dissociated portions, is a constant.

Oh. X Ch ^**

Moreover, the gas and osmotic pressures are proportional to the con-
centration, hence

and also ^a ^»

therefore ^ = — r*

Pi Fl

Recently quantitative measurements of the electromotive force of
such cells have been made, the results of which are in agreement
with the predictions. A somewhat complicated case will now be
considered.

A hydrogen sulfide concentration cell has been investigated by
Bemf eld.^ Hydrogen sulfide dissociates according to the equation,

H,S5tH+H8',

and to an extremely slight extent according to the equation,

and always in such a manner that an equal number of positive and
negative ions are formed. Hence it is evident that this gas would
produce no current in such an arrangement as is used for the hydrogen
concentration cell. However, by means of an artifice, a reversible
hydrogen sulfide concentration cell can be made.

The following reaction takes place between hydrogen sulfide and
lead sulfide : —

H^ + PbS^Pb + 2HS'.
^ Zt$chr. phy$. Chem^ tt, 46 (1898).

ELECTROMOTIVE FORCE

197

If now two lead electrodes which have been covered with a thin
layer of lead sulfide be partially submerged in a solution of sodium
Bulfhydrate of a definite concentration and partially enveloped by
hydrogen sulfide gas of different concentrations, two systems are ob-
tained which, with the exception of the concentrations of the hydro-
gen sulfide gas, are identical. Upon connecting the two electrodes
thus formed by means of a wire, an electric current is obtained. As
the current passes, the hydrogen sulfide gas under the greater pres-
sure enters the following reaction : —

H,S + PbS-^Pb + 2H8';

while at the other electrode, the following reaction occurs : —

2HS' + Pb-^PbS + H^.

Since in this cell negative ions form and disappear, the direction of
the current is the reverse of that of the hydrogen celL The values
of the electromotive force of the two cells are, however, the same
when the respective gases are maintained under the same pressures.
That of the hydrogen sulfide cell is as follows : -^

— p =

InSst.

Hi0

It is evident that the nature of metal sulfide forming the elec-
trodes does not come into consideration, and it would be expected,
therefore, that the same value of the electromotive force would be
obtained if, instead of the lead-lead sulfide, silver-silver sulfide or
bismuth-bismuth sulfide electrodes were used. This conclusion is
well confiirmed by the results contained in the following table : —

EUOTBODM «

Pb-PbS

Ag-AgS

Pas.

37.50 37.61 87.44
15.60 6.26 12.91

35.1 34.6
4.2 5.2

37.50 37.50 37.50
1.71 4.27 2.92

MilliTolts calc. =
liiUivolts found =

-11.0 -22.4 -13.3
- 8.9 -21.1 -10.9

-26.6 -23.7
-25.0 -21.4

-38.6 -27.2 -84.8
-36.8 -25.8 -32.7

The consideration of a second kind of concentration cell will now
be taken up.
2. Different Concentrations of the Ions. — (a) The combination,

Ag — AgNOs sol., dilute — AgNO^ sol., concentrated — Ag,

may be considered as a type of these cells. In such a cell, where

198 A TEXT-BOOK OF ELECTRO-CHEMISTRY

the electrode furnishes positiye ions, the current always flows
through the cell (not through the external circuit) from the dilute
to the concentrated solution. Silver is dissolved into the dilute
solution and precipitated from the other, this process continuing
until the two solutions become of the same concentration. That the
silver ions must precipitate from the more concentrated solution is
evident when it is remembered that the osmotic pressure here di-
rected against the solution pressure is greater than in the dilute
solution. If the electrodes furnish negative ions, then the current
flows through the cell from the solution most concentrated, to that
most dilute, in respect to the negative ions. It will be remembered
that by current direction is meant the direction in which the posi-
tive ions migrate.

Leaving out of account for the present the potential-difference
which exists at the point of contact between the two solutions, the
electromotive force of such a cell is given by the equation,

ir«^ln|,-^ln^,

where p is the electrolytic solution-pressure of silver, and P and Pi
are the osmotic pressures of the silver ions in the concentrated and
the dilute solution, respectively^ Since the solution pressures are
the same, the formula may be simplified to

K = ^ln|.

This expresses the fact that the electromotive force of such a
cell is dependent only upon the relation between the osmotic pressures
and upon the valence of the metal ions, and is indepetident both of
the nature of the metal and of the negative ions of the electrolyte.

The electromotive force may also be ascertained by the second
method, through calculating the maximum of energy represented by
the osmotic change when one ion equivalent of silver migrates from
one electrode to the other. For this purpose the conditions of the
cell before and after the electrolysis are compared.

If one ion equivalent of silver dissolves in the dilute solution,
the silver concentration is increased by one ion equivalent, but at
the same time some silver also passes from the dilute to the concen-
trated solution. If (1 — n^y be the transference number of the
silver, 1 ^ n^ ion equivalents leave the dilute solution, and the actual

^ See page 70.

ELECTROMOTIVE FORCE 199

increase in the concentration of the latter when one ion equivalent
dissolves is n« ion equivalents. The more concentrated solution
must evidently have its concentration reduced by this amount. A
migration of NOs ions also takes place. If n^ represent the share
of transport for this ion, then n«,NOs ion equivalents pass from the
concentrated to the dilute solution, since the motion is in the direc-
tion opposite to that of the silver ions. Consequently 1 — n« ion
equivalents of silver and the same number of ion equivalents of NO3
move from the concentrated solution to the dilute during the passage
of 96,640 coulombs, i,e. from osmotic pressure P to Pi. The rela-
tion of the osmotic pressures of the anions as well as of the cations

is — . The work is expressed by the equation,

and i, = 2«^lni.

On comparing this equation for the electromotive force in the
case of univalent metals with that obtained above, it is seen that
when n^ = ^, i.e. when the two ions have equal velocities of migra-
tion, the equations become identical. When this is not the case, a
potential-difference exists (see later) at the point of contact between
the solutions, and this requires the application of a correction to the
previous equation ; consequently the formula just derived is more
general in its application. It will be assumed for the present that

Wa = i-
The following formula is the most general one : —

F(v9) = n,n„ijrin-^,

or F = ^iJ!rin~.

(V9) A

Here yq is the quantity of electricity which must flow through
the cell in order to cause n^ mols of the electrolyte to pass from the
concentrated to the dilute solution. The highest valency repre-
sented by the ions in a given case gives the value of v directly. If
zinc chloride be the electrolyte, v =3 2. In the concentration cell,

Tl - TljSO* sol., cone. - ^,804 sol., dilute - Tl,

y is also equal to 2. If the electrolyte be thallium nitrate, v a= 1,

200 A TEXT-BOOK OF ELECTRO-CHEMISTRY

and so on. The number of ions formed from a molecule of the
electrolyte is n^

For dilute solutions the relation between the concentrations may
be used| instead of that between the osmotic pressures.. For ex-
ample, in the cell,

Ag - AgNOa sol., 0.01 (7» - AgNO, sol., 0.001 CJ. - Ag,

the yalue 10 may be substituted for — in the equation, and the

yalue of the electromotive force so obtained should agree closely
with that measured.
Nemst^ measured the electromotiye force of the cell,

Ag - AgNO, sol., 0.1 CL - AgNO, sol., 0.01 CL - Ag,

and found, at 18*" t, f = 0.055 yolt.

From conductiyity measurements, it was calculated that the ratio of
the two concentrations of silver ions, instead of being 1 : 10 was
1 : 8.71. Hence the calculated value of the electromotive force is
as follows: —

F « 0.000198 X 291 log 8.71 = 0.054 volt

In this calculation it was assumed that the transference numbers of
the anion and cation are equal. If the fact that, instead of the two
values being equal, the value of the transference number of the
nitrate ion is 0.53 is taken into consideration, the calculated value
of the electromotive force becomes

F = 0.057 volt

Hence the agreement between the calculated and the experimen-
tally found value is very satisfactory.

The following statements will serve to give a general idea of the
magnitude of the numerical values. Since at 17°, when

til = 2 and n. = 0.5,
,»0:^log|volt8,

it follows, where the concentrations of the ions to be considered are
in the ratio 1 : 10 and the metal univalent, that

F = 0.0575 volt

1 Ztschr. phffs, CKem,, 4, 129 (1889).

ELECTROMOTIVE FORGE 201

If the ratio of the concentrations is increased to 1 : 100 or 1 : 1000,
the value of f becomes twice or three times as great, since f in-
creases in logarithmic ratio.

It may be stated in general, that if a concentration cell inTolving
uniYalent ions possesses an electromotiye force,

F s a X 0.0575,

under the conditions stated above, the ratio of its ion concentra-
tions is,

§.= 10-.

If the ion be other than univalent, the corresponding values must
be divided by the valency. Thus the cell consisting of copper and
copper sulfate solutions, in which the concentrations of the copper
ions are 1 : 10, would give an electromotive force of about one half
that of the corresponding silver concentration celL Measurements
by Moser corroborate this statement.

The equation used above for the calculation of the electromotive
force, which is sometimes known as the Nemst equation, appears to
hold, not only for aqueous solutions, but also for solutions in fused
salts. At least, Gordon ^ has measured the electromotive forces of
different concentration cells of silver nitrate, dissolved in a fused
mixture of potassium and sodium nitrates, at temperatures between
200^ and SO(f t, and found that the values of the electromotive force
calculated by means of the above equation, under the a8SU|nption of
complete dissociation, agree with the values found by experiment
He observed further, that when the concentration of the silver
nitrate was greater than ten per cent, the value found by experiment
was always less than the calculated value. This indicates an appre-
ciably incomplete dissociation at this concentration.

Concentration cells are involved in most electrolytic work, espe-
cially in metal refining and in galvanoplastic work. In these cases
the solution becomes more concentrated about one electrode, and less
concentrated about the other. When the stirring is insufficient, the
electromotive force of the concentration cell which results may be of
a considerable magnitude. Since this force must be overcome by
the electromotive force of the primary current, energy is thus un-
necessarily lost. Furthermore, disturbances due to the decrease in
the ion concentration about the cathode may injure the quality of
the deposition of metal. Concentration cells may even be formed

1 Ztichr.phys, Chem,, S8, 802 (1809).

202 A TEXT-BOOK OF ELECTRO-CHEMISTRY

at one electrode alone when the current is not evenly distributed.
Such cells may make themselyes unpleasantly evident by causing
the metal already deposited to redissolve in places. This is con-
firmed by the following simple experiment: If a dilute layer is
placed above a concentrated layer of stannous chloride solution in a
test tube containing a rod of tin, it will be observed that the part of
the rod in contact with the dilute solution is very soon eaten into,
while crystals of tin separate out on the part in contact with the
concentrated solution. The formation of concentration cells at one
electrode can be prevented by an efficient stirring of the solution.

The fact that standard cells can only be used for small current
densities may now be understood. Because of the slight solubility
of the mercury salts nsed in them, the concentration of the ions is
very small. Moreover, the ions removed from the solution by the
passage of the current are but slowly replaced from the excess of
solid salt. Consequently, the electromotive force of the cell must
decrease when it produces a considerable current. While at the
cathode a state of under saturation is produced, at the anode the
solution becomes slightly supersaturated. When the cell is aUowed
to remain inactive for a time, the concentrations of the solution
about the two electrodes change spontaneously until the original
uniform value is reached. This discussion leads directly to the con-
sideration of a second kind of concentration cells.

6. A type of this kind of concentration cells is represented by the
combination^

Ag — AgNOt sol. — KCl sol. — Ag (covered with Ag CI).

In spite of the apparent differences between this and the cell last
described, the two are entirely analogous. In the calculation of the
electromotive force only the osmotic pressures of the silver ions in
the nitrate solution and in the solution of the silver chloride require
to be taken into account. The potassium chloride is used merely to
increase the conductivity of the silver chloride solution. In practice
a solution of potassium nitrate is inserted between the potassium
chloride and silver nitrate solutions, in order to prevent the forma-
tion of a precipitate. The equation

, ^ 0.0001983 r^^p

holds good.

ilculation of f the ratio

In the calculation of f the ratio -- alone need be known. The

ELECTROMOTIVE FORCE 203

Talae of y in this case is unity. In the nitrate solution the concen-
tration of the silver ions may be known, if a solution of a certain
strength be prepared; for if not very dilute, so that complete
dissociation may be assumed, the degree of dissociation may be
determined. In the case of the solution of silver chloride, the
concentration of silver ions is not so easily ascertained. On account
of the slight solubility of the chloride, it is certainly very small.
By means of the electrical conductivity (page 137), the solubility in
pure water may be determined. It has thus been found that the
saturated silver chloride solution at 26^ is 0.0000144 normal. In
such a dilute solution the salt is doubtless practically all dissociated
into the ions, Ag' and Gl'; moreover, as they are present in equiva-
lent amounts, the solution is 0.0000144 normal in respect to silver or
chlorine ions, and the product of these concentrations is

Ag X CI' = (0.0000144)* = iS"

when S represents the solubility of the salt.

Instead of a pure aqueous solution of silver chloride, that of the
cell also contains potassium chloride. From x>age 202 it is seen that
the product of the concentrations of the ions, divided by the con-
centration of the undissociated molecules, is a constant independent
of the dilution, or,

"p ^«

WfCl

and, since in a saturated solution the undissociated portion must be
considered to remain constant, the same is true also of the product
of the concentrations of the ions, or

When a relatively large amount of potassium chloride is added
to a saturated aqueous silver chloride solution, the number of
chlorine ions is greatly increased, and, in consequence, a certain
amount of undissociated silver chloride must form and be precipi-
tated, since the solution is already saturated with it. If G is the
concentration of the silver ions after the addition, and also that of
the chlorine ions derived from the silver chloride, while Oi is the
concentrfktion of the added chlorine ions, then

and since Ci is very great compared with C, the equation may be
written oi

204 A TEXT-BOOK OF ELECTRO-CHEMISTRY

To obtain the ooncentration of the ion corresponding to the mate-
rial of the electrode, the square of the solubility S of the salt used
is divided by the concentration of the other ion, of which an excess
is added. Supposing a 0.1 normal potassium chloride solution to be
used, Oi for complete dissociation would be 0.1, but since at this
concentration it is only about 85 per cent dissociated, Ci ss 0.086;

and therefore

p^ (0.0000144)'

0.086

Since the osmotic pressures are proportional to the concentrations,
and the silver nitrate is 82 per cent dissociated, when the silver
nitrate solution is 0.1 C«, the following holds for 2S^ t : —

F - 0.000198 X 298 X log ^^^=0.44 Tolt

The corresponding value, experimentally determined by (Goodwin,
is 0.46 volt. The agreement is satisfactory.
The following arrangement is another example of such cells: ^ —

Ag - KNOs sol., sat with AgBrOs 7

Ag - KBrOg soL, sat with AgBrOi 1'

The concentration of the silver ions in the nitrate solution is nearly
the same as in pure water, since the nitrate yields neither Ag nor
BrOg ions, and consequently has but slight influence on the state of
dissociation of the AgBrO^. The concentration of the silver ions la
the potassium bromate solution may be calculated as before, from
the solubility of the silver bromate in water and the concentration
of the BrO, ions added. When the values so obtained are substi-
tuted in the formula,

F = 0.0612 volt for 0.1 0^
and F =s 0.0464 volt for 0.06 C7»

solution of potassium bromate solution. The experimentally deter-
mined magnitudes are 0.0620 and 0.0471. The current, as before,
passes through the cell from the weaker to the more concentrated
solution of silver ions, t.€. from the bromate to the nitrate solution.
Electrodes in which the metal is in contact with one of its diffi-
cultly soluble salts, and also in the presence of a solution of a soluble
salt with the same negative ion, were called by Nemst electrodes of
the second order, or, as regards the negative ions, reversible eleo-

1 ZUchr. phys. Chem,, 18, 677 (1894).

ELECTROMOTIVE FORCE 205

trodes. Ostwald showed that these are not to be distinguished from
metal electrodes in a solution of one of their salts.

c. A third kind of concentration cell consists of those in which
one of the electrolytes is a complex salt. As a type of this class,
the following combination may be given : —

Ag - AgNO, sol. - KCN sol. (+ a little AgCN) - Ag.

In the latter solution the complex salt KAg(CN)| is formed, the
ions being K' and Ag(CN)s '. This negative ion is in turn dissoci-
ated to an extremely slight extent into 2(CN)' and Ag', and it is the
concentration of this latter silver ion which, in this solution, is to
be taken into account in considering the electromotive force of the
cell. It is evidently somewhat dependent upon the quantity of
silver cyanide. Since it is at present impossible to. measure the
concentration of this small quantity of ions in the solution of the
complex salt by an independent method, it is impossible to calculate
the electromotive force of such cells. On the other hand, the meas-
urement of the electromotive force gives a means of calculating the
concentration. This is also true, naturally, of the cell previously
described.

The calculation of the concentration from the measured electromo-
tive force will now be carried out for the parallel case of the cell,^

Hg-HgNO, solution, 0.1 C»- -

Hg — HgsS dissolved in Na,S solution ^1

The value of the electromotive force at 17^ t was found to be 1.262
volts. Hence,

1.262 » 0.000198 x 290 log ^,,

where P and JP may represent either the osmotic pressures, or the
concentrations of the mercury ions in the nitrate and sulfide solu-
tions. Furthermore,

log J = 21.8,

and — = 10 -

Assuming complete dissociation, there are 20 grams of mercury
ions in a liter, or 1 mg. of ion in 0.00006 liter, of the 0.1 normal

1 Behrend, Ztsi^r, phys. C%em., 11, 466 (18d8); w&b9^Zt9chr,ph,y9. Chem.,
15, 495 (1894).

206 A TEXT-BOOK OF ELECTRO-CHEMISTRY

mercurous nitrate solution. This latter number, multiplied by 10*^,
gives the number of liters of the sodium sulphide solution contain*
ing 1 milligram of mercury ions.

A means of determining the solubility of the difficultly soluble
salts, and thereby the ion concentration, has already been found in
the measurement of electrical conductivity. These considerations
furnish, however, a second method far surpassing the first in deli-
cacy. In fact, it is exactly at those extremely low concentrations,
where all other methods are without avail, that the advantages of
this one are most prominent, since the electromotive force becomes
higher the greater the difference in the concentrations. In order to
avoid error, however, what has been said on page 163 in regard to
the capacity of the measuring instruments must be borne in mind.

Extrapolations such as the above ^ into the domain of extremely
small ion concentrations are naturally accompanied with some un-
certainty, since it is tacitly assumed that the regularities which
have been found to exist in the case of ions of moderate concentra-
tion also exist in the case of ions of such small concentrations.
Moreover, that the formation of potential and the activity of such
cells can depend upon such slight concentrations of the metal ions
is scarcely conceivable. It would seem necessary to ascribe an
active part to the complex ions. Nevertheless, as will be shown in
the section on the formation of potential at the electrodes, as long
as it is assumed that the concentrations of the various substances,
including the ions, are always related in a definite manner, and are
in equilibrium with each other according to the law of mass action,
the calculation of the potential is the same whichever the actual
process taking place at the electrode may be. Bearing this in mind,
it may be said that the measured values of the potentials correspond
to the calculated small ion concentrations.

Attention may be called to the following important fact : In the
three cells, —

- Silver — AgNOs solution, 0.1 C^ -,

* Silver — KCl solution, 0.1 C^ saturated with AgCl— i'

2 Silver — AgNOs solution, 0.1 C. - i

* Silver — KBr solution, 0.1 C^ saturated with AgBr.- J.*

o Silver — AgNOj solution, 0.1 C, -— :

' Silver — KI solution, 0.1 C„ saturated with Agl 1 '

1 See the dificussion between Haber, B5dlander, Abegg, and Danneel, Ztsckr,
JBlelaroehem., 10, 403, 604, 607, 609, and 773 (1904).

ELECTROMOTIVE FORCE 207

the electiomotiye force increases from the first to the third
cell.

This is a consequence of the fact that the silver chloride is more
soluble than the bromide, and this in turn more soluble than the
iodide, and of the fact that all three salts are practically completely
dissociated in their saturated solutions. In such cells as these the
electromotive force is greater the less soluble the salt. With the
complex instead of the insoluble salts, as is illustrated by the 0.1
normal potassium cyanide solution, to which some silver cyanide
was added, the electromotive force is the greater the fewer the metal
ions furnished by the salt (in this case silver). If a series of such
cells be arranged in the order of their electromotive forces, begin-
ning with the lowest, the order is also that of the solubility, or of
the decomposition. Each salt in the series will dissolve in, and
will react with, any of the saturated solutions of the cells following
in the series. For example, silver chloride added to the potassium
bromide solution forms silver bromide; silver bromide in the potas-
sium iodide solution forms silver iodide, etc. When silver cyanide
is added to a solution of sodium sulfide, it is changed iuto silver sul-
fide because the electromotive force of the cell,

Silver — AgNOs solution, 0.1 C»- ;

Silver — Na^S solution, 0.1 G^ saturated with Ag^S — I '

is greater than that of the corresponding cyanide cell. On the
other hand, silver sulfide does not dissolve in dilute potassium
cyanide solution. The reason for this is easily seen when it is
remembered that the more insoluble or complex a salt is, the
lower is also the value of the product of the corresponding ions. If
to a saturated silver chloride solution an amount of iodine ions (as
in potassium iodide) be added equal to the chlorine ions present,
silver iodide must precipitate ; otherwise the product of concentra-
tion of the iodine and silver ions woidd be greater than its stable
value. The concentration of the ions must, then, decrease in the
only way possible, t.e. by the precipitation of solid silver iodide. This
precipitation proceeds until the product of the ion concentrations has
reached the constant value corresponding to the saturated silver
iodide solution.

Such an arrangement of concentration cells is given in the follow-
ing table :^ —

lOstwald, Lehrb. der Allg. ChemU If, 1, 882.

208

A TEXT-BOOK OF ELECTRO-CHEMISTRT

BlLTCE NlTBATB, 0.1 Ok AOAIUST

SilTer chloride, in potaaBium chloride of 1 C»

Ammonia, I Cn

Silyer bromide, in potaasiam bromide of 1 C.

Sodium thiosolfate, 1 (7« .

Silver iodide, in potaaaiam iodide of 1 OSi

Potaaaium cyanide eolation

Sodium sulfide, 1 C»

r, IB Volts

0.51
0.54
0.64
0.84
0.91
1.31
1.36

A few drops of silver nitrate solution were added to the solutions
of ammonia^ sodium thiosulfate, and potassium cyanide, respectivelj.

Evidently the order of such a series may be changed by altering
the concentrations of the electrolytes added to the silver salts. This
might be done, for example, by adding a very concentrated solution
of potassium chloride to the silver chloride solution ; the concentra-
tion of the silver ions would thus be reduced below that of the 0.1
normal bromide solution, which contains silver bromide. In this
case the electromotive force of the chloride cell would be greater
than that of the bromide, and even if 0.1 normal potassium bromide
solution be added to the chloride solution, silver bromide would not
be precipitated ; on the other hand, silver bromide coidd be dissolved
in it Similarly, silver sulphide would dissolve in concentrated
potassium cyanide solution.

i/. Finally, a concentration cell, which might also be included
under description a, may be here considered, because of its peculiar
characteristics. Attention was first called to it by Ostwald. A cell
consisting of one hydrogen electrode in an acid solution, and another
in an alkali solution, the two solutions being in contact, is a concen-
tration cell with regard to hydrogen ions. It has already been
learned that water is slightly dissociated into H and OH ions, and
consequently a certain quantity of H ions is present in the alkali
solution. The electromotive force of this ceU is

RT , P

P being the concentration or osmotic pressure of the hydrogen ions
in the acid solution, and Pj that of the ions in the alkali. Suppose
the alkali and acid used to be normal solutions. The concentration
P of the H ions in the acid solution, when the incomplete disso-
ciation is taken into account, is about 0.8, and Pi may be calculated
from the measured electromotive force of the cell. In this case a
considerable potential-difference exists at the surface of contact he-

ELECTROMOTIVE FORCE 209

tween the two solutions, which must be taken into consideration^
since the sum of the potentials at the electrodes alone is desired.
With the correction given by Nemst/ the value of f at 18^ is 0.81
volt; that is,

0.81 = 0.0577 log ^,
or J=10"^

The concentrations of the hydrogen ions are proportional to their
respective osmotic pressures. Then, since

0=0.8,

the value of the concentration of the hydrogen ions in the alkali
solution is as follows : —

(7 = 0.8x10-".

Now according to the law of mass action, the product of the hydro-
gen and hydroxyl ions must, in this case also, give a constant when
divided by the concentration of the undissociated water, or,

^MHl2LC(olOH5 = const.
C(pt H,0)

The concentration of the undissociated water is so great in compari-
son with that of the ions, that it may be considered as a constant.
Consequently, the product of the concentrations of the two ions
must be a constant, or,

0(of H*) X <7(of OH') = const

But the concentration of the hydrogen ions in the alkali solution is

C = 0.8xlO-",

and that of the hydroxyl ions, according to the supposition, is

(7=0.8.
Hence C x C = (0.8)» x 10"".

From this result, the dissociation of water may be directly ascer-
tained, for the product of the concentrations of the hydrogen and
hydroxyl ions in pure water is the same as that of these ions in an
alkali solution. Hence, for pure water,

C(of H-) X (7(of OH') = (O.Sy X 10

^Zuehr, phys. Chem., 14, 1&6 (1894).

k-14

210 A TEXT-BOOK OF ELECTRO-CHEMISTRY

But, in this case, the concentration of the two ions is the sama
Theref ore^ if O represents this concentration^

0»=.(0.8)«xlO-",
or C7=s 0.8 X 10-'.

In other words, pure water is 0.8 x 10~' normal with respect to its
hydrogen or hjdroxyl ions. The conductivity measurements of
Kohlrausch gave 0.75 x 10^'. This is a very remarkable agreement,
and its significance is made greater by the fact that other methods
for reaching the same end, as through the study of the hydrolysis
of salts and the saponifying effect of water, have led to very nearly
the same value.

Oxygen electrodes may be used instead of hydrogen, and the cell
still have the same electromotive force, because the concentrations
of the hydrogen ions in the two solutions are in the same relation to
each other as those of the corresponding hydroxyl ions. This fol-
lows from the fact that the product of the concentrations of the H
and OH ions of the solutions in the cell is a constant. The fact
that the platinum does not absorb oxygen as readily as it does hydro-
gen, and that it reaches a state of equilibrium with the surrounding
gas more slowly, makes it more difficult to obtain constant results.
In both cases, die current flows through the cell from the alkali to
the acid solution.

It may be repeated here that, except for the potential-difference
existing between the solutions at their point of contact, the electro-
motive force of such cells does not depend upon the nature of the
negative ion of the acid, nor upon the positive ion of the alkalL On
the other hand, when acids of the same molecular concentrations
are used, the degree of dissociation comes into play. The cell

Hydrogen — Acetic acid solution ;

Hydrogen ^ Potassium hydroxide solution- !

would exhibit a lower electromotive force than the cell of correspond-
ing concentrations,

Hydrogen — Hydrochloric acid solution —
Hydrogen — Potassium hydroxide solution-

!•

The slightly dissociated acetic acid contains less hydrogen ions than
the highly dissociated hydrochloric acid ; consequently in the latter
cell the difference in concentration between the hydrogen ions of the
acid and alkali solutions is greater than in the former, and there-

ELECTROMOTIVE FORCE 211

fore its electromotive force is also greater. That the same consid-
erations apply to bases may be safely concluded from the measure-
ments which have already been made in that direction.

3. Concentration Donble-Cells. — Another kind of concentration
cell may be formed by combining two simple cells into a double-
cell. The so-called calomel cell, which is veiy often used, serves as
a type of such a double-celL Its combination is as follows : —

Zn — ZnCls solution, cone. 1

„ yHgCl solution, sat. !

\HgCl solution, sat ,

Zn — ZnClj solution, dil I

The mercurous chloride is in excess, and covers the mercury.
This cell differs from the simple cell,

Zn — ZnCls solution, cone. -~ ZnGl^ solution, dil. -^ Zn,

in having the combination, —

HgCl - Hg - HgCl,

between its two differently concentrated solutions of zinc chloride.
Consequently, the processes of electrolysis and the electromotive
forces of such double-cells differ from those of the simpler cells. In
the case of the simple cell, when 2^ coulombs of electricity pass,
there is a migration of zinc and chlorine ions from one solution to the
other, and a simultaneous solution and precipitation of two equiva-
lents of zinc at the electrodes. In the calomel concentration cell such
a migration cannot occur. When 2 q coidombs pass through this cell,
two equivalents of zinc dissolve in the dilute chloride solution, and
two of mercury separate from the mercurous chloride. Here the
current always passes from the dilute to the concentrated solution
within the cell. The mercury ions come from the dissolved mercu-
rous chloride, and those precipitated are immediately replaced by
the further solution of mercurous chloride. In the concentrated
solution, on the other hand, two equivalents of zinc separate at the
electrode, and two of mercury are dissolved. It must be borne in
mind that when two equivalents of metallic mercury have been pro-
duced from the solid mercurous chloride in the dilute solution, two
equivalents of chlorine ions have also been formed ; and when two
equivalents of metallic mercury have changed to mercurous chloride
in the concentrated solution at the same time, two of chlorine ions
have disappeared. When the quantities of the solutions are imag-

212 A TEXT-BOOK OF ELECTRO-CHEMISTRY

ined so great that these changes take place without sensible influ-
ence on the concentration, the processes may be summarized as
follows : Two equivalents of zinc and two of chlorine — that is, one
mol of zinc chloride — have been transferred from the concentrated
solution to the dilute, while the quantity of mercury and of mercu-
rous chloride remains unaltered. If the osmotic pressure of the
zinc ions in the concentrated solution be P, and in the dilute solu-
tion P], then the corresponding osmotic pressures of the chlorine
ions are 2 P and 2 Pj. The maximum osmotic work is easily calcu-
latedi and is given by the equation,

Tr^ = 5rin§ + 2Brhi|4=3JKrhi§.
Pi 2 P| Pi

The electrical energy is 2 fq, therefore

2 2q Pi
In general, p««i:^lnj,

where n^ is the number of ions formed from one molecule of the
electrolyte, and y the number of electrochemical units 3 required
to transfer one mol of the electrolyte from the concentrated to the
dilute solution. It is evident from a comparison of this equation
with that given on page 199 that here we have another method for
the calculation of the transference numbers of an electrolyte.

From the formula it may be seen that only the ratio -p , n^ and

V have influence on the value of the electromotive force v. As
Ostwald predicted, and as Ooodwin ^ experimentally demonstrated,
it follows that : —

1. The mercurous chloride and mercury of the calomel cell may
be replaced by silver chloride and silver without altering the electro-
motive force.

2. Instead of zinc chloride, zinc bromide or iodide may be used
when the depolarizer" is a difiicultly soluble bromide or iodide,
without changing the electromotive force.

3. The electromotive force of the cell will not be changed if cad-
mium chloride and cadmium be substituted for zinc chloride and zinc.

^Zt$ehr,phy8. Cftem., 18, 677 (1894).

* The difficultly soluble salt is here called a depolarizer, because, through its
presence, the electrode is made unpolarizable for small conents.

ELECTROMOTIVE FORCE

213

4 If the zinc and zinc chloride be replaced by thallium and thal-
lium chloride, the electromotive force will be considerably increased.

5. If instead of the chloride of zinc, the sulfate be used, with a
difficultly soluble sulfate as depolarizer, the electromotiye force
will be less than before. Whether lead or mercurous sulfate be
used as depolarizer can make no difference. The accompanying^
tables confirm these statements. For the sake of breviiy the cells
are designated by their soluble salts and depolarizers.

ZnCl, - HgCl and ZnClj - AgCl Cells at 25 "*

COHOnrTBATIOH

Obmkvbd E. M. F.

Obsbbybd E. M. F.

Cavouiated

OF THS ZnClf

or ZnCls - HgCl

OF ZnCl^ - AgCl

B. M. F. nr Voltb

0.2 -0.01

0.0787

0.0767

0.0797

0.1 -0.01

0.0800

0.0780

0.0818

0.02 - 0.002

0.0643

0.0848

0.0844

0.01 - 0.001

0.0861

0.0847

0.0868

Considering the experimental errors of 1 to 2 thousandths of a volt,
the agreement is very satisfactory.

ZnBr, - HgBr and ZnBr, - AgBr Cells

CONCBVTSATION OF

Obsketxd E. M. F.

OBSmysD £. M. F.

Oaloulatbd

THS ZnBrs

OF ZnBra - HgBr

OF ZnBr, - AgBr

E. M. F. or YoLis

0.2 -0.02

0.0703

0.0793

0.0797

0.1 -0.01

0.0808

0.0802

0.0818

0.02-0.002 •

0.0860

0.0862

0.01 - 0.001

0.0863

0.0868

Through replacement of zinc and its chloride by cadmium and
cadmium chloride, the value of the electromotive force could not be
calculated, the concentration of the cadmium ions not being deter-
minable with exactness (by the conductivity method). This is ex-
plained by the fact that CdCls dissociates not only into Gd" and CI',
CI', but probably also, in concentrated solutions, into CdCl' and Gl'.
In dilute solutions, where only the former dissociation is consider-
able, the values calculated agree with those experimentally found.

214

A TEXT-BOOK OF ELECTBO-CHEMISTBT

TlCl - HgCl fJftllB

ofthbTIGI

Obabktsd
E.M.F.

Oalouiatid
E. M. F.

0.0161 - 0.00161
0.008 -0.0008
0.0161 - 0.008

0.102
0.100
0.0828

0.114
0.116
0.038

The ezperimental errors in this case are greater than those in the
two previous tables.

IV
ZnS04 - PbSO* Cells

OONOBHTBATIOV
OF Tn ZDBO4

Obustbd
S.M.F.

OALOVLAnV

S.1LF.

0.2 -0.02
0.1 -0.001
0.02 - 0.002

0.0427
0.0440
0.0622

0.0468
0.0471
0.0600

ZnS04 - HgjSO* CeUs

OONOSHTKATIOir

OF ma Z11BO4

OBMBTin

E.M.F.

Oalovlatbd
E.M.F.

0.2 - 0.02
0.1 - 0.01

0.047 - 0.084
0.046 - 0.038

0.046
0.047

The formula

F= — In^

V Q Pi

is only applicable when the solubility of the depolarizer is inappre-
ciable. If, for example, the difiicultly soluble mercurous chloride
of the calomel cell be replaced by the comparatively easily soluble
thallium chloride, it must be taken into account that the concentra-
tions of the zinc and the chlorine ions are no longer in the same re-
lation. Chlorine ions from the thallium chloride are thus added to

ELECTROMOTIVE FORCE 215

those of the zinc chloride, and from the law of mass action the prod-
uct of the ion concentrations of the thallium and chlorine in the
saturated thallium chloride solution is constant, and more chlorine
ions must enter the dilute than the concentrated zinc chloride solu-
tion. From this consideration, taking into account the previous
deduction, P and Pi being the osmotic pressures or the concentra-
tions of the zinc ions, and P* and Pi those of the chlorine ions,

2FS=jBrin^ + 2 5Tln^.

