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ELECTROLYTIC DISSOCIATION

THE THEORY

ELECTROLYTIC DISSOCIATION

AND

SOME OF ITS APPLICATIONS

HARRY C. 20NES

PROFESSOR OF PHYSICAL CHEMISTRY IN THE
JOHNS HOPKINS UNIVERSITY

THIRD EDITION

THE MACMILLAN COMPANY

LONDON : MACMILLAN & CO., Ltd.

1906

COPYRitiHT, xgooy
By the MACMILLAN COMPANY.

Set up and electrotypcd. Published January, X900. Reprinted
June, Z904 ; November, 1906.

Nottnooti 9n00

J. S. Cashing & Co. — Berwick & Smith Ck).

Norwood, Ma«8., U.S.A.

PREFACE TO THE THIRD EDITION

At the time when this book first appeared in 1900, the
Theory of Electrolytic Dissociation was recognized by
physical chemists to be a well-established and fundamental
generalization. They regarded it not only as one of the
three or four generalizations upon which the new physical
chemistry rests, but as being of scarcely less importance
for the whole subject of general inorganic chemistry.

At that time the wide-reaching significance of this
theory for general chemistry was not fully appreciated
by those who have to teach this subject.

In the last few years a marked change has come about.
The Theory of Electrolytic Dissociation has found its way
not only into the teaching of advanced inorganic chemis-
try, but is now introduced by the progressive teachers into
their elementary courses. This change has been brought
about largely by the recognition of the fact that this
generalization correlates great masses of facts which hith-
erto have been regarded as more or less disconnected, and
thus an important step is taken towards placing chemistry
on the basis of an exact science.

The recognition of the fact that it is the charged parts
or ions, and not the uncharged atoms or molecules that
are the chemically active agents, has changed, funda-
mentally, the teaching and study of general chemistry.

The next few years will probably see a still more general
adoption of the newer conceptions.

283327

PREFACE TO SECOND EDITION

When this little volume was first written, the Theory
of Electrolytic Dissociation was well established, but was
much less known than at present. During the past few
years it has become the household word of practically
every scientific chemist, and is now recogjnized to be
indispensable to the development of chemical science.
Indeed, it has become of such fundamental importance
that it is now introduced into the very early stages of
the teaching of chemistry, and the chemistry of atoms
and molecules is rapidly giving place to the chemistry
of ions.

The Theory of Electrolytic Dissociation has thus ac-
quired a new interest, and will doubtless ingraft itself
more and more deeply into general chemistry.

A number of minor changes have been made, but the
plan of the second edition of this book is essentially the
same as the first; the reception with which the work
has met having led to the conviction that serious changes
might injure rather than improve the work.

H. C. J.

PREFACE

During the last few years the writer has been frequently
asked, directly and by letter : Where can an account of the
newer developments in physical chemistry be obtained?
Where can we learn something about the relation between
osmotic pressure and gas pressure, and about the origin
and significance of the theory of electrolytic dissociation ?
The most satisfactory reply which could be made was,
read certain original papers. But these were not always
accessible, and, in some cases, not quite adapted to the
state of development of the reader. While it is true that
certain chapters in some of the text-books on physical
chemistry are helpful in the direction indicated, yet no
one of them seemed to meet entirely the demands of a
large number of students.

This little volume has been written with the hope of
supplying students of chemistry, physics, and physical
chemistry with at least a part of the information which
they desire. It aims to give an account of the origin and
significance of these newer developments. A student
who has a fair knowledge of the origin of the theory of
electrolytic dissociation, of the evidence upon which it
rests, and of its applications, has already acquired an ele-
mentary conception of many of the fundamental principles
which underlie modem physical chemistry.

In order that the relation between the newer and the
older physical chemistry may be the better understood, a

vi PREFACE

chapter is devoted to the latter. A few typical pieces
of work in the earlier period are considered very briefly,
and some of the conclusions reached are pointed out. It
is hoped, in this way, to show clearly the nature of the
problems solved, the methods employed, and some of the
results obtained.

The origin and development of the theory are then taken
up. This is followed by an examination of some of the
more important lines of evidence bearing upon the theory ;
and, finally, some applications of the theory in chemistry,
physics, and biology are considered.

The attempt is made to answer, in part, the questions :
What was physical chemistry before the theory of electro-
lytic dissociation. arose ? How did the theory arise ? Is it
true } What is its scientific use ?

It is believed that a closer acquaintance with the facts
will but serve to increase the interest in physical chemistry,
which is already manifesting itself in so many directions.

I wish to express my indebtedness to my friend Dr. S.
H. King, for valuable assistance in reading the proof of
this volume.

HARRY C. JONES.

Johns Hopkins University,
October, 1899.