In general, vfq = n^RT In ^ +n/ RTln :^,

A Pi'

where Ui and n^ represent the number of cations and anions which
the molecule of the electrolyte produces, and v the number of q units
corresponding to the transference of one molecule of the electrolyte
from the concentrated to the dilute solution.

The electromotive force of the cell may also be calculated from
the electrolytic solution pressures of the two metals coming into con-
sideration (in the calomel cell, the zinc and mercury). In this case
the electromotive force of the cell consists of four potential-differ-
ences, existing at the four points of contact between metal and
liquid. If Pzn and Ph^ represent the solution pressures of the zinc
and mercury respectively, and P, Pi, P', and Pi' the concentrations
of the zinc and mercury ions in the concentrated and in the dilute
solutions, while Vzn and Yhii are the valencies of the metals, then
taking into consideration the fact that the current passes through the
cell from the dilute to the concentrated solution, the electromotive
force is represented by the following equation : —

P = ^fAln]^ + -Lln^ + _lln^+JLlnZV
8 \Vza A Vh^ Phi ^Hg P' V«n PW

This may be shortened to the form

Equations (1) and (2) lead to the same result, in spite of their

216 A TEXT-BOOK OF ELECTRO-CHEMISTRY

apparent difference. In (1) ----represents the concentration relation

of all the negative ions of the solutions, while in (2) -pf represents

that of the cations of the depolarizer. It must be remembered that
saturated solutions of the depolarizer are being considered; conse-
quently the product of the concentrations of all the anions and cat-
ions of the depolarizer is a constant (the anions of the electrolyte
and depolarizer being always alike, as in the case of ZnCl^ and
HgCl). The separate concentrations are also in a definite relation
to each other. When, for instance, the cations and anions are of the
same valency, as in the example, their different concentrations in
the solutions are inversely proportional to each other. If the anion
be bivalent and the cation univalent, the concentration of the latter
is inversely proportional to the square of that of the former, and so
on. This explains the agreement of the two equations.

TTse of the Electrometer as an Indicator in Titration. — After the
explanation of the above concentration cells, the interesting use of
the electrometer as an indicator will be easily understood. In order
to illustrate this application, consider the concentration cell

Ag - AgNO, sol., 0.1 CL- AgNO, sol., 0.1 C7. - Ag,

the electromotive force of which is equal to zero. If to one of the
two solutions potassium chloride is added, the difficultly soluble
precipitate, silver chloride, is formed, the concentration of the silver
ions is decreased, and an electromotive force is produced in the cell.
As more potassium chloride is added, the electromotive force of the
cell increases, at first slowly, then faster and faster until a sudden
change takes place, and then slowly again. This behavior may be
at once understood from a consideration of the equation,

F = 0.0675 log J,

in which P and P represent the two concentrations of the silver
ions. If, for example, while P is maintained constant the value of
P is decreased to one hundredth of its original value, the electro-
motive force becomes

F = 2 X 0.0576 volt

In order to produce this decrease in concentration, it would be
necessary to add to 1000 cubic centimeters of the 0.1 normal solu-
tion of silver nitrate about 980 cubic centimeters of a 0.1 normal
solution of potassium chloride, if both solutions are completely dis-

ELECTROMOTIVE FORCE 217

sociated. The new value of P' may be decreased to one hundredth
of its value by the further addition of 19.8 cubic centimeters, and
the value of JP so obtained may be decreased to the same extent by
the addition of 0.198 cubic centimeter of 0.1 normal potassium
chloride solution, etc. With each successive decrease in the value
of P'; the electromotive force of the cell is increased by 2 x 0.0575
volt. As follows from what has just been stated, the greatest
change of the electromotive force with the addition of the potas-
sium chloride solution occurs when the last portion of silver nitrate
disappears, or, better expressed, when the concentrations of the
silver and of the chlorine ions are nearly equal. The increase of
the electromotive force with further additions of potassium chloride
is very slight, being due to the decrease of the silver ions by the
ma8S4U3tion effect of the added chlorine ion& When the original
concentration of the silver is known, this method may also be used
for the determination of the halogens.^ With the aid of two hydro-
gen electrodes it may be used in acid and alkali titrations.'

LIQUID CELLS

It has already been stated in the consideration of the concentra-
tion cells that potential-differences occur at the points of contact
between the solutions. This assumption has been entertained a
long time, but a clear conception of the origin of such potentials
did not exist. The Becquerel acid-alkali cell is well known ; two
platinum electrodes connected together are placed one into acid
and the other into alkali solution. That in the acid becomes posi-
tively, and the other negatively, charged ; the potential-difference,
varying with the conditions, often amounts to more than 0.6 volt.
Formerly the source of this electrical energy was erroneously
thought to be in the heat generated by the neutralization of the
acid and alkali. As previously explained, this is practically a con-
centration cell. Oxygen of the air is present at the two electrodes,
and in the acid solution there are few, while in the alkali there are
many, OH ions. Since the electrodes are of ordinary platinum
instead of being coated with platinum black, it is easily explicable
that the electromotive force of such a cell is variable. Ordinary
platinum does not absorb oxygen to a very great extent, so that the
condition of equilibrium which should be established, in which the
concentration of the oxygen dissolved in the platinum corresponds

1 Ztsehr. phya. Chem,, 11, 466 (1808).
* Ztschr.phys. C%em., M, 268 (1897).

218 A TEXT-BOOK OF ELECTRO-CHEMISTRY

to the pressure of the sorrounding oxygen, as in the case of plati-
nized platinum, is practically unrealizable; consequently the cell
has an uncertain and varying value. This cell cannot generate a
perceptible current, because the quantity of oxygen absorbed by
the electrodes is very small, and, being exhausted, is replaced by
that of the air only very slowly. The presence of other gases, such
as hydrogen, also has an influence upon the electromotive force of
this cell.

We are indebted to Nemst^ for satisfactory explanations of the
phenomena of these liquid cells, their theory having been developed
by him. If a solution of hydrochloric acid, for example, be placed
in contact with a more dilute solution or with pure water, the acid
will diffuse into the water. The hydrogen and chlorine ions of the
acid are, to a certain extent, independent particles capable of mov-
ing with different velocities from places of higher osmotic pressure
to those of lower. Since the hydrogen ions migrate more rapidly
than those of chlorine, the foremost of the diffusing ions are hydro-
gen, and since these possess positive charges, the water or the dilute
solution as a whole exhibits a positive, and the stronger solution a
negative, charge. Owing to the mutual attraction of the positive
and negative charges of the hydrogen and chlorine ions, this sepa-
rating process does not actually take place to any measurable extent,
the hydrogen ions are delayed, and the chlorine ions increase their
speed, so that a condition is reached in which both migrate at the
same rate. The electrostatic attraction, as well as the potential
difference between the solutions, exists until both solutions are
homogeneous.

The unequal velocities of migration ofihe ions are therefore the cause
of the potentiaMifferences at the contact surfou^es of differently concenr
trated solutions^

If the negative ions have the greater velocity of migration, the
more dilute solution will evidently be negative to the concentrated.
In other words, the dilute solution always presents the electricity of the
more rapidly moving ion.

Moreover, it is thus not only possible to foresee the nature of
the potential-difference at the point of contact between two liquids,
but also in many cases quantitatively to calculate the magnitude
of such potential-differences, and to prove the calculations by actual
experiment. To illustrate this point, two differently concentrated
solutions of an electrolyte, consisting of two univalent ions, may
be imagined in contact Let (1 — n«) be the share of the transport

^ Ztsehr.phys, (Jhem,, 4, 129 (1880).

ELECTROMOTIVE FORCE 219

of the positiye ion, and consequently n« that of the negative. The
quantity of electricity q is now conducted through the solutions from
the con<:e7itr(Ued to the dilute, then (1 — n.) positive gram-ions pass from
the concentrated into the dilute, and at the same time n. negative
gram-ions from the dilute into the concentrated solution. Let P
represent the concentration of the positive and negative ions in
the concentrated solution, and Pi the same in the dilute solution.
The maximum work, the process being completed osmotically, is

Tr= (1 - n.) ijrin|. - n. Urin ^

or Tr=(l-2n.)iJ!nn^

or if n. be replaced by — ^a — jj^ being the velocity of migration of

Ue + u. •" ^

the positive, and v^ that of the negative, ions,

Ue + U. Pi

Consequentiy f = H<liL2. :^ln^, (a)

because fq s W.

If Vc be greater than u., the electric current passes from the con-
centrated to the dilute solution in the cell itself ; if u« be greater
than Vc the current passes in the opposite direction. If, finally,
Ue = u«> 110 potential-difference exists between the solutions, and
consequently there is no current.

Nemst constructed such liquid cells so that the potential ob-
served was only that appearing at the point of contact of two solu-
tions, and compared the experimentally determined values of the
electromotive force with those calculated from the equation derived
above. The following arrangement was used : —

Hg-KCl solution, 0.1 0^ sat with HgCl ;

, KC1,0.01 0., ^ ^

-HC1,0.01 O^-- ;

HCl, 0.1 C«- •

-KOI solution, 0.1 Cn, sat with HgCl — Hg.

Since the two ends are identical, the potential-differences occurring
there neutralize each other, and therefore only those differences at
the four contact points 1, 2, 3, and 4 are to be taken into account.

220 A TEXT-BOOK OF ELECTRO-€HEMISTRY

It is to be observed that, as far as experience has gone, the rule
holds also for liquid cells that (yrdy the ratio, not the absoLuU valves of
the osmotic pressures, comes irUo consideration, (Nemst's principle of
superposition. Each system may be imagined to be formed from
the others by means of n-fold superposition.) Therefore the poten-
tial-difference of 2 is equal and oppositely directed to that of 4.
Thus the potential-differences at 1 and 3 alone remain, and may be
calculated from the above formula. If u^ and'u'. are the velocities
of migration of the potassium and chlorine ions respectively, while
Tx''e and u' « (= u « because the negative ions are the same) are the
migration velocities of the hydrogen and chlorine ions, then the sum
of the potential-differences is represented by

U'e + U'. Q P^V", + V\ 9 P/

and as

P ^P
P, P,"

therefore ^^(<-< ^^''c-rj".\BT^P.

P and Pi are the osmotic pressures or concentrations of the po-
tassium and chlorine ions in the concentrated and dilute potassium
chloride solutions, P' and P/ the corresponding values of the hydro-
gen and chlorine ions in the corresponding hydrochloric acid solu-
tions. The actual measured potential-difference was —0.0357 volt.
The negative sign is used, since the current in the cell flows in the
direction 4 to 1, and since, in the calculation, it has been considered
positive when it passed from the concentrated to the dilute potas-
sium chloride solution. The potential-difference resulting from cal-
culation by the formula, taking into consideration the incomplete
dissociation of the substances, differs from the above by about four
to five per cent.

The equation (a) only permits of calculation of the potential-dif-
ference at the points of contact of two differently concentrated
solutions of one and the same binary electrolyte. If it is desired to
make it applicable to electrolytes whose ions have different valen-
cies, it takes the form

T representing the valence of the positive and y' that of the nega-
tive ion.

ELECTROMOTIVE FORCE 221

If two different electrolytes are in contact, as, for instance,
potassium chloride and hydrochloric acid, the calculation is more
difficult. Only for the case in which the total concentration of ions
in each of the two solutions is the same, the following simple ex-
pression holds : —

, = ^lnH;^±4-, (c)

where v'c and u « are the migration rates of the ions of one electro-
lyte, u"e and v"a those of the other. The electromotive force is here
independent of the ratio of the concentrations.

The calculation is still more difficult when one of the electrolytes
contains polyvalent ions. If all the ions of the two solutions of
binary electrolytes are polyvalent and of the same valency, then
when the ion concentrations are the same,

VQ U"c-hu'a

It is worthy of special attention that in general there can be no
arrangement of solutions in an electromotive series such as Yolta
formed for the inetals. This is evident from the fact, already men-
tioned, that such solution cells as the one measured by Nemst (see
pages 219 and 220) produce a current. A circuit
consisting of metals only, at a common tempera-
ture, does not generate an electric current. If,
on the other hand, the solutions of the above
cell, without the mercury and the mercurous
chloride, be arranged in a circuit as shown in
Figure 45, an electric current is obtained whose
electromotive force is that previously calculated. FroTtf

The existence of this current may be demon-
strated by its power of induction, and it lasts until the concentra-
tion of the various ions is the same throughout the system.

The law of electromotive series applies only to differently concen-
trated solutions of the same electrolyte in juxtaposition. That it
holds in this case may be shown by adding the potential-differences
occurring at the different points of contact, and comparing the sum
with the potential-difference actually observed between the first and
last solutions placed directly in contact. The intermediate members
of the series are thus shown to play no part.

In considering concentration cells, siibh conditions were usually
chosen that the potential-differences occurring at the contact points

222 A TEXT-BOOK OF ELECTRO-CHEMISTRY

of the solutions were negligible.^ Under such circumstances the elec-
tromotive force as previously given^for a cell in which the metal
electrodes dip into the two differently concentrated solutions of the
salt, is

va Pi

This equation was obtained by adding the potential-differences exist-
ing at the electrodes — that is, with the application of the idea of
electrolytic solution pressure. In the addition the solution pres-
sures were cancelled from the equation, as they have the same value
for the two similar electrodes and are oppositely directed.

It was also found possible to obtain the value of f, without any
assumption of solution pressure, by the so^^alled purely energetic
method. It was only necessary to take into account the condition
of the system before and after the passage of a certain quantity of
electricity, without attempting to understand why a potential-differ-
ence and electric current are manifested. The maximum work
obtainable osmotically by the change of the system from its original
to its ultimate state is calculated, and this maximum is considered
as the equivalent of the electrical energy obtainable from the process.
The values of f calculated in both ways agreed without exception.

It remains to be seen whether, when a potential-difference occurs
at the point of contact of the liquids, the two methods of calculation
still yield the same result. For this purpose, the following concen-
tration cell is selected : —

Zinc — ZnCls solution, concentrated •

Zinc — ZnCl, solution, dilute- r

1. Calculation ofv by means of the electrolytic solution pressure.

The electromotive force of the cell consists of three potential-
differences, namely, the two at the electrodes and that at the point of
contact between the two liquids. The sum of the first two is

Fj -h F, = F^i+j) = -::;7- In — J

RT. P

where Pand P^ are the osmotic pressures of the zinc ions in the con-
centrated and dilute solutions, respectively, the corresponding pres-
sures of the chlorine ions being 2 P and 2 P^.

1 For a description of a means for attaining this end, see Ztschr. phys. CT^em.,
14, 146 (1897).

ELECTROMOTIVE FORCE 228

The third potential-difference is calculated according to the
formula (b), and is

2 IBT.P

irheie v, and t;, are the yelocities of migration of the zinc and
chlorine ions. The stun of Fd^.^ and r, is

or if the transportation ratios are introduced, n^ ss — H2 —

u ^. + u«

andl-n« = — -^,

and 'a+w, = |^*ijrinj^.

F3 must be subtracted from v^+t) as indicated, since the calculation
of F, presupposes the direction of the« positive current from the con-
centrated to the dilute solution 'within the cell, while with f^i^s) the
current passes in the opposite direction.

2. CalculaHon of f by meaTia of the principles of energetics. The
process is exactly that outlined on page 198. If 2 q be allowed to
pass through the cell, an ion-mol of zinc passes into the dilute, while
the same quantity is deposited from the concentrated, solution. In
addition, the quantity (1 — n^) ion-mols of zinc passes from the dilute
to the concentrated solution, (1 — na) being the transference share of
the zinc ions. The dilute solution is now richer by n. ion-mols of zinc,
while the concentrated one has lost this amount. Simultaneously,
however, an amount of chlorine ions equivalent to the n^ zinc ions
has also passed from the concentrated to the dilute solution ; conse-
quently the quantity n^ ion-mols of zinc and its equivalent of chlorine
ions have been moved from the concentrated to the dilute solution.
The maximum osmotic work corresponding to the zinc ions is

TF'=n.-Brin^,

and since there are two chlorine ions to each zinc ion, it has for the
chlorine ions the value

W=2naBT In^,
or, added together, W^ 3 n. iJT In ^.

224 A TEXT-BOOK OF ELECTRO-CHEMISTRY

The electrical energy is 2 f^^ and therefore

which is the same as the equation derived aboye.

This agreement in the methods gives also a method for determin-
ing the magnitude of potential-differences at the contact points of
liquids. It is only necessary to calculate, as above, the sum of the
potential-differences occurring at the two electrodes, and subtract it
from the actually measured electromotive force of the whole cell, to
obtain the desired value.

Finally, it should also be mentioned that the electromotive force
of concentration cells may also be calculated by means of an appli-
cation of the principles of energetics to processes other than the
osmotic process used in this book. For instance, the process of
isothermal distillation, first used by Helmholtz,^ is well adapted to
the calculation of the electromotive forces of concentration cells.
In making use of this process, a knowledge of the vapor pressures of
the differently concentrated solutions is essential.

On the whole, the process involving osmotic pressures is to be
preferred in the case of dilute solutions because the requisite knowl-
edge of the osmotic pressure, or the proportional concentration of the
ions, is readily available.

GENERAL CONSIDERATION OP CONCENTRATION AND

LIQUID CELLS

All the cells thus far described have the common characteristic
that their electriooU energy is not generated Jrom chemical energy. In
every case there was simply a passage of material from a higher
to a lower pressure, and whether it be gas or a dissolved substance
which undergoes this change, the process does not affect the internal
energy. The work done does not therefore come from the internal
energy, but is derived from the heat of the surroundings. Conse-
quently the galvanic ceUa thus far considered are ready machines for
transforming the heat of their surroundings into electrical energy.

According to the generally applicable formula of Helmholtz (see
page 173),

1 Wied. Ann,, 8, 201 (1878), and 14, 61 (1881).

ELECTROMOTIVE FORCE 225

In the present case Q, the heat generated by the chemical reaction,
is zero ; therefore

FQ = Qr^: orl = ^; and f= T^.
- - dT' T dT' dT

This, on integration, gives

In F = In !r+ Ic or ^= k.

The change of the electromotiye force of these cells with the tem-
perature is determined by the relation existing between the electro-
motive force and the corresponding absolute temperature. The
electromotive force itself is proportional to the absolute tempern-
ture. When in activity, the cell cools itself and takes up heat from
the surroundings.

The same conclusions are reached on proceeding in still another
way. The electromotive force of one of the previously mentioned
concentration or liquid cells is, in general,

, = »^ln£, («)

from which \^x^\a~. (b)

On differentiatioa irith respect to T

^^x^ln^ (c)

dT q Pi ^^

is .obtained, if x and In ~ for '< ideal '' solutions are considered as

practically independent of the temperature.
By combination of (&) and (c),

F ^dw

T'^dT
is again obtained.

It will be well to bear in mind that the electromotive force is only
correctly calculable by this method when the solutions are so dilute
that the laws of gases are applicable, for it is upon this assumption
that the maximum work is estimated. As a matter of fact solutions
are often used which, on being mixed, generate considerable quanti-
ties of heat, and are therefore far from being ideal solutions. For

226 A TEXT-BOOK OF ELECTRO-CHEMISTRY

such solutions the Q of Helmholtz's formula is evidently not zero^

and the lelation,

F dv

T^dT
no longer holds good.

It is, then, to be noticed that the Helmholtz equation in its aboTe
form applies only when the chemical process resulting from the
passage of a definite quantity of electricity is not a function of the
temperature. This is, however, not the case for most concentration
or liquid cells, since the transference number n^ and, among other
properties, also the valence v, is a function of the temperature. For
this reason, the quantity x which appears in the second equation
derived cannot be considered as independent of the temperature. In
agreement with these considerations it is found that the electro-
motive force of such cells in general is not at all proportional to the
absolute temperature.

In still another respect the application of the Helmholtz equation
is of interest. G-enerally the electromotive force of a cell cannot, as
has often been emphasized, be calculated from the value of its heat
effect alone. In the following case, however, the electromotive force
can be so calculated, or, more strictly speaking, the value of

dF
dT'

which, together with the value of Q, must be known in order to cal-
culate F, may, in the case of many concentration cells, be calculated
directly from the value of Q. This has been shown by van't Hoff,
Cohen, and Bredig.^
Consider the concentration cell,

Hg, HgsSOf, solid, — Na^SOf, saturated ,

Hg, Hg,S04, solid - NajSO^, 0.26 O,- 1'

It is evident that the electromotive force of this cell will be equal
to zero at the temperature at which the saturated solution of sodium
sulfate is 0.25 normal. If at this temperature, which is — 16.2^ f, a
current be allowed to pass through the cell, sodium sulfate goes

1 ZUchr. phys. Chem., 16, 463 (1805). As has been mentioned by Nemst,
here also the modified Helmholtz equation,

Jp Qvdng _. Fa — ^
dT nJiT T

must be used beoanse of the variability of n«.

ELECTROMOTIVE FORCE 227

into solution on one side and separates on the other. The value of
Q is easily calculated from the heats of solution and dilution of the
salt. The following form of the Helmholtz equation may now be
applied : —

dF\ ^ _ Q.

If this value of ;r^be multiplied by 16.2^^ the preliminary value

of F at O^f is obtained. With the aid of this value and the exact
value of Q at 0^ ty the value of

may be calculated. If, f urther, the average of the two values

(^\ and m

be multiplied by 16.2, a more accurate value of f at zero is obtained.
By a repetition of this calculation the value of f at 0**t becomes
more and more nearly correct. The value of the electromotive force
obtained experimentolly agrees well with the value calculated in
this manner.

It is especially evident from this example that it is not in harmony
with fact to consider the heat of solution, or of dilution, etc., exclu-
sively as the source of the electrical energy, for, at —16.2^ for
example, the heat of solution of sodium sulfate is very great, while
the electrical energy is equal to zero. On the other hand, there is a
close relation between the temperature coefficient of the electro-
motive force and the heat of solution. This appears accountable
when it is considered that the heat of solution is closely related to
the temperature coefficient of the logarithm of the concentration, and
that the electromotive force depends upon the latter value.

In the concentration cell,

Hydrogen in platinum black — alkali solution ,

Hydrogen in platinum black — acid solution **^

the electromotive force depends principally upon the difference
between the concentrations of the hydrogen ions in the two solutions.
When the cell is in operation, the neutralization of acid and base
takes place, not at the point of contact of the two solutions, but at
the electrodes. The electromotive force of this cell can be calculated

228 A TEXT-BOOK OF £L£GTRO-CH£MISTBY

from the heat effect of the process, ue. the heat of neatralization,
only with the aid of its temperature coefficient.

THERMOELECTRIC CELLS — THE ELECTROMOTIVE SERIES

In connection with the foregoing a few words may well be devoted
to thermoelectric cells. Heat is here subjected to a transformation
into electrical energy caused by a difference of temperature. On
the other hand, in the concentration cells heat at a constant tem-
perature is changed into electricity, accompanied by the simultaneous
passage of a substance from a higher to a lower concentration. This
cannot be considered as contrary to the second law of thermody-
namics, because, according to this law, it is only in a cyclical process
that no heat at constant temperature can be changed into work. In
other processes such a transformation may well occur.

The potential-difference at one electrode may be expressed by the
equation,

va p

and is accordingly proportional to the absolute temperatura The

arrangement

Zn — ZnS04 solution, — Zn

will produce no electrical energy at constant temperature, since the
two potential-differences of such a cell are equal and oppositely
directed. But if one of the contact points between electrode and
solution be warmed, the corresponding potential-difference changes
and an electric current is produced. As the potential-difference at
the point of contact between two solutions is also proportional to the
absolute temperature, it is immediately clear that the following
cyclical arrangement should produce an electric current:

Solution Ci at Ti — Solution C, at li -

Solution Ci at T, - Solution C, at T, - !'

Here Oi and Q represent the concentrations of the solutions.
Since the osmotic pressure^ the solution pressurCy and transference
numbers are functions of the temperature, the electromotive force of
a thermoelectric cell cannot be calculated in a simple manner. For
further considerations of this point the reader is referred to the
original work of Nernst,* in which this theory was first developed.

Another kind of thermoelectric cell is that discovered by Seebeck

1 Ztschr.phya. Chem., 4, 160 (1889).

ELECTROMOTIVE FORCE 229

in the year 1821^ in whicli only conductors of the first class enter.
The following arrangement represents such a cell : —

First metal at Ti — Second metal at T^-
First metal at T^ — Second metal at T^

These cells are of special importance since by means of them the
numerical values of the potential-differences between the metals
may be determined.

Since a thermoelectric cell generates an electric current only by
the change of heat into electrical energy^ the equation given on
page 225 applies : —

T dT' dt

and this applies equally well to the combination as a whole as to
the individual potential-differences, since a cell can always be con-
ceived in which there exists only the potential-difference considered.
It is, therefore, only necessary to know the change of the potential-
difference with the temperature [ ;=^] at the point of contact be-
tween two metals, in order to be able to calculate f, or the potential-
difference at the temperature T. The value of -— may be directly

obtained from the electromotive force of a thermoelectric cell con-
sisting of the two metals in question, the temperature at one contact
point being 2\ and that at the other T-^-dT. If the temperature
T is common throughout, the electromotive force is zero, as the
two potential-differences are equal and opposite. It is only because
one of the potential-differences may be changed by a temperature
change that the electromotive force assumes a certain value, namely,
that of the alteration in the potential-difference. From the formula
it is evident that if dT is unity, the electromotive force of the cell is
Tdv.

The values of f, calculated for pairs consisting of the most widely
differing metals at the ordinary temperature, are very small, and
amount, even in exceptional cases, to but a few hundredths of a volt.
In the preparation of thermoelectric piles the latter metals or alloys
are especially valuable. A notably high electromotive force, namely,
from 0.2 to 0.3 of a volt, results from the combination,

Copper sulfide — Copper,

if the point of contact is heated to about 500^ t

230 A TEXT-BOOK OF ELECTRO-CHEMISTRY

It may be wondered whether or not it would be possible to pro-
duce electrical energy commercially by means of thermoelectric
piles instead of steam engines. In each case, the process which
furnishes the energy is the passage of heat from a higher to a lower
temperature. The maximum efficiency may, in each case, be calcu-
lated in the same manner with the aid of the second law of ener-
getics. The pile equals the steam engine in simplicity and excels
it especially in that it may operate through a greater temperature
difference. As a matter of fact, there is a possibility of making
such a change from the steam engine to the thermoelectric pile,
eyen if at present it is not feasible because of the expense of con-
struction, of the great loss of heat by conduction, and of the con-
sumption of a part of the electrical energy produced (which means
that the quantity of work obtainable from this electrical energy is
decreased) in overcoming the great internal resistance of the pile.
Furthermore, recent experiments seem to indicate that the problem
of transforming heat into electrical energy in this manner is not at
all hopeless.^

The results of the calculations of the electromotiye force which
have been carried out are in good agreement with the assumption,
made earlier, that the chief source of the electromotive force of a
cell is the contact surface between the electrode and electrolyte.
It seems, however, upon a closer consideration of actual measure-
ments, that the deduction itself is not satisfactory, at least in some
cases; for the measurements show that the electromotive force is
not always, but only in the case of certain metal combinations and
within narrow temperature limits, proportional to the absolute
temperature.

Many thermoelectric couples show so-called reversal points, t.e.
their electromotive forces decrease with rising temperature, finally
becoming zero. The current then changes its direction. Other
processes besides those assumed must, therefore, take place at the
point of contact of the two metals.

At all events, there is no reason for supposing a considerable
potential-difference to exist between metals ; while, on the contrary,
the existence of slight potential-differences has been shown to be
probable.

The law of the electromotive series must evidently apply to the
minute potential-differences existing between the metals themselves.
A cell composed of only two metals cannot, therefore, generate an
electric current when the temperature is the same throughout.

1 Zuchr, Elektrochemie, 9, 91 (1908).

ELECTROMOTIVE FORCE 281

This conclusion is necessitated by the second law of energetics.
Otherwise any desired quantity of heat at constant temperature
could be changed into electrical energy without any permanent
alteration taking place in the system; which is equivalent to saying
that a cyclical process may continually change heat into work.
That this electromotive series exists does not explain that discov-
ered by Yolta, since in the latter the forces are very much greater.
Yolta thought that the potential-difference now ascribed to the sur-
face between liquid and metal was really produced at the contact
point between the metals. To corroborate his conclusions, the exist-
ence of a similar law governing the potential-differences at the
surface between metals and liquids must be demonstrated.

In the following pages it will be seen that, theoretically, a certain
definite potential-difference exists between a metal and an electrolyte.
If, for example, zinc, in contact with an electrolyte whose potential
is zero, exhibits a potential of 3, while that of cadmium is 2 and of
copper 1, then, according to the electromotive series, the potential-
difference between zinc and copper must be equal to the sum of that
between zinc and cadmium and that between cadmium and copper.
As this is actually the case, the law of electromotive series may be
considered correct.

The electromotive series is roughly applicable to galvanic cells.
The arrangement,

Zn » ZnSOf solution ^ CdS04 solution Ny^^
Cu - CuSO* solution - CdSO* solution/ '

in accordance with this law, should exhibit the same eleotromotiye
force as the arrangement,

Zinc — zinc sulfate solution ---

Copper — copper sulfate solution ••'

if the concentrations of the zinc and copper sulfate solutions are
the same in both cases. This is, however, only exceptionally the
case. Because of the potential-differences which exist in most
cases at the point of contact of two liquids, the law is only approxi-
mately true. That the law applies to simple liquid cells only in a
certain definite case, has already been mentioned.

CHEMICAL CELLS

The cells thus far described, in which the electrodes are always of
the same nature, may in most cases be characterized as ooTusentraition

282 A TEXT-BOOK OF ELECTRO-CHEMISTRY

cells. To be distinguished from these cells are those in which the
electrodes are different and in which chemical energy is transformed
into electrical energy. They may be called chemical cells. ^ A type
of this latter class is the well-known Daniell cell.

Zinc — ZnS04 solution —
Copper — CUSO4 solution-

When in activity^ zinc passes from the metallic into the ionic, and
copper from the ionic into the metallic state. In this process (in
contradistinction to the ideal concentration cells) a change in the
internal energy of the system takes place, and this difference in
energy may be considered as the principal source of the electrical
energy produced. Instead of the change of positive ions to metal at
one pole, and the metal to ions at the other, the negative ions may
also perform this^ process. The cell,

Oxygen (platinized Pt) — KOH solution- ,

Chlorine (platinized Pt) — KCl solution -1'

causes hydroxyl ions to be produced in the alkali solution and
chlorine ions to change into molecular chlorine in the potassium
chloride solution. (The current and process may be reversed under
certain circumstances.)

Finally, positive ions may form at one electrode simultaneously
with the negative ions at the other. An example is seen in the
combination.

Zinc — ZnS04 solution

Chlorine (platinized Pt) — KGl solution-

It is also well to remember that in all such cells there is always a
small potential-difference produced at the surface of contact of the
solutions.

As already noted, the electrical energy may be calculated by the
Helmholtz equation, from the heat generated by the chemical pro-
cesses and the experimentally determined temperature coefficients
of the electromotive force. The cell during activity yields as elec-
trical energy the maximum work obtainable through the change
which takes place in it. This work bears that relation to the heat
of the chemical reactions measured in the calorimeter which is given
by the Helmholtz equation. As this equation shows, there may be
elements in which the chemical or internal energy chan^ is exactly
equal to the electrical energy obtained. These may be considered

ELECTROMOTIVE FORCE 288

as machines which, in their action, will change all the energy put
into them into another energy form. There are, secondly, cells in
which only a portion of the chemical energy is transformed into
electrical energy, and these may be looked upon as machines which
transform only a portion of the energy introduced into another form
of available energy, while the remainder is lost as heat. A third
kind of cell is also known, by which more electrical energy is pro-
duced than corresponds to the chemical reactions taking place, and
such elements may be considered as machines transforming not only
the applied energy into work, but absorbing and changing into work
the heat of the surroundings. Imagine in this last class the amount
of work which really comes from the heat of the surroundings con-
tinually increased; cells are finally reached in which (as in the
concentration cells) the internal energy remains unaltered and the
electrical energy is derived entirely from the heat of the surround-
ings. It then becomes a question whether or not these are to be
designated chemical cells. From these remarks it may be seen that
a sharp line of demarcation between the chemical and other cells
does not exist, but one form graidually passes over into the other.
The distinction is justifiable in so far as the chemical reaction is the
chief characteristic of the cells.

The influence of concentration changes in the electrolytes of any
cell upon the electromotive force may be predicted from the princi-
ples established for concentration cells. When, for example, the
Daniell cell is in operation, zinc ions enter the zinc sulfate solution
and copper ions separate out from the copper sulfate solution. If
now the concentration of the zinc ions be increased, it is evident
that zinc ions can less easily enter the solution. The electromotive
force is, therefore, diminished. If, on the other hand, the concen-
tration of the copper ions be increased, the deposition of copper ions
is facilitated, and hence the electromotive force is increased.
Finally, if the concentrations of the ions in the two solutions
are changed equally, the electromotive force remains unchanged,
since the effects produced at the two electrodes compensate each
other.

In general the rule holds, that the electromotive force of a cell is
decreased when, at an electrode, the solution is made more concen-
trated in respect to the ions which this electrode sends into the
solution during the activity of the cell. On the other hand, the
electromotive force is increased when the concentration of the ion
which s^Mirates at the electrode is increased. For example, when
both solutions of the cell,

284 A TEXT-BOOK OF ELECTRO-€HEMISTRT

Zinc — Zinc sulfate solution ,

Chlorine — Hydrochloric acid solution. J

are dilutedi the electromotive force ia increased.

The magnitude of the change of the potential-difference or of the
total electromotive force may be calculated directly from the equation
which applies to concentration cells : —

RT, P

VQ P'

If, for example, only univalent ions are involved and at one eleo-
trode the ion concentration 1 normal is replaced by the ion concen-
tration 0.1 normal, the change in the electromotive force is equal
to 0.0575 volt at 17^ t (see page 200). These conclusions have been
finely confirmed by experiment.

The electromotive force of a cell, as already emphasized, is always
made up of the sum of at least two separate potential-differences,
namely, those which exist at the points of contact of the two elec-
trodes with the liquid of the cell. (In a similar manner, the tem-

dF
perature coefficient of the electromotive force of the cell, — , is the

sum of the temperature coefficients of the component potential-
differences.) It was endeavored for a long time to find a means of
obtaining a knowledge of these component, or single, potential-
differences. The results of this endeavor will now be considered.

DETERMINATION OF SINGLE POTENTIAL-DIFFERENCES

By the experimental investigations of Lippmann upon the rela-
tion existing between the surface tension of mercury in sulfuric
acid and the potential-difference at the point of contact, the meas-
urement of single potential-differences was first ma4e possible. The
principal result of Lippmann's research was expressed by him as
follows: The surface tension at the contadt surface between mercury
and dilvte sutjuric acid is a continuous function of the electromotive
force of ^ polarization at tJiat surface.

Helmholtz later made the researches of Lippmann better under-
stood by an application of the theory of the electrical double-layer.
If mercury be brought into contact with a liquid, e,g. dilute sulfuric
acid, it assumes a positive electrical charge. This may be explained
by assuming that the electrolyte contains mercury ions, very possi-
bly from the dissolving of a little oxide, which may be present on
the surface of even the purest mercury. The work of Warburg has

ELECTROMOTIVE FORCE 235

also shown that the mercury may be oxidized by the oxygen dis-
solved in the liquid, and may thus enter the ionic state. Because
of its yery low solution pressure the mercury itself is positively
charged in a solution even when it contains very few of its ions.

At all events, there exists at the surface of contact of the mer-
cury and the solution a certain potential-difference which depends
upon the concentration of the mercury ions in the layer of solution
directly in contact with the mercury. If now a weak current of low
electromotive force be sent from an auxiliary electrode through the
solution to the mercury, mercury is deposited and the concentration
of the ions is decreased, and the potential-difference is changed by
the magnitude of the primary electromotive force, whereupon the
current ceases to flow. Since the ion concentration has been de-
creased, the positive charge of the mercury has decreased and the
surface tension increased.

This is the result of the mutual repulsion of the quantities of
positive electricity on the surface of the Mercury as well as of the
negative electricity in the electrolyte, with the consequent expansion
of the surface in opposition to the surface tension. If a portion of
this electricity be removed, the surface tension naturally increases.
By continued increase of the primary electromotive force, a condition
may be reached in which the electrical double-layer disappears and
the surface is electrically neutral. Evidently at this point the
surface tension has reached its maximum value. The potential-
difference between the mercury and the liquid is now zero, and
the applied electromotive force of the polarizing current is exactly
equal and opposed to the single potential of the auxiliary electrode,
which may in this way be found. If still more negative electricity
be introduced, the mercury becomes negatively charged, and the
attracted positive ions of the solution form a new electrical double-
layer, differing from the former only in the relative position of the
two kinds of electricity. The surface tension of the mercury must
now decrease with increased negative charges at the surface because
of the mutual repulsion of the quantities of electricity.

The execution of the above experiment is simple in principle ; the
difficulties which must be overcome in accurate investigations need
not be discussed here. The apparatus shown in Figure 46^ may
be used. The capillary c, as well as the greater part of the tube A,
attached to c by a rubber tube, are filled with mercury, e dips into
the cup Bf which contains a little mercury, and above this is the elec-
trolyte. The position of the mercury in the capillary is observed by

^ Zt9chr.phy9, Chem,, 16, 1 (1804).

286

A TEXT-BOOK OF ELECTRO-CHEMISTRY

means of a microscope. The bulb Oy which contains mercoiyy per-
mits of the application of desired pressures through its elevation
and depression ; it is attached to the manometer Jf by a rubber
tube. A bent glass tube D leads from the latter to A, the connec-
tions being made with short pieces of rubber tubing. ParafiKn oil
serves as the liquid of the manometer, increasing the delicacy
of the reading. A small Tessel, as shown at F^ containing both
paraffin oil and mercury, is connected to the apparatus between
the manometer and rubber tube. P is an arrangement for impress-
ing any desired potential-difference on the mercury in the capillary
tube.

It is to be recalled that when a capillary is placed in water, the
latter rises to a level above that of the surrounding liquid, as it
wets the surface of the glass. On the other hand, with mercury the
level in the capillary is below that of the surrounding liquid, and,
if the surface tension be increased, sinks still lower, that is, it
moves against the pressure of the mass of mercury. It is only in
this way that a diminution of the surface, the result of increased
surface tension, can occur.

If now a certain potential from the source of electricity P be
applied to the mercury in the capillary c, the surface tension of the
mercury increases and the meniscus begins to rise. In order to hold
this in its original position, a certain pressure must be exerted by

ELECTROMOTIVE FORCE 287

means of the manometer. As the applied potential-difference is
increased the necessary pressure also increases^ until at a certain
potential-difference a maximum in the pressure is obseryed, which,
on further increase of the potential-difference, again diminishes.
The potential-difference corresponding to the maximum pressure is
that which is naturally assumed by the large mercury surface, the
auxiliary electrode, in the electrolyte at B.

In order that the results may not be variable, it is necessary to
add some mercury salt to the electrolyte, that this may have a
certain concentration of mercury ions throughout, since the potential-
difference at the surface of the metallic mercury is dependent thereon.
The question is naturally raised : Is not the electrode an unpolarizable
one when suficient mercury ions are present, i.e. is it not an electrode
the potential-difference of which remains nearly constant during
electrolysis ? In answer, attention is directed to the following : By
adding mercury ions to the liquid, the mass of mercury in B, the
auxiliary electrode, becomes a nearly unpolarizable electrode, which
maintains the same potential-difference towards the electrolyte, no
matter what other potential-differences are inserted at P. Because
of its small surface the metallic mass in the capillary only comes
into direct contact with a very small part of the electrolyte. Conse-
quently, on the application of a potential-difference, only very few
mercury ions pass from the electrolyte into metallic mercury, and
new ions can diffuse into the layer at the surface but slowly ; there-
fore this electrode is practically polarizable. Evidently, the relative
extent of tJie surfaces of mercury, or, better, the relative density of the
currents at the ttoo mercury surfaces, plays the important part. What
is actually measured is the potential-difference at the larger mercury
surface, since this alone is constant. When the two quantities of
mercury are connected by a conductor, that in the capillary changes
its surface tension until it possesses the same potential-difference
as the lower mass. This is essential to the equilibrium which the
current first flowing tends to establish. This is particularly evi-
dent when the larger electrode is an amalgam instead of pure mer-
cury. For instance, if it be copper amalgam and the solution above
it contains a copper salt, the potential-difference between metal and
liquid will be less than before, since the amalgam assumes a less
positive charge. The mercury in the capillary again assumes the
potential of the lower electrode when the two are connected, and on
introducing independent potential-differences a lower value than
with pure mercury is sufficient ta bring about the maximum surface
tension.

238 A TEXT-BOOK OF ELECTRO-CHEMISTRY

By this method it is possible, by avoiding the potential-difference

which occurs at the point of contact of the two liquids by a suitable

choice of electrolytes, or by applying a calculated correction (see

page 219) for this potential-difference, to determine the single

potential-difference,

Mercury — Electrolyte,

and, further, neglecting the potential-difference between the two
metals, to determine any potential-difference,

Metal— Liquid.

The method of procedure is as follows: The potential-difference,

for example, of

Hg - HgCl (solid) in KCl, O.

is first determined. The value found is 0.56 volt, when the electrode
is positively charged. This combination, or electrode, is then
connected with the combination of which the potential-difference is
desired. Supposing the potential-difference

Ag - AgNO» (7n,

to be desired, the electromotive force of the combination^

Hg-HgCl (solid) in KCl solution, O*. ,

Ag — AgNOs solution, Cn ••'

would be measured. If, from this value, the potential-difference
between mercury and potassium chloride solution (0.56 volt) be
subtracted, the required value is obtained.

In this connection, the investigations of Eothmund^ with the
Lippmann method are of interest. Instead of mercury, he used
amalgams of the base metals, which even at a concentration of about
0.01 per cent exhibit the potential of the pure metal. He measured
the potential-differences of the combinations,

Pb amalgam - H,S04, Cny sat. with PbS04 ,

Cu amalgam - H2SO4, On, -f CuSO*, 0.01 0« ,

Hg - H^O^ (7„, sat with HgjSO* ,

and also of the cells formed by connecting the latter combination
with the others in succession. He then compared the latter values
with the sum of the corresponding single potential-differences. The
values obtained are given in the following table : —

^Ztachr, phys. C%em., 16, 1 (1894).

ELECTROMOTIVE FORCE

239

AlLlLGAin

BlBOTBOLTIB

Bdioli PoTBirr.-Dirr.

Ck>ppeT

Mercury

Lead

H,804 (1 On) + OnR04, 0.01 Cn,
HsSOi (1 Cn) saturated with HgsSOi
HtS04 (1 Cn) saturated with FbS04

0.445 Tolt
0.926 Yolt
0.008 Yolt

The electrodes were positively, and the electrolyte negatively,
charged.
According to the above values, the electromotive force of the

Copper — Mercury cell « 0.481 volt,
and of the Lead — Mercury cell s 0.918 volt

The values actually measured are 0.458 and 0.923 volt, respectively.
In other cases the agreement between the value of the electromotive
force taken as the sum of the two single potential-differences and
that actually measured was less satisfactory.

To sum up, the following should be noted: The theory which
has been outlined is based on the supposition that the surface ten-
sion of the mercury is related to the electrical double-layer at its
surface only in the way already described, and especially that the
nature of the ions forming one side of the double-layer, as well as
the nature of the electrolyte in the general, is without influence upon
the surface tension of the mercury. Since, however, according to
recent investigations of Kemst, the surface tension of the mercury,
in contradiction to the theory, is strongly influenced by noneleo-
trolytes, the theory and therewith the significance of tiie experi-
mental results is rendered uncertain. Furthermore Billitzer,^
together with other objections to the theory, has called attention
to the fact that the electrolytic solution pressure of mercury must
not be considered as a constant, but as a variable increasing with the
surface tension.

There is a second method which can be used for the determina-
tion of single potential-differences, the principle of which was ex-
plained by Helmholtz. Ostwald ' first showed that it could be used
for this purpose, and through his efforts, as well as those of Paschen,
the method has-been developed.

If an insulated mass of mercury be allowed to flow in a stream
through a fine opening and drop into an electrolyte, there can be,
according to Helmholtz, no potential-difference between the mercury

^Ztachr. phys. Chem.y 48, 613 (1904), and 61, 106 (1006).
* Ztsehr. phya. Cfhem,, 1, 683 (1887).

240

A TEXT-BOOK OF ELECTRO-CHEMISTRY

aad the electrolyte. Helmholtz expressed himself on this point in
the following manner : —

<' CQnsequently I conclude that when a quantity of mercury is con-
nected with an electrolyte by a rapidly dropping fine stream of the
mercury, and is otherwise insulated, the two cannot possess different
electrical potentials, for if a potential-difference did exist, for
example, if the mercury were positive, each falling drop would form
an electrical double-layer on its surface, requiring the removal of
positive electricity from the mass, and diminishing its positive
charge until that of the mercury and solution reached equality."

An experiment by A. Eonig has already shown that the charge on
the mercury can be partly removed by allowing it to drop through

a solution. This result was later con-
firmed in other ways. Figure 47 repre-
sents the arrangement employed by K5-
nig. The mercury cup a, beneath dilute
sulfuric acid, was connected by a wire
with mercury dropping from the capillary
into the acid. A galvanometer G was
connected into the circuit as shown. This
indicated that the positive electricity was
removed with the dropping of the mer-
cury in agreement with the previous ex-
planations. If the upper mercury, through
the dropping, be brought to practically
the same potential as the solution, the
polarizable mercury in the cup has the same potential, and therefore
the maximum surface tension. This could be determined by means
of an ophthalmometer. As still further proof, a weak electromotive
force, positive or negative, on being introduced into the circuit on
the wire connecting the two electrodes, caused the surface tension to
decrease, since a potential-difference was produced between the
liquid and the mercury of the cup.

According to the Nemst osmotic theory, the following statements
concerning the drop electrode may be made : ^ If a fine stream of
mercury be allowed to flow out of a tube into a solution of an elec-
trolyte containing some mercury salt, as for example mercurous
chloride, mercury ions deposit on the fresh surface of the mercury,
each drop becomes positively charged and surrounded by the negar
tive chlorine ions corresponding to the ions deposited. Arriving at
the bottom, it joins the constant mercury surface there and gives up

1 Zt9Chr, phys. CKem., U, 265 (1896), and 88, 267 (1890).

Fio. 47

ELECTROMOTIVE FORCE 241

the excess of its positive charge by sending merourous ions into the
solution. These ions, with the chlorine ions, which up to this time
constituted the outer part of the double-layer, form mercurous
chloride again. As a result of this process, the mercury salt is
transferred from the upper to the lower part of the solution, thus
forming a concentration cell. Since the solution becomes more con-
centrated below than above, it would be expected that the current
would flow through the solution from the upper to the lower part.
This is actually the case. Furthermore, it may be stated that the
concentration of the mercury ions in the upper part of the solution
must finally become so small, if no diffusion takes place, that the
potential-difference there will be zero. This state is not changed
nor is there a further transference of salt from the upper to the
lower part of the solution when more mercury is allowed to drop
through the solution.

The end sought has, then, been attained; for by throwing an
electromotive force into the circuit, the potential-difference of the
lower mercury electrode can be measured.

As a matter of fact, however, the presence of diffusion prevents
a complete freedom of electric charge, and thus causes the measure-
ments to be both difficult and uncertain. However, all errors
arising from the fact that an electric charge is still present may be
avoided by a method recently proposed by Nemst. It depends on
the preparation of a solution of so small a concentration of mercury
ions that the potential-difference between it and a mercury surface is
equal to zero. A means of preparing such a solution is offered by
potassium cyanide. It has been found that in a concentrated solu-
tion of potassium cyanide, the direction of the current is reversed,
i.e. it flows from the stationary mercury through the solution to the
mercury drops. If now a solution of potassium cyanide of such a
concentration be prepared that no electric current is produced when
mercury is allowed to drop through it, the desired zero electrode is
obtained. Experimental results obtained by Palmaer^ have con-
firmed the correctness of this conclusion. With the use of a zero
electrode made as above described, he obtained nearly the same value
for the single x>otential-difference,

Hg - KCl, 0.1(7^ saturated with HgjCl,,

as he did with the aid of the capillary electrical method.
In view of this work, it might with good reason have been thought

1 Ztschr. mek$rochem., 9, 764 (1003).

242 A TEXT-BOOK OF ELECTRO-CHEMISTRY

that the values so f ouad although questioned are yet near the correct
one.^ The recently published investigations of Billitzer,' however,
which lead to entirely different values, diminished even more the
probable correctness of the values obtained by the above methods.

As has already been explained in Chapter YI, at the surface of
contact of a solid and a liquid there is always formed, according to
Helmholtz, an electrical double-layer. Hence an electrically charged
particle which is suspended in an electrolyte through which an elec-
tric current is flowing, will, according to the nature of its charge,
migrate toward the positive or toward the negative pole. If all
other influences which also may cause the particle to move be
excluded, then the sign of the charge upon the particle may be
known from the migration direction of the particle, and, further, it
may be concluded that at that point at which the direction of
migration is reversed, i.c. the point at which the double-layer
disappears, a system of two bodies with a potential-difference
between them equal to zero exists. If the solid particle is a metal,
the system is a zero electrode which may be used directly for
the determination of the single potential-difference of any otiier
electrode and its solution.

The investigations were carried out with colloidal platinum, silver,
and mercury, and also with fine metallic wires with one end fused
forming a small sphere, which were suspended perpendicularly from
a quartz thread. The movement took place and the reversal could
in every case be brought about by changing the ion concentration, in
agreement with the Nemst equation relating to the potential-differ-
ence between a metal and its solution. The same results were
obtained by reversing the experiments. When metallic powder was
allowed to fall through a tube containing a solution, an electric cur-
rent was obtained. The direction of this current could be changed
by changing the ion concentration of the solution. At a definite
concentration, by the first method the particles or wires ceased
to move, and by the second method the electric current ceased to
flow.

It is very remarkable that the value of the potential-difference of
the mercury electrode in contact with a normal solution of potassium
chloride saturated with mercurous chloride, as measured by the
method just described, differs from that obtained by the surface ten-
sion method by not less than 0.74 volt. Since, however, the value

1 See also Krtlger, ** Theorie d. Elektrokapill. nnd d. Tropfelektr.,** Getting.
Oes. d. Wiss., 1904, Vol. 1.

> Zt8ehr. Elektrochem., 8, 638 (1902), and loc, cU.

ELECTROMOTIVE FORCE 243

obtained by the new method may contain errors/ Nemst' has
repeated his recommendation that until the subject is further inves-
tigatedy the value at present usually given^ i.e. for the mercury
electrode,

?Hg - MiadoB = + 0.66 volt,

be disregarded, and that the potential-difference of the hydrogen
electrode with hydrogen at atmospheric pressure and hydrogen ions
at one normal concentration, placed arbitrarily equal to zero, be taken
as a standard. It should especially be noted that up to the present no
special significance has been attached to the absolute zero point of
the electrode potentials. Not to the slightest degree has it a signifi-
cance such as that which the absolute zero point of the temperature
scale possesses ; for it has not been found possible to find a numeri-
cal relationship between solution pressure and other physical proper-
ties. Hence, from this point of view, no objection can be raised to
the choice of an arbitrary zero point, t.e. an arbitrary zero electrode.
The choice of the hydrogen electrode as such a zero electrode
possesses advantages in the direction of systematization, siuce a
division of the metals into those which do, and those which do not,
evolve hydrogen is thereby effected. On the one side there are the
metals which are less, and on the other side those which are more,
negative than hydrogen, if the metals be considered to be in contact
with their respective normal sohitions. Finally, hydrogen is the best
reducing agent, and in this respect also divides the electrodes into
two classes.

A hydrogen electrode of sufficient constancy for general use is
easily prepared. It is only necessary to place a well-platinized
platinum electrode into a sulfuric acid solution which is normal in
respect to hydrogen ions, and to pass a stream of hydrogen into the
solution, and past the electrode for fifteen minutes, in order to obtain
the correct potential-difference within 0.001 of a volt. The deter-
mination of single potential-differences and their signs is then in the
main very simple, if the potential-difference which always exists at
the place of contact of the two liquids be left out of consideration.
The electrode which is to be investigated is connected with the above
standard or normal hydrogen electrode, and the electromotive force
of the cell thus formed and the direction of the electric current in the
cell are determined according to the usual methods. This electro-

1 Ztschr. Elektrochem., 18, 192 and 281 (1906).

s Ztschr. EUktrochem., 7, 263 (1900) ; ZUchr. phy$. Chem., 85, 291 (1900)
and 86, 91 (1901).

244 A TEXT-BOOK OF ELECTRO-CHEMISTRY

motive foroe is directly the value of the single potential-diffeTence
desired, and its sign is plus or minus according as the electrode in
question is the positive or the negative pole of the celL The
direction of the current is represented by an arrow.

What has just been stated is illustrated by the following example.
If the electromotive force of the cell

Zn-Zn",l CL-H,1 OL-H,

is equal to 0.770 volt, and the electric current flows from the zinc
electrode through the solution to the hydrogen electrode, then the
single potential-difference between the zinc and the solution of zinc
ions is equal to — 0.770 volt. Representing single potential-differ-
ence by V as will be done from now on, this may be expressed as
follows : —

?Zb -► lohittoii = "■ 0.770,

or F ^tatt^ <- zn = + 0.770 volt.

The sign plus or minus is always that of the electrical charge of the
first-mentioned component in the equation, i,e, in the former equa-
tion, the sign of the electrical charge of the zinc, and in the latter,
that of the solution of zinc ions.

In the manner just illustrated, any single potential-difference may
be determined. Moreover, the electromotive force of a cell com-
poseS of any two electrode combinations may be obtained by taking
the sum of the single potential-differences of these combinations. It
should be noted that the direction of the arrow in the case of single
potential-differences is always that of the current when the electrode
combination under consideration is connected with the normal
hydrogen electrode. If now the two single potential-differences
composing a cell be written one after the other in the order in which
they are combined in the cell, and if the two arrows have the same
direction, then their signs are the same. If the arrows have opposite
directions, the signs are unlike. In the latter case, the direction of
the current in the cell is that of the larger single potential-difference.
This is illustrated by the following equations: —

(1) ?Zn — ^ ML + fwL — ^ Cu = ^Zn— >>Cay

- 0.770 - 0.329 - 1.099

®' ?Ca<<— Ml. + 1'm>1. •4»Zii = ^Ca-<— Zbi

-M.099

(2) Jzto — ► mL + ? ML .<— Cd = ^ Zn — ► Cdt

-0.770 -1-0.420 -0.350

ELECTROMOTIVE FORCE 245

- 0.420 -f 0.770 + 0.360

Hence it makes no difference whether we write

'zii-».cd= —0.350, or Pcd<-zi»= +0.350.

In either case the meaning is the same and the arrow shows the
direction of the current in the couple, i.e. from one electrode through
the liquid to the other. In the case represented by the latter equa-
tions, the current flows from the zinc, the negative pole, through the
liquid to the cadmium, the positive pole.

This method of representation is employed in exactly the same
way in the case of electrodes which send negative ions into the solu-
tion, such as oxygen, chlorine, bromine, etc., electrodes. When
these electrodes are in combination with the hydrogen electrode, the
single potential difference,

? elMtrode— liquid;

receives the positive sign when negative ions are formed, and the
negative when they are discharged. By means of this method of
representation, which was in principle suggested by Luther, the sur-
vey and comprehcDsion of the subject has been greatly facilitated.
It ahouldf howevery be noted that U is not in general use in electro-chemir
cal literature.

Although the hydrogen electrode possesses certain advantages as
a standard electrode, it is not always to be recommended for general
use in the measurement of single potential-differences. When used
in carrying out measurements with neutral or very concentrated
alkaline solutions, diffusion potential-differences of considerable
magnitude arise, due to the great difference in the migration veloci-
ties of the ions, which can be calculated only with difficulty if at all.
In such cases the so-called calomel electrode, which is very constant
and easily duplicated, possesses advantages over the hydrogen
electrode.^

A form of the calomel electrode such as is shown in Figure 48 may
be prepared in the following manner:^ At the bottom of a small
upright vessel, about eight centimeters in height and from two to
three centimeters iu diameter, a small quantity of pure mercury is
placed and then covered with a layer of mercurous chloride. The

1 See also the discussion, *^ Ueber die Zahlung der Elektrodenpotentiale,'*
Ztschr. Elektrochem,, 11, 777 (1906).

'For further parUculais see Ostwald-Luther, PhysiJ>chem, MeMSungen^
page 881.

246

A TEXT-BOOK OF ELECTRO-CHEMISTRY

Teasel is then filled with a normal solution of potassinm chloride and
•closed with a rubber stopper carrying two glass tubes. Through one
of the latter, a platinum wire is connected with the mercury. The
other tube, bent as shown in the figure, is, together with the rubber

tube attached to it, filled with the
solution of potassium chloride.
The bent glass tube B of the calo-
mel electrode thus made, is dipped
into the liquid of the electrode
combination the potential-differ-
ence of which is desired, and the
electromotire force of the cell
thus formed is measured as usual.
If the potassium chloride solution
produces a precipitate with the
solution of the electrode combina-
tion under consideration, as would
be the case, for example, if the
latter contained a solution of sil-
ver nitrate, a third and indifferent
solution, e.g. of potassium or am-
monium nitrate, must be intro-
duced between them. It is often
advantageous to use a solution of potassium chloride because, since
the migration velocities of the respective ions are nearly the same,
there is no tendency to form a large potential-difference at the place
where the two solutions meet. Since the Value of this potential-
difference cannot always be calculated with certainty, it is a disa-
greeable factor in the measurement of single potential-differences.
In the case of a contact between a solution of potassium chloride
and one of a neutral salt, however, its value is sufficiently small to
be neglected. Even when it cannot be neglected, it may easily be
made calculable.^

It was recommended by the International Congress at Berlin* that
in all cases the directly measured values be given, and that the 1
normal calomel, or the above4efined Nernst hydrogen, electrode be
employed as the auxiliary electrode. Following these recommendar
tions, the correct measured values will always be available for
possible future recalculation. These values may be considered as
single potential-differences referred to the hydrogen or the calomel

I Sammet, Ztschr.phya. Chem., 58, 068 (1905).
* Zt8chr, JEUarochem., 9, 686 (1903).

Fig. 48

ELECTROMOTIVE FORCE 247

electrode as a zero electrode. In this case it must be borne in mind
that these values still include the potential-differences which exist
at the point of contact of the two solutions.

In the following table are given the most reliable values of the
single potential-differences,

£ electrode - eleetrdljte f

when, at room temperature, the electrodes are in contact with their
respective solutions containing one ion-mol per liter. ^ The ion con-
centration is in many cases still uncertain.'

In column I are given the calculated or measured single potential-
differences against the calomel electrode. These values will be
represented by r*-

In column II are given the calculated or measured values against
the hydrogen electrode. They will be represented by f*.

The values inclosed in parentheses have been calculated solely
from heat effects.

Since the potential-difference between the calomel and the hydro-
gen electrode is equal to 0.283 volt, and since in this combination
the current flows from the hydrogen electrode through the solution
to the mercury, the following relation exists,

la ^ ,.^H^ = + 0-283,

'Hg-^^eleelroljte ' '

when the calomel electrode is referred to the hydrogen electrode as
zero electrode; and

?H-<-eleetrol7te = — 0.283,

when the hydrogen electrode is referred to the calomel electrode as
zero electrode. Hence we have the following relation between the
values referred to these two standard zero electrodes, —

!* = ?« + 0.283 volt.

This series may at least be considered as the approximately cor-
rect electromotive series. The values are often called '^electrolytic
potentials'^ and represented by the letters (ep) when they refer to

1 Wilsmore, loc. cit. The values for Fe, Co, and Ni were obtained from the
work of Muthmann and Fraunberger, '^ Math.-phyB. KI. d. K. Bayr. Ak. d. W.
84," Vol. 2 (1004) ; those for Ag and O under atmospheric pressure against 1
normal OH' from an investigation of Lewis, Ztschr, phys. Chem,^ 65, 473 (1906);
and those for CI, Br, and I from an investigation of Luther and Sammet,
Ztschr, ElektrocJum.y 11, 205 (1006). The latter values were obtained by extra-
polation and are referred to a halogen concentration of one mol per liter.

> Abegg-Labendzinski, Ztschr. Elektrochem.^ 10, 77 (1004).

248

A TEXT-BOOK OP ELECTRO-CHEMISTRY

ELECTROLYTIC SINGLE POTENTIAL-DIFFERENCES

EuMBim

PotaBsium

Sodiom

Barium

StroDtiam ....

Calciam

Magnesium ....
Magnesium ....
Aluminium ....
Manganese ....

Zinc

Cadmium ....

Iron

Thallium

Cobalt

Nickel

Tin

Lead

Hydrogen

Copper

Arsenic

Bismuth

Antimony ....

Mercury

Silver

Palladium ....

Platinum

Gold

Fluorine

Chlorine ^ f , .
Bromine ^ 26^ *{ . .
Iodine J I . .
Oxygen

< +

< +
+
+

< +

+
+
+
+

8.48)

3.10)

8.10)

8.06)

2.84)

2.82)

1.774 ?

1.560 f

1.868

1.063

0.708

0.0401

0.606

0.730*

0.8801

0.476

0.481

0.288

0.046

0.010

0.108 *

0.188

0.467

0.615

0.606

0.680

0.796

1.68)

1.120

0.812

0.845

0.1 10

II (p,)

(-8.20)
(-2.82)
(-2.82)
(-2.77)
(-2.66)
(-2.64)
-1.491?
-1.276?
- 1.076
-0.770
-0.420
-0.6601
-0.822
-0.4601
-0.6001
< -0.192
-0.148
:i: 0.000
+ 0.829

< + 0.293
<+ 0.891

< + 0.466
+ 0.760
+ 0.798

< + 0.789

< + 0.868

< + 1.079
(+1.96)

+ 1.400
+ 1.095
+ 0.628
+ 0.398

room temperatura According to the Nemst equation (see page 183),
for a metallic electrode,

(ep)=-:^1iip,«

since in the above measurements P has been made equal to unity.
Hence in general the potential-difference which exists between an
electrode and a solution of an ion concentration P, at a temperature
T, is as follows: —

1 Approximately.

* The sign becomes + when negative iona are formed.

ELECTROMOTIVE FORCE 249

SdMtiode- electrolyte =* (^^) + ~ ^ ^9

when the electrode sends positive ions, and

when it sends negative ions, into the solution.

The electrolytic potentials for solvents other than water cannot
yet be given, since the degrees of dissociation involved are not known.
The potential-differences of a large number of couples with organic
solvents have been measured by Kahlenberg.^

Finally, attention is called to the fact that the Helmholtz equation,

is applicable, not only to the electromotive force of the entire cell,
but also to the constituent potential-differences of each individual
reversible electrode. This has been shown to be true experimentally
by Jahn' for several metal electrodes. In this equation Q represents

dF
the heat effect of the reaction at the electrode in question, and —

the temperature coefficient of the potential-difference in question.

Just as the total electromotive force of the cell is made up of two or

more independent potential-differences, so the temperature coefficient

of the former is made up of the sum of the individual temperature

coefficients of the latter.

dv
The expression, - ^d7^

represents what is known as the Helmholtz — or Peltier — heat
effect. It was first applied to simple metallic contacts. In the
case of such contacts, the Peltier effect is understood to mean the
quantity of heat which is evolved or absorbed when, at the tempera-
ture of the contact, a unit quantity of electricity passes through the
contact. The Peltier effect is the reverse of the thermoelectric phe-
nomenon discovered by Seebeck which was mentioned on page 228.
Influence of Negative Ions upon the Potential-difference : Ketal —
Metal Salt Solution. — The question may still be asked: Is the
nature of the negative ion without influence upon the potential-dif-
ference ? To answer this question, Neumann prepared 0.01 nor-

1 J. Fkys. Chem., 8, 879 (1899).

a Zt8chr. phys, Chem,, 18, 399 (1896).

250 A TEXT-BOOK OF ELECTRO-CHEMISTRY

mal solutions of oyer twenty different thallium salts (mostly of
organic acids), and determined the potential-differences between
them and pure metallic thallium. In these solutions, these salts
may be considered to be equally dissociated, and the same potential-
differences might be expected in each case. As the measured values
do not differ by more than 0.001 of a volt, it is a justifiable conclu-
sion that the nature of the negative ion is without influence upon the
potential-difference between metal and solution.

Nevertheless nitrate solutions differ considerably from chloride
solutions. These apparent exceptions to the above-stated general-
ization may be explained by the fact that in the latter case the con-
centration of the thallo ions, which determine the poteLtial-difference,
is less than in the former case, due to the formation of complexes.
On the whole, such an indirect influence of the anion is not seldom
in the case of metal salt solutions. The degree of complex forma-
tion depends on the electro-af&nity of the anion.^

CELLS IN WHICH THE ELECTROMOTIVELT ACTIVE
SUBSTANCES ARE NOT ELEMENTS

A class of chemical cells, apparently very different from that rep-
resented by the Daniell element, will now be considered. If a plat-
inized platinum electrode is surrounded by a solution of stannous
chloride, and another by one of ferric chloride, and the two are
placed in metallic connection, an electric current is obtained, which
passes through the cell from the former solution to the latter. The
trivalent ferric ions g^ve up an equivalent of electricity, becoming
ferrous ions, while each stannous ion takes up two electrical equiva-
lents, becoming a stannic ion, as follows : —

Sn" f- 2 Fe"- = Sn"" + 2 Fe".

The process may be imagined in detail as follows : The stannous
ions change into stannic, and thereby positiye electricity is con-
sumed. This is shown by the equation,

Sn"H-2Q(-h) = Sn-".

Since this can never take place alone in a change of chemical into
electrical energy, the same quantity of negative electricity must
be produced upon the electrode. This electricity passes through
the wire to the other electrode, where it unites with the positive

1 Abegg-Labendzinaki, Ztschr, Elektrochem., 10, 77 (1904).

ELECTROMOTIVE FORCE 251

electricity deriyed from the change of ferric into ferrous ions, ac-
cording to the equation^

2Fe" + 2Q(-)=:2Fe".
The cell

Hydrogen (in platinum) — electrolyte -4—,

Chlorine (in platinum) — electrolyte B — !

is evidently completely analogous to the above combination. It
was previously stated (page 194) that platinized platinum in hydro-
gen may be considered as a hydrogen electrode. In a similar man-
ner the above combination may be characterized as stannous and
ferric electrodes, and just as a tendency to go into the ionic (or of
the ions to go into the neutral) state was ascribed to the hydrogen
and chlorine electrodes, so a tendency of the stannous and ferric to
form stannic and ferrous ions may be recognized. The electromo-
tive force of this cell also consists principally of the two indepen-
dent potential-differences occurring at the electrodes. But these
potential-differences depend not only upon the transformatian pres-
sures (which are analogous to the solution pressure) of the sub-
stances in question, but also upon the osmotic pressures of the ions
forming. Therefore the concentrations of the stannic ions formed
at the one electrode, and of the ferrous ions at the other, are
important factors; a certain constant potential-difference, as in
the Daniell cell, could only be expected when the solutions
already contained stannic and ferrous ions. Moreover, the con-
centration of the altering compounds must be considered, for the
transformation pressure of a substance at constant temperature is
invariable only at a definite concentration.

From wTiat has been said, it is obvious that there is essentially no
difference between the Daniell and the so-<xdled reduction and oxidation
cells. The laws governing the former may be expected to control the
latter.

Already in the first edition of this book (1895) this same ex-
planation was given. At that time, however, a proof of them was
not possible because of lack of experimental results. Thus the in-
fluence of the concentration of the substances formed at the elec-
trodes has been almost entirely neglected, and it is probable that
the varying values of such cells are due to this. The non-reversi-
bility of these cells may be similarly accounted for. If, instead of
allowing the stannous chloride ^ ferric chloride cell to act, it be
opposed by a cell of greater electromotive force, oxygen must sepa-
rate at one electrode (at least in dilute solution) and metallic tin at

252 A TEXT-BOOK OF ELECTRO-CHEMISTKY

the other. Stannic and ferrous chlorides being present, a change
of the stannic into the stannous, and of ferrous into ferric salt,
when the current is not too strong, would certainly take place in-
stead of the above, and the cell be reversible.

A cell which consists of zinc and chlorine electrodes, and of electro-
lytes which do not contain zinc and chlorine ions, is also not a reversi-
ble cell. If a stronger opposing current be sent through such a cell,
the positive ions of one electrolyte separate at the zinc, and the
negative of the other at the chlorine electrode, while zinc and chlo-
rine ions are liberated through its own activity as a cell.

Equations may be deduced for the calculation of the electromo-
tive force of such cells. They are analogous to those formulated
for the Daniell cell.^

Every process which takes place at an electrode of a cell during
its activity may be represented by the following scheme : —

aA + bB hVQ {+):^dD + eE"'.