CONTENTS

CHAPTER I
THE EARLIER PHYSICAL CHEMISTRY

PACK

Relations between Properties and Composition, and

Properties and Constitution i

Introduction i

The Boiling-Points of Liquids 4

Specific Heat of Liquids 8

Atomic and Molecular Volumes 11

Viscosity 14

Refraction of Light 16

Rotation of the Plane of Polarization 21

Magnetic Rotation of the Plane of Polarization ... 27

Conclusion from the Preceding Work 29

The Study of Solutions 30

Other Lines of Work 31

The Development of Thermochemistry .... 32

Work of Hess 32

Favre and Silbermann 33

Work of Berthelot 34

Work of Julius Thomsen 35

Thermochemical Results 36

The Development of Electrochemistry . . . .39
Davy's Electrochemical Theory . . . '. . .40

Berzelius's Electrochemical Theory 40

Faraday's Law 44

Electrolysis 45

Theories of Electrolysis 46

Clausius's Theory of Electrolysis 48

• •

Vll

• ••

viii CONTENTS

PAGE

Williamson's Theory of Electrolysis 50

Hittorf 's Work on the Migration Velocity of Ions . . 52

Kohlrausch's Work on the Conductivity of Solutions . . 52

The Development of Chemical Dynamics and Chemical

Statics 53

Wilhelmy's Discovery of the Law of Reaction Velocity . 56

Work of Berthelot and P^an de St. Gilles .... 58

Guldberg and Waage's Law of Mass Action ... 60

The Application of Thermodynamics to Chemical Processes 64

Methods of Measuring Affinity 67

Conclusions from the Earlier Physical Chemical Work . . 68

CHAPTER II

THE ORIGIN OF THE THEORY OF ELECTROLYTIC

DISSOCIATION

Pfeffer's Osmotic Investigations . . . . . 71

Introduction 71

PfefFers Method of Measuring Osmotic Pressure ... 72

Some of Pfeffer's Results 75

Relations between Osmotic Pressure and Gas Pressure

DISCOVERED BY VAN'T HOFF 76

Historical 76

Boyle's Law for Dilute Solutions 82

Gay Lussac's Law for Dilute Solutions 84

Experimental Evidence in Favor of both the Laws of Boyle

and Gay Lussac for Solutions 85

Avogadro's Law for Dilute Solutions 87

General Expression of the Laws of Boyle, Gay Lussac, and

Avogadro for Solutions and Gases 89

Exceptions to the General Applicability of the Gas Laws to

Osmotic Pressure 91

On the Dissociation of Substances Dissolved in Water.

By Syante Arrhenius 93

Summary loi

CONTENTS IX

CHAPTER III

EVIDENCE BEARING UPON THE THEORY OF ELEC-
TROLYTIC DISSOCIATION

PAGB

The Physical Properties of Completely Dissociated

Solutions should be Additive 104

Specific Gravity of Salt Solutions 105

Change of Volume in Neutralization 107

Specific Refractive Power of Salt Solutions . . . .108

Rotatory Power of Salt Solutions no

The Color of Salt Solutions no

A Demonstration of the Dissociating Action of Water . -113
Conductivity is Additive. The Law of Kohlrausch . .116

Properties of Completely Dissociated and of Undisso-

ciated Mixtures

Mixtures of Two Completely Dissociated Compounds .
Mixtures of Two Completely Undissociated Compounds

Heat of Neutralization in Dilute Solutions .

Strong Acids and Bases

Weak Acids and Strong Base

Hess's Law of the Thermoneutrality of Salt Solutions .

117
117
118

119
121
121
122

Osmotic Pressure — Lowering of Freezing-point — Rise

IN Boiling-point — Conductivity . . . .123

Relation between Osmotic Pressure and Lowering of Freezing-
point 126

Relation between Osmotic Pressure and Lowering of Vapor-
tension. Rise in Boiling-point 127

Relation between Osmotic Pressure and Conductivity . .128

Relation between Lowering of Freezing-point and Rise in
Boiling-point 129

Relation between Lowering of Freezing-point and Conductivity 1 29

Connection between Osmotic Pressure and Lowering of Freez-
ing-point, established by Thermodynamics . . -131

Relation between Osmotic Pressure and Lowering of Vapor-
tension (Rise in Boiling-point). Theoretical Demon-
stration 134

X CONTENTS

PAGB

Experiment to show the Presence of Free Ions . .137
Illustration of a Solution charged Electrostatically . .138
Experiment of Ostwald and Nemst . . • . • 139

The Ostwald Dilution Law 142

Ostwald^s Deduction 143

Rudolphi^s Dilution Law 147

Effect of an Excess of One of the Products of Disso-
ciation 149

Further Relation between Dissociation by Heat and Electro-
lytic Dissociation . . 149

Determination of Electrolytic Dissociation by Change in
Solubility 151

Agreement between Dissociation determined by Conductivity,
Freezing-point Lowering, and Solubility . . . .152

The Relation between the Two Kinds of Dissociation an
Analogy 153

Dissociation and Chemical Activity 154

Conductivity and Reaction Velocity 155

Dissociation measured by Chemical Activity . . ' ^57

Chemical Reactions usually take Place between Ions . .158
Dissociating Power of Different Solvents . . . •160

Effect of Water on Chemical Activity . . . .160

Action of Dry Chlorine on Metals 161

Comparative Inactivity of Dry Oxygen . . . .162

Dry Hydrochloric Acid does not decompose Carbonates . 163
Dry Acids exert no Action on Litmus and do not form Salts 165
Dry Hydrochloric Acid does not precipitate Silver Nitrate in