Here a &,••• represent the number of mols of the substances A^
JB, ••• which by taking on the quantity of positive or giving off
the quantity of negative electricity, vq,' form d, e, ••• mols of the
substances Z>, JE7, •••. By an application of this scheme to the
ferri-f erro electrode, the f oUowing equation is obtained : —

The left-hand side of this equation represents the higher state of
reduction or the lower state of oxidation. The upper arrow of the
transformation sign, then, represents an oxidation, while the lower
one represents a reduction.

As already indicated, the assumption that the potential-difference
at the electrode, not only in the case of the Daniell cell but in gen-
eral, is dependent on the concentration of the substance being formed
as well as on that of the substance being consumed, in the manner
required by the Nemst logarithmic equation, seems plausible. If all
the substances under consideration be taken at unit concentration,
i.e. usually one mol (or one ion-mol) per liter, and if the value in
this case of the potential-difference,

feleetrode — deetrolytey

1 See also Ostwald-Lnther, Physiko-chemisclie Messungen, p. 878 ; Ztschr.
Elektrochem., 7, 1043 (1901).

> In passing from metallic to ionic state, v = valence of the ion formed. See
also page 182.

ELECTROMOTIVE FORCE 253

be represented by Fq, then, accepting the correctness of the above
assumption, the following equation is obtained for the potential-
difference at an electrode when the electrolyte is of any concentra-
tion (7: —

?«l«etrade-tlMtro|jto ~ ?0 + ^/v "^

^5 C^xC]...

The higher state of oxidation is represented in the numerator and
the lower state in the denominator. The former, then, becomes trans-
formed into the latter by giving up positive or taking on negative
electricity. In regard to the sign of f or Fq, the rule given on page
244 is to be followed. The value of f^ may also appropriately be con-
sidered as the electrolytic potential (ep). For the ferri-ferro elec-
trode, the following equation should hold : —

?«leelra<to-cleetroljte= Fo + ^^ "^ Te"*

where Fe'" and Fe" represent the concentrations or the osmotic
pressures of the ferro and ferri ions respectively. This expression is
entirely analogous to that which holds for metal electrodes. Applied
to the hydrogen and chlorine electrodes, the equation assumes the
following forms : —

^ i^r. ITf .

?tleoferod«-«leetiol7te'~ ?0 T~ o Q nVt

For an oxygen electrode, two different expressions hold according

as the equation,

0, + 4q (-) = 2 0",
or the equation,

0, + 2H,0 + 4q (-)^40H',

be considered to take place.^ The equation which holds in the
former case is as follows : —

^ The foUowlng relation exists : —

2 OH' ^ HjO + 0".

The concentration of the OH ions, but not that of the ions, can be obtained
experimentally. The latter ia certainly very small. In a consideration of equi-
librium states it makes no difference whether OH' or O" ions are involved.

264 A TEXT-BOOK OF ELECTRO-CHEMISTRY

Here Fq" represents the (ep), or, in words, the potential-diiference

which exists when the oxygen is under a pressure of one atmosphere

and is in contact with a solution which contains one gram-ion of

oxygen ions per liter. The equation which holds in the second

case is

RT O

The yalue of ^J" is determined by the fact that the oxygen is under
a pressure of one atmosphere and is in contact with a normal solu-
tion of hydroxyl ions. Strictly speaking, the value H^G should
appear in the numerator of the fraction the logarithm of which is to
be taken. Since, howeyer, the concentration of the water is not appre-
ciably changed during the reaction, its mass-action effect can be left
out of consideration. In fixing the value of Fo'"> the concentration
of the water in the solution may be placed equal to unity. It very
often happens that water takes part in a reaction in this manner.
Assuming that the following reaction tsikes place at a permanganate
electrode,

MnO'4 + 8 H* + 69 (-) :^ Mn" + 4 H,0,

then the strict equation would be

,RT MnO^ X H'

F'electrod.-dectrolTte - Fo+ g^ Mn"x(H,0/*

As in the case of the metals, so in the case of other oxidizing or
reducing substances, the determination of (ep) is of importance.
Very little in this direction has, however, been done. Below a
few accurate values are given : —

ElEOTBODB 1'Blbozxodb<<— Euotsolttb

Ferri-f erro -F 0.46 volt

Cupri-cupro + 0.13 volt

Ferri-ferrocyanide -F 0.153 volt

Thalli-thallo + 0.908 volt

Measurements have been made to confirm the statement that the
electromotive force varies with the concentration of the substances
involved as required by the above equation by Peters,^ Schaum,' Fre-

1 Ztichr, phya. Chem., 96, 103 (1898).

^ Sitzber. d. G. zur Befordemng d. Naturw., Marburg, No. 7, 1896.

ELECTROMOTIVE FORCE 266

denhagen,^ Spencer-Abegg,^ Maitland-Abegg,' and Sammet-Luther.^
Their results are in good agreement with the theory.

The results giyen in the last-named investigation will be consid-
ered again in the discussion of equilibrium constants. Other (ep)
values will then be given. At this point attention will be called
only to the possibility of determining the electromotive valence, i,e.
the number of chemical equivalents of electricity q required for
the electrolytic oxidation or reduction of the reacting substances,
from the dependence of the electromotive force on the concentration.
If the process takes place in stages, as in the case of the reduction
of molybdic acid solutions through intermediate pentavalent to
trivalent molybdinum, it may be perceived by means of continued
potential measurements, the influence of the concentrations of the
individual reacting substances being taken into consideration. An
insight into the mechanism of electrolytic processes may thus be
obtained.^

It scarcely needs to be mentioned that, when two single potential-
differences are combined to form a cell, the electromotive force of
the cell is essentially equal to their sum. This was proven by Ban-
croft.' Although his results suffered from the lack, at that time, of
known ion concentrations, the values of the single potential-differ-
ences measured are given here because they are of considerable
interest and because they are a measure of the strength of the oxi-
dizing or reducing power of the substances. They were obtained
with the use of platinized electrodes surrounded by the liquids men-
tioned. Most of the solutions contain about ^ mol per liter.

It is evident from the preceding discussion that in electrical pro-
cesses it is possible to distinguish sharply between oxidations and
reductions. In the case of such processeSy a stihatance is said to be oxi-
dized when its positive charge of electricity is increased or its negative
charge decreased. It is said to be rediuxd when, conversely, its nega-
tive charge is increased or its positive charge is decreased.

An actual oxidation, i.e. interaction with oxygen, although for-
merly always believed to take place, is in many cases not involved.
The action consists, instead, of a change of the charges on the ions.
The term oxidation is, however, still retained.

^Ztschr. anorg. Chem.j 89, 396 (1902).

^ZUchr. anorg. Chem., 44, 379 (1905).

*Zt$chr, JSlektroehem,j 12, 263 (1906).

^Ztachr. Slektrochem., 11, 298 (1906); Ztschr. phys, Chem,, M, 641 (1905).

^ChilesoUi, Ztschr, ElektrocKem., 12, 173 (1906).

« Ztschr. phys. Chem., 10, 387 (1892), and 14, 228 (1894).

256

A TEXT-BOOK OF ELECTRO-CHEMISTBY

SoLunom or

£* altotrad* • atoetroljte

SoLunons

^' ^'oiMttoiii aigjmuii

Sn Clfl + KOH . .

-0.861

FeSOi, neuti

Ml . + 0.078

NasS

-0.061

UydroxylaoL

ine + 0.076

HydroxyUmine,

NaHSOt .

. . . +0.108

KOH ....

- 0.610

H,SOi .

. . . ^0.158

Ohromoiu acetate,

Fe804+HsS<

34 . . + 0.234

KOH ....

-0.680

Potaeainin

ferric

Pyrogallol, KOH .

-0.482

oxalate

. . . +0.286

Hydrochinone . .

-0.829

Iff KI .

. . . +0.328

Hydrogen, HCl .

-0.811

K,Fe(CN)«

. . . +0.422

Potafisiam ferrooa

KsCrsOf . .

. . . +0.602

oxalate . . .

- 0.276

KNOs . . .

. . . +0.677

Chromous aoetate

-0.106

Clt, KOH

. . . +0.626

K4Fe(CN),, KOH

-0.086

FeCU . .

. . . +0.678

I,, KOH ....

- 0.070

HNOi . . .

. . . +0.697

Sn Cls, HCl . . .

-0.064

HCIO4 . .

. . . +0.707

PotaaBlam arsen-

Br,, KOH .

. . +0.755

ate

-0.064

HfCrtOT . .

. . + 0.837

NaHiPOi . . .

-0.044

HCIO, . .

. . +0.866

CuCli

+ 0.000

Brs, KBr

. . + 0.866

NasStOi ....

+ 0.016

KIOs . . .

. . + 0.929

NatSOt ....

+ 0.023

MnOs,KCl .

. . + 1.068

NajHPOt . . .

+ 0.083

Cl,,KCl . .

. . + 1.106

K4Fe(CN)« . . .

+ 0.036

KMn04 . .

. . +1.203

According to these definitions there must be, in every galvanic
cell, an oxidation at one electrode and a reduction at the other.
In the Daniell cell the reduction takes place at the zinc electrode
and the oxidation at the copper. The precipitation of one metal by
another, the process of substitution, is thus to be considered as one
of oxidation and reduction. It is evident, then, that the metals can
only serve as reducing agents, since they are only capable of produc-
ing positive ions, followed by the formation of negative or the dis-
appearance of positive ions. The metals themselves are thereby
oxidized.

On the other hand, all of those elements which produce negative
ions act exclusively as oxidizing agents. Solutions of electrolytes
in general may be reducing as well as oxidizing agents, for they con-
tain both positive and negative ions, and are therefore capable of
yielding positive or negative electricity. If zinc be placed in a so-
lution of cadmium bromide, cadmium is precipitated, the solution
acting as an oxidizing agent ; but if chlorine be conducted into the
solution, bromine separates, the solution acting as reducing agent.

ELECTROMOTIVE FORCE 267

Similarly, the substances in the above table may be examined to
discover whether they are reducing or oxidizing agents. From the
above it is, moreover, not surprising that a dissolved substance may
have a reducing or oxidizing action according to circumstances.
This may even be the case when only the single ion enters the reac-
tion ; the bivalent ferrous ion may change into the trivalent ion, on
the one hand, or into metallic iron, on the other ; that is, it may act
reducing or oxidizing.

Attention has been called by Luther^ to the fact that since the
change in free energy in an isothermal, reversible process is inde-
pendent of the path and dependent only on the original and final
states, the work required to transform the lower directly into the
highest state of oxidation is equal to the work required to effect the
transformation from the lower to the next higher state plus the
work required to transform the latter to the highest state of oxida-
tion, etc. Since, now, the work for the reversible oxidation is meas-
ured by the quantity of electricity consumed, the following holds : —

(a + 6) QF s= oqf' + &qf".

Here a and b represent the numbers of electrical units q of elec-
tricity consumed in changing the state of oxidation from the lower
to the intermediate, and from the intermediate to the higher state,
respectively. The electromotive force required during the first
stage of the oxidation is f', and during the second stage f^', while
that required when the entire oxidation takes place in one stage is
F. From the above equation the following is obtained : —

, ttF' -f- &f"

F = ;; •

a + b

In the case of iron, which may furnish either di- or trivalent ions,

this equation becomes

_ 2f^ + f^'

and in the case of copper, which may furnish uni- and bivalent ions,
it becomes

"""■ 2 •

These equations state that the electromotive force which is re-

1 Ztsehr. phys. Chem., M, 488 (1000), and 86, 885 (1901). The numerical
values have been cbanged to agree with more recent measurements. See preyi-
ous pages.

268 A TEXT-BOOK OF ELECTRO-CHEMISTRY

quired to oany out the oxidation in one stage from the lowest to the
highest state, is always between the two electromotive forces which
are required to carry out the oxidation from the lowest to the inter-
mediate, and from the intermediate to the highest state, respect-
ively. Hence, such a relation as,

which at first sight one might hit upon, does not hold.

Nothing can be predicted in regard to the order of the three elec-
tromotive forces, since they depend both upon the nature of the
substances and upon the concentrations involved. If the latter con-
dition be eliminated by taking all substances involved at a concen-
tration unity, then two typical cases may occur.

Casb I. Iron is an example of this case. When two of the values
are known, evidently the third one may be calculated. Thus for
iron

Z'^Eew-^T^" B — 0.94 volt, and

Z =JEe KUetrodt.^— Xlaitioljto jT = + ^'^ VOlt,

has been found. It follows, then,

JC as Fe r«— ► F.- " — ^"^^ VOlL

The order is, therefore, f', f, and e",

or, in other words, the strongest reducing process is that correspond-
ing to £' and the strongest oxidizing process is that corresponding

tOF".

Leaving out of consideration the negative ions, in the cell,

Iron— ferrous ions . ^-v

Platinum — ferrous and ferric ions !' ^

the iron electrode is negative, and the platinum electrode positive.
When the cell is active, the quantity of iron and ferric ions de-
creases, while that of the ferrous ions increases. In the cell, there>
fore, the same action takes place as would take place if the
substances at the same concentration were directly mixed, i.e. for-
mation of the intermediate state of oxidation at the expense of the
other two, according to the equation,

2 Fe " + Fe = 3 Fe'.

Besides the above cell (1), two more may be formed by combin-
ing the three potential-differences. They are as follows : —

and

ELECTROMOTIVE FORCE

Iron — ferrous ions

Iron — ferric ions !'

Iron — ferric ions

Platinum — ferrous and ferric ions-

259

(2)

(3)

In these cells also, when a current flows, the intermediate stage
of oxidation is formed at the expense of the other two.

There are interesting relations which exist between these three
cells. If the electromotive forces of the cells be calculated from
the single potential-differences, the following values are obtained : —

Obll

Elbotbomotitb Fobob

(1)

(2)
(8)

1.40 Yolto
0.47 Yolt
0.03 volt

If, further, the number of units of electricity q which must be
passed through each cell in order to dissolve 56 grains of metallic
iron be calculated, the values obtained are as follows : -—

Cmi.1.

OOULOXM

(1)

(2)
(«)

2S
8Q

Hence the quantity of energy obtainable from the process,

2Fe • + Fe = 3Fe",

may be obtained in any one of the following three forms according
to the cell used : —

Obll

FOBM

(1)

(2)
(«)

1.40 volte x2q
0.47 volt X 6 Q
0.93 volt x8q

Naturally, the product is in all cases equal to 2.80 x 96,540 joules.
It is evident that here a true galvanic transformation of energy is
being dealt with, which is thereby characterized that only such

260 A TEXT-BOOK OF ELECTRO-CHEMISTRY

transformation relations can appear as can be expressed in whole
numbers. Whetiier or not all these cells can be realized is another
question.

Case II. Copper is an example of this case. The action is here
the opposite of that in the case of iron, t.e. the lower and higher
states of oxidation increase spontaneously at the expense of the
intermediate state, as follows : —

2 Cu = Ctt + Cu".
YHien the cell,

Copper — cuprous ions •

Platinum — cuprous and cupric ions ^'•

(which, however, cannot be directiy realized because of the unstable

character of the cuprous ions), is in action cuprous ions must disappear

and cupric ions appear. In other words, the platinum pole must be

negative and the copper pole positive. Corresponding to this, the

order of the electromotive forces is the reverse of that in the case of

the iron, being

f", f, and f'.

In this case, the process corresponding to f" is most strongly
reducing, while that corresponding to f' is most strongly oxidizing.

It is characteristic of all such cases as that of copper that on the
one hand the intermediate stage Cu' is more strongly oxidizing
than the highest stage Cu", and on the other, it produces a stronger
reducing influence than does the lowest stage Cu. Furthermore,
other conditions remaining the same, the activity of the intermediate
stage both as an oxidizing and as a reducing agent increases with
increasing concentration.

Although it sounds paradoxical, by the oxidation of metallic
copper a stronger reducing agent Cu*, and by the reduction of
cupric ions a stronger oxidizing agent Cu, is obtained. In other
words, it may be stated that, by the addition of a positive charge,
the oxidizing power, and by the removal of a positive charge, the
reducing power, of a substance may be increased.

Considering, finally, an iron electrode (the same holds for a cop-
per electrode) in contact with a solution with ferrous and ferric
ions in such concentrations that

f = f'
and equilibrium exists at the electrode. The relation

F"s3E = F'

ELECTROMOTIVE FORCE 261

is then obtained directly from Luther's equation. Hence when
equilibrium is established, the three potential-differences are always
equal to each other.

It may be well to say a word here concerning the conditions whick
determine the actual production of the electric current.^ It has been
seen that in all galvanic cells a reduction and oxidation take place ^
that is, at one electrode ions come into existence, and at the other
ions disappear. That the reaction may be the source of an electric
current, the two processes must take place at points separated from
each other. If they both occur at the same point, no electric
current ean be obtained. Zinc being placed in a copper sulfate
solution, both the oxidation and reduction proceed simultaneously
at the surface of the metal. The electric charges of the dissolving
zinc and precipitating copper have the opportunity of neutralizing
each other there, and the possibility of a removal of this neutraliza-
tion to some other point (and thereby the production of an electric
current) is lost. Hence the general statement, that a chemical reaction
between two substances can only be used as a source of electrical
energy when electricity is produced or disappears during the reaction
(i.e. by changes in the charges of the ions), and also when the two sub-
stances separated from each other are still capable of undergoing this
reactioTL

If zinc be in contact with a solution of zinc sulfate, and a
platinum wire be placed therein, only a feeble current is obtained
on connecting the wire with the zinc. If it be desired to dissolve
the zinc rapidly, that is, to cause it to pass into the ionic state and
produce a large current, this may be accomplished by surrounding the
platinum with a solution such as that of a copper salt, or of an acid
whose positive component has a smaller tendency to produce ions
than zinc. The addition of the copper or acid solution directly to
the zinc solution would evidently not produce an electric current.

In the production of galvanic currents many different oxidizing
agents have been used to achieve the highest possible efficiency,
without the theory of the phenomena being clearly understood. One
of the most common cells is the bichromate cell, consisting of

Zn - HjCr A(Na,Or A + HjSO*) - C.

The process consists essentially in the formation of zinc ions at the
n^ative (zinc) electrode, and the reduction of chromium ions at the
positive (carbon) electrode from higher to lower valency, whereby
electricity is given up to the electrode.

1 Ostwald, " Chemifiche Fernewirkung,*' Ztschr. phys. Chem., 9, 640 (1802).

262 A TEXT-BOOK OF ELECTRO-CHEMISTRY

The electromotiye force of this cell is great, because the zinc has
« strong tendency to go into the ionic state, and the chromium ions of
high valency also tend strongly to change into ions of lower valency,
the two tendencies additively producing the high electromotive force.
Furthermore, it is clear that the electromotive force of this cell,
when active, must gradually diminish, because zinc ions are con-
tinually forming, while the concentration of the chromium ions of
higher valency is decreasing, and that of those of lower valency in-
creasing. Each of the three changes reduces the electromotive force.

The energetic oxidation of the zinc and the high electromotive
force of the cell is therefore obtained by the addition of the oxidiz-
ing agent, not to the zinc, but to the carbon.

It is also possible to dissolve the noble metals or to change them
into the ionic state in a similar manner. A cell consisting of

Pt — NaCl solution — Au

produces no electric current, though one is produced when chlorine
water is introduced at the platinum electrode, the gold dissolving.
The great tendency of the chlorine to yield ions may be looked upon
as forcing the resisting gold to act similarly. Addition of the
chlorine water to the gold electrode alone would not result in the
production of a current (the platinum being unaffected), and the gold
would oxidize very slowly.

The free energy of other processes, such as that of solution, can be
made to produce an electromotive force by being coupled or combined
with oxidation or reduction processes.^ Thus the double cell,

Hs(in Pt) — saturated solution over solid salt — Oj(in Pt)

H,(in Pt) - pure water .0,(in Pt) !'

produces an electric current which flows from the saturated solution
through the oxygen electrode to the pure water. The process which
takes place when the cell is in action is merely the combining of
water with solid salt to form a saturated solution. Since this pro-
cess can in this manner be carried out reversibly, the electrical
energy derivable from it gives directly the maximum available work
of the process. As a matter of fact, the same relations have been
considered, only from a different standpoint, earlier in the book,
especially in the section on double concentration cells (see page 211).
Finally, the above cell shows clearly that the active mass of the
water in the solution is not, as has been tacitly assumed up to this

1 Ostwald-Lather, Hand- und HUfabucht p. 888.

ELECTROMOTIVE FORCE 268

point, equal to that of pure water. It is proportional to the vapor
pressure. In the case of dilute solutions, however, the difference
between the active masses of pure water and solution, and therefore
also the electromotive force of the cell, is very small. Since the
active mass varies, the product H' x OH' must also change; for if it
remained constant, then, considering the abbve cell as a combina-
tion of

Hydrogen H'

and Oxygen OH'

electrodes, no electromotive force could arise.

FORMATION OF POTENTIAL-DIFFERENCE AT THE ELEC-
TRODES. SPONTANEOUS EVOLUTION OF OXYGEN OR
HYDROGEN. THE PROCESS OF CURRENT PRODUCTION »

In considering any electrode and an aqueous solution of the cor-
responding ions, between which there exists an electromotive force
F, it must not be forgotten that there are also hydrogen and hydroxyl
(or oxygen) ions present in the water. Hence in order that equilib-
rium may be established, each electrode must become charged with
hydrogen and oxygen to such an extent that the potential-difference
of the combination, —

Hydrogen — hydrogen ions — ,
and of the combination, —

Oxygen — oxygen ions — ,

is equal to f. In this connection, the reader is referred to the dis-
cussion on page 187 and to the note on page 254. This process is
of special importance in the case of platinized platinum electrodes,
because they dissolve large quantities of gases, and, further, because
a state of equilibrium is established in a short time. At a platinized
ferri-ferro electrode, for example, the following equilibrium equa-
tions must be satisfied : —

2re +^^2re" +0".

If the tri- and bivalent iron ions are of normal concentration in the
solution, then the potential-difference, —

!• •!«<««• -•toetroIyt«= +0.46 VOlt

1 See also Fredenhagen, Ztschr. anorg, Chem^ W, 896 (1QQ8.)

264 A TEXT-BOOK OF ELECTRO-CHEMISTRY

It follows from this that, at a given concentration of hydrogen and
oxygen ions, the concentrations of the hydrogen and the oxygen in
the electrode may be calculated. The latter must, naturally, be
changed by a change in the concentration of the hydrogen and oxy-
gen ions if that of the iron ions remains unchanged. A short con-
sideration shows that to a higher charge of oxygen there always
corresponds a lower one of hydrogen, and conversely. Kow it is
evident that when the concentration of the gas in the electrode be-
comes too great, it escapes from the electrode. Assuming that this
takes place if the hydrogen or oxygen exerts a pressure of one atmos-
phere, then it may be stated that every oxidizing agent for which

or, what is the same thing,

1a dMtroda - dwtndjte > 1*22 VOltS,

must cause the evolution of oxygen from a solution which is normal
in respect to hydrogen ions. This action must, moreover, continue
until the concentrations involved have been so diminished as to
lower the potential-difference to the value 0.94 or 1.22 volts, accord-
ing to the standard of reference adopted. On the other hand, a re-
ducing agent for which the potential-difference ^ or Em ^s less than
—0.283 or 0.00 volt respectively, will cause hydrogen to be evolved
from a solution of hydrogen ions of normal concentration. Thus it
is seen that oxidizing and reducing agents in aqueous solutions are
relatively stable, and capable of measurement only within narrow
limits. Outside these limits only states in transition exist, and
therefore the deduced equations are no longer applicable. This is
true, for instance, of solutions of persulfates which break down
into sulfates with the evolution of oxygen. Only when the per-
sulfate concentration becomes very slight is the potential-differ-
ence corresponding to its relative stability reached. itelative
stability only can be spoken of because all oxidizing and reducing
agents undergo such a change with hydrogen and oxygen ions (and
consequently with the corresponding charges of gases on the elec-
trode) that their electrode potential-differences always approach that
value corresponding to the atmospheric oxygen. Since this oxygen
is present in an inexhaustible quantity, its concentration remains
constant The iron electrode mentioned above is in stable equilib-
rium in the air only when in a solution of such a concentration in
respect to the oxygen (or hydroxyl) ions that the electrode of atmos-
pheric oxygen in it also produces a potential-difference of 0.46 volt.

ELECTROMOTIVE FORCE 265

The assTunption is here made that the existing hydrogen concentrar
tion in the electrode remains unchanged. Since, strictly speaking,
this would only be the case when the corresponding pressure of
hydrogen exists in the atmosphere, which certainly is not the case,
the conclusion is now reached that a state of complete equilibrium
is never attained. However, since as long as the pressures of the
gases do not exceed one atmosphere they diffuse from the electrode
into the surroundings very slowly, it may be assumed in practice
that, below this limit, the relations may be calculated.

Another important result may be obtained from these considera-
tions. If for a reducing agent,

r* electrode - electrolyte "< 0.00 VOlt,

it will no longer be stable in a 1 normal solution of hydrogen ions,
but will be stable in a solution containing less hydrogen ions, as,
for example, in a solution containing hydroxyl ions. The lower the
hydrogen ion concentration, the greater (counting negatively) will
be the potential-difference between the hydrogen under atmospheric
pressure and the solution, and the greater can also be that between
the reducing agent and the solution without causing hydrogen to be
evolved. The less noble metals, such as iron, furnish the simplest
illustration of this behavior. In a 1 normal solution of ferrous
ions, which is neutral and therefore contains but few hydrogen ions,
iron does not evolve hydrogen. On the other hand, if the solution
is acid and therefore contains many hydrogen ions, the iron evolves
hydrogen immediately.

An analogous discussion may be applied to the case of oxidizing
agents, or substances producing high positive potential-differences.
They are more stable and evolve oxygen less energetically and after
a longer time in acid than in alkali solutions.

In the previous discussion it was assumed that the potential-dif-
ference in the case of such oxidizing or reducing agents as a ferri-
ferro solution, the changes of which do not involve hydrogen or
hydroxyl ions, is independent of the concentration of these ions, i.e.
is the same in acid or alkali if the concentration of the ions of the
oxidizing or reducing substance is not changed. Within certain
limits, experimental measurements have confirmed this assump-
tion. The magnitude of the concentration of the gases hydrogen and
oxygen on the electrodes naturally changes, as already explained,
corresponding to the changes in the concentrations of the hydrogen
and oxygen ions.

If there is a possibility of further reactions taking place at the

266 A TEXT-BOOK OF ELECTRO-CHEMISTRY

electrodes, as would be the case, for example, if iodine be added,
then in this case, when equilibrium is again established, the poten-
tial-difference between the iodine and iodine ions must be equal to
that just considered above. If the electrolytic potential-difference
for the individual reactions be known, then very interesting calcu-
lations may be carried out. For example, we may calculate the
ratio of ferrous to ferric ions which may exist in a normal solution
of iodine ions which is saturated with iodine.^

If it is so desired, all galvanic cells, especially those with plati-
nized electrodes, may, therefore, be considered as hydrogen and
oxygen concentration cells. It is not possible to say with certainty
just how in the individual cases the electric current comes into
existence. It is, in all probability, different in different cases. In
the case of the ferri-ferro electrode it may be assumed, as has been
done in the preceding pages, that the current results from the direct
transformation of ferric into ferrous ions, but it also seems permis-
sible to assume that the current, or a part of it, results from such a
reaction between the ferric and hydroxyl (or oxygen) ions as is rep-
resented by the equations given on page 263. As a result of this
reaction, the electrode may become laden with hydrogen, and there-
upon become electromotively active. In the case of the oxidation
of thiosulf ate to tetrathionate according to the equation,

2S,0;'-f2Q = SA",

it has been shown by Thatcher ' to be very probable that the process
only takes place through the agency of oxygen. Likewise in the
case of organic oxidizing agents, for example chinone, which are
not measurably ionized, the above assumption seems plausible. In
an analogous manner, through a reaction taking place at the elec-
trode by which a reducing is transformed into an oxidizing sub-
stance, e,g. ferrous into ferric ions, the electrode may become laden
with hydrogen, and then exhibit an electromotive force. In the
case of the metal electrodes we will assume that the current is not
produced by such an indirect process, but by the direct passage of
the metal into the ionized state, although opposition to this view
has already become strong.

There are many metals which, upon being dissolved electrolyti-
oally, are capable of forming more than one kind of ions. This fact
raises a question as to the nature of the process of solution in such

1 For farther particalan, see Abegg, Ztm^r, EUetroehem,, 9, 569 (1903).
> Zt9ehr.phy8. Chem,, 47, 641 (1904).

ELECTROMOTIVE FORCE 267

oases.^ Kow the metals must dissolve in such a manner that the
potential-differences between the electrode and the various ions shall
be the same. The relation between the concentrations of the ions
being formed is thereby determined. If another substance, which
forms a complex compound with one kind of ions, be added to the
solution, it is at once evident that the valence with which the metal
goes into solution will be more or less changed in favor of the ion
thus constantly removed to form the complex compound. Undoubt-
edly ccnnplications often appear during the solution of metals.
They will be considered further in the section on the passive
state.

ELECTROMOTIVE FORCE AND CHEMICAL EQUILIBRIUM

When an electromotively active reaction takes place at an elec-
trode, and all effective concentrations are equal to unity, the
measured value of the potential-difference of this reaction has been
called its '' electrolytic potential '' (see page 253). Absolute values
of the " electrolytic potentials " cannot be obtained with certainty at
present The question now arises whether or not such values may
be calculated directly from purely chemical data.

In order to calculate the value of the electrolytic potential, it is
only necessary to know the maximum quantity of work obtainable
when, by means of a non-electrical, isothermal, reversible process, the
substances involved on one side of the reaction equation at unit con-
centration are transformed into the substances involved on the
other, likewise at unit concentration. If now the transformation be
imagined to take place electrically, the maximum work obtainable is

We = VQF.

Since the maximum quantity of work is, according to the second law
of energetics, the same whatever the process used,

W
or FsB — .

The value of W can, in the case of gases and dissolved substances in
dilute solutions, be calculated.
Consider the system,

oA + bB hVQ(-f )^cfD-f 6Jr —

1 Le Blano, Ztsehr, Electrockem.f 9, 686 (1903) ; Abegg-Sknkoff, Zt$ehr.
Jgleetrockem.j 19, 467 (1906).

268 A TEXT-BOOK OF ELECTRO-CHEMISTRY

in equilibrium, that is to say, under such conditions of concentration
that no work is required to carry out the process in either direction.
Further, let these concentrations be represented by

•• •.

C'Vj G By ••• Cdj Gg,

and the number of mols of the substances inyolyed by

respectiyely (see page 253). Then according to the mass action law,
the following relation exists between the quantities of the substances
entering the reaction : —

cy X Ci' ... ^'

where KJ is the equilibrium constant.

In order to calculate the maximum work TTof the process, we may
proceed as follows : —

1. With the aid of the simple gas laws which apply to dissolved
substances (see page 168), the work expended or gained in bringing the
given number of mols of the substances on one side of the above
reaction equation from the concentration unity to the concentrations
Oj', CTfl', ... may be calculated.

2. Under equilibrium conditions, these substances at the above
concentrations may be transformed into the substances on the other
side of the reaction equation at the concentrations Cd', Ce\ .••»
without the expenditure of work.

3. Finally, the quantity of work involved when the concentrations
of the latter substances are changed from C^} GJy *** to unity may
be calculated.

If T is the room temperature and W the maximum work of this pro-
cess, the following equation is obtained from the above calculations.^

Therefore the absolute value of the '^ electrolytic potential '' is given
by the equation,

(BP)«:^lnJS^;.

By combining this equation with that given on page 253, the follow-
ing general expression is obtained : —

^ For further particalars see Nemst, Theorem. Chem.^ 4th edition, p. 090
(1908).

ELECTROMOTIVE FORCE 269

, (absolute) - ^f In ^J-^^^ + In ^lii^:::)

<w 5 (absolute) = ^fla KJ + In ^^^f'"\

where CTj, CTb, ••• Cj>y C7^» **- represent any concentrations of the
substances inyolved.

The ralue of K„ the equilibrium constant of the single reaction
which takes place at one electrode, cannot, however, be experimen-
tally determined, for a chemical reaction always consists of an oxida-
tion and a simultaneous reduction; never of one of them alone. By
chemical methods, it is only possible to determine, in a given experi-
ment, the equilibrium constant of the total reaction taking place at
the two electrodes. It is, therefore, not possible by means of deter-
minations of equilibrium constants to obtain a knowledge of the
values of the potential-differences of single electrodes. However,
with the help of such determinations, and a knowledge of the con-
centrations of the substances reacting at the electrodes, it is possible
to calculate the electromotive force of the cell, which is, if the po-
tential-difference between liquids be disregarded, equal to the sum of
the two single potential-differences. This may be done with the
help of the equation,

= :K?flnJr.+ln-^l->i%:\

^9 V c: X c], .../

in which K^ is the equilibrium constant of the total reaction taking
place in the cell, f is the electromotive force of the entire cell, and
the terms after the logarithm sign are the concentrations of the
substances which react at the two electrodes respectively.

In this connection it should be remembered that the electromotive
force of any galvanic cell may be calculated by a second method with
the aid of the heat of reaction Q, and the temperature coefficient of

the potential-difference -— . The equation is that formulated by
Helmholtz (see page 173) : —

Q dT

The former equation, first put forward by van't Hoff in the year
1886, has recently, at the instance of Bredig, been tested experimen-
tally by Knlipffer.^ The results obtained will now be considered.

1 ZUchr, phyi. Chem,y M, 266 (1898); also, ZUchr, Elektrochem.^ 4» 644 (1808).

270 A TEXT-BOOK OF ELECTRO-CHEMISTRY

The double reversible chemical tranBformatioiii

TlCl + KSCN 2: TISCN + KCl,
■olid dissolved solid dissolved

was investigated. Since the transformation is independent of the
quantity of the solid salts, and since the concentrations of the latter
may be regarded as constant^ it is only necessary to consider the sub-
stances in solution. It is, moreover, assumed that the solutions are
dilute and that the dissolved substances are completely dissociated,
t.e. are present in solution in the form of potassium, sulf ocyanate,
thallium, and chlorine ions. The potassium ions take no part in the
reaction. The equilibrium conditions are, then, given by the equa-
tion,

0x1' X Cqr Oqi' ___ y

On- X Cscvf Cbcii-

Attention is called to the &ct that

is the solubility product of a saturated thallium chloride solution,

and that Civ X Csgm- "=> S'

is that of a saturated solution of thallium sulfocyanate. Hence the
equilibrium constant is in this case equal to the ratio of the two
solubility products and may be calculated from these quantities. It
was, in fact, determined by ascertaining the concentrations of the
chlorine and sulfocyanate ions in solutions formed by shaking a solu-
tion of potassium chloride with solid thallium sulfocyanate, and by
shaking a solution of potassium sulfocyanate with solid thallium
chloride. The following average results were obtained for this re-
action: —

TSMPBBATUSB (f)

BQUIUSSIVM COMRAIIT

0.8»

1.74

20.0»

1.24

39.9»

0.85

Using these values of the equilibrium constant, it is possible to
calculate, for any known concentrations of chlorine and sulfocyanate
ions, the values of the electromotive force of this process at these
temperatures. By placing

CI I ^

ELECTROMOTIVE FORCE 271

io the equation given on page 269, the following expression is ob-
tained: —

In order to be able to measure directly this electromotiye force, it is
necessary to devise a cell by means of which this reaction may be
made to produce an electric current. Such a cell is the following
combination : —

Thallium amalgam — EGl solution sat. with TlCl- •. ^

Thallium amalgam - KSCN solution sat with TISCN . J *

If 9 when this cell is in action, the positive electric current flows in
the cell from the upper to the lower thallium amalgam in the above
scheme, thallium and sulfocyanate ions are formed while simul-
taneously thallium and chlorine ions disappear. Hence only the
chlorine and sulfocyanate concentrations are changed. The electro-
motive force of the cell must, therefore, depend upon the ratio of
these two concentrations to each other.