Ether or Benzene . 165

Comparative Inactivity of Dry Hydrogen Sulphide . .165
Other Reactions which do not take Place without Water . 168
Dry Hydrochloric Acid does not act on Dry Ammonia . .168
Dry Sulphuric Acid does not act on Dry Metallic Sodium . 169
Conclusion 170

CONTENTS xi

CHAPTER IV

SOME APPLICATIONS OF THE THEORY OF ELECTRO-
LYTIC DISSOCIATION

PAGB

Application of the Theory of Electrolytic Dissocia-
tion TO Chemical Problems 171

The Theory of Electrolytic Dissociation as applied to

Solutions 172

Osmotic Pressure 173

Diffusion 174

Lowering of Freezing-point . . . ' . . . .176
Lowering of Vapor-tension, Rise in Boiling-point . . .178
The Theory of Electrol3rtic Dissociation as applied to Electro-
chemistry 182

Electrolysis 183

Modes of Ion Formation 189

Velocity of Ions 191

Relative Velocity of Ions 192

Kohlrausch's Law of the Independent Migration Velocity of

Ions 197

The Absolute Velocity of Ions 198

The Conductivity of Solutions 201

Specific Conductivity 202

Method of Measuring the Conductivity of Solutions . . 203

Carrying out a Conductivity Measurement . . . . 206

Conductivity of Water 207

Calculation of Dissociation 209

The Conductivity of Solutions in the Different Solvents varies

very greatly , .211

Thomson's Theory 213

Conductivity at Elevated Temperatures . . . .215

Electromotive Force 216

Strength of Acids and Bases 216

Relations between Acidity and Composition and Constitution 219

Bases 223

Application of the Theory of Electrolytic Dissocia-
tion TO A Physical Problem 226

XU CONTENTS

PACE

The Seat of the Electromotive Force in Primary Cells 226

Calculation of Electromotive Force from Osmotic Pressure . 227

Electrolytic Solution-tension 231

Constancy of Solution-tension 236

Calculation of the Difference in Potential between Metal and

Solution 237

Types of Cells 238

Concentration Elements of the First Type . • . . 239

Concentration Elements of the Second Type . . . 243

Liquid Elements 247

Theory of the Liquid Element 247

Sources of Potential in a Concentration Element . . . 252

The Electromotive Force of the Daniell Element . . . 254

The Gas-battery 256

Chemical Action at a Distance 261

Experiment to demonstrate Chemical Action at a Distance . 262

Conclusion 267

Application of the Theory of Electrolytic Dissocia-
tion TO Biological Problems 268

Toxic Action and Electrolytic Dissociation .... 268

Toxic Action of the Phenols and their Dissociation . . 272

Dissociation and Disinfecting Action 273

Toxic Action of Substances on Certain Fungi . . . 275

Application of the Dissociation Theory to Animal Physiology 276

Physical Chemical Methods applied to Animal Physiology . 278
Application of Osmotic Pressure and Dissociation to the

Mechanics of Secretion 281

Conclusion 282

ELECTROLYTIC DISSOCIATION

CHAPTER I

THB EARLIER PHYSICAL CHEMISTRY

RELATIONS BETWEEN PROPERTIES AND COMPOSITION, AND

PROPERTIES AND CONSTITUTION

Introduction. — Such marked advances have been made
in physical chemistry during the last few years, that it
is sometimes thought that this is distinctively a new branch
of science. Indeed, the beginning of physical chemistry
is often regarded as contemporaneous with the origin of
the theory of electrolytic dissociation.

While it is true that the new physical chemistry, which
has revolutionized so many of our chemical conceptions,
has grown up around the theory of electrolytic dissocia-
tion, nevertheless, we must not forget that the newer is
built upon, and incorporates, the entire work of the cen-
tury. Indeed, the theory of electrolytic dissociation itself
had its beginning, as we shall see, about the middle of the
century.

What was termed physical chemistry, prior to 1885, was
largely a study of the physical properties of chemical
substances, and work of this kind is in progress up to
the present. . At first, the physical properties of the ele-

B I

2 ELECTROLYTIC DISSOCIATION

ments, and of compounds, attracted attention, with the
result, that the laws of gases, liquids, and solids were dis-
covered. The earlier workers in this field, however, were
not content with a disjointed knowledge of the properties
of substances ; they began to look for, and discover, rela-
tions ; for the highest aim of scientific investigation is to
find out relations between apparently disconnected facts —
to discover generalizations. The first point which would
naturally be taken up was the relation between properties
and chemical composition. How would the introduction
of an oxygen or a chlorine atom into a compound affect
the physical properties of the compound ; or the intro-
duction of a CHg group into organic compounds alter
their properties.? The study of this relation was com-
paratively simple. It was only necessary to prepare
a compound, study its properties, then introduce an
oxygen or chlorine atom, or a CHj group, and study the
properties of the new compound formed. By applying
this process to a large number of substances, relations
between composition and properties could be discovered,
and much valuable work was done along this line.

But it was well known that there are many chemical
compounds which have the same composition, but very
different physical properties. Isomeric substances in gen-
eral have different physical properties. Isomeric sub-
stances have the same kind of atoms in the molecule ; but
there is the possibility that the molecule of one isomeric
substance may be the simplest possible, and the molecule
of the other isomeric substance may be an aggregate of
the simplest molecules; and this might account for the
difference in properties of isomeric substances.