The values of the electromotive force found by experiment agree
well with those calculated with the aid of the equilibrium constants,
as may be seen from the following table : —

Elbctbomotivx Fobcb
Tbmpbratum CalciOated Found

0.8* 17.1 17.6 millivolts

20.0** 9.8 10.6 millivolts

39.9** 0.6 1.0 millivolt

It may be remarked, further, that this cell can also be considered
as a concentration cell in respect to the thallium ions, and that its
electromotive force can also be calculated by means of the equation
applying to such cells.

One further interesting relation is shown by the equation given
above. If a is made equal to JS^, i.e. if equilibrium concentra-
tions are maintained, then the electromotive force of the cell is
equal to zero. This follows from the fact that, when chemical
equilibrium exists in a cell, electrical equilibrium must also exist.
Utilizing this fact, the appearance of a state of equilibrium may be
shown by electrical measurements. Thus Cohen ^ determined transi-
tion points by means of measurements of electromotive force. Zinc
sulphate crystallizes at room temperature with seven molecules of

I ZtBchr, ph^B. Chem,, 14, 63 and 686 (1894).

272 A TEXT-BOOK OF ELECTRO-€HEMISTRY

water, while at a somewhat higher temperature it crystallizes with
six molecules. Hence with the combination^

Zn — Z11SO4 • 7 H^O in contact with the solid salt ;

Zn - ZnSO* • 6 H,0 in contact with solid salt 1'

which is a concentration cell (or in this case a transition cell), an
electric current may be obtained because the two hydrates are not
equally soluble. Its construction is conditioned by the fact that
below the transition temperature the metastable hydrated salt,
ZnSOi • 6 H,0, may exist for some time. This condition can, how-
ever, be avoided by an artifice. If the temperature of such a cell be
varied, so slowly that the solution is always saturated, to the transi-
tion temperature, the electromotive force decreases and finally at
this temperature becomes equal to zero, since here the solubility
curves of the two hydrated salts intersect each other. From what
has already been stated in reference to concentration cells, evidently
the relations existing in this cell may be calculated.
The reaction.

Metal oxide ^ metal + oxygen,

and also the reaction.

Metal halide ;j± metal + halogen,

forms an especially simple case. Here the following equation holds,

where p^ represents the dissociation tension or pressure of the metal
oxide at the temperature T,^ for it alone determines the equilibrium.
In this equation TT represents the work obtainable when one mol of
oxygen passes from a pressure p^ atmospheres to a pressure of one
atmosphere. It may be obtained in the form of electrical energy
with the aid of the cell.

Metal — solution of metal oxide (sat.) — oxygen (atm. pressure).

When one mol of oxygen is transformed in this cell, the electrical
work.

Hence we have the following equation: —

^ Rothmund, Zt9chr. phys. Chem.^ 82, 69 (1899); and Lewis, Zuchr. phys.
Chem., 65, 449 (1906).

ELECTROMOTIVE FORCE 273

Therefore, the value of f being known, that of p^ may be calculated.
This cell may also be considered as a concentration cell in respect to
oxygen.

The investigation of Luther and Sammet^ furnishes an example
of a somewhat more complicated relation between the electromotive
force and the equilibrium constant. The equilibrium constant of
the reaction,

6H- + IOa' + 5r5t3I, + 3HA

was determined chemically, giving the following: —

ir.,^== («rxTOx(ir ^2.8(+o.3)xio^.

The above reaction may now be considered to be made up of the
following individual processes : —

2 I0, + 12 H- +10 a (_)5tI, + 6 H,0; (a)

r + 3H,0 + 6<>(+) 5tI0', + 6H-; (6)

4r + 4a(+) ^21r (c)

A summation in the usual manner of the members on either side of
the ^ sign of these equations gives the above original reaction
equation.

If now all three processes exist in equilibrium in a mixture, and
if a reversible electrode for each process be placed in the mixture,
then it follows from what has been said in the last two sections that
the three potential-differences between the respective electrodes and
the solution must be equal to each other. Under these circum-
stances these potential-differences will be represented by the follow-
ing equations : —

(a) (a)

(6) (P)

r _, , Jgr ■ (IT)* X go.') .

— ttlMtrod* - •iMtrolTte "" — o "^ o q

1 ZUehr. ph^i. Ohtm., U, 041 (1906) ; Zt$ehr. Xleetrochem., 11, 808 (1005).

274

A TEXT-BOOK OF ELECTRO-CHEMISTRY

and when the potential-differences are equal we obtain the follow-
ing:—

(ft) (a)

^ -• 6q '

For prooess (a) it was possible to obtain a reyersible platinum
electrode. The concentrations of H', 10^', and Ij were found to be
of considerable magnitude and also measurable. Hence it was pos-

(«x

0>).^A (c)

sible to determine^ '^and therefore also ^and

Fo Fo F0.

In an analogous manner the reaction,

6 H+ BrO; + 6 Br' 5t 3 Br, + 3 H/),

was investigated. It was found possible to calculate the corre-
sponding values for chlorine. The following results referred to the
calomel cell were obtained : —

FoclMtrod* -<- cleetrolTto

lODIKS

BBOMim

CHU>sm

Process (a)

Process (b)

Process (c)

1
P P P

1.186
1.138
0.812

1.26
1.28
1.12

In the case of bromine and of iodine there exists a considerable
potential-difference between the liquids. By means of an artifice
this has been made calculable, thus permitting it to be taken into
consideration in calculating the above values. The temperature of
the measurements was 25**.

It being known that at the transformation temperature, or, more
generally speaking, at the point of equilibrium of two systems, the
potential-difference is equal to zero, it may at once be concluded
that no potential-difference exists between a solid and a fused metal
at its melting point. It is impossible, therefore, to obtain an electric
current from a cell composed of an electrolyte, and of a fused and a
solid electrode of the same substance at this temperature. From

ELECTROMOTIVE FORCE 275

this it is evident that the heat of fusion, no more than the heat of
solution (see also page 227) can be considered exclusively as the
direct source of the electrical energy. This conclusion has been
confirmed by the results of experiment. ^ If such a cell be placed in
surroundings of a temperature other than the melting point, whereby
either the liquid or the solid phase must become unstable, naturally
an electric current is obtained because the two phases are no longer
in equilibrium ; but the one is capable of undergoing transformation
into the other with the simultaneous production of free energy.

VELOCITY OF IONIZATION. PASSIVITY. CATALYTIC

INFLUENCE

Up to the present the velocity of the passage of a substance to and
from the ionized state has been left entirely out of consideration under
the tacit assumption that, in comparison with the velocities usually
measured, it is infinitely great. In the case of the Daniell cell, for
example, at a constant temperature, the electromotive force is depend-
ent only on the concentrations of the two solutions. Constant prop-
erties are ascribed to the zinc (which furnishes the ions) which are
also independent of the strength of the electric current. It may
now be questioned whether there are not cases in which the velocity
of the formation of ions is no longer infinitely great, but possesses
very different values under different circumstances. What would
happen in the case of the Daniell cell if suddenly the velocity of
the formation of zinc ions should fall to zero ? In answer to this
question it may be stated that the zinc would then behave like
a noble metal and that the cell would no longer of itself furnish an
electric current. If, furthermore, with the aid of an independent
electromotive force, an electric current should be sent through the
cell in the direction of the current of an ordinary Daniell cell, oxy-
gen would be evolved at the zinc electrode.

In general there are a number of possible processes which may
take place at an electrode upon the passage of an electric current,
and of these processes, that one takes place which gives rise to the
highest electromotive force. Here again it is assumed that the veloc-
ity of ionization is infinitely great. If this velocity is not suffi-
ciently great, the above principle becomes invalid.

It sometimes happens that a base metal which under ordinary
circumstances is dissolved as required by its valence and Fara-
day's law, under other conditions behaves like a noble metal.

1 Ztschr. phy8. Chem., 10, 469 (1892).

276 A TEXT-BOOK OF ELECTRO-CHEMISTRY

This behavior is called poMivity, It was first observed with iron
at the end of the eighteenth century. In concentrated nitric acid
iron loses the power of dissolving with the evolution of hydrogen
which it possesses in dilute acids. Even when used as an anode in
dilute nitric acid it does not go into solution, but instead permits an
evolution of oxygen. Recently it has been found that this phe-
nomenon of passivity is of frequent occurrence, occurring with iron,
nickel, and other metals in alkali solutions, with nickel also when
it is used as an anode at ordinary temperatures in salt solutions
which are neutral, or acid with nitric or sulfuric acid.

Until recently, the phenomena of passivity were explained on the
assumption of the existence of a film of oxide covering the metal and
protecting it mechanically from corrosion. There is no doubt but
that this explanation is a satisfactory one for a large number of
cases. This is sometimes evident from the appearance alone. For
example, lead when used as an anode in a pure sulfuric or chromic
acid solution with a sufficiently small current density is insoluble
and becomes covered with a visible layer of lead sulfate or peroxide
at which oxygen is evolved. Analogous behavior is always observed
when a salt, the anion of which forms a difficultly soluble compound
with the anode metal, is used as the electrolyte.

It is a remarkable fact that the anode metal is easily dissolved
when, besides a salt of the above description, the electrolyte contains
another one in excess which is indifferent and which furnishes an
anion which forms an easily soluble salt with the anode metal.
This behavior is utilized technically in the preparation of difficultly
soluble compounds (Luckow's process).^ For example, lead, when
used as an anode in a solution of sodium chromate and sodium
chlorate, dissolves easily, and a beautiful precipitate of lead chro-
mate is formed which rolls from the electrode, leaving it still bright.
This is explained by assuming that, due to the action of the indiffer-
ent ions in the mixed solution, a liquid layer free from chromate
ions is formed directly at the surface of the electrode soon after
the electrolysis is started. The adhesion of the precipitate to the
electrode is thus prevented. Hence only at the beginning of the
electrolysis can a precipitate of lead chromate be formed directly on
the anode, and this precipitate does not protect the electrode, for
a covering impenetrable to ions can only be formed when it can be
continually patched or repaired.

After the above presentation of the subject, it would be justifiable

1 Le Blano and Bindschedler, iBenbmg, Just ; Zuckr, Xlektrochem.f •, 265
(1902); 9, 276 and 647 (1008).

ELECTROMOTIVE FORCE 277

for one to expect that, if the passivity of a metal in an electrolyte
is goyemed by the formation of a precipitate, the addition of a
second electrolyte in which the same metal as an anode dissolves^
forming a soluble compound, would oyercome the passivity and
cause the solution of the metal with the simultaneous formation of
a precipitate which would fall from the electrode, as in the case
of the lead chromate.^ This holds for individual cases, as for
example nickel and iron in alkali solutions, but not in others. For
instance, although nickel as an anode dissolves in sodium nitrate,
upon the addition of sodium chloride no precipitate is formed. It
seems scarcely possible to explain this case of passivity in the
above manner, i,e, on the assumption of the formation on the
originally active metal of a protective coating. Some kind of an
insoluble oxide or other compound may gradually form. It can-
notf however, be the cause of the passive state of the metal, but, on the
other hxind, mtist be the result of previously existing passivity. The
same can be said of a film or coating of a gas which may appear.
Up to the present, the optical investigation of the electrode surface
has not led to a conclusive result. It would only be of decisive sig-
nificance if it furnished certain proof that in individual cases of pas-
sivity no oxide layer or coating is formed: A proof of the presence of
such a coating, on the other hand, could not, as already emphasized,
be considered as a conclusive result in the opposite direction.

The above discussion brings us to the idea already indicated, that
here we are often dealing with nothing more than the phenomenon
of reaction velocity. It is well known that the velocity of a large
number of reactions is not only greatly changed by temperature
changes, but also by the addition of substances which are apparently
inert. Furthermore, it is known that a large number of reactions
proceed with such a moderate velocity that they can be easily fol-
lowed. It should not surprise us especially, therefore, to know that
the velocity with which a metal goes from the elementary state to
the ionic state is not always very great. This tracing back of real
passivity to an exceedingly small ionization velocity of the metal
is a gain in that it uncovers the real character of this phenomenon.
It is then only a special, if also an especially interesting, case of
reaction velocity.*

Platinum as an anode does not dissolve in a solution of potassium

1 Le Blanc and Levi, Boltzmami-Festschrift, 1904, and Ztschr. Elektrochem,,
11, 9 (1906). V

^ Less general conceptions of passiyity are given by W. MtlUer, Ztschr, Elek-
trochem^ 11, 755 and 823, and by O. Sackur, in the same volume, p. 841 (1905).

278 A TEXT-BOOK OF ELECTRO-CHEMISTRY

oyanide, but according to F. Glaser,^ it dissolves like a base
metal in the same solution without the aid of the electric current,
although yery slowly, accompanied by the evolution of hydrogen.
This must be considered as a case of true passivity.

The investigations of Hittorf on chromium* may be interpreted in
a similar manner. According to the choice of solvent, tempera-
ture, etc., the chromium is dissolved at the anode in a di-, tri-, or
hezavalent state. In dilute hydrochloric acid,' for example, the
chromium dissolves at moderate temperatures in the divalent state.
If, however, solutions of the alkali sulfates be subjected to elec-
trolysis at lOVt, using metallic chromium as an anode, chromic acid
is obtained. In the former case the process is spontaneous and
therefore is capable of doing work. Here the chromium plays,
in all respects, the part of a base metal, simulating zinc In the
second case work must be expended in order to bring the chro-
mium into solution. The chromium now behaves like a noble
metaL This process especially directs our attention to the fact
that tJie electromotive force depends, not upon the mbstaThce, btU upon the
process. Moreover, calculated results can only be correct when the
assumed process actually takes place alone. It may be said that in
the first case the velocity of the formation of bivalent chromium
ions is very great, while in the second case it is so small that the
formation of hexavalent ions takes place. Here is an example of a
real transmutation, \,e, a transformation of a base metal into a noble
one, although of a different kind from that sought by the alchemists.
At present nothing further is known of the conditions upon which
this change in reaction velocity depends.

Analogous relations exist, according to Luther,' in the case of
ozone. Ozone possesses different electromotive activity and enters a
reaction with different valences according to the nature of the indif-
ferent electrode. At a polished platinum anode it is univalent,
while at a polished iridium anode it is divalent.

Furthermore, in the case of metals such changes in valence often
take place with changes in the anodic treatment. For example, zinc
and copper, as anodes, dissolve at least partly in the univalent state
in the presence of oxidizing agents. Since these univalent ions are
strong reducing agents, the oxidizing agent is reduced or hydrogen is
evolved at the anode. Thus we have, as a noteworthy result, a
reducing action at the anode.^

1 ZUchr. Elektrochem., 9, 11 (1908). ^Ztschr, phys. 0%em., 86, 720 (1806).

• Ztschr. Elektrochem. , 11, 832 (1005) .

« Lather and Schilow, Zttchr.phys. Chem., 46, 777 (1008).

ELECTROMOTIVE FORCE 279

It does not seem impossible that the latter change in yalence may
be explained in a manner similar to that given on page 267 for the
formation of complex compounds when a metal is dissolved. In
both cases there may be a continual removal of one kind of ions
and thus a tendency to favor the formation of this kind of ions.
However, a definite statement of the cause of the phenomenon can-
not be given until the subject is further investigated.

In closing this discussion of passivity, a number of cases in which
a catalytic influence on an electro-chemical process has been observed
will be presented.

From the cell,

Zn - ZnS04 solution -HNO, solution - Pt,

an electromotive force of 0.7 of a volt according to the investigation
of Ihle ^ is obtained if the nitric acid solution is dilute and free from
nitrous acid. During the action of the cell, hydrogen is evolved at
the platinum electrode. If now a small quantity of nitrous acid
be added near the platinum, the evolution of hydrogen ceases and
simultaneously the electromotive force rises to about one volt.

The explanation is as follows : The nitric acid is an oxidizing
agent, i.e. it is capable of producing hydroxyl ions by undergoing
decomposition into the lower oxides of nitrogen. The velocity of
the formation of these ions is, however, under ordinary circum-
stances practically equal to zero. Hence the nitric acid does not
behave like an oxidizing agent, but like any other acid, and therefore
causes hydrogen to be evolved at the cathode as usual. The nitrous
acid accelerates the formation of the hydroxyl ions, and since this
process takes place spontaneously with a much higher electromotive
force, it replaces the evolution of hydrogen. Consequently the elec-
tromotive force of the cell rises.

Finally, the observations of F5rster ' and Voege ' on the reduction
of potassium chlorate shotdd be mentioned in connection with this
subject. The former found that when high-current densities are
used, this salt is scarcely at all reduced when the cathode is of
platinum, lead, zinc, or nickel, very strongly reduced when the elec-
trodes are of wrought iron, and only moderately when the electrodes
are of cobalt The latter investigator found that in acid solutions
the activity of the reduction is dependent upon the material used for
the cathode.

1 Zt9chr, phy$. Chem., 19, 577 (1896).
*Zt8chr, EUktrochem., 4, 886 (1807).
• J. i%y«. Chem,, 8, 677 (1809).

280 A TEXT-BOOK OF ELECTROCHEMISTRY

It is veiy remarkable that, according to the choice of cathode
metal, reducing action can be made to take place to different stages
of the same depolarizer. Thus with the use of mercury as an elec-
trode, TafeP was able to reduce nitric acid quantitatively to hydroxyl-
amine, while with a copper electrode covered with spongy copper
he was able to reduce it almost quantitatively to ammonia. If blank
copper electrodes are used, a yield of about 15 per cent of hydroxyl-
amine may be obtained. It is evident that observations such as
these may become of commercial importance. They will be referred
to again at the end of the chapter on electrolysis and polarization.

The influence of the anode material on the course of electrolytic
oxidation processes is shown in the use of platinum and lead perox-
ide as anodes in the electrolytic regeneration of chromic acid. Only
when the latter is used is a satisfactory yield obtained. The same
difference has been observed in the oxidation of hydriodic to perhy-
driodic acid. According to E. MUller and SoUer' both of these
cases are examples of the catalytic effect of the cathode material

Although apparently they do not belong to this discussion, a few
observations of Luther' will be mentioned. He found that the
addition of a small quantity of a dissolved substance which exists
in several different states of oxidation to the oxidizing or reducing
agent being investigated, is without influence upon the potential-
difference, but facilitates its measurement. Thus with the use of
platinum electrodes it is difficult to measure the potential-difference
of a chromi-chromate solution, evidently because of the slowness of
the reaction, —

CrO/' -I- 8H> 35(-) ^tCr- + 4HA

By the addition of a small quantity of an iron salt, this difficulty

Ye"
is removed. The concentration ratio ^=r-n- becomes so adjusted that

the corresponding potential-difference is equal to that of the chromi-
chromate solution. Now since the velocity of the reaction

Fe" + S(-f.)^re"

is comparatively great, the platinum electrode has become to a

greater extent unpolarizable. Naturally by means of such an addition

it is not possible to obtain a continuous large current of electricity.

From these examples, which might easily be increased, it is suffi-

^ZUchr, anorg. Chem., 81, 280 (1902).
*Zt9chr. Elektrochemie, 11, 863 (1006).
^Ztsehr. phys. Chem., 86, 400 (1001).

ELECTROMOTIVE FORCE 281

ciently evident that catalytic influences which are apparently insig-
nificant produce very considerable effects in electro-chemistry. It is
probable that in the future very remarkable discoveries may be made
in this little-investigated field.

GENERAL THEORY OF THE COURSE OF THE ELECTRO-
CHEMICAL REACTIONS

The idea that possibly the process of evaporation may be
explained by the formation of a layer of saturated vapor directly on
the surface of the liquid which gradually diffuses into the surround-
ingSy and that the rate of evaporation depends on the rate of this
diffusion, was first presented by Stefan.^ Somewhat later, and
apparently without knowledge of Stefan's work, Noyes and Whit-
ney' came to an analogous conclusion in studying the velocity of
solution of solid bodies. They found that the latter is proportional
to the difference in concentration of the saturated solution and that
of the solution surrounding the body at the time the velocity of
solution was measured.

The theory put forward for these two special cases was generalized
by Nernst,' and in this form it was endeavored to apply it to *all
chemical reactions taking place in heterogeneous systems. Accord-
ing to the expanded theory, equilibrium always exists at the boundary
surface of two reacting phases, so that the reaction velocity is deter-
mined solely by the rate of decrease of the difference between the
concentration at the surface and that in the interior of the phase.
K now more comprehensible relations be obtained by reducing the
thickness of the layer in which the fall in concentration takes place
to a certain value I by suitable stirring of the solution, then the -
velocity of reaction is represented by the equation,

D; = 5££2ii(C-C7'),

where d^^ represents the diffusion coefficient, 8 the contact surface of
the reacting phases, and C^CP the concentration-difference involved.
The value of I is dependent on the temperature, the solvent, and the
speed of stirring.
From this theory a number of interesting conclusions may be

1 WUd, Ann,, 41, 726 (1800).
s ZtKhr, phys, Chem,, 28, 689 (1897).

* Ztsehr. phys, Chem., 47, 62 ; and also Bronner, ZUehr. phys. Chem.^ 47, 60
(1904).

282 A TEXT-BOOK OF ELECTRO-CHEMISTRY

drawn. The Telocity of solution of a lod of benzoic acid in pure
water would be for a gi^en surface, temperature, and speed of stir-
ring, proportional to the product of the coefficient of diffusion and the
concentration of the saturated solution, i,e,

it; 8 const. X Do. X C.

In this case (7 is equal to zero. If now at the same temperature
and 'the same speed of stirring, a rod of any difficultly soluble oxide
or hydroxide, with a surface equal to that of the rod of benzoic acid,
be placed in a saturated solution of benzoic acid, then its rate of
solution will be equal to that of the rod of benzoic acid in pure
water, i.e. equal to a const. xv^xC, This must be so, for there is
always at the surface of the solid oxide a layer of liquid saturated
with it, i.e. a layer of a solution of hydrogen ions of a very small
concentration corresponding to the slight solubility of the oxide.
The benzoic acid which diffuses to the surface of the oxide is com-
pletely neutralized; its concentration is thus reduced practically to
zero. Hence the rate of solution of the oxide is governed by the
coefficient of diffusion of the benzoic acid j>„ and the concentration
of the saturated solution C (not considering the constant inyolved).

Plainly nothing essential is changed if a large rod of some base
metal such as magnesium be substituted for the rod of oxide. Since
the concentration of hydrogen ions at the surface of the metal is very
small, it may be considered to be practically equal to zero. The rate
of solution of the metal would then depend only on the Telocity of
diffusion of acid to its surface where hydrogen ions lose their
charges, magnesium ions form, and hydrogen gas is evolved. As
above indicated, this is true provided all processes which consist
in the simple giving up or taking on of electrical charges by a sub-
stance at the boundary surface between metallic and electrolytic con-
ductors are like those which consist in mere transition through a
boundary surface without electrical change, taking place so rapidly
that equilibrium is constantly maintained at the boundary surface.
It makes no difference here whether or not the substance goes over
into another phase, t.e. electrolytic separation and solution, or
whether or not one of the substances dissolved in the electrolyte is
transformed into another soluble substance, i.e. real electrolytic
oxidation and reduction.

We may proceed a step farther. If the rod used in the above-
cited case be replaced (other conditions remaining the same) by any
unattacked electrode of the same form and size, and if a cathode
potential be imparted to it such that the concentration of H ions

ELECTROMOTIVE FORCE 283

formed directly at its surface is very small, then the electric current
(which can pass only through the discharging of H ions) is equiv-
alent to the quantity of H ions furnished by the diffusion of the
acid and the electrolytic transference. The transference of H ions
can be eliminated by taking a solution containing a sui&cient excess
of salt. The velocity of reaction, that is, the current-strength, must
then be equal to the velocity of solution of the oxide rod in the same
acid solution. Hence after a certain cathode potential is reached,
the current-strength remains constant and independent of a further
increase of this potential. This holds only within certain limits, i.e.
until some other process begins also to take place.

Experimental results which have been obtained are in good agree-
ment with this theory.

In the case of all electrolytic reductions and oxidations for which
the assumption holds that all reactions coming into consideration
are very rapid as compared with the velocity of diffusion, the
velocity of diffusion and the kind of stirring are the chief &ctor8
influencing the processes at the electrodes.

There are also processes which take place at the electrodes which
not only consist in the giving up or taking on of electric charges, but
also are accompanied by pure chemical reactions (in a homogeneous
system). Such a reaction is the following : —

Chinone ^i Hydrochinone.*

According to the discussion on page 267, we must consider that
this reaction results from the discharging of hydrogen or hydroxyp
ions at the electrode, and the reacting of the gas so formed with the
chinone or the hydrochinone, as the case may be. The latter pure
chemical reaction, however, proceeds very slowly. In such cases
the velocity of reduction of chinone or the velocity of oxidation of
hydrochinone is independent of the more rapid process of diffusion
and is characteristic of the process in question. It is dependent on
the character of the depolarizer. Such slow reactions as the oxida-
tion or reduction reaction just mentioned are often met with in the
case of organic substances. With such depolarizers hydrogen or
oxygen is evolved at the electrode at a less current density than it
is, under otherwise the same conditions, in the case of very active
depolarizers.

Even in these latter reactions, it should particularly be noted that
it has been assumed that the transference of substances or electrical

1 Haber and Rubs, Ztschr, phy9, Chem.j 47, 267 (1004).

284 A TEXT-BOOK OF ELECTRO-CHEMISTRY

charges from one phase to another takes place with infinite rapidity.
The fundamental assumption of Nemst therefore still remains.
Whether or not this assumption is untenable in many cases is still
an open question. As far as the process of electrical charging or
discharging is concerned, it is probably always rapid, for in
homogeneous systems reactions between ions are generally (always?)
very rapid. Nevertheless we know of no reason at present why of
necessity it must be rapid. There is still less reason for thinking
that other processes taking place between phases are generally (or
always) rapid. It is known that reactions in homogeneous systems
often take place slowly, and no reason is apparent why reactions in
heterogeneous systems may not also take place slowly.

It is evident that these questions are most intimately related to
the phenomenon of passivity (see page 275). The assumption of a
lack of a velocity of ionization made in considering passivity does
not necessarily contradict the fundamental assumption of Nemst.
It is quite possible that the transition from the metallic to the
ionic state may consist, not only of the taking on of an electrical
charge, but also of a number of other processes, any one of which
by taking place slowly may cause the appearance of the phenomenon
of passivity. This latter case is very similar to that of the reaction^

Chinone ^ Hydrochinona

A further explanation must be left to the future.

ELEMENTS POSSESSING DOUBLE NATURES

Although up to the present we have always spoken of substances^
like the metals, which can furnish only positive ions, or of substances,
like oxygen, which can furnish only negative ions, it is not unreason-
able to question whether or not a single substance may possess the
power of forming both negative and positive ions. In the year
1900 I stated the following in the second edition of this book.
^* There are many indications that such cases exist. Thus if a solu-
tion of selenous or selenic acid be electrolyzed, a deposition of
metallic selenium is obtained at the cathode. This indicates the
existence of positively charged selenium ions. On the other hand,
a study of hydrogen selenide or sodium selenide leads to the con-
clusion that selenium also forms negative ions. The behavior of
sulfur and of tellurium is similar to that of selenium, and even in
the case of the halogens, it is not entirely certain that under sM
circumstances they form negative ions.'' In the meantime Walden

ELECTROMOTIVE FORCE 286

has carried out condaotiyity measurements in solvents other than
water which substantiate this view. He^ found that the conduc-
tivity of liquid sulfur dioxide is considerably increased when
bromine is dissolved in it, and that of sulfuryl chloride is also
increased by the addition of iodine. If now we maintain that the
electrical conductance of solutions is due to the presence of ions,
then we come to the conclusion that the bromine and iodine in these
two solutions dissociates according to the equations, —

Br, 5t Br + Br',
and Ij^tr + r.

Closely related to the question of the possibility of an element
existing in solution both in the form of positive and of negative
ions is that of the possibility of one and the same element
going into solution by being electromotively active both as an anode
and as a cathode. As a matter of fact, this remarkable behavior is
exhibited by tellurium when used in a completely symmetrical arrange-
ment* in an alkali solution. At the anode it goes into solution as
Te,"y where x varies between 1 and 2 according to the conditions
of experiment, and at the cathode as Te**** which unite largely
with the OH ions to form the complex ion TeO^''. This explanation
at least seems the simplest one offered up to the present time. Al-
though investigations of other elements have not yet been concluded,
they appear to behave in a similar manner.

It is, at all events, of great interest to learn that there is no
sudden change between ^^ positive'' and ^'negative" elements, but
rather a gradual transition through a number of elements which
may be either positive or negative according to circumstances, i.e.
through elements which possess double natures.

^ ZUi^r. phy8, Chem., 4S, 885 (1903).

s M. Le Blanc, Zt9chr. Mektroehem.^ 11, 813 (1906) ; and IS (Spring of 1906).

CHAPTER VIII

BLBCTBOLTSia AND POLARIZATZOH

Thx phenomena observed when an electric current is conducted
through an electrolyte between inactive electrodes, as gold, platinum,
carbon, etc., will now be considered. It has long been known that
the current produces a decomposition of the electrolyte at the eleo-
trodes, and that its electromotive force is thereby reduced. The
two facts are evidently related. The performance of an amount of
work, more or less considerable according to circumstances, is neces-
saiy to bring about the decomposition of an electrolyte (as, for
example, hydrochloric acid into hydrogen and chlorine), and this
work is done by the electric current. When such reduction of the
electromotive force occurs, polarization is said to take place. The
phenomenon was formerly very little understood, and it is only
within the lap t few decades that its explanation has become possible.

If a current flows for a time through the above-described arrange-
ment, and is then interrupted, the two electrodes being connected
through a galvanometer, it wiH be observed that an electric current,
which rapidly becomes weaker, passes between the electrodes in a
direction opposite to that of the first or applied current. This is
spoken of as the pdlarizatioti current, and its electromotive force is
called the dectrornative force of polarizatum. From the following it
will be evident that this current is derived from the tendency of the
materials separated in the neutral condition to return to the ionic
condition.

Ohm's law, applied to a circuit possessing a certain primary
electromotive force F], and containing a '' polarization cell," is rep-
resented by

""" B '

where Fs is the electromotive force of polarization, o the current,
and B the total resistance of the circuit.
Methods of measuring Polarization.^ — As already seen, the electro-

^ For farther partdcolars, see Ostwald-Luther, Phyaiko^hemitche JfeMun^en,
I».890.

280

ELECTROLYSIS AND POLARIZATION 287

motive foice of polarization is not a constant^ but rapidly diminishes
when the primary electromotive force is removed; its magnitude is
therefore best determined during the passage of the primary current
The accompanying figure represents an arrangement which may be
used for the measurement^

One circuit is represented by 1, 2, a, 1, and the other by 2, e, b,a,2'f
1 is the source of the electricity, 2 the polarization cell, e a compen-
sation electrometer, b a known electromotive force, which may be
altered at will, and a a tuning fork commutator (or, better, a double
commutator driven by a motor), which vibrates very rapidly. The
arrangement is such that at a one circuit is opened and the other
simultaneously closed, then the latter opened and the former closed,
etc., with each vibration of the tuning fork. The result is practically
the same as though both primary and polarization current were inde-
pendentiy active. Thus the electromotive force of the latter may be
measured under the same conditions as if the primary circuit were
continually dosed. It is only necessary to alter b until the electrom-
eter shows a condition of equilibrium ; b is then the desired value.

t —

Fio. 49

As the electromotive force of galvanic elements is due to two or
more potential-differences, so also in the electromotive force of po-
larization two single potential-differences are found located at the
two electrodes. In order to measure them separately, the method of
Fuchs is employed. Its arrangement is shown in Figure 50. A
double U-tube is filled with the solution of the electrolyte e whose
polarization is to be measured, a and b are two indifferent electrodes
connected with the source Q of the primary or polarizing current.
K the potential-difference at 6 is to be measured, the bent glass tube
of the normal electrode N (page 246), filled with normal potassium
chloride solution, is inserted at c in the electroljrte e, and b is con-
nected with the mercury of the normal electrode by means of the
platinum wire of the latter. An element thereby results, consisting

1 Le Blanc, Ztschr. phy$. Chem,, 6, 409 (1890).

288

A TEXT-BOOK OF ELECTRO-CHEMISTRY

of two electrodes and two electrolytes, and the electromotiye force
of the combination is measured by the usual apparatus at M. The
potential-difference between h and e may then be determined by sub-
traction of the normal electrode potential, and that at the surface
of contact between the liquids from the total electromotire force.
For determining the potential-difference between a and e the process
is analogous, and using a primary or polarizing current, whose
electromotive force gradually increases from zero, it is observed that
the electromotive force of polarization is at first very nearly equiva-
lent to that of the primary current. As the latter becomes higher
the former falls gradually away from it in magnitude, nevertheless
always increasing to some extent. The much-sought-after maTJmnm
of polarization does not actually exist.

Fio. 00

Deoomposition Values of the Slaetromotive Foroe. The Hydrogen-
Oxygen Cell. Primary and Secondary Decomposition of Water. —

There is another characteristic point for the different electrolytes.
A continuous current flows and a continuous decomposition only
takes place when the electromotive force exceeds a certain value.
If an electromotive force less than the above be impressed, only an
instantaneous passage of electricity takes place, which may be made
evident by inserting a galvanometer into the circuit. The needle of
the galvanometer is at first deflected, but returns very nearly to its
original position (the effect of secondary disturbing influences will
be considered later). This does not happen when the applied elec-
tromotive force has reached the value in question.

A better view of these relations may be obtained by plotting the
current on the ordinate and the corresponding electromotive force on
the abscissa of a coordinate system. The curves thus obtained (see
later, Figure 51) all show a more or less abrupt turning point at
which the curve changes its direction.^

1 As has already been indicated, the potential-fall due to the reststance of the
electrolyte mast either be avoided or taken into oonsldeiation in the calculations.

ELECTROLYSIS AND POLARIZATION

289

Le Blanc determined the magnitudes of these decomposition valt^es
for a great many electrolytes, chiefly in normal solutions. They
may be very exactly determined for salts from which a metal is pre-
cipitated by the current, but for other salts, as well as for acids and
alkalies, they are less easily found. The following decomposition
yalues were found for salts from which the metal is deposited.^

ZnS04 = 2.36 volts

Cd(NO,),

= 1.98 volts

ZnBr, =s 1.80 volts

CdSO*

=s 2.03 volts

NiS04 = 2.09 volts

CdCl«

» 1.88 volts

NiCl, = 1.85 volts

Pb(NO,), = 1.52 volts

C0SO4

= 1.92 volts

AgNO, = 0.70 volt

CoCl,

= 1.78 volts

The decomposition values for sulfates and nitrates of the same
metal, as shown by the experiments with cadmium salts and other
experiments with the alkalies, are nearly equal. As is evident, the
values for the various metals are different. The conclusion to be
drawn from the corresponding values for the acids and bases is that
there exists a maximum decomposition point, which is exhibited
by most of the compounds and exceeded by none. This is about
1.67 volts. Among the acids, however, several gave values below
this maximum. The following tables contain the values for acids
and bases : —

Sulfuric

Nitric

Phosphoric

Monochloracetio

Dichloracetio

Malonic

Perchloric

Dextrotartario

Pyrotartaric

Trichloracetic

Hydrochloric

Hydrazoic

Oxalic

Hydrobromio

Hydriodic .

5= 1.67 volts
= 1.69 volts
= 1.70 volts
« 1.72 volts
s: 1.66 volts
= 1.69 volts
= 1.65 volts
s= 1.62 volts
= 1.57 volts
= 1.51 volts
« 1.31 volts
= 1.29 volts
= 0.95 volt
= 0.94 volt
= 0.52 volt

1 ZtKhr.phys. Chem., 8, 209 (1891).

290

A TEXT-BOOK OF ELECTRO-CHEMISTRY

Sodium hydrate

Potassium hydrate

Ammonium hydrate .

\ n. Methylamine

I n. Diethylamine

^ n. Tetramethyl ammonium hydrate

8 1.69 volts

8 1.67 volts
8 1.74 volts
8 1.76 volts

8 1.68 volts
8 1.74 volts

The alkali and alkali earth salts of the highly dissociated acids
with maximum decomposition values, as sulfates and nitrates, have
nearly the same decomposition pointy i.e. about 2.20 volts. The
chlorides, bromides, and iodides have lower values, independent of
the nature of the alkali metal. Additivity is exhibited, owing to the
mutual independence of the potential-differences produced at the two
electrodes. Differences between the values for the various halogen
compounds of the alkalies, hydrogen, and the metals are nearly
equal ; for example, the difference between hydrochloric and hydro-
bromic acid is the same as that between sodium chloride and
sodium bromide.

The salt bf a slightly dissociated acid, as sodium acetate, or of a
slightly dissociated base, as ammonium sulfate, always exhibits a
lower value than that of a highly dissociated acid or base, providing
the acid and base possess the maximum decomposition value. The
halogen salts of ammonium have lower decomposition values than the
corresponding salts of the alkalies; and, in fact, the differences
between corresponding salts are equal.

Concerning the effect of dilution in the case of bases and acids
which on electrical decomposition evolved oxygen and hydrogen at
the electrode, the decomposition values are independent of the
dilution, and this is true for all the acids excepting those whose de-
composition values are below the maximum. For these, the value
rises with increasing dilution, and finally reaches the maximum.
This is very marked in the case of hydrochloric acid.

OOKOKNTRATION

DsooMPMiTioH Pocrr

4 Normal hydrochloric acid
) Normal hydrochloric acid
\ Normal hydrochloric acid
•^ Normal hydrochloric acid
^ Normal hydrochloric acid

1.20 volts
1.34 volts
1.41 volts
1.62 volts
1.69 volts

ELECTROLYSIS AND POLARIZATION 291

It is also worthy of note that when the maximum yalue is reached,
the acid solution is no longer decomposed into chlorine and hydrogen^
but into hydrogen and oxygen.

The above experiments were carried out with platinum electrodes.
If other electrodes be used, as gold or carboui different nimierical values
are obtained, but the general relations between them remain unaltered.

In order to obtain a better insight into polarization phenomena
Le Blanc ^ investigated the potential-difference at the electrode
where the metal is electrolytically deposited (the cathode), when the
electromotive force of the primary current is gradually increased
from zero. He found that the potential-difference at the decomposi-
tion point is equal to that which the precipitating metal would itself
exhibit in the solution. For example, a normal solution of cadmium
sulfate was decomposed at a primary electromotive force of 2.03
volts. The potential-difference of the electrode where the cadmium
separated was, —

Metallic cadmium placed in the solution also gave — 0.72 volt. In
many solutions the electrode exhibited the potential-difference due
to the separating metal before the decomposition point of the solu-
tion is reached. For instance, in silver nitrate the electrode had
the value of pure silver in silver nitrate even below the decomposi-
tion point (0.70). This is due to the great tendency of the silver
ions to separate as electrically neutral metal.

It was also possible to demonstrate that the material of the indif-
ferent electrodes, providing no alloy is formed,' is without influence
upon the magnitude of these potential-differences. The results were
the same whether gold, platinum, carbon, or any other metal more
positive than that in solution was used. From this it is evident that
the electrode itself possesses no '' specific attraction" for the elec-
tricity, as formerly was imagined.

The process of precipitation and solution of the metals is, there-
fore, to be considered as reversible. It may be represented as fol-
lows : If an indifferent electrode be placed in the solution of a salt of
a metal, a very small quantity of the ions leave the ionized state and
deposit upon the electrode in the metallic form. This process goes
on until the tendency of the ions to deposit in the metallic state is
exactly compensated by the electrostatic attraction which exists be-
tween the positively charged electrode and the negatively charged

1 Ztschr.phyB, Chem., 12, 833 (1893).

1 For farther particulars, see Coehn and Dannenberg, ZUchr.phys. Chem., S8»
609, 1901.

292 A TEXT-BOOK OF ELECTRO-CHEMISTRY

Bolation. The quantity of ions deposited is, therefore, dependent
upon the tendency of the ions to persist in the ionized state. Up
to the present we have always spoken of the tendency of the metal
to pass into the ionized state. Now we will speak, as naturally we
may with equal right, of the tendency of the ions to remain as such.
To express this exertion of the ions to hold their electrical diarges,
the expression holding power (Haftintensitat) is often used. Ku-
merically this holding power is equal to the electromotive force
which is required to deposit an ion in the neutral state.

A certain potential-difference must, therefore, exist at the elec-
trode, there being some metal upon it and the corresponding ions in
the solution. The magnitude of this potential-difference need not
be, and almost never is, the same as found when the massive metal
is in contact with the solution, for the metal deposited upon the elec-
trode does not reach the concentration of the massive metal. The
conclusion seems strange at first, for it is customary to consider the
concentration of a metal as unalterable. This is only the case above
a definite limit. If the metal is not present, at least to the extent
of a molecular layer, it does not act as the massive metal. This has
been shown by Oberbeck^ and E5nigsberger and Muller.* When
the metal of a salt solution was precipitated upon a platinum plate,
the latter exhibited in the corresponding metal solutions the poten-
tial-difference characteristic of the massive metal as soon as a certain
amount had been deposited. Below this point the electrode ex-
hibited smaller potential-differences corresponding to the lower con-
centrations of the metal. This fact need not be surprising when it
is recalled that gases and dissolved substances have solution pres-
sures dependent upon their concentration.

If the source of an electromotive force be connected with the
electrode in such a manner as to tend to separate a metal from the
solution, it works against the electrostatic attraction, and more ions
can separate as metal. The concentration of the metal upon the
electrode is thereby increased, and consequently also its solution
pressure p, which tends to prevent a further deposition of the
metal, and soon entirely prevents it. To deposit more metal it is
necessary to impress a still greater potential-difference. This con-
tinues until the maximum concentration of the metal is reached —
that is, until the electrode acts as the massive metal. A continual
deposition may then take place without further increase of the ap-
plied electromotive force, providing, naturally, that the osmotic pres-

1 Wied, Ann., 81, 336 (1887).

* Phy$. Ztschr., 6, 847 and 849 (1906).

ELECTROLYSIS AND POLARIZATION 298

snre of the ions P remain unaltered. When strong cnrrents are
used P does not remain constant, but gradually diminishes, and con-
sequently the potential-difference at the electrode increases.

It must be observed that the separation of positive ions at on&
electrode as neutral substance is necessarily accompanied by the
simultaneous deposition of the corresponding amount of negative
ions at the other. Considerations analogous to the above evidently
apply to the negative electrode. If, for example, oxygen is set free,
the concentration of the gas gradually increases; and, when the
solution is saturated, has its greatest value, and consequently also
its maximum solution pressure (which opposes the further decom-
position of the electrolyte). If more separates, it escapes into the
air. It will now be understood why a certain electromotive force
is necessary to induce continuous decomposition in an electrolyte ;
this only occurs when the concentrations of the two substances
separating at the electrodes have reached their maximum values.
It is also evident that the electrodes upon which metals are de-
posited should exhibit the potential characteristic of the massive
metal when the decomposition point is reached. But it is evi-
dently unnecessary that these maxima of concentration for both
electrodes should be reached simtdtaneotidy ; it may sometimes be
reached at an electrode before the decomposition point of the solu-
tion can be attained, as is the case with a silver solution. The
decomposition point of normal silver nitrate is 0.70 volt, but the
potential-difference at the electrode upon which silver is deposited
is of the same magnitude as that between massive silver and the
solution long before this decomposition value is reached.

The polarization due to metal ions having been considered, atten-
tion will now be directed to the phenomena presented when gaseous
or dissolved substances are separated. These are somewhat more
complicated, and have greatly increased the difficulty of understand-
ing the process of polarization. As a simple case, the following cell
will be considered : —

Pt (platinized) in hydrogen — water (with a dis-
solved electrolyte, such as H^SG^) ,

Pt (platinized) in oxygen !

Consider the two gases to be under atmospheric pressure.

The cell at 17^ has an electromotive force of about one volt, and
is, as was first shown by Le Blanc, to be considered reversible for
small current densities. If an equal opposing electromotive force
be connected with this cell, a condition of equilibrium exists ; when

294 A TEXT-BOOK OF ELECTRO-CHEMISTRY

s, lower electromotive force is applied, water is produced bj the
oxygen and hydrogen of the cell, and when the electromotiye force
of the opposing current is greater, water is decomposed. Smale ^
calculated the temperature coefficient of this cell from the Helm-
holtz formula, using the known heat of formation of water under
constant pressure (67,534 caL at 17^ and the measured electro-
motiye force as data : —

96640 X 1.07 - 33767 x 4.189 = ST^;

38152 dw

96640x290 dT'

^= -0.00136.
dT

A7/S5M.

Q is ^^, since the heat effect corresponding to one equivalent of

the substance is employed. Experimental determinations gave as a
mean value between 0^ and GS"*, 0.00141, and between 0"* and 100^,
0.00143 (obtained later by L. Olaser), which is a satisfactory agree-
ment with the calculated value.

It has recently been shown' that the electromotive force of the
hydrogen-oxygen cell at atmospheric pressure and room temperature
must be 1.22 volts, a value which is considerably higher than that
obtained by earlier investigators, who, perhaps because of the forma-
tion of oxides, never succeeded in completely saturating the oxygen
electrode. The highest value which has been found is 1.14 volts.
This change in the value of the electromotive force of the cell
has, however, no influence upon the above calculation, because the
cell is capable of producing work reversibly, whatever the pres-
sures of the gases.

Furthermore, at high temperatures, the agreement between the
value of the electromotive force calculated from thermodynamical
considerations and that found experimentally is very satisfactory.*

It may now be predicted that if the hydrogen and oxygen, instead
of being at atmospheric pressure, be at a lower pressure, the electro-
motive force of the cell will be lower. In fact, if the pressures Qf
the gases be reduced almost to zero, the electromotive force will
nearly disappear. Under such a condition water may evidently be

1 ZUdiT, phy$. Chem., 14, 677 (1804).

< See, for example, Zt9chr. phys, Chem., 66, 478 (1906).

• Haber, ZJBJcAr. EUktroehemU, 18, 416 (1006).

ELECTROLYSIS AND POLARIZATION 296

decomposed by currents of minimum electromotive f orce, it being
only necessary to apply one which exceeds that of the cell itself
by a yery small amount. From this it is clear that the electri-
cal energy obtainable through the formation of water from oxygen
and hydrogen, or necessary for its decomposition (the two being
equal and of opposite sign), may assume any magnitude from zero
to a certain value dependent on the pressures of the gases or their
concentrations. The heats of formation at constant pressure, on the
other hand, are independent of the pressure, within such limits as
the gas laws hold. This is the most direct evidence that a simple
relation cannot exist between the heat of reaction and the electrical
energy obtained. It is, however, possible in this case to calculate the
amount of one of these two forms of energy from a knowledge of the
other when the changes of the temperature coefficient due to pressure
changes are known.

That water may thus be decomposed by minimum quantities of
electrical energy seems at first a contradiction of the law of the con-
servation of energy. This is, however, in no wise the case. The
law referred to declares that by the reversible changes of a system
from one condition to another, the same amount of work must
always be done, and this condition exists in the present case. The
decomposition of water into hydrogen and oxygen at atmospheric
pressure may be accomplished, on the one hand, by the application
of electrical energy alone. A gas cell such as described, the gases
being under atmospheric pressure, may be used, an opposing electro-
motive force just exceeding that of the cell being connected with it.
Electrical energy alone then causes the decomposition of the water
into hydrogen and oxygen at atmospheric pressure. This same
result may, however, be brought about in another way. For instance,
a hydrogen-oxygen cell in which the pressure of the gases is one
tenth atmosphere may be employed. • The electromotive force of
this cell being lower than the previous one, less electrical energy is
required to produce the hydrogen and oxygen at the reduced pres-
sure. But the work which corresponds to the difference between
the two quantities of electrical energy employed must exactly suffice
to compress the gases produced at one tenth atmosphere to the pres-
sure of one atmosphere, and thus the total work in the two cases,
although done in different ways, has remained the same.

When platinized electrodes are used, the formation and the decom-
position of the water are reversible. At atmospheric pressure water
may be decomposed by an electromotive force of 1.22 volts. If the elec-
trodes lire not platinized, the electrolysis does not take place until the

296 A TEXT-BOOK OF ELECTRO-CHEMISTRY

electromotive force is 1.67 volts. This is the maximnm value for de-
composition found for the acids and bases, hydrogen and oxygen being
the products. It was long considered surprising that the decomposi-
tion point in the latter case is so high, notwithstanding the fact that
only the partial pressure of the atmosphere is exerted upon each of
the gases. Furthermore, the fact that the decomposition point
is dependent upon the nature of the indifferent electrode appeared
curious.

These results can now be understood. In the first place, when
electrodes such as ordinary platinum or gold ^ are employed, the
process is no longer a reversible one. These electrodes have too feeble
absorbing power to remove the gases as rapidly as they are formed.
With platinized electrodes there is equilibrium between the gas
dissolved in the solution, that dissolved in or taken up by the
electrode, and the volume of gas surrounding the electrode. If the
applied electromotive force be great enough to overcome that of
the gas cell, gas separates at the electrodes, and thereby its concen-
tration in the solution as well as in the electrode is increased. The
former condition of equilibrium is soon reproduced, for the electrode
yields its excess of gas to the space about it (which is considered so
great that no change in the concentration of this gas in it is pro-
duced), and in this manner prevents supersaturation of the liquid.
The gas formed by continued decomposition of the electrolyte thus
always escapes into a space filled with a gas at constant concentra-
tion. The generation can therefore always take place under the
same electromotive force.

The conditions are entirely different when the electrodes are of
gold or of unplatinized platinum. These have practically no absorb-
ent action on the gases, aud there is thus no medium to bring about
equilibrium between the solutions of the gases as formed in the cell
and the gases in the space about the electrodes. Proceeding on this
assumption, the result of a gradually increasing electromotive force

^ If carbon be used as an electrode, the kind of carbon is an important factor.
Carbon is capable of taking up gases to a considerable extent, and this property
increases its value as positive electrode of a galvanic element. In the Le-
clanch^ element, for example, hydrogen is evolved at the carbon pole, and the
property of carbon just mentioned causes the gas to pass quickly from the liquid
to the air, thus reducing the polarization at this electrode. For long-continued
activity of the cell, the carbon is often incapable of removing the hydrogen with
sufficient rapidity, and polarization is the result. If the action of the cell be
stopped for a time, the hydrogen dissolved in the liquid has an opportunity to
escape, and the element, becoming thus depolarized, again exhibits its original
electromotive force, i.e. it recuperates.

ELECTROLYSIS AND POLARIZATION 297

opposing such a gas cell would be exactly as observed. Beginning
with a low electromotive force, a scarcely perceptible decomposition
of water would take place, the concentrations of the hydrogen and
oxygen in the water being at first inconsiderable. At each subse-
quent increase of the applied electromotive force so much water at
the most may be decomposed that the concentration of the gases in
solution at the electrodes is made exactly that which would produce
an equivalent electromotive force with platinized electrodes. A
higher concentration of the gases can evidently not be produced,
otherwise perpetual motion would be possible. This explains the
temporary current observed in the galvanometer. Diffusion alone
causes disturbances, the gases being thereby very slowly removed
from the electrodes and the concentration reduced so that further
decomposition takes place. The galvanometer corroborates this,
since, after the first deflection, the needle does not return quite to
its former position. It thus indicates a slight residual current.^
Upon gradually increasing the electromotive force, the concentration
of the separated gases continually increases, until finally a point is
reached at which gas is evolved. The resistance which opposes
the formation of bubbles, or another passive resistance of an un-
known nature which opposes the escape of the gas into the space
above, is then overcome. When this point has been reached, water
may be decomposed without causing a further increase in the con-
centration of the gases dissolved at or in the electrodes. The gases
are then continually evolved as bubbles, and the so-called decomposi-
tion point is observed, that is, that point above which water may be
continually decomposed withotit the aid of diffusion. The less the dif-
fusion of separated substance from the immediate neighborhood of
the electrode, the more marked is the decomposition point, and in-
deed often (in the case of metals) the galvanometer exhibits a clearly
defined sudden rise in the strength of the current at this point.

However, even this conception does not embrace all actual relation-
ships. It has been observed that the decomposition point is not
always identical with the point at which bubbles of gas are formed.
The latter point, the observation of which is to a large degree sub-
ject to chance, very often is later than the former. Finally, it has
been proven that the decomposition point is indei)endent of the pres-
sure.* It must then be assumed that, at the decomposition point,
the metal is saturated with gas to such an extent that it gives the
gas off to the surrounding liquid as rapidly as it is brought up to

1 Nernst and Merriam, Ztschr. phys. C%em., 5S, 236 (1905).
* Wulf, Ztschr. phys. Chem., 48, 87 (1904).

298 A TEXT-BOOK OF ELECTRO-CHEMISTRY

the metal by a farther increase of the electromotive force. This
process, which takes place without inyolying a change in Tolume, is
independent of pressure. From this, the degree of the dependence
of the decomposition point on the solubility of the separated gas in
the electrode is very evident It is also evident that the greater the
solubility of the gas in the liquid, the farther apart will be the
decomposition point and the point at which bubbles appear. This
conclusion is confirmed by experience.

The great influence of the electrode material is shown by the in-
vestigations of Coehn and Dannenberg,^ and Gaspari.' The former
two investigators determined the decomposition points at cathodes
of various metals, for the most part, in a normal solution of sulfuric
acid. If the potential-difFerence at the reversible platinized plati-
num electrode be placed equal to zero, the results obtained by them
are as follows : —

Mral

DBooMPoemoir Voltaob
(Ea •lcctiod»-etoetralyta)

FaUAdinm

PlatiDum

Iron •••••••..

+ 0.26 TOlt

- 0.00 volt

- 0.08 Toit

Gold

- 0.05 Tolt

Sllyer

— 0.07 volt

Nickel . . '

- 0.14 Yolt

Copper .••••••••

-O.IOyoU

Alamininm

Lead

- 0.27 volt

— 0.S6 volt

Mercury

- 0.44 volt

Only in the case of palladium is the separation of hydrogen facili-
tated, and this is most certainly due to the formation of an sllay.
In all the other cases, a considerable retardation or hindrance of the
separation, or in other words a considerable over^uoUagey exists. This
over-voltage appears to be greatest in the case of metals which pos-
sess the smallest occlusion capacity.

In the case of the cathodic polarization of metals in a solution of
potassium hydroxide it was found that the order of, and the differ-
ences between, the decomposition voltages are the same as those given
above. From this it is to be concluded that no alkali-alloy is formed
at the decomposition point, but only a separation of hydrogen takes
place. Mercury at no time left its place in the above order, and

1 Zt$chr. phif$. Chem.t SS, 000 (1001).
• ZUchr. phifs. Cham., 80, 80 (1809).

ELECTROLYSIS AND POLARIZATION 299

only when high potential-differences are reached is the phenomenon
of disintegration or powdering of the cathode, as in the case of tin
and lead, which was studied by Haber, Sack,^ and Bredig, observable.
This behavior of tin and lead is explained on the assumption of the
formation of an alkali alloy.

If, as in Gaspari's work, the electromotive force which is required
to produce a visible evolution of gas be determined, the values will
be found to be somewhat greater but in the same order as those in
the above table. His highest values, obtained with zinc and mercury,
are — 0.70 and — 0.76 volt, respectively.

These values are of interest in connection with the chemical solu-
tion of metals in acids. It may be seen from the table given on
page 248 that zinc tends to separate from a normal solution of
hydrogen ions with an intensity of 0.80 of a volt. Therefore, since
the over-voltage is equal to 0.70 of a volt, zinc dissolves in a solution
which is normal in respect to the hydrogen and zinc ions only very
slowly. By increasing the concentration of the zinc ions, as, for
example, by the addition of zinc sulphate, the solution of the zinc
may be made even slower or brought to a standstill, while by
increasing the concentration of the hydrogen ions, or, what is the
same thing, of the acid, the action may be accelerated.

Goinmercial zinc possesses a smaller over-voltage, and therefore is
more easily dissolved than is pure zinc. If it be amalgamated, it
dissolves less easily and its over-voltage increases ; while if pure zinc
be amalgamated, the ease with which it dissolves and its over-voltage
do not suffer any considerable change.

Not only in the case of hydi/bgen, but also in that of oxygen, an
over-voltage which varies with the nature of the electrode (in this
case the anode) is produced by the separation of the gas. Ooehn
and Osaka,' making use of a normal solution of potassium hydroxide
as an electrolyte, measured the anode voltage against a constant
hydrogen electrode which was also in contact with a normal solution
of potassium hydroxide. The values obtained by them are given in
the table on the following page.

It should be noted that the decomposition point in this case is iden-
tical with that at which visible evolution of oxygen takes place and
that the order of the metals is quite different from that in the case of
the hydrogen. The results given here indicate that the commercial
decomposition of water could be carried out with the least expendi-
ture of energy with the use of nickel electrodes.

1 ZtBchr. anorg. Chem., M, 286 (1908).
* Zuchr. anorg. Chem., M, 86 (1903).

800

A TEXT-BOOK OF ELECTK0-<3HEMISTRT

Gold

Flatinnm (polished)

Falladinm

Cadmiam

Silver .

Lead

Copper .

Iron

Platinam (platinized)

Cobalt .

mckel (blank)

Kickel (spongy) .

DaooMPOsmov Yoltami

1.76
1.67
1.66
1.66
1.63
1.63
1.48
1.47
1.47
1.86
1.36
1.28

Even with the same substance used as au anode the decomposition
value varies with the treatment to which the substance has been
subjected^ i.e, with its previous history. This was mentioned on
page 296 in reference to carbon. This subject will be further con-
sidered later on.

Both bromine and iodine separate reversibly at platinum anodes.

It may be questioned whether the order of the over-voltages ob-
tained under practically zero^nirrent conditions is the same as the
order which is obtained during electrolysis with a high current
density. Furthermore, is the latter series of values noticeably higher
than the former ? These questions have been investigated by Tafel.^
The maximum values thus far obtained are given in the following
table. They were obtained at 12^ in a 2-normal sulfuric acid

MiTAL

OVKB-TOLTAOBB (^)

Mercury ,

1.80

Lead (polished)

1.30

Lead (rouflh)

1.28

Cadmiam

1.22

Tin

1.16

Bismuth ■•••••«*...

1.00

Gold

0.96

Silver

0.03?

Copper

0.79

Nickel

0.74

Flatinnm (platinized)

0.07

^Ztschr. phy$, CTtern,, 60, 712 (1906). The change in potential due to the
change in the concentration of H ions at the electrodes is, as the experiments
with platinized platlnoms show, negligible.

ELECTROLYSIS AND POLARIZATION 301

solation with a current density maintained constant at 0.1 of an
ampere per square centimeter of electrode surface. The anode sec-
tion was separated from the cathode section.

It should be noted that the value of the over-yoltage for a given
current density is for many metals dependent on the previous treat-
ment to which the electrode has been subjected, as for example, upon
the current density maintained when the cathode was previously
polarized. The over-voltage of all metals changes slowly as time
passes. This change and the dependence of the potential on specific
influences is not the same for different metals. An access of the
anode solution to the cathode compartment generally lowers the
potential-difference. The maximum value of the potential-differ-
ence is reached at once with mercury and lead, but very slowly with
copper, nickel, and gold, and not at all with polished platinum. The
potential decreases with increasing temperature.

The investigations of Fdrster and MtQler, ^ and F5rster and Piguet,'
of anode potentials in 2-normal potassium hydroxide show relation-
ships similar to the above.

Finally, it should be mentioned that E. Mtlller' has found that
the over-voltage at the anode, in the case of platinum, is greatly
increased by the addition of fluorine ions. It follows from this fact
and also from the above-mentioned work of Tafel that the over-
voltage depends also on the nature of the electrolyte.

According to the explanations already given, the electromotive
force of the hydrogen-oxygen cell is dependent upon the concentra-
tions of the gases, but nearly independent of the nature of the elec-
trolyte. The electrolyte may almost equally well be an acid or a base.
The electromotive force is the sum of the potential-differences pro-
duced at the hydrogen and oxygen electrodes. That of the former is
dependent upon the concentration of the hydrogen ions, that of the
latter upon the concentration of the hydroxyl ions, for a given con-
centration of the gases. According to the law of mass action, the
product of the concentrations of the hydrogen and hydroxyl ions is
(nearly) always constant without regard to other substances present;
therefore, although the values of the single potential-differences may
vary considerably on changing the homogeneous solution, their sum
always remains the same.^

Leaving out of account metal salt solutions reducible by hydrogen,

^Ztachr. Elektrochem,, 8, 627 (1902).

*Zt8chr. Elektrochem,^ 10, 714 (1004).

•Ztschr. Elektrochem., 10, 768 (1904).

*For farther parUcolani see L. Qlaser, Ztachr, XlectroeKem.y 4, 866 (1898).

802 A TEXT-BOOK OF ELECTRO-CHEMISTRY

and chlorides, bromides, iodides, etc., reducible by oxygen, the ions
of water alone take part in the decomposition, instead of those of the
dissolved electrolyte, so that with the limitations given, the principle
may be expressed : In electrolysis a primary decompositioji of the uxxter
takes place. The actual electrical conductance is brought about by
all the ions in the solution, but at the electrode that action takes
place which proceeds most easily, and this is usually the separation
of the hydrogen and hydroxyl ions. When, for example, a solution
of potassium sulphate is being electrolyzed, and the current is not
too strong, there is no reason for assuming the separation of potas-
sium and the SO4 radical at the electrodes, and the subsequent or
secondary action of these upon the water. The fact that every acid
and base, in so far as they do not possess a lower decomposition
voltage, decomposes at 1.67 volts can scarcely be otherwise explained
than by the assumption that in every case the same process takes
place. If a secondary action, i.e. a separation of the radicals at the
electrodes and a subsequent reaction of these with the water, takes
place, it would be expected that the decomposition point would not
be the same in all cases but would vary with the velocity of the
action. In the case of acetic acid, for example, a higher potential
would be expected, since during electrolysis of it with a strong cur-
rent only a small quantity of oxygen is found mixed with the gas
evolved at the anode. The reaction,

4 CH,COO' -h 2 H,0 = 4 CH,COOH + 0»

must therefore take place slowly. Whether or not a primary de-
composition of water takes place when strong currents are used
evidently depends, for a given concentration, on the velocity of the
formation of hydrogen and hydroxyl ions from undissociated water.
This subject will be touched upon again.

It shoidd be emphasized that the assumption, made earlier, that
the ions carried to the electrode by the electric current always sep-
arate on the electrode directly and then react with water or other
substances does not appear to be in agreement with facts. That
the conduction of the electric current and the decomposition of
the electrolyte at the electrodes are not as closely related as was
formerly supposed is evident from the simple fact that during the
electrolysis of every electrolyte more ions are separated at each
electrode than are brought to it by migration (see page 67). Hence
in every case some of the ions originally in the solution near the
electrodes which have not taken part in the conduction of the current
are deposited.

ELECTROLYSIS AND POLARIZATION 303

The following oonception, which has already been mentioned
briefly^ appears to me to be decidedly preferable to that formerly
accepted. The conduction of the electric current and the chemical
changes or separations at the electrodes are not closely related. AU
of the ions in the solution take part in the conduction of the electric car-
rent, but only those ions the separation of which require the least expen-
diture of work or energy are deposited or separated at the electrodes.
Thus it may happen tiiat ions which conduct scarcely a Ineasurable
part of the current play the most important part in the chemical de-
compositions at the electrodes^ in so far as they are formed with
sufficient rapidity.

The following example is well adapted to show the greater sim-
plicity of the newer conception. Suppose that a fairly concentrated
solution of a mixture of potassium, cadmium, copper, and silver salts
be electrolyzed with a moderate current between platinum electrodes.
In conducting the electric current, potassium, cadmium, hydrogen,
copper, and silver ions migrate to the cathode. At the cathode,
from actual experiment, it is known that the silver is first deposited.
This deposition goes on until the number of silver ions remaining is
no longer sufficient for the current density maintained, when the
copper begins to separate in the same manner. Following copper,
cadmium, and finally hydrogen, is deposited. Is not the simplest
conceivable explanation of these experimental results that given in
the following statement?

Those ions separate first which give up their electric charges most
easily. The other ions must wait their turn in the order of their ease of
deposition. The process takes place smoothly and comprehensively.

The other conception may now be applied to the same process.
According to this conception, potassium, cadmium, hydrogen, copper,
and silver ions separate simidtaneously at the cathode. The potas-
sium may then set free hydrogen from the water, cadmium from the
cadmium salt, copper from the copper salt) and silver from the silver
salt. This must be considered to take place, for the assumption
cannot well be made that there is always a particle of silver ready to
be precipitated in the immediate vicinity of each particle of potas-
sium. The potassium must then separate those ions of whatever
kind which happen to be in its vicinity. Of these substances sepa-
rated by the potassium, the hydrogen sets free cadmium from the
cadmium salt, copper from the copper salt, and silver from the silver
salt. Of this group of separated metals, the cadmium may set free
copper from the copper salt, and silver from the silver salt. Finally,
the copper sets free, or deposits, silver from the silver salt. The

804 A TEXT-BOOK OF ELECTRO-CHEMISTRT

final result of all this is that as long as sufficient silver is present^ it
alone is deposited permanently on the cathode. This conception of
the process of electrolysis certainly cannot b6 said to be as simple as
the one given above, and it involves the assumption of all these sec-
ondary reactions which no one has ever observed. The question at
once arises, why make this complicated assumption when, as has
been shown, it can, with greater simplicity, be avoided ?

After this discussion, the values obtained during the determination
of the decomposition voltage with the use of platinized platinum
electrodes is easily understood. Those substances which decompose
water will be considered first. Both acids and bases must have the
same value, since, as already stated, the product of the concentrations
of the hydrogen and hydroxyl ions at the electrodes, and conse-
quently the sum of the potential-differences at the electrodes, is the
same in the two cases. In the case of salts, higher values should be
obtained, since at the cathode a base is formed whereby the concen-
tration of the hydroxyl ions is greatly increased, with the conse-
quent driving back of the concentration of the hydrogen ions and
increase of the potential-difference. A similar line of reasoning
holds for the anode at which acid is formed, increasing the con-
centration of the hydrogen and decreasing that of the hydroxyl ions.
The less the dissociation of the acid or base formed, the less the
increase in the potential-difference. This has been observed to be
the case.

Since that ion is always separated at the electrode which requires
the least electromotive force for its separation, no ions other than
hydrogen and hydroxyl ions (providing the concentrations of the
latter are sufficiently great) come into consideration except when the
electromotive force required for their separation is less than that
required for the separation of hydrogen and hydroxyl ions. For this
reason, the decomposition voltage of the halogen acids, etc., which
do not cause a separation of oxygen is lower than that of those acids
which do cause the separation of oxygen. Furthermore, while in
the case of acids and bases which are decomposed with the separa-
tion of hydrogen and oxygen, the decomposition voltage is indepen-
dent of the concentration (since the product of the concentrations of
the hydrogen and hydroxyl ions remains the same), in the case of
the halc^en acids the decomposition voltage rises with decreasing
concentration, since an increase in the concentration of the hydroxyl
ions takes place corresponding to the decrease in that of the hydro-
gen and of the halogen ions. A dilution is finally reached at which
oxygen is continuously evolved more easily than is the halogen. At

ELECTROLYSIS AND POLARIZATION 805

this dilution, the decomposition voltage is equal to that of water.
Such a case has been realized with hydrochloric acid.

In the foregoing pages the current-voltage curve of any electrolyte
has always been discussed as if there existed but a single decomposi-
tion value which, by means of measurements with an auxiliary elec-
trode, can be divided into an anode and a cathode potential-difference.
The recent measurements of Nemst/ Glaser,' Bose,'Coehn {loc. cU.),
and others have shown that, when the measurement is more accu-
rately made, more than one decomposition point may be found under
certain circumstances. Such measurements may best be made as
follows : The electrode being investigated, together with any other
electrode, a galvanometer, and an electromotive force which is
changeable at will, are introduced into a circuit. The electrode in
question is, furthermore, combined with an auxiliary nonpolarizable
electrode. Now in obtaining the current- (or better, current density-)
voltage curve, the electromotive forces of the cell,

Auxiliary electrode — Unknown electrode,

are taken as the voltage values. With this arrangement, the nature
of the third electrode does not come into consideration because the
same electromotive force always corresponds to a definite current
density (referred to the unknown electrode) for a given solution. By
making the unknown electrode changeable, it is possible by this
method to isolate better than formerly Uie processes which take place
at the anode and the cathode, respectively. It has been possible
with the use of platinum electrodes to establish two anodic decom-
position values, namely,

Za»1.14 and » 1.67 volts,

but only one cathodic value,

i;= 0.0 volt,

for a 1 normal solution of an acid.