THE EARLIER PHYSICAL CHEMISTRY 3

There are also other substances, called metameric, which
have not only the same kind of atoms in the molecule, but
the same number of the same kind of atoms; and yet
have different physical properties.

The composition of the molecules in the two cases is
exactly the same, so that the difference in properties, in
such cases, cannot be attributed to a difference either in
the kind or number of atoms in the molecule. To what
then is the difference in properties in such cases to be
attributed? If it is due neither to the kind, nor to the
number of atoms in the molecule, it must be due to the
way in which the atoms are combined with one another in
the molecule. This brings us to the second problem
which was investigated by the earlier physical chemists,
the relation between properties and constitution.

In investigating this point, such questions arose as what
would be the effect on the physical properties, produced
by oxygen in the carbonyl condition (CO), with respect to.
oxygen in the hydroxyl condition (OH).? Or how would

carbon atoms combined as in ethylene Ml j differ in their
effect on the physical properties of the compound, from

carbon atoms combined as in ethane ( > )? By using

metameric compounds such questions could be, and in a
number of cases have been, answered.

Work of this earlier kind had to do with gases, liquids,
and solids, but we will confine ourselves to that which
has been done upon liquids; since relations have been
more fully developed here than for either gases or
solids.

4 ELECTROLYTIC DISSiOCIATION

•

The Boiling-points of Liquids. — A relation between the
boiling-points of liquids and their composition was first
pointed out by Kopp,^ in 1842. An elaborate investigation
on the boiling-points of a large number of organic com-
pounds was published in 1855,^ ^^^ result of which was to
show that his earlier generalization was, in the main, cor-
rect. The following are a few of the data obtained by
Kopp, and these will suffice to bring out the relation be-
tween composition and boiling-point discovered by him : —

SUBSTANCB BoiLING*POIMT

Methyl alcohol, CH4O 65°

78C

Ethyl alcohol, CjHcO , ^

>i8

Propyl alcohol, CsHgO 96°^^

Butyl alcohol, C4H10O 109°^

>3"

Amyl alcohol, C5H12O 132®^

Ethyl formate, CgHeO, S5\

Ethyl acetate, C4H80j 74*^

Ethyl propionate, QH10O2 96°'^^

22**

Formic acid, CHjOj 105

N12
Acetic acid, C2H4O2 iiy^

Propionic acid, C8H«02 ^4^\

>i4'

Butyric acid, C4H8O2 156**^

Valeric acid, C5H10O2 176°'^

20°

I Liebig's Ann., 41, 86, 169 (1842). ^ /did,, 96, i (1858).

THE EARLIER PHYSICAL CHEMISTRY 5

Take succeeding members of any of the above three
groups of compounds ; they differ in composition by one
carbon atom and two hydrogen atoms, — by the group CHj,
— and there is, in every case, an approximately constant dif-
ference between the boiling-points of succeeding members.
This relation between composition and boiling-point, Kopp
formulated from data obtained much earlier, as follows :
Equal differences in the chemical composition of organic
compounds correspond to equal differences in the boiling-
points.

It is obvious from the above data that this relation holds
only approximately.

If the above relation held rigidly, then isomeric sub-
.stances having the same composition must have the same
boiUng-point. The following data will serve, in part, to
show the validity of this conclusion : —

SuBSTiOfCB BOIUNG-POINT

f Methyl acetate 56**

t Ethyl formate 55°

{Methyl butyrate 95

Ethyl propionate 96

Methyl val(erate 115

Amyl formate 116

Ethyl butyrate 115

We might conclude from the above data, that isomeric
compounds have the same, or very nearly the same, boiling-
point. It should be observed, however, that the above
isomeric compounds have similar constitution. As soon as
isomeric compounds which have different constitution

6 ELECTROLYTIC DISSOCIATION

were compared, it was found that they have very different
boiling-points; which shows that boiling-point is con-
ditioned not simply by the number and kind of atoms
in the molecule, but also by the way in which these atoms
are combined with one another.

Subsequent work has shown that these relations,
pointed out by Kopp, are only rough approximations.
Dittmar^ has proved that metameric compounds, such as
methyl acetate and ethyl formate, do not have the same
boiling-point, and more accurate work on the boiling-
points of homologous series of compounds has shown that
the difference between the boiling-points of succeeding
members is not constant, but usually decreases as the com-
pounds become more complex. This is illustrated by the
following data,, taken from the work of Schorlemmer :'— -

SUBSTANCB BOIUNG-POINT

C4H10

>"'

C,H„ 38

C.Hm 70°/

CtHm 99"/

I a?*'/

CgH„ las'

QHjCl ia.5

QH^l 46.4"'/

>3i-
C4H,a 77.6"/

CHuCl

Na8.
105.6°/

Liebig's Ann. Suppl., <t, 313 (1868). * Liebig's Ann., 161, 381.