The question now arises, how can the existence of this lower value
of the decomposition point of water be explained ? In addition to
the assumption previously made that the decomposition potential
of 1.67 volts is the result of supersaturation phenomena, and, as
observed, varies with the material of which the electrode is com-
posed, it may be stated that even ordinary platinum electrodes pes-

1 Bar., SO, 1647 (1897). *Zt9ehr, Eleetrochem., 4, 866 (1806).

^Ztschr. EUctrochem., 6, 163 (1898).

806 A TEXT-BOOK OF ELECTRO-CHEMISTRY

8688, although a very slight, yet a sufficient degree of reversibility to
produce a oontinuous decomposition at 1.14 yolts which is distinctly
detected by very exact measurements. The reversibility may be due
to the formation of an intermediary compoimd between oxygen and
water. The decomposition value of 1.14 volts is that of the reversi-
ble reactioui

4 0H'+4 a(+) Z^ 4 OH 1^2 H,0+0„

when the oxygen is at atmospheric pressure and the hydrogen ion
concentration is 1 normal.

The lower anodic decomposition value then corresponds to a rever-
sible process, while the higher value is plainly due to the supersatura-
tion phenomena. This is in agreement with the fact that the former
value is independent^ of, and the latter value dependent upon, the
electrode material. The process corresponding to the value 1.67
volts may be represented as follows : —

40H'-|- 4q (-h) 5^ 4 OH 5t H,0 -h 0, -> 0,,

where Of represents traces of oxygen dissolved to a high concentra-
tion, and 0], oxygen at atmospheric pressure. The part of the pro-
cess indicated by the single arrow can proceed in but one direction
and is accompanied by a loss in free energy.

It might be expected that metals which exhibit a considerable
over-voltage in respect to the separation of hydrogen would also give
a reversible cathodic decomposition point at

?jk == 0.0 volt

in a solution of 1 normal concentration in respect to hydrogen
ions. Up to the present time, however, this has not been found to
be the case.

It has been endeavored to explain the existence of the two
decomposition values given above in another manner, based partly
on the assumption, which is certainly theoretically justifiable, that
there are present in the water oxygen as well as hydroxyl ions. In
this connection see note on page 254. It seems to me that, in order
to explain this electrolytic phenomenon, it is not necessary to
involve the oxygen ions which are present, if at all, in a very small
concentration. In the case of the electrical phenomenon under con-
sideration, it does not appear advisable to involve in the explanations

^ In view of the irregularities of the oxygen electrode mentioned on page 296»
there cannot be a complete independence of the material of the anode.

ELECTROLYSIS AND POLARIZATION 807

such slight concentrations as those of the ions. Haber^ has with
reason pointed out that there are considerable objections to the
assumption of even a moderate yelocitj of formation of ions in the
case of such extremely small ion concentrations. This point of view
must always be taken into consideration in reference to electrolysis.
If by means of the formation of a complex compound, or otherwise,
the concentration of an ion falls below a certain value, the separation
of this free ion at the electrode is no longer to be assumed. Finally,
the results of the experiments of Hof er and Moest ' also lead to the
assumption of the discharge of OH ions at the anode. They found
that, during the electrolysis of such mixtures as that of sodium
acetate and sodium sulfate, besides ether and carbon dioxide, methyl
alcohol was formed in considerable quantities at the anode. This
formation of methyl alcohol can scarcely be explained otherwise
than on the assumption of a direct union of OH- and CH^radicals.

By the very recent investigations of Grafenburg,' Brand,^ and
Luther and Inglis' it has been demonstrated that the electromotive
force of an ozone-hydrogen cell at atmospheric pressure and room
temperature, using a 1 normal acid solution, is equal to 1.66 volts.
The cell is, moreover, reversible. Consequently, in the case of the
anode potential,

Ij,^ 1.66 volts,

we have a third characteristic point which corresponds to a re-
versible process and which is also independent of the nature of the
material of the noble anode. In the case of platinum this point is
nearly identical with the second decomposition point already
mentioned. At the present time it is not possible to give a scheme
representing the electrolytic formation or decomposition of ozone.

Finally, there is another result obtained in the investigation men-
tioned on page 305 which is of great interest. It was found that still
other anode decomposition values may be detected above the value
1.67 volts. When sulfuric acid, for example, is electrolyzed between
platinum electrodes, four such values have been found, namely,

?*deetn.i— i«et«,iyf = 1.14; 1.67; 1.95; and 2.6 volts.

At each of these points, the electrolysis receives a sudden accelera-
tion. A similar behavior may also be observed in the case of bases.
These results seem to indicate that other ions besides hydrogen and

1 Ztwhr. Elektrochem., 10, 443 and 778 (1004). « Dnid Ann., 9, 468 (1902).
* Liebigs Ann., 888, S04 (1902). « Ztsehr. phy$. Chem., 48» 208 (1908).

^Zuehr. Elektrochem., 8, 297 (1902).

808

A TEXT-BOOK OF ELECTRO-CHEMISTRY

hjdroxjl ions take part in the electrolysis. It would seem probable
that the value 1.95 volts corresponds to that point at which the sulfate
ions, and the value 2.6 volts to that at which the acid sulfate ions,
begin to take part in the electrolysis. It may further be concluded
from these results that the velocity of formation of hydrogen and
hydroxyl ions cannot be especially great, for otherwise it would not
have been possible to find the above decomposition points. This
leads to the conclusion that the hydrogen and oxygen set free by
the action of strong electric currents is, to a great extent, of second-
ary origin, resulting from the action of the liberated radicals on the
water.

In the following table the values of the anodic decomposition
voltage,

£ft alMtvodt-tlMtroljrte,

(except at the point 1.14 volts) for a number of acids are given : —

▲OD

Daooicpooxnov Volta«v

Ftarot

Saeond

ThM

Nitric

2.8

1.06

1.88

Phosphorio

2.8

i.e7

1.96

2.18

Formic

8.6

i.e9

1.88

—

Acetic

8.6

1.67

2.06

—

Propionic

8.6

1.68

2.20

—

Bu^ric

8.6

1.67

2.86

Yalerianio

8.6

1.67

—

— .

Tkrtario

1.2

1.66

1.86

Benzoic

saturated

1.67

2.00

—

Phthalio

Batorated

1.68

1.07

2.6

The assumption just made that each decomposition voltage, or^
in other words, each factor of irregularity of the current-voltage
curve, indicates that a new reaction is beginning to take place is, in
a way, confirmed by the investigation of Bose {loc. cU., Figure 51). As
an electrolyte, he used a 0.966 normal solution of hydrochloric acid
to which various quantities of potassium bromide had been added.
When the bromine ion concentration was large, he obtained but one
anode decomposition point, namely, that of the bromine ions. Like-
wise when the bromine ion concentration was small, only a single
value was obtained, this time that of the chlorine ions. Only at a
definite concentration of the bromine ions (0.001 n. KBr) did he
obtain both the value for bromine ions and that for chlorine ions

ELECTROLYSIS AND POLARIZATION

309

Solvent » 0.965 Ha
Sol. I ^ 1.0 KBr
Sol. U » 0.1 KBr
Sol. m » 0.01 KBr
Sol. IV - 0.001 KBr
Sol. y - 0.0001 KBr I

(see the two breaks in curve IV). Between these two turning
points the curve follows first a vertical, then a moderately upward
sloping direction, which in many cases becomes completely horizon-
tal and even may slope

downward again. It is ^<>^^^ Cubvbb fob Br akd Cl Sbparatzon
assumed that the curve ^"^ °^ ooNTAnrnio Solutions of KBr

follows such a horizontal
course when the primary
substance which is disap-
pearing during the elec-
trolysis is nearly con-
sumed at the electrodes.^
To be sure, it should be
taken into consideration
that in these experiments
the appearance of a new
turning point in the curve
is accompanied by the ap-
pearance of a new phase
at the electrode, while in
earlier cases a new phase
could not be detected.

The significance of the former turning points is, therefore, not yet
established with certainty. However, according to Luther and Bris-
lee^ it is possible that in many cases the different turning points do
not correspond to different processes taking place in the electrolyte,
but to different changes taking place as time passes on the surface of
the electrode. This agrees with the remarks made on page 301 in
regard to the potential of the electrodes.

OhloriN* t »p frt on.

Fio. 51

IMPORTANCE OF THE DECOMPOSITION VOLTAGE IN MAK-
ING ELECTROLYTIC SEPARATIONS AND IN PREPARING
NEW COMPOUNDS

As already shown, different decomposition points characterize the
various metals. From this fact it was inferred by Le Blanc that it
should be possible to quantitatively precipitate* metals one after
another from their mixed solutions by a gradual increase in the

1 See also the recently published investigation of F. Weigert, ZUchr. Eltktnh
them., 19, 877 (1006).

^Ztsehr. phys. Chem,, 18, 97 (1893).
* Ztschr, phys, Chem,, 46, 216 (1908).

810 A TEXT-BOOK OF ELECTRO-CHEMISTRY

electromotive force of the decomposing current That this may be
done has been shown by Freudenberg.^

If through a solution containing salts of copper and cadmium a
current be passed, the electromotive force of which is insufficient for
the continuous deposition of the cadmium but capable of precipitat-
ing the copper, the latter metal alone is completely precipitated.
When all the copper is precipitated the current ceases, it being thus
unnecessary to pay attention to the electrolysis. The electromotive
force necessary for the precipitation of the copper increases with the
dilution of the solution, according to the formula,

F = In^;

VQ P

but since an increase in dilution from -^ to 100^^1^^ normal (the
limit of analytical determinations) causes an increase of less than
0.3 volt for a monovalent and half as much for a divalent metal,
this does not hinder the separation if the solution pressures differ
moderately from each other.

After the precipitation of the copper the electromotive force may
be increased and the cadmium precipitated. In this way a number
of separations have become possible, which had not succeeded when
attention was given to changing the current-strength instead of the
electromotive force. In the future this must be kept in mind in all
processes of electrolysis. Complications may, however, arise through
the formation of alloys or of chemical compounds, which may pre-
vent a complete separation.

Besides the neutral or acid solutions, those of the double com-
pounds of the metal salt with ammonium oxalate or potassium

^ It should, however, be noted that about ten years ago M. Kiliani called atten-
tion to the possibility of electrolytic separations by a gradation of the electro-
motive force, and carried out the separation of silver and copper. He came
upon the idea in considering the heat effects characterizing individual metals,
and calculated from them the electrical energy necessary for their precipitation.
This method of calculation has been shown to be inapplicable, for which reason,
and perhaps more especially because of the general uncertainty regarding polar-
ization conditions introduced, his work did not receive much attention. That
when the electromotive force is above a certain value a metal may be continuously
precipitated from its solution, while below this point only an analytically negli-
gible or absolutely unweighable amount precipitates, was not at that time clear.
The opinion was then much more commonly held that even with low electro-
motive forces not inconsiderable quantities of the metal were precipitated,
according to which view the separation of two metals by a proper regulation
of the electromotive force appeared as an accident rather than as a neceesazy
result of recognized relations.

ELECTROLYSIS AND POLARIZATION 811

cjanide are especially adapted to such separations. In the latter
many metals can be separated from one another which cannot be sep-
arated in acid solution. Thus in acid solution platinum cannot be
separated from gold, mercury, and silyer, i.e. from the metals with
slightly different solution pressures, but is easily separated in potas-
sium cyanide solution. This depends upon the formation of the com-
plex salt 2 K', TtiCl^J', the negative ions of which are dissociated
to an extremely slight extent into Pt"" and 6 CN'. As a result of the
extremely low concentration of the ions, the platinum cannot be pre-
cipitated by an electromotive force which is sufficient to precipitate
the other metals the ions of which are more niunerous. Such arti-
fices are also often utilized in technical work, as, for example, in the
electrolytic purification of gold.^ If a warm dilute solution of hydro-
chloric acid be used as the electrolyte, the gold and platinum of the
anode of impure gold go into solution, but only the gold separates
at the cathode. The platinum thus becomes accumulated in the
solution in the form of complex ions.

Previously, in the quantitative separation of the metals, only the
current-strength was altered. In a mixture of zinc, copper, and
silver salts in acid solution the silver must separate first, since that
process occurs requiring the least expenditure of work, which is also
the case even though the electromotive force be very high, provided
that sufficient silver ions are present at the electrode. In making
this statement it is assumed that the reaction velocities involved are
sufficiently great. The current must be stopped at the proper
moment, otherwise the second most easily separated metal will be
precipitated. After silver and copper, hydrogen follows. To pre-
cipitate zinc simultaneously with the latter from an acid solution,
the current-strength must be made so great that the hydrogen ions
present are insufficient to convey all the electricity from solution to
electrode, and zinc ions must take part in the process. It is evi-
dently more rational to choose to regulate the electromotive force
instead of the current-strength, whenever possible, for then it is
not necessary to watch over the electrolysis. Until within the last
few years most electrolytic separations were carried out empirically,
without knowledge of these theoretical principles.

Not only the metals, but also the halogens, can, even though not
directly, be separated in stages by changing the electromotive force.
For further information in regard to these separations, the work of
Specketer' and E. MuUer* may be consulted.

1 ZUchr. Elektroehem., 4, 402 (1808). * Ber., S6, 960 (1902).

s Ztsehr. Electrochem., 4, 639 (1898) .|

812 A TEXT-BOOK OF ELECTRO-CHEMISTRY

Thus far in the discussion of the phenomena of polarization at-
tention has been directed chiefly to insoluble electrodes at which
the products of electrolysis, especially hydrogen and oxygen, are
separated directly from the solution. Attention will now be given
to those cases in which the product of electrolysis reacts either
with the electrode itself or with some substance in its vicinity.
A general idea of such cases may be obtained from the following
consideration : —

Whenever the evolution of hydrogen or oxygen at the electrodes
is prevented, elepoktmo^ton is said to have taken place. Depolariza-
tion may then consist of a reduction at the anode or of an oxidation
at the calhode. When the electrodes are thus freed of hydrogen
and oxygen, the electromotive force which is required to effect a
continuous decomposition is less than that required before they
were freed. This may easily be shown by a determination of the
electrode potentials. This decrease is due to the fact that the two
gases can no longer accumulate, to high concentrations -at the
electrodes, but must react with the substance, or depolarizer, in
question while at a low concentration. The more energetic the
depolarizer (or mixture of depolarizers), the lower is the concentra-
tion of the hydrogen and oxygen at the electrodes, and consequently
the lower is the electromotive force required to carry on the elec-
trolysis. Indeed, in many cases a spontaneous electrolytic process
results, and the cell, of itself, produces electrical energy.

The velocity with which the hydrogen and oxygen are consumed
naturally plays an important part For example, an oxidizing
agent which, for small currents, appears much stronger than
another, may for large currents appear much weaker. The follow-
ing general statement may be made : —

An oxidizing or a redvcing agent is electromotivdy active in propor-
tion to its power of reducing the concentration of the separated hydro-
gen or oxygen.

The electromotive activity itself is dependent on the concentration
of the depolarizer at the electrode, and therefore indirectly on the
rapidity of stirring, the velocity of diffusion, and the current
density in the case of depolarizers which react rapidly, and on the
specific character of the depolarizer, catalytic action, and above all,
on the temperature in the case of depolarizers which react slowly.
These points have already been touched upon in the discussion of
electro-chemical reactions on page 281.

In the above consideration, it has been assumed that hydrogen
and oxygen first actually separate and then react with the depolar-

ELECTROLYSIS AlfD POLARIZATION 313

izer. In many cases this may be true, but in others it certainly
is not true. For instance, if zinc is made an anode in a dilute solu-
tion of sulfuric acid, it is very improbable that the formation of
zinc ions is the restdt of a secondary reaction between zinc and the
separated oxygen. It is uniyersally assumed that the zinc ions are
formed directly. The above method of viewing the phenomena of
depolarization is, however, allowable if it is only desired to obtain
a clear idea of the formation of potential-difference at the electrodes,
providing, however, that a state of equilibrium exists, ue. that all
of the potential-differences existing at the electrode are equal. (See
also pages 263 to 267.)

Oxidizing and reducing agents are extensively used in electrolysis
on a commercial scale with more or less success in order to decrease
the electromotive force required and thus to effect a saving in
electrical energy. Naturally in this case it is of first importance
that the cost of the substance used as a depolarizer be not greater
than the resulting saving in electrical energy. In his well-planned
process for the refining of copper, Hdpfner makes use of a solution
of sodium and ferric chlorides. This solution dissolves the copper
from its ores in the cuprous state with the simultaneous reduction
of the ferric to ferrous chloride. This copper-containing solution is
sent through the cathode compartment of the electrolytic apparatus,
where the copper is deposited. It is then sent to the anode com-
partment, where the ferrous iron is oxidized to the original ferric
state. The solution may now be passed through the same cycle
again. By the reducing action of the ferrous chloride at the anode
the separation of chlorine and the corresponding high electromotive
force is avoided.

Soluble electrodes are used to attain the same end, namely, the
saving of energy.

The nature of the reacting substances and the conditions of the
experiment determine which specific reactions will take place in
any individual case. By the electrolysis of alkali chlorides, for
instance, it is possible to obtain metal and chlorine, alkali liquor
and chlorine, hypochlorite, chlorate, or perchlorate. Although con-
siderable success has already been attained, this is still a field of
great promise for experimental research. Space in this book is too
limited for a consideration of specific cases, hence the student is
referred to the compilation of F. Fdrster, "Elektrochemie wasserigen
Losungen" (1905). Here we must confine ourselves to the more
general points of view and their characterization by citation of
individual cases.

814 A TEXT-BOOK OF ELECTRO-CHEMISTRY

From one and the same substance, it is possible, especially in
organic chemistzy, by means of simple oxidation to obtain different
new substances which, under comparable circumstances, exhibit
different oxidation voltages. If now this original substance be
used as a reducing agent at the anode, it is evident that, according
to the magnitude of the applied anode potential, the first, second,
third, and perhaps still higher oxidation stages of the compound
may be formed. In such a case the determination of the decomposi-
tion voltages might be of great importance. Each decomposition
point indicates the beginning of a new reaction. If it is desired to
exclude the product of one of the reactions, the electrolysis must
be carried out with an electromotive force which is less than the
decomposition voltage which corresponds to this reaction.

In this manner, Goehn ^ was able, by passing a stream of acety-
lene through the anode compartment during the electrolysis of
potassium hydroxide under an electromotive force which was be-
tween the first and the second decomposition points, to demonstrate
that as a matter of fact formic acid may thus be formed quantita-
tively. Hence in this case the entire electrical work was expended
in the formation of formic acid. If a higher electromotive force be
employed, a mixture of substances is obtained, in which carbon
dioxide, formic acid, and oxygen have been found.

This method for the preparation of formic acid is of interest in
that it indicates how a substance may be prepared without the
formation of troublesome by-products. Unfortunately there is but
slight probability that this process will become of value commer-
cially, because with the limited electromotive force, the available
current density is very small, and therefore the quantity of formic
acid formed per unit of time is insignificant compared with the size
of the necessary apparatus.

Previous to this work of Goehn, other similar investigations had
been carried out, especially by Haber.' He succeeded in show-
ing that by reducing nitrobenzene at a given electrode with the
use of different constant electromotive forces, different products are
obtained.

It is evident that in many cases it is of importance to find some
means of increasing the potential at which, for a given current
density, oxygen is evolved. With such a means at hand, it might
be possible that other oxidations, which are desired, would take
place for which the previous potential was either quite too low or at

1 Ztsehr, Elektrochem.^ 7, 681 (1901).

*Zt9ehr. Elektroehem,, 4, 606 (1806) ; Ztsehr. phya, Chem,, Sd, 103 (1900).

ELECTROLYSIS AND POLARIZATION 815

least too low for a good yield of the desired oxide. Such a means
has been found in the form of fluorine ions. It is a fact that the
yield of oxidation processes taking place at a platinum anode is con-
siderably increased by the presence of these ions.

If, after a knowledge of the facts described above has been ob-
tained, the catalytic influence of the electrode material upon the for-
mation of new substances mentioned on page 276 be recalled to mind;
the thought is at once suggested that the different potentials existing
at the electrodes during the passage of an electric current is the
cause of this different or catalytic behavior of the metals. This
subject is elucidated by the recently published work of Haber
and Buss.^ In this work they have shown that velocity of reduc-
tion at the surfaces of different metals is very different even for the
same voltage. The specific influence of the material of the cathode
plainly follows as a consequence of this fact. They investigated
especially the depolarizing action of the substances : —

Nitrobenzene, p-Nitrophenol,

Hypochlorite, and Quinhydrone,
at electrodes of

Gold, Platinum,

Silver, Iron,

and NickeL

Furthermore, they were able to confirm the peculiar influence which
in many cases the past treatment of an electrode exerts upon the
electrolytic process. By subjecting an electrode to continuous
cathodic polarization, it may be made '' active," Le. the rapidity of
depolarization at it may be increased. This increase in activity be-
comes evident in the following manner : Starting with a definite
current and a definite electrode potential, such that hydrogen is
rapidly evolved, it may be observed that the current increases, the
potential falls, and the evolution of hydrogen slackens or ceases.
This active state is very unstable. A short interruption of the cur-
rent is sufficient to restore the original state of the metal.

Summing up, the conclusion is reached that the catalytic influence
of the electrode material, as well as the electromotive force, plays an
important part in the electrolytic process. This is shown also by
the recent investigation of Tafel and Naumann' on the electrolytic
reduction of coffeine and succinic imide. The process can be
carried out only with the use of a cathode of cadmium, mercury,

^ Zttehr. phy9. Chem,,\t, 267 (1004).
> Zt9chr. phys. Chem., 00, 718 (1905).

816 A TEXT-BOOK OF ELECTRO-CHEMISTRY

or lead. In the case of the lattet metal, the cathode potential most
not exceed a certain value. This fact shows clearly the influence of
potential on the process. The influence of the electrode material is
shown by the fact that with the same cathode potential the reducing
action obtained with mercury is different from that obtained with
lead. The latter influence also occurs in the process mentioned on
page 280, involving PbO^.

The phenomena of the electrolysis of fused salts are, as shown by
the investigations of B. Lorenz,^ entirely analogous to those of aque-
ous solutions.

Eieotrolyiis with an Alternating Current.* — If, instead of a direct
current, a symmetrical alternating current be used, it is at once
evident that, with so-called reversible electrodes, no change would be
detected either in the solution of the electrolyte or at the electrodes.
The change which is produced by the momentary flow of electricity in
one direction is exactly compensated by that produced by the next
momentary flow in the opposite direction. On the other hand, if the
electrolysis is carried out with such an arrangement as :

Copper — Acid solution of sodium sulfate — Copper,

whether or not copper goes into the solution depends upon the rapid-
ity of alternation. If the current be but slowly alternated, a greater
or less quantity of copper ions sent into the solution by the momen-
tary current in one direction is removed from the immediate
vicinity of the electrode by diffusion or convection so that an insuf-
ficient quantity of these ions are available at the electrode for
precipitation by the next momentary flow of electricity in the
opposite direction, then this deficit is supplied by hydrogen or
sodium ions. Experiments have shown that for a current density
of 0.046 ampere per square centimeter and a frequency of alterna-
tion of 1000 per minute and higher, only a small per cent of copper
goes into solution. The same holds for the system,

Platinum — Sulfuric acid — Platinum.

1 See also Le Blanc and Brode, "The ElectrolysiB of Eased Sodium and
PotasBium Hydroxides,** Ztschr. MeJarochem,, 8, 697 (1902). More detailed
information will be found in Lorenz*8 ** Die Elektrolyse geschmolzener Saize,**
VolnmeB 90, 21, and 88 of the ** Monographien tiber angewandte Elektro-
ehemie,** W. Knapp, publlBher, Halle, Saxony.

* Le Blanc and Schick. Ztschr. phys, Chem,^ 46, 213 (1908) ; A. LOb,
2k9chr, Elektrochem., 18, 79 (1906). The reader is referred also to the inter-
esting experiments of Drechsel, J. ftakt. Chem,, 88, 84, and 88, which cannot
be considered here.

ELECTROLYSIS AND POLARIZATION 817

In this case the quantity of hydrogen and oxygen evolved by an
alternating current of high frequency is practically equal to zero.

The relations are quite different when, for instance, two copper
electrodes are placed in a 4 normal solution of potassium cyanide.
In this case, with an alternating current of a frequency of 1000 per
minute, the copper dissolves in the form of cuprous ions almost
quantitatively, accompanied by the evolution of an equivalent
quantity of hydrogen. Thus the same results are attained as with
the direct current. As the frequency of the alternating current is
increased, the quantity of copper dissolved decreases. However,
when the frequency has reached 38,000 reversals per minute, and
the current density is 0.046 ampere per square centimeter, the yield
is still about 33 per cent.

The most probable explanation of this phenomenon is found in
the formation of complex substances. Copper ions may unite with
potassium cyanide, or cyanide ions, to form a complex ion from
which copper cannot be separated at the cathode. If now the
reversal of the current is so slow that the copper ions sent into the
solution by the momentary current in one direction have sufficient
time to form the complex ion with the cyanide ion, the reverse cur-
rent cannot redeposit the copper. The greater the frequency of
reversal of the current, the greater is the per cent of copper sent
into the solution which will be deposited out again. This offers a
means of obtaining an idea of the velocity of a reaction between
ions. Thus the reaction between copper ions and potassium cyanide
during the electrolysis of a 4 normal solution of potassium cyanide
between copper electrodes, with a current density of 0.046, is prac-
tically completed in y^ of a minute, while at the end of ^^ of a
minute it has not proceeded far enough to be detected. The alter-
nating current also throws some light on the velocity of the forma-
tion of difficultly soluble precipitates, although in most cases the
precipitate formed by the current in one direction is completely
decomposed again by that in the opposite direction.

It will only be mentioned here that with the alternating current
remarkable passivity phenomena occur.

Electrolysis without Electrodes. — If a platinum cathode be placed
in a potassium iodide solution and a platinum anode a few milli-
meters above the solution, and an electric current from a powerful
electric machine be sent from one electrode to the other, then iodine
separates at the boundary surface of air and liquid. The quantity
of iodine which so separates is that required by Faraday's law.^

i Klupfd, Drud, Ann., 16, 674 (1906) ; Gabkin, Wied. Ann,, Z% 114 (1887).

818 A TEXT-BOOK OF ELECTRO-CHEMISTRY

Hence ander these oircumstanoes the negatively charged iodine ions
give up their charges to the space occupied by gas or vapor. It is
possible that these charges pass through this space to the anode as
free electrons. If instead of the anode the cathode be placed above
the solution, the corresponding quantity of potassium hydroxide is
formed at the surface of the liquid, accompanied by the evolution of
hydrogen gas. If, with this same arrangement of electrodes, a solu-
tion of a salt of a heavy metal be used, then a separation of metal
takes place at the surface. In this case it may be considered that
the cathode throws off free negative electrons, constituting cathode
rays. The question then at once arises as to the possibility that
real cathode rays may have a reducing action on the surface of elec-
trolytes. As a matter of fact, Bose^ found that, under favorable
circumstances, hydrogen is evolved when the surface of a hot
saturated alkali solution under a vacuum is exposed to the action of
cathode rays. The quantity of hydrogen evolved is, however, con-
siderably greater than required by Faraday's law. Besides the pure
electro-chemical action another takes place in this case which may be
ascribed to the kinetic energy of the particles of the cathode rays.
It may be shown by calculation that the mechanical energy of the
cathode rays may, in the most favorable case, produce a much
greater chemical action than corresponds to the quantity of elec-
tricity involved. Now even if by far the greater part of this energy
becomes transformed into heat, the assumption that at least a small
portion of this energy is consumed in the evolution of detonating
gas is still plausible. The oxygen gas, which would be expected
under this assumption, is at first dissolved by the electrolyte. It
may, however, with continued action finally be detected.'

In the case of the Becquerel rays it is probable that, due to the
higher kinetic energy, the dynamical exceeds the purely electro-
chemical effect to a greater extent than in the case of the cathode rays.

Deoompoiition Voltage and Solubility. — That the voltage at which
the ions of a salt in a 1 normal solution are separated from the
solution marks the upper limit of the solubility of the salt has been
IX)inted out by Nernst * For example, since the decomposition value
for iodine ions is

?e dttrod* < e to e t rolyte = + 0*24 VOlt,

and that of silver ions is

1 ZUehr. Wi88. Phot, %, 228 (1904).

s It is also aasumed in the case of the formation of OKone that the action of
the cathode rays is a purely chemical one. See page 24.
»Ber., 80, 1647(1897).

ELECTROLYSIS AND POLARIZATION 819

silver iodine conid not exist in solution to a concentration of 1 nor-
maly because at such a concentration it would become spontaneously
decomposed with a force of 0.25 of a volt. Hence in order that
silver iodide should be capable of existence, its solubility must
be exceedingly small. This is in agreement with facts. If the
solubility be calculated for which the decomposition voltage is equal
to zero, t.e. at which the salt just becomes stable, a value is obtained
which is much larger than that actually observed. Bodlander ^ states,
what had already been indicated by Luther, that it is possible to
calculate exact solubility values if the decomposition voltage of the
solid salt be taken into consideration.

Equilibrium constantly exists between the saturated (but dilute)
solution of a practically completely dissociated electrolyte and
the anhydrous solid salt. Then the work which must be done
during electrolysis in order to discharge the ions is equal to that
which is required to break up the solid salts into the same con-
stituents at the same concentration. Hence we may consider the
decomposition voltage as a measure of the tenacity with which these
constituents are held together in the solid state.

The decomposition voltage of the saturated solution is now, at 17^,

F. = 0.0576 log^jV* +0.0575 log f^\ (1)

where Pe and v^ refer to the cation. Pa and v. to the anion, and P
represents the equal concentrations, expressed in equivalents, of the
two ions in the saturated salt solution.

The individual decomposition voltages of the cation ^ and of the
anion ?« ^^r an ion concentration of 1 normal is as follows:—

le « 0.0575 log p/«j

i:a=0.05751ogPa^«.J
From (1) and (2) the following is obtained: —

(2)

J-+i.

F. = !!.+!:„ -0.0576 log P^« ^•.
If the cation and anion aie both univalent,

(8)

V^ = Va=l.

^Zt9chr, phya. Chem., ft!, 65 (1896).

820 A TEXT-BOOK OF ELECTRO-CHEMISTRY

By substituting this value in (3), the following equation is ob-
tained:-^

'.-^• + ?.-0.1151ogP.

In the case of highly dissociated and slightly soluble electrolytes^
the value of P represents the solubility. From this quantity, the
values of l^ and I^ being known, the free energy f^ which is lib-
erated during the formation of the solid substance from the corre-
sponding constituents may be calculated. Conversely, the quantities,
F., Ig, and ?« being known, the value of P may be calculated. Of
these quantities, £« and Z. are easily determined experimentally, and
F, may in many cases be taken as approximately equal to the
equivalent heat of formation Q, expressed in calories. Hence

F^ = Q X 4.189,

0X4:18? Q_,

96640 23045

Considering the sources of error involved, the calculated values are
in remarkable agreement with those actually observed.

Finally, attention is called to an empirical rule which holds in
many cases, and which, further, may be established theoretically by
deductions from the above equation. It may be stated as follows: —

The aolubUUy of different mUs of the same metal (or of the same
acid) ia the greater j the greater the tendency of the acid radical (or
metal radical) to pass from the electrically iveutral to the ionized state.

Thus in the case of compounds of tiie metals, the solubility ior

creases in the order, —

Iodine,

Bromine,

Chlorine,

and in the case of the organic acids, in the orderi*^

Silver salt,
Acid,
Alkali salt.

Beoentiy, it has been endeavored to bring a large number of prop-
erties into relationship with the decomposition voltages.^

1 Abegg and Bodiander, Ztschr. anorg. Chem., M, 463 (1809).

CHAPTER IX

Supplement

STORAGE CELLS OR ACCUMULATORS

SiKGB storage cells are to^ay used to an extraordinary extent for
many purposes, a brief presentation of the chemical processes which
take place in them is here given.

Storage cells o]; accumulators are arrangements in which electrical
energy may be stored as chemical energy, whence it may again
be obtained at will in the form of electrical energy. Any reversible
cell may be used as an accumulator. If a current be sent through
a used Daniell element in the direction from copper to zinc, copper
is dissolved and zinc precipitated — in other words, electrical energy
is stored up in the form of chemical energy. In practice lead
storage cells are used almost exclusively.^ The electrodes consist
of lead plates coated with a specially prepared layer of lead oxide
or sulfate, and the electrolyte is 20 per cent sulfuric acid. When a
current is sent through this arrangement, lead peroxide (or a cor-
responding hydrate) is formed on that electrode at which the positive
electricity enters the acid, while at the other electrode metallic lead
in spongy form is produced. The storage cell is charged after the
conduction of sufficient electricity through it. In the discharge
both the peroxide and the metallic lead return to sulfate. The
chemical process on charging is then essentially the change of lead
sulfate to lead at one electrode and to peroxide at the other, while
the discharge is simply the return of these substances to lead sul-
fate. The corresponding heat of reaction is given by Streintz' as
follows : —

PbO, + 2H,S04 aq. -f Pb = 2Pb804 + 2H,0 -|- aq. -t- 87,000 cal.

If the electromotive force of the storage cell be calculated from

^ For particnlars concerning the making and use of accomulaton, attention
Ib called to the following works : —

Heim, '* Die Akkomulatoren ** (Oskar Lehier, Leipzig).
Elbe, ** Die Akkumulatoren ** ( Johann Ambroeius Barth^ Leipsig).
3 Wiener Monatsheftef. Chemie, 16, 286 (1894).
Y 321

822 A TEXT-BOOK OF ELECTRO-CHEMISTRY

the known heat of reaction, assuming complete transformation into
electrical energy, 1.885 volt is obtained. This agrees yeiy well with
the experimentally determined value for dilute sulfuric acid. From
this agreement it also follows that the electromotive force of the
storage cell is nearly independent of the temperature (page 173), and
this has also been demonstrated by Streintz. If this shows that
it is probable, the work of Dolezalek ^ removes all doubt, that the
process takes place in the manner indicated. Dolezalek showed
that the entire behavior of the storage cell is in agreement with the
reaction equation. He investigated especially the relation between
the electromotive force and the concentration of the acid, and estab-
lished the fact that the values calculated from thermodynamical
considerations agree finely with the values found by experiment,
and that therefore (for small current densities) the storage cell is
reversible. These results are in complete agreement with the theory
advanced by Le Blanc' by which the processes taking place in the
storage cell were, for the first time, explained with the aid of the
ionic theory.