THE EARLIER PHYSICAL CHEMISTRY

SUBSTANCB

BoiUMG-rOIMT

7i.o»/

100.4

\28.;
128.7^/

CjHjBr
C^HeBr

C5HuBr

Some interesting facts in connection with the relation be-
tween constitution and bo^ing-point have been discovered.
Take the benzene hydrocarbons, and compare those in
which one hydrogen has been replaced by a group, with
those having two hydrogen atoms replaced ; and these, in
turn, with those having three hydrogen atoms replaced.

Compounds with Onb

Hydkogbn Atom Rbplacbd

BOIUNG-POIMT

QH5CJH5

134'

CeHjCsHy

15a*

C«HaC4H9

(172^ calculated)

C6H5C5H11

•

IPS'*

Compounds with Two
Hydkogbn Atoms Rbplacbd

BonJNG-ponrr

C.H,(CH,),

139-140^

/CH,

c,hZ
N:.H.

159-160®

/CH,

c,hZ
m:,h,

175-178®

QH4 (€2115)2

178-179®

Compounds with Thrbb
Hydrogbn Atoms Rbplacbd

BOIUNG-POINT

C,H,(CH,),

165-166®

/(CH,).
C.H/

183-184®

•^ ELECTROLYTIC DISSOCIATION

By comparing these three classes of substances, we see
that the second boils higher than the first, and the third
higher than the second. Between the first and second
there is almost a constant difference of about 6°, and
between the second and third the difference is just about
6°, and is nearly constant.

The study of a number of classes of primary and
secondary compounds has established the fact, that the
same difference in constitution produces approximately the
same difference in boiling-point.

Specific Heat of Liquids. — The specific heat of a liquid
is different at different temperatures. In determining
specific heats it is, therefore, necessary to choose some
temperature for making the measurements, in order that
the results may be comparable.

Reis ^ took the mean specific heats between 20° and the
boiling-points of the substances investigated. That speci-
fic heats may be comparable, it is necessary to refer them
to comparable quantities of substances. Mbleciilar quanti-
ties are taken, and the molecular heats are compared, to
bring out any relations which might exist. A few results
for homologous series of alcohols, acids, and hydrocarbons,
will serve to bring out any relation between composition
and this property.

SuBSTANCB Molecular Heat

Methyl alcohol, CH4O 2 1 .6

Ethyl alcohol, CaHeO 30 3^

^10.2
Propyl alcohol, CgHgO 40-5\

Butyl alcohol, C4H10O 50.9^

/9-6

Amyl alcohol, C5H12O 60.5^

1 Wied. Ann., 13, 44-,

THE EARLIER PHYSICAL CHEMISTRY

SUBSTANCB MOLBCULAE HbAT

Formic acid, CH2OS 24.2

77.4

Acetic acid, C2H4OS 31-6^

y>2 X 7.9

Butyric acid, C4H8OJ 47.4^

^8.6
Isovaleric acid, CsHioOj 56.0^^

>9.6
Caproic acid, CeHiaO^ 65 .6^^

Benzene, QHe 33.8

>8.o

.i.8r

Toluene, QHg

Ethyl benzene, CgHio ^ ^^^

)>8.

Mesitylene, CgHu 56.8^

48.8C

7.0
o

The difference between the molecular heats of any two
members of a series is nearly constant. This difference
corresponds to a difference in composition of CHj, in each
series of compounds ; yet its value varies somewhat from
one series to another.

The effect of constitution on molecular heat can be seen
from the following examples of isomeric substances : —

SUBSTANCK

Molecular Heat

Propyl aldehyde,

•

Acetone,

CgHeO
CsHeO

32.6
32.6

Butyric acid,
Isobutyric acid.

C4Hg02

CiHgO,

47.4
47.6

Allyl alcohol,
Propyl aldehyde,

CgH«0

38.1
32.6

Isomeric compounds, having similar constitution, have
very nearly the same molecular heats ; but if the constitu-

lO ELECTROLYTIC DISSOCIATION

tions are markedly different, as in the last example, then
the molecular heats differ widely from one another. This
conclusion has been, in the main, confirmed by the work
of de Heen.^

Schiff ^ found the further relation between specific heat
and composition ; that the specific heat is nearly the same
for large groups of closely related substances. If we
represent the specific heat at / degrees, by 5/, we have
the following results : —

Substance

SpBanc Hbat

Methyl benzoate

^/= 0.3630 -f 0.00075 ^

Ethyl benzoate

S/= 0.3740 + 0.00075 /

Propyl benzoate

S/= 0.3830 -f 0.00075 /

Benzene

S/= 0.3834 + 0.001043 '

Toluene

5/= 0.3834 + 0.001043 /

M'Xylene

S/= 0.3834 -f 0.001043 ^

/'-Xylene

Sf= 0.3834 -h 0.001043 /

Acetic acid

.S/= 0.444 +0.001418/

Propionic acid

5/= 0.444 +0.001418/

Butyric acid

•S'/= 0.444 +0.001418/

This relation can be generalized as follows : —

TAe specific heat of homologous compounds is represented
by the formula c =^ a '\- bt, in which b always has the same
value for the different members , and a often has the samcy
but sometimes slightly different values for the different
members.

Later work by Schiff ^ confirmed his earlier results.
Considerable work has been done on the specific heats

1 Essai de phys. comp., Brussels, 1883. < Liebig's Ann., 234, 30a

• Ztschr. phys. Chem., i, 376.

THE EARLIER PHYSICAL CHEMISTRY II

of aqueous solutions. That of Marignac^ is to be espe-
cially mentioned. He carried out an elaborate investiga-
tion of closely related compounds, as chlorides, bromides,
iodides, sulphates, nitrates, acetates, etc., with the object of
discovering any relations which might exist. The molec-
ular heats of solutions of a number of svibstances were
found to be the sum of two parts ; the one depending upon
the acid, the other upon the base — they belong to that
class of properties which are known as additive. But a
large number of substances did not show this regularity, so
that no comprehensive generalization was reached.

Atomic and Molecular Volumes. — Here, again, to find
relations we must use comparable quantities of substances,
and it is most convenient to use molecular quantities. If

g is the specific gravity, - is the specific volume. If m

is the molecular weight, — is the molecular volume, A

g
number of relations were pointed out by Kopp.*

For closely allied compounds, the same difference in
composition corresponds to the same difference in molec-
ular volume. This is seen from the following examples :—

SUBSTANCB

MOLBCULAR VOLUMB

CH4O

42.Iv

^20.1

62.2^

CjH^O

\20.I

775^

1 Ann. Chim. Phys. [5], 8, 41a • Liebig*s Ann., 41, 79 ; 96, 153, 303,

12 ELECTROLYTIC DISSOCIATION

SuBSTAKCB Molecular Volume

CHjOa 41.4.

C,HA 63.7/

N2I.7

C,HaO, 85.4/

CiHgO, 107.1/

The following generalization was also reached by Kopp :
When two atoms of hydrogen are replaced by one of
oxygen, the molecular volume is only slightly changed.
Thus : —

Substance Molecular Volume

Methyl alcohol, CH4O 42.1

Formic acid, CH2O2 41.4

Ethyl alcohol, C2H6O 62.2

Acetic acid, C2H4O2 63.7

The relation between molecular volume and constitution
was also worked out. A few results for isomeric sub-
stances will serve to bring out the conclusion reached.

Substance Molecular Volume

r Acetic acid, C2H4O 63.7

\ Methyl formate, C2H4O 63.4

{Methyl valerate, C6H12O2 149.2

Ethyl butyfate, C6Hi202 ^49*3

r Propionic acid, C3He02 85.4

I Ethyl formate, CsHeOa 85.3

Isomeric liquids have the same molecular volumes.
Kopp found, also, that the atomic volumes were not
constants, independent of. the nature of the atpms\with

THE EARLIER PHVSICAL CHEMISTRY 1 3

which any given atom is combined, but varied somewhat.
Thus, oxygen in hydroxyl has a different atomic volume
from oxygen in carbonyl. Similarly, carbon and nitrogen
in their different forms of combination have different
atomic volumes. Yet the molecular volumes are, in gen-
eral, approximately the sum of the atomic volumes.
The following atomic volumes, —

Atomic Volums

25-5

26.4

323

40.2

show the relation which was pointed out by Kopp, that
the atomic volumes of the elements are nearly multiples
of . a constant, the value of the constant lying between
5.1 and 5.9.

The more recent work of Thorpe^ has shown that
isomeric liquids, at their bbiliiig-points, do not always
have exactly the same molecular volume, though the dif-
ference is not great. While Schiff found that isomeric
liquids, in general, have somewhat different molecular vol-
umes, the differences corresponding to the law, that the
higher the boiling-point of the substance the higher its
molecular volume.

W. Losseri*^ concluded, from a number of pieces of
work carried out by his pupils, that we cannot say, in
general, that the molecular volume is additive — that
it is the sum of the atomic volumes of its constituents.
The molecular volume depends not simply on the kind of

1 Journ. Chem. Soc, 141, 327 (1880). 2 liebig's Ann., 254, 42, 1889.

14 ELECTROLYTIC DISSOCIATION

atoms in the molecule, but also on the way in which the
atoms are combined in the molecule.

It may, however, be stated, that while the molecular
volumes of liquids at the boiling-point, are not exactly the
sum of the constant atomic volumes, yet they are approxi-
mately so; and molecular volume is approximately an
additive property.

Viscosity. — Some interesting relations between the vis-
cosity of liquids, and their composition and constitution,
have been recently pointed out by Thorpe and Rodger,^ in
their elaborate investigation along this line. Although this
work has been done very recently, yet it is typical of the
earlier work, and, therefore, belongs in this place.

The viscosities were measured by the time required for
a liquid to flow through a capillary tube. To calculate
the viscosity coefficient, the formula of Slotte was used, —

V =

{i+bt)n

in which i; is the coefficient of viscosity, in dynes per
square centimetre, ^, by and n are constants, varying with
the nature of the liquid. To test the influence of com-
position and constitution on viscosity, this property of
some seventy liquids was determined in absolute measure,
at all temperatures from o^ to the boiling-points of the
liquids.

To compare viscosity coefficients, we must use compara-
ble temperatures, and we will use first the boiling-points
of the liquids. As we ascend a homologous series of com-

1 Thorpe and Rodger, Proceed. Royal Soc, 1894 ; Bakerian Lecture, Royal Soc.
Chem. News,<S9, 123. 135 ; Journ. Chem. Soc., 71, 360 ; Ztschr. phys. Chem., 14,361.

THE EARLIER PHYSICAL CHEMISTRY 1 5

pounds, the coefficient generally decreases ; in a few cases
it remains the same, and in one series increases. If we
compare corresponding compounds, we find that the one
with the highest molecular weight has the highest coeffi-
cient. The effect of increase in molecular weight, however,
may be more than counterbalanced by constitution. Iso-
compounds have, in general, a larger coefficient than
normal compounds. The degree of symmetry of the
molecule can have a marked influence on the size of the
coefficient.

The following relations between the molecular viscosi-
ties at the boiling-point, were established by Thorpe and
Rodger. An increment of CHg in compounds, with the
exception of the alcohols, dibromides, and lowest members
of the homologous series, corresponds to an increase in the
molecular viscosity. The compound having the highest
molecular weight, with the exception of the compounds
mentioned above, has the highest molecular viscosity.
The dififerences in the molecular viscosities, between
corresponding members of two correlated series, are
fairly constant.

An attempt was made to calculate the viscosity constants
of a number of atoms and groups, but since constitution
comes so largely into play, it is evident that these con-
stants are only approximations. Yet, the molecular vis-
cosity of forty-five liquids, calculated from these constants,
differs in few cases more than 5 per cent from those
found. There are, however, many exceptions to this rule.

The above relations were all obtained by comparing the
viscosities of liquids at their boiling-points. But another
method of comparison was also used.

1 6 ELECTROLYTIC DISSOCIATION

The general shape of the viscosity curves, toward the
boiling-point, was practically the same. If tangents are
drawn to the curves at points corresponding to the boiling-
points of liquids, the inclinations of the tangents to the
axis, i,e, the slopes of the curves, varied but little. Curves
for the alcohols, etc., were an exception.

The temperatures of equal slope of curves were then
taken for comparison. At this point, the effect of tem-
perature would be the same for different substances.

It was found that at the temperature of equal slope,
there were more definite relations between the viscosity
coefficients and the chemical nature of the compounds. At
this temperature a CHg group exerts a positive influence
on the coefficient, which decreases as the series ascends.
Exceptions are the alcohols, acids, and dichlorides. Of
corresponding compounds, that with the highest molecular
weight has the highest coefficient. Iso-compounds invari-
ably have a larger coefficient than normal compounds;
while for other isomeric substances a branching of the
atomic chain has an influence on the magnitude of the
coefficient.

The molecular viscosity at constant slope can be calcu-
lated from the fundamental constants for the constituents,
but here, again, water and the alcohols are exceptions.

It is evident from the above, that the relations found,
thus far, between viscosity and composition and consti-
tution, are, at best, only approximately correct, and apply
only to a limited number of cases.

Refraction of Light. — A number of attempts have been
made to formulate a relation between the power of sub-
stances to refract light and their densities. Of these, that

THE EARLIER PHYSICAL CHEMISTRY \*J

proposed by Dale and Gladstone^ is probably the most
general. If we represent the index of refraction by «,
and the density by d^

— - — = constant.
d

They showed that this relation holds for a large number
of liquids, within very wide ranges of temperature.

Landolt ^ tested this relation very accurately, for a small
range of temperature, and found almost exactly a constant
for a number of substances. Others® have, however,
obtained results to which the above expression did not

accurately apply, the value — — - either increasing or de-

creasing with the temperature.

The formula of Dale and Gladstone is far more accurate

w — I
than the expression — - — , which was proposed earlier,

d
and it is preferable to that of Lorenz-Lorentz, * which

df?-\-2

Recently, Edwards^ has tested the formula —

n — I
nd '•

and has shown that it holds for a number of substances,
over a considerable range of temperature.

None of these expressions, however, are perfectly gen-
eral, and without the introduction of specific constants,
they do not show an exact relation between refractivity

1 Phil. Trans. (1858), 887. Ibid., 1863. « Ibid., 132, 202; 133, i.
* Pogg. Ann., 123, 595. * Wied. Ann., 11, 70 ; 9, 641.

5 Amer. Chem. Journ., 16, 625 ; 17, 473.
c

1 8 ELECTROLYTIC DISSOCIATION

and density. Indeed, it is not at all certain that such a
relation exists.

Relations between refractivity, and composition and con-
stitution, have, however, been worked out, and a few of
these will now be considered.

Dale and Gladstone ^ found that isomeres of similar con-
stitution have very nearly the same specific refractivity.
In homologous series this quantity increases regularly.
They drew the general conclusion, that " every liquid has a
specific refractivity, composed of the specific refractivities
of the elements in the compound, modified by the kind of
union."

Landolt^ compared the "refraction equivalents" of sub-
stances, calculating them from the formula —

d '

in which m is the molecular weight of the substance, and
the other symbols have the same significance as in the
Dale-Gladstone expression.

The relation between composition and refraction equiva-
lents was worked out, and it was found that equal differ-
ences in composition correspond to equal differences in
refraction equivalents.

Landolt showed, also, that the refraction equivalent of a
compound is approximately the sum of the refraction
equivalents of its parts.

He investigated, further, the relation between constitu-
tion and refraction equivalents, by studying metameric
substances. A few results are given : —

i Phil. Trans., 1863. 2 Pogg. Ann., 117, 353 ; 122, 545; 123, 595.

THE EARLIER PHYSICAL CHEMISTRY 19

Substance

Refraction Equivaijint

Propionic acid,

CsHgOj

28.57

Methyl acetate,

QH.O,

29.36

Ethyl formate,

C8H6O2

29.18

Valeric acid,

C5H10O2

44.05

Methyl butyrate.

C5H10O2

43.97

Butyl alcohol.

C4H,oO

36.11

Ethyl ether.

C4H10O

36.26

Isomeric substances are thus seen to have the same
refraction equivalents.

J. W. Briihl has carried out elaborate investigations, since
the year 1880,^ on the refractive power of liquids. His
work, which has now extended over nearly twenty years,
has brought to light many interesting and important rela-
tions. He took up the effect of carbon, in its different
forms of combination, upon refractive power, and showed
that doubly united carbon exerted a different influence
from carbon united by single bonds. Each double union
in a gompound increases the refraction equivalent about
two units. He thus showed the influence of constitution
on refractivity. He also found that oxygen, in its different
forms of combination, had different effects on refractivity.

The question of the effect of symmetry on refractive
power has also been studied. Two isomeric compounds,
the one symmetrical, the other asymmetrical, have been
studied with the following results : —

Substance Rbpraction Equivalbnt

j Ethylene chloride 20.95

[ Ethylidene chloride 21.08

{Ethylene bromide 26.84

Ethylidene bromide 27.31

1 Liebig's Ann., 200, 139.

20 ELECTROLYTIC DISSOCIATION

The unsym metrical compound has a larger refraction
equivalent than the symmetrical.

The refraction values of a number of elements have
been worked out, and also the differences in the refraction
values of certain elements in different forms of combina-
tion. Refractivity, therefore, can be and has been used to
throw light on the question of constitution. Briihl has
applied the method of refractivity to the problem of the
constitution of benzene. How are the carbon atoms
united in benzene ? If by a single bond, they will have
a different refractive power than if they were doubly
united. From the power of benzene to refract, Briihl was
led to the conclusion that there are three single and three
double bonds in the molecule, which is expressed thus : —

This is the well-known benzene formula of Kekul6.

It should be stated, that it is not safe to place unlimited
confidence in a method like the above for determining the
constitution of chemical compounds. The same problem
has been attacked by Julius Thomsen, with very differ-
ent result, using a thermochemical method. Thomsen's
method is based upon the principle, that when a compound
is burned a different amount of heat is liberated if the
carbon atoms are united by single or double bonds, than
if they are united by triple bonds. He determined the
heat of combustion of benzene, and found that it cor-

THE EARLIER PHYSICAL CHEMISTRY

responds to nine single bonds between the carbon atoms,^
which would be expressed thus : —

+10

This is the well-known prism formula of benzene, sug-
gested and defended by Ladenburg. This apparent di-
gression is made, to show the caution which is necessary in
accepting conclusions based upon work such as that above
described.

Rotation of the Plane of Polarization. — When a beam of
polarized light is passed through certain liquids, the plane
of polarization is changed. Sometimes it is turned in the
one direction, sometimes in the other. This property is
not confined to liquids, but is possessed also by solids and
gases. Substances which have this property are said to
be optically active. According as the substance rotates
the plane of polarization in the one or in the other direc-
tion, it is termed dextro- or laevo-rotatory.

The direction and amount of rotation depend chiefly
upon the nature of the substance. The rotation depends,
also, upon the thickness of the layer, the wave-length of
light, and the temperature. Comparable results can,
therefore, be obtained only by keeping all of the con-
ditions constant, and then studying the kind and amount
of rotation which different compounds produce.

1 Ber. d. chem. Gesell., 13, 1808.

22 ELECTROLYTIC DISSOCIATION

The specific rotatory power of a liquid has been defined
by Biot, as the rotation produced by a layer one decimetre
in length. But since different liquids have different den-
sities, this would contain different amounts of substance.
The specific rotatory power r is obtained by dividing the
angle a, through which a column of liquid of length /, and
density d^ rotates the plane of polarization, by Id,

^^ Id

In order to compare the rotatory power of liquids we must
deal with comparable quantities, and most conveniently
with molecular quantities. If m is the molecular weight
of the substance, this must be multiplied into the above
expression. The molecular rotatory power mr would
then be : —

fKOb

This unit is usually divided by one hundred.

Some exceedingly interesting relations between rotatory
power, and composition and constitution, have been worked
out. There is quite a large number of substances which
exist in different forms, one rotating the plane of polariza-
tion to the right, the other to the left. Pasteur^ pointed
this out in connection with the tartaric acids. There is
a dextro-rotatory tartaric acid, and a laevo-rotatory tartaric
acid, and inactive racemic acid. The latter is produced by
mixing solutions of the dextro- and laevo-varieties, and, on
the other hand, racemic acid can be separated into dextro-
and laevo-tartaric acids. This separation is accomplished

1 Ann. Chim. Phys