When the storage cell is charged and ready for use, the positive
electrode is coated with lead peroxide and the negative with spongy
lead. Between the two electrodes is sulfuric acid. It may be
assumed that lead peroxide in contact with water forms tetravalent
lead ions together with the corresponding hydroxyl ions, and that
while the cell is in action the tetravalent ions are transformed into
divalent lead ions. This process is the chief source of the electromotive
force of the storage ceU, The tetravalent ions which disappear are
constantly replaced from the solid lead peroxide, and the bivalent
ions which are formed do not remain in the solution, but since lead
sulfate is difficultly soluble, i.e, since the product of the concentra-
tions of the divalent lead ions and the sulfate ions is a small value,
they combine with the sulfate ions in the solution, forming solid
lead sulfate.

At the negative pole metallic lead changes into bivalent ions, a
process taking place without producing any considerable potential
difference. Here also insoluble lead sulfate is formed from the
Pb" and SO/'.

The ionic theory not only renders clear the changes of peroxide
and metallic lead into sulfate, but also explains the gradual
diminution of the electromotive force of the cell in action. While

1 Wied, Ann., 66, 894 (1808), and *' Theorie des Bleiakkamulatois," W.
Knapp, Halle, Saxony (1901).

3 First edition of this book, page 223 (1895).

SUPPLEMENT 823

the magnitude of the potential-difference at the positive electrode
depends upon the concentration of the quadrivalent and bivalent
lead ions (see page 250), that of the potential-difference at the
negative electrode depends upon the concentration of divalent lead
ions in contact with an excess of metallic lead. The concentration
of the quadrivalent ions decreases with time^ and that of the bivalent
increases, as may be seen from the following: At the peroxide
electrode there is a saturated solution of this compound — that is,
the product of the concentration of Pb- and the fourth power* of the
concentration of the OH' ions is here constant. On the other hand,
there must be definite relations between these ions and those of the
sulfuric acid. The product of the concentration of the H and OH
ions in the solution must have a constant value equal to that for
water. It has been seen, in the first place, that during the discharge
of the cell, lead sulfate is formed at the peroxide electrode, and in
the second, that newly formed OH ions produced by the peroxide
cannot exist as such, but must combine with the H ions of the acid
to form undissociated water. There is thus a continual removal of
H and SO4 ions taking place. The removal of the former allows of
an increase in the concentration of the OH ions, and therefore causes
a reduction in that of the quadrivalent lead ions. The removal of
SO4 ions permits an increase in the concentration of the Pb" ions,
since the solution is saturated with lead sulfate. This latter
process also takes place at the negative electrode. When the supply
of peroxide is exhausted, the electromotive force falls very rapidly to
an exceedingly low value.

After the cell has been discharged, there is lead sulfate on both
electrodes, consequently bivalent lead ions are present. The process
of charging consists simply in the change of bivalent lead ions to
quadrivalent at the electrode at which the positive electricity enters
the solution, and to metallic lead at the other electrode. The Pb"
ions used are replaced from the solid lead sulfate. The Pb- ions and
the OH' ions present, having reached that concentration in the solu-
tion determined by the dissociation constant for peroxide of lead,
combine to form this oxide (or a hydrate). Thus the lead sulfate
at one electrode gradually changes into peroxide, and into metallic
lead at the other. The opposing electromotive force of the cell
increases during the charging, because the processes described as
taking place during discharge are reversed. The concentration of
the bivsdent lead ions at both electrodes diminishes with time, while
that of the SO4" ions is continually increasing. The concentration of
1 Because four OH ions correspond to one of the lead ions.

824 A TEXT-BOOK OF ELECTRO-CHEMISTRY

the Pb" ions increases with the increase of H ions fonned with equiv-
alent quantities of OH ions from the undissociated water. The
OH' ions continually combine with the Pb'* to form peroxide, and
their ooncentration must diminish as that of the hydrogen ions in-
creases. The lower the concentration of the OH ions the greater is
that of the Pb- ions. If no more bivalent lead ions are present^
hydrogen ions separate at one electrode and hydroxyl ions at the
other. Thus the rapid generation of hydrogen and oxygen at the
electrodes in charging shows that the accumulator is over-charged.
In order to cause a considerable generation of hydrogen and oxygen
in the cell a somewhat higher electromotive force is required than is
necessary to charge it, since the separating gases can accumulate to
high concentrations in the electrodes, or, in other words, since the
electrodes possess a considerable over-voltage. When platinum elec-
trodes are used in sulfuric acid, an electromotive force of two volts is
sufficient to produce a rapid evolution of gas. If this was also the
case in the lead cell, the latter could be charged only with a great
loss of energy.

The above theory of the processes which take place in the storage
cell has received considerable support from the recent work of Elba
and Rixon,^ which has established the fact that acid which has been
in use in such cells contains comparatively large quantities (as much
as 0.17 of a gram of Pb(S04)t per liter) of tetravalent lead, and hence
of tetravalent lead ions. By a special experiment it was proven that
the equilibrium corresponding to the reaction equation, —

Pb(SO0, + 2H,0:^PbO, + 2 HjSO*,

is attained in about five hours, when a mixture of freshly precipitated
lead peroxide and sulfuric acid is continuously stirred. The presence
of the above-mentioned considerable quantity of tetravalent lead in
the acid furnishes a plausible explanation of the spontaneous dis-
charge of accumulators. The tetravalent lead migrates from the
peroxide electrode, where it is formed, to the spongy lead electrode,
where it is reduced to the bivalent state.

It must not, however, be supposed that only the assumed process,
especially the formation of tetra- or bivalent lead ions at the anode,
takes place. According to Liebenow, it is possible that the ion
PbOj" is present, and is transformed reversibly into ordinary PbOj.
In describing states of equilibrium, as, for example, in measurements
of potential, it makes no difference to which of the reactions of the

1 Ztschr. Ulektrochem,, 9, 267 (1903).

SUPPLEMENT

825

equilibriiun the source of the electiomotive foroe is ascribed. In
describing the process of electrolysis, however, it is absolutely neo'
essary to emphasize the reaction in which the greatest quantities
are involved. Which of the reactions this is depends upon the
respective velocities of reaction, and must be determined for indi-
vidual cases. In the case in question it appears more in accord with
facts to give prominence to Pb'-, and not to PbOj" ions, because the
concentration of the latter is insignificant in comparison with that
of the former. (See also page 307.)

Of the storage cells using metals other than lead, the Junger-Edison
accumulator is the most interesting.^ When charged it consists of
the combination,

Fe - KOH - NiA, aq.

During the charging and the discharging of the cell, the following
processes take place: —

Fe + 2 Ni(OH) :5:Fe(0H) + 2 Ni(OH)„ or
Fe + NiA, w H,0 ± r H,O^FeO, m H,0 + (NiO),, p HjO.

Hence in this cell water plays the greatest part in the reaction.
For this reason, but little alkali is required in the cell. This is in
contrast to the lead accumulator, in which much sulfuric acid is used.
The normal initial voltage is 1.36 volts. The value of this storage
cell in practical service remains to be determined.

ENERGY-EQUIVALENTS (see page 18)

Eses

JOUl^BS

Oalobibb *

KlUM&AM-
MBTSBfl

LinBR-

▲TMOePHBBBS

Kilowatt-

BOVBS

HOBSB-
POWBB

10-T

2.887xlO-»

1.020x10-8

9.872X10-M

2.778xl0-»*

8.776xl0-»«

0.2887

0.1020

9.872x10-*

2.778xl(^-»

8.776xlO-»

4.189x107

4.189

0.4272

4.186x10-"

1.164xl0-«

1.682x10-*

9.BMxW

9.806

2.841

9.861x10-

2.724x10-*

8.708x10-*

1.018x10*

101.8

24.18

10.88

2.814x10-*

8.826x10-*

a.oooxiou

8.600xl0>

8.598x10*

8.672x10*

8.668x10*

1.869

2.649x10"

8.649xl0«

6.825x10*

2.702xl0«

2.616xl0«

0.7860

1 ElbB, Ztschr. JSlektrochem., 11, 734 (1906) ; Gr&fenberg, Ztschr. Elektro-
e?tem^ 11, 786 (1005) ; Zedner, Ztschr. Elektrochem,^ 11, 800 (1905) ; FSrster,
Ztschr. JElektrochem., 11, 048 (1005). See also the discusBion following the above
papem.

* The calorie (15^ gm-cal.) here is that recommended by the International
Congress for Applied Chemistry at Berlin, namely, equal to 4.180 x lO' ergs.

326

A TEXT-BOOK OF ELECTRO-CHEMISTRY

ELECTRO-CHEMICAL CONSTANTS (see page 43)

M^ represents electro-chemical equivalents, or the quantity or mass
of substance in milligrams which is separated by one ampere-second,
and 3000 • Jf«. represents the quantity or mass in grams of various
anions and cations which is separated by one ampere-hour of elec-
tricity (= 0.0373 equiv.).

CATiom

Equiv.

Mac

seoo-M^

AHiom

EqiriT.

Mae

aeooir^

JAl

0.08

0.00864

0.8367

70.06

0.8282

2.082

iSb

40.07

0.4161

1.404

BrOs

127.06

L826

4.772

JAb

26.

0.2600

0.0822

86.46

0.3672

1.322

iBa

68.7

0.7116

2.662

CIO,

83.46

0.8644

3.112

IPb

108.46

1.072

8.868

CHOa

46.01

0.4662

1.678

|Cd

66.2

0.6821

2.006

CHsO,

60.02

0.6114

2.201

iCa

20.06

0.2077

0.7477

26.04

0.2607

0.0710

iCr

17.87

0.1700

0.6477

iCO,

30.00

0.3108

1.110

}Fe

27.06

0.2806

1.042

1C,04

44.00

0.4668

1.641

iFe

18.68

0.1080

0.6047

iCr04

68.06

0.6013

2.166

\am

66.78

0.6808

2.461

10.

0.1068

0.7086

80.16

0.4066

1.460

126.07

1.316

4.736

(Co

20.6

0.8066

1.100

10,

174.86

1.811

6.620

68.6

0.6688

2.372

NO,

62.04

0.6426

2.318

(Ca

81.8

0.8204

1.186

0.08287

0.2068

7.08

0.07282

0.2621

17.01

0.1762

0.6848

IMg

12.18

0.1262

0.4642

iSiO,

38.20

0.8067

1.424

(Mn

27.6

0.2840

1.026

16.03

0.1660

0.6078

28.06

0.2888

0.8606

iSe

80.6

0.4102

1.477

iNl

20.86

0.8040

1.004

iS04

48.08

0.4076

1.701

200.0

2.072

7.468

^Te

68.8

0.6600

2.870

107.08

1.118

4.026

JSr

48.8

0.4687

1.688

JTe

81.0

0.8804

1.100

204.1

0.2114

0.7611

1.008

0.01044

0.03760

iZn

82.7

0.3387

1.210

iSn

60.6

0.6168

2.210

iSn

20.76

0.3082

1.100

APPENDIX

NOTATION

Since there is no recognized system of notation in electro-
chemistrj, it has been endeavored in this translation to devise and
introduce a system of notation which shall be simple, and shall avoid
the difficulty and confusion often caused by the use of complicated
or unsystematized notation. While the system given here is
original as a whole, yet in nearly every case the individual symbols
have been used with a similar meaning in some other work on
chemical or electrical science. Hence it will scarcely be necessary
for any one at all familiar with chemical or electrical literature to
study the system. It is also believed that students and general
readers of the book will experience no difficulty or confusion in
keeping the notation in mind.

In devising the system, each class of properties, quantities, etc.,
has been represented by a Roman letter which, while avoiding
ambiguity, readily suggests the class in question. Thus concentra-
tion has been represented by the letter C, and dilution by the letter
D, Whenever the names of two or more classes have the same
initial letter, the use of a single character to represent them has
been avoided by the use of small letters, small capitals, and large
capitals, or of different letters which may be substituted for the
initial letters without materially affecting the sound of the class
names. This may be illustrated by the following examples: —

Concentration (of a gas) = c

Current (electric) as o

Concentration (of a solid or liquid) = C
Conductance (electrical) =k

Constant = K

The class notation adopted is given in the following table:—
A . . . Acidity.
B • • . Basicity.
o • • . Eleotbio Cubbent.

327

828

APPENDIX

O
d

E
F
H

n
P

T
U

F
W

i-h)

(4)

Concentration.

DiFFEBENTAL.

Diffusion.
Dilution.

Energy.
Force. (Factor or function ss/)
Heat or Heat Capacity.
Electrical Conductance. («=-•)

Constant. (Capacity = k).

Length, Height, Distance.

Mass or Weight.

Number. (Normal concentration a jy.)

Pressure.

Quantity.

Electrical Resistance. ( = ^-]

Gas and Solute Constant, f =^. i

Surface or Cross Section.

Solubility.

Time.

Temperature.

Velocity.

Valence or Number of Charges on an Ion.

Volume.

Work.

Fractional Part. Degree of Dissociation.

It should be noted that electrical quantities are in general repr^
sented by small capitals.

The whole system is based on the class notation just given, the
individual members of a class being represented by the class letter
with distinguishing sub letters. This is illustrated by the following
example: —

Concentration (general) ss O,

Concentration in grams per liter = C^,

Concentration in equivalents per liter = C. or C,.
Concentration in mols per liter = C^.

APPENDIX 829

In the case of oondnctance, a different rule has been followed.
The yarioos kinds of condnctances have been distingnished as

ows: Conductance (general) s=k.

Specific Conductance s= s.
Equivalent Conductance = £.

Symbols have been distinguished by an underline also in the
following cases: —

Quantity of Electricity (general) =q.

Quantity of Electricity, 96540 coulombs = 9.
Quantity of Heat (general) as Q.

Quantity of Heat, 1 calorie &s^.

Electromotive Force (general) bs f.

Single Potential-difference s 1.

The complete system of notation is given in alphabetical order
in the following table: —

a . • . Acceleration.

A . . . Acidity.

B . • . Basicity.

c • • . Concentration of a gas. fes-.j

Cg Grams per liter.

c^ Mols per liter.

c« Equivalents per liter.

• • • Electric current or current-strengtL (bs'.j

C • • . Concentration of a solute, [^^y;*)

Cg Grams per liter.

Ge Equivalents per liter.

Cm Mols per liter.

d . . • Differential.

d • • • Dilution of a gas. (^'-•J

D • . • Dilution of a solute.

Dg Volume in liters containing one gram.

D« Volume in liters containing one equivalent.

Dm Volume in liters containing one mol.

880 APPENDIX

D • • • DiffasioiL

D«» Coefficient

E • • , Energy.

E^ or s Electrical energy.
E^ External energy.
Ef Free energy.
Ei^ Heat energy.
Ef^ Internal energy.
E^ Mechanical energy.
E^ Volume energy.

/ • • • Factor (or function).

F . . . Force.

F^ or V Electromotiye force.

Fe Beferred to the standard calomel celL
Va Beferred to the standard hydrogen celL
Z Single potential-difference.
£0 Single potential referred to calomel celL
Zh Single potential referred to hydrogen cell.
£0 or (ep) Single potential at unit concentration.

F^ Mechanical force (pressure).

JET . • • Heat or heat capacity.

H. Electrical heat effect (Joule's heat effect).
Hr Heat of reaction.
H^ Heat of dissociation.
H^ Heat of neutralization.

ft • • . Electrical capacity.

K • • • Electrical conductance.

S Specific conductance or conductiyity.
2 Equivalent conductance.

JT • • • Constant.

Ke Cell constant.

K4 Dissociation constant.

K^ Equilibrium constant.

Kd Dielectric constant.

K, Solubility constant.

K^ Velocity constant.

{ . • • Length, height, or distance.

m • . • Mass or weight of a gas.

m^ Atomic mass in grams (gram-atom or atom).
m^ Molecular mass in grams (gram-mol or mol).

APPENDIX 881

Jf • • • Mass or weight of a solute, liquid or solid.

Mag Atomic mass in grams (gram-atom or atom).
M^ Equivalent mass in grams (gram-equivalent or

equivalent).
Mi Ion mass in grams (gram-ion or ion).
M^ Molecular mass in grams (gram-mol or mol).

n • • • Number.

Ua Transference number for anions (= 1 — n^>
tie Transference number for cations ( = 1 — n^).
Ui Number of ions formed from one molecule of an

electrolyte.
Yi^ Number of molecules formed from one molecule.

N . . . Normal concentration.

p . • . Pressure of a gas.

p . . . Electrolytic solution pressure.

P . . . Pressure of a solute, i.e. solute or osmotic pressure.

(f • . • Quantity of magnetism.

Q . • . Quantity of electricity.

^ Electrochemical unit of quantity of electricity, i*.e.
96540 coulombs.

Q . • . Quantity of heat.

Q Quantity of heat required to raise the temperature
of one gram of water one degree, i.e. 1 calorie.

r • • • Internal electrical resistance of cells.

B . . . Electrical resistance. External resistance of a circuit

JB . • . Gas or solute constant. I =J^A

(■

nTj
«... Surface or cross section.

8 . . . Solubility.

t . . . Temperature, centigrade scale.

T • • . Time.

T^, Time in days.
Tji Time in hours.
T^ Time in minutes.
T« Time in seconds.

jP • • • Temperature, absolute scale.

u • . • Migration velocity of ions.

Va Of anions.
u„ Of cations.

832 APPENDIX

. Yelooity of soluticnL
. • Velocity of reaction.
, • Volume of a gas.

V . .

. • Valence. Number of electrical charges on an ion.
. • Volume of a liquid or solid.

w . ,

, . Work.

W^ MechanicaL
Tr« Electrical.
W„ Osmotic.

9 • ,

» • Fractional part Degree of dissodatioiL

» Fractional change.

A| Due to temperature change of one degree.

AUTHOR INDEX

Abegg, 122, 123, 206, 2i7, 250, 266, 206,

267,320.
Adolph, 82.

Arrhenius, 49, 62, 68, 69, 89, 94^ 136, 136.
Ayogadro, 62.

Bancroft, 266.

Basset, 76.

Behiend, 206, 217.

Bender, 136.

Bemield, 196.

Berzelios, 40, 41, 44, 46.

BiUitzer, 169, 239, 242.

Biltz, 143, 168.

Bindsohedler, 276.

Blake, 123.

Bodlander, 128, 206, 319, 820.

Borchers, 20, 21.

Bose, 154, 306, 306, 318.

Bottger, 93, 217.

Boyle, 62.

Brand, 307.

Braun, 61, 169, 166.

Bredig, 79, 116, 117, 128, 226, 209, 299.

Brislee, 309.

Brode, 23, 40, 316.

Bronner, 181, 281.

Bagarsky, 173, 222.

Gantoni, 82.

Carlisle, 36.

Carrier, 82.

Caspari, 296, 299.

Castner, 39.

Centnerszwer, 142.

Chilesotti, 266.

Claosias, 48, 49, 91, 166.

Coehn, 169, 291, 298, 299, 306, 814.

Cohen, 226, 271.

Coolidge, 132.

Czapski, 173.

Daniell, 46.
Danneel, 38, 93, 206.
Dannenberg, 291, 298.
Davy, 38, 39, 40, 123.
Des Condres, 180, 19L
Dolezalek, 322.
Drechsel, 316.
Dofay, 31.

Elbs, 821, 824, 895.
Ermann, 37, 164, 168.
Eoler, 135, 160.

Fanjung, 136.
Faraday, 42, 43, 44.
Fansti, 81.

Forster, 279, 301, 818»
Franklin, 31.
Frazer, 66.
Frannberger, 247.
Fredenhagen, 254, 263.
Freadenberg, 310.
Fritsch, 164.

Galyani, 32, 33.
Qay-Lussac, 62.
Oibbs, 51, 166.
Oilbert, 31.
Glaser, F., 82, 277.
Olaser, L., 294, 301, 306.
Gockel, 173.
Goodwin, 93, 204, 212.
Gordon, 201.
Graetz, 153.
Grafenberg, 307, 325.
Grotthns, 45, 47, 49.
Gnbkin, 317.

Haagn, 104.

Haber, 186, 206, 282, 283, 294, 299, 807, 814,

315.
Haskell, 93.
Heil, 230.
Heilbron, 81.
Heim, 321.
Heimrod, 43.
Helmholtz, 26, 61, 168, 166, 224, 234, 239,

240,242.
H^ronlt, 21.
Herschkowitz, 186.
Heydweiller, 129.
Hisinger, 40.

Hittorf, 47, 49, 63, 71,76, 76, 79 80, 91, 278.
Hofer, 307.

HoflF, yan't, 52, 66, 95, 96, 226, 269.
Holbom, 83.
Hollemann, 140.
Hopfner, 313.
Hulett, 163.

838

884

AUTHOR INDEX

Ihle, 279.
IngliB, a07.
iMDburg, 276.

J&ger, 162, 168.
JahD, 83, 173, 2tf.
JoDet, 76, 131.
Jast, 106, 276.

Kahlenbeig, 142, 2ia

KaDoIt, 79.

Kettenbeil, 62.

Kiliaoi, 310.

KItipfel, S17.

Knupffer, 200.

Kohlrauach, 47, 49, 76, 68, 86, 69, 92, 93,

99, 119, 128, 129, 130, 131, 140, 146, 103,

210.
Konig, 240.
Konigsberger, 292.
Rruger, 178, 242.
KOster. 140.

Labendzlnskl, 247, 2B0.

Lash Miller, 276.

Le Blanc, 40, 82, 83, 180, 194, 987, 276, 2n,

286, 287, 289, 291, 293, 809, 816, 822.
Lehmann, O., 24.
Leyl, 277.
Lewis, 247, 272.
Liebenow, 324.
Llppmann, 234.
Lobry de Bniyn, 79.
Lodge, 122, 128.
Loeb, A., 316.
Loeb, M., 78.
LoreDZ, 81, 164, 816.
Lnckow, 276.
Lather, 181, 246, 247, 266, 267, 878, 378,

280, 307, 309, 819.

Maitland, 266.

Masson, 122.

Merriam, 297.

Meyer, 186.

Moest, 307.

Morgan, 79.

Morse, 06.

Moser, 201.

Miiller, E., 280, 301, 811.

Miiller, W., 277, 292.

Muthmann, 247.

Naamann, 316.

Nernst, 73, 76, 78, 104, 146, 146, 147, 154,

166, 173, 176, 181, 200, 204, 209, 218, 219,

221, 226, 228, 289, 241, 248, 281, 297, 306,

318.
Neumann, 249.
Nicholson, 36.
Noyes, A. A., 76, 78, 88, 94» U4, 126, 182,

139, 261.

Oberbeck, 202.

Ogg, 186.

Ohm, 8, 166.

Osaka, 299.

Ostwald, 47, 64, 89, 94, 96, 99, 101,

106, 114, 126, 176, 166, 206^ ,^12, 280,

261.

Palaz, 146.
Palmaer, 241.
Pa8chen,230.
Peters, 264.
Pfeffer, 64.
Pigaet, 301.
Planck, 66, 124.
Poincar^, 163.

Quincke, 167.

Ramsay, R. B., 19S.
Ramsay, W., 146.
Raoalt, 66.
Beinden, 186.
Reoss, 107.
Richards, 48.
Riesenfeld, 76.
Bitter, 34.
Rizon, 324.
Rose, 140.

Rothmund, 238, 27&
Ross, 283, 316.

Sack, 299.

Saekur, 277.

Sammet, 246, 247, 286, 9178.

Schaam, 264.

Schick, 316.

Schiller, 180.

Schilow, 278.

Scudder, 107.

Seebeck, 228.

Shields, 148.

Shukoff , 267.

Simon, 38.

Smale, 294.

Smith, 114.

SoUer, 280.

Specketer, 311.

Spencer, 2S6,

Steele, 122, 128.

Stefan, 281.

Steiner, 82.

Storbeck, 128.

Streintx, 321, 322.

Tafel, 280, 800, 801, 81A.
Thales, 31.
Thatcher, 266.
Thomson, 146, 166b
Tower, 83.

AUTHOR INDEX

886

yo6g8y279.

Volta, 83, 31, 36, 36, 49, 00, 221, 231.

Walden, 76, 142, 143, 147, 151,
Walker, 79, 116.
Warburg, 24, 104, 234.
Wegscheider, 116, lift
Weigert, 309.
West, 13L

Whetham, 122, 128.
Whitney, 123, 281.
Wiedemann, 157.
Wilke, 31.
Wilgmore, 243, 247.
WohlwiU, 311.
Wnlf,297.

Zedner,825.

SUBJECT INDEX

Aocnmulaton, 321.

Aoids, bases, «nd salts, abnomuJltj of, 87.

Activltj ooefflcient, 58.

Additiye properties, 90.

Addittrity of electrical oondactanoa, 89.

Affinity constant, definition, 9fi.

Affinity constant, relation to chemical
constitation, 116.

Affinity of adds and bases, 96.

Alternating cnnent, electrolysis by means
of, 316.

Ampere, definition, 8.

Amphoteric electrolytes, 79.

Analysis by means of condoetanoe meas-
urements, 136.

Application of migration Telocity to oom-
meicial processes, 81.

Ayogadro's principle, generalized, 82.

Basicity law (k,^ — k,^, 126.

Bell process for the mannfactnre of cans-
tic soda, 82.

Cadminm, or Weston, standard cell, 163.

Capacity, electrical, 24.

Catalytic inflnence on the electromotlYe
force, 278.

Cell constant, 103.

Chemical analysis by electrical conduct-
ance, 136.

Chemical and electrical energy, relation,
49, 166.

Chemical cells, 231.

Chemical compounds as electrodes, 188.

Chemical constitution, relation to disso-
ciation constants. 111, 116.

Chemical equilibrium and electromotiye
force, 267.

Chromic acid, regeneration by electrolysis,
83.

Clark standard cell, 163.

Clausius theory of electrolysis, 47.

Colloidal metal-solutions, preparation, 24.

Colloidal suspensions, 186.

Compensation method of determining
electromotiye force, 161.

Concentration cells, 184.

Concentration double-cells, 211.

Concepts of electrical science, 1.

Conductance, at high temperatures, 133.
Conductance, calculation from mi^atloa

Telocity, 91.
Conductance, determination, 98. ^
Conductance of electrolytes, 85.
Conductance of solid and fused salts, 188.
Conductance of water, 128.
Conductance, specific and equiTalent, 86.
Conductance, table, 88.
Conductance, technical importance, 186.
Conductors, first and second class, 38.
Constitution of ions, 45.
Corresponding, or isohydric, solutions,

136.
Coulomb, definition, 10.
Course of electro-chemical reactions, 281.
Current density, 168.
Current production, process of, 268L

Daniell cell, 60.

Decomposition of water, primary and
secondary, 288.

Decomposition point, 297.

Decomposition voltage and solubility, 318.

Decomposition voltages, importance, 30O.

Degree of dissociation, calculation, 88.

Depolarization, definition, 312.

Dielectric constant, definition and meas-
urement, 142.

Dielectric constant, relation to dissociat-
ing power, 147.

Displacement of equilibrium by temper-
ature changes, 132.

Dissociating power, or capacity, of liquids,
142.

Dissociation constant, calculation from
conductance values, 106.

Dissociation constant, definition, 97.

Dissociation constant, relation to chemi-
cal constitution. 111.

Dissociation heat, 134.

Dissociation of dibasic acids, first and
second hydrogen, 113.

Dissociation of water, 128.

Dissociation pressure or tension, 272.

Dissociation theory of Arrhenius, 82.

Distant-action, chemical, 261.

Double-natured elements, 284.

886

SUBJECT INDEX

837

Doable-nataied ions, 80.
Drop-electrode, 239.

Electric furnace, 18.

Electrical and chemical energy, relation,
166.

Electrical oondactanoe In chemical analy-
sis, 136.

Electrical condnctanoe of electrolytes, de-
termination, 98.

Electrical discharge, dark or silent, 23.

Electrical double-layer, applied to col-
loids, 242.

Electrical double-layer, applied to lipp-
mann electrometer, 235.

Electricity, material conception of, 00.

Electro-chemical change, Faraday's law,
42.

Electro-chemical constant, 43.

Electro-chemical nomenclature, 44.

Electro-chemical theory of Berzelius, 40.

Electro-chemical reaction, theory, 281.

Electrode potentials, importance, 267.

Electrolysis and polarization, 286.

Electrolysis, conceptions of, 44.

Electrolysis with an alternating current,
316.

Electrolysis without electrodes, 317.

Electrolytic dissociation, theory, 284.

Electrolytic frictional resistance, 123.

Electrolytic gas constant ( ^ ] , 182.

(1)

Electrolytic potentials (bp), 247.

Electrolytic preparations based on decom-
position voltages, 309.

Electrolytic separation based on decompo-
sition voltages, 309.

Electrolytic solution pressure, 176.

Electrolytic versiu gaseous dissociation,
69.

Electrometer, use of, as an indicator in
titration, 216.

Electrometric measurements, 28.

Electromotive force and chemical equi-
librium, 267.

Electromotive force at reversible elec-
trodes, calculation, 181.

Electromotive force, conception of, 7.

Electromotive force, determination, 161.

Electromotive series, law of, 34, 221, 230.

Electromotive valence, 266.

Electro-stenolysis, 169.

Elements, double-natured, 284.

Empirical rules relating to oonductance
of electrolytes, 126.

Endosmose, electrical, 167.

Energetics, first law, 166.

Energetics, second law, 166.

Energy forms, 1.
z

Energy transformations, galvanic, 269.
Equilibrium at an electrode, conditions,

261.
Equivalent conductance at 18°t, table, 88.
Equivalent conductance, definition, 86.

Farad, definition, 26.
Faraday's law, 42.
Ferri-ferro electrode, 263.
First law of enezgetics, 166.
Fused salts, conductance of, 163.

Gas constant, R, 67.

Gas electrodes, preparation of, 194.

Gaseous and electrolytic dissociation, dif-
ferences between, 69.

Gravity, influence on electromotive phe-
nomena, 193.

Grotthns theory of electrolysis, 44.

Heat of dissociation, 133.
Heat equivalent, electrical, 17.
Heat equivalent, mechanical, 17.
Helmholtz equation, application to OOB-

centration cells, 224.
Helmholtz heat effect, 249.
Helmholtz standard cell, 163.
Holding-power of ions, 292, 308.
Hydration of ions, determination, 78.
Hydrogen electrode, reversibility, 194. '
Hydrogen-oxygen cell, 288.
Hydrogen, spontaneous evolution, 263.

Indicator, electrometer in titration, 216.
Internal friction, relation to conductance,

161.
Ionization, according to the materialistio

theory of electricity, 60.
Ionization, regularity, 62.
Ions, absolute migration velocity, 119.
Ions, constitution, 76.
Ions, double-natured, 80.
Ions, hydration, 78.
Ions, relative migration velocity, 71.
Ions, velocity of formation, 276.
Irreversible and reversible cells, 104.
Isohydric solutions, 136.

Joule, definition, 2.
Joule's law, 18.

Kohlransch's law, 89, 91.
Kohlrausch method of determining eleo-
trical conductance, 98.

Law of Dilution, Ostwald's, 124.

Law of Faraday (electro-chemical

change), 42.
Law of Joule, 18.
Law of Kohlrausch, 91.

838

SUBJECT INDEX

Law of mass-action, 96.

Law of Ohm, 8.

Law of pressare-Tolume product (Boyle-
Hariotte), 63.

liquid cells, 217.

Luckow's process, preparation of chem-
ical compoauds, 27d.

Mass-action law, 95.
Mercury process, caustic soda, 82.
Metallic mixtures as electrodes, 186.
Migration of ions, 62.
Migration Telocity of ions, 71.
Migration velocity of ions, absolute, 119.
Migration Yelocity of ions, table, 121.
Mixed solutions, conductance, 136.
Mobility, or migration velocity, of ions, 71.
Molecular weight determination, electri-
cal method, 184.

Nitrogen, fixation from the atmosphere,

22.
Non-polarizable electrodes, 166.
Normal or standard cells, 163.

Ohm, definition, 8.

Ohm's law, 8.

Osmotic pressure, 62.

Ostwald's dilution law, limited applica-
tion, 124.

Over-voltage, 296.

Oxidation and reduction cells, 260.

Oxidation, electrolytic, 266.

Oxidizing agents, electromotive activity,
312.

Oxygen, spontaneous evolution, 263.

Passivity, 275.

Peltier heat effect, 249.

Physical constitution of metals, influence

on electrolytic phenomena, 193.
Polarizable electrodes, 165.
Polarization, measurement, 286.
Potential-difference, formation at the

electrode, 263.
Pressure, influence on conductance, 135.

Reactivity of electrolytes, 141.
Reducing agents, electromotive activity,

312.
Reduction and oxidation cells, 250.
Reduction, electrolytic, 255.
Relative migration velocity, 71.
Relative strengths of acids and bases, 95.
Residual current, 297.
Resistance, electrical, 7.
Resistance, electrolytic frictional, 123.
Reversible and irreversible cells, 164.

Second law of energetics, 166.

Siemens units, 85.

Single potential-differences, 234.

Solubility, calculation from electromotive
force, 206.

Solubility, determination by means of
electrical conductance, 140.

Solubilitv, relation to decomposition volt-
age, 318.

Solution pressure, electrolytic, 175.

Solutions of metals, behavior as elec-
trodes. 186.

Solvents other than water, electrical con-
ductance, 142.

Solvents other than water, electromotive
force, 249.

Specific conductance, or conductivity,
definition, 85.

Standard, or normal, cells, 163.

Strength of acids and bases, 96.

Storage cells or accumulators, 321.

Superposition principle of Nemst, 220.

Supersaturated solutions, conductance
of, 129.

Surface tension of mercury, relation to
polarization, 234.

Suspended particles, migration of, 157.

Temperature changes, effect on electrical
conductance, 130.

Thermo-electric cells, 228.

Transference numbers, definition, 70.

Transference numbers, determination, 72.

Transference numbers, table, 84.

Transference phenomena, technical im-
portance, 81.

Transformation of an alternating into a
direct current, 155.

Transformation pressure, 251.

Transition points, determination by
means of E. M. F. measurements, 271.

Unipolar conduction, 154.

Valence, electromotive, 256.

Velocity of ionization, 275.

Velocity of migration, individual ions,

116.
Volt, definition, 7.
Voltaic pile, 33.

Water, electrical conductance and degree
of dissociation, 128.

Water, primary and secondary decom-
position, 302, 308.

Watt, definition, 1&

Weston, or cadmium, standard cell, 163.

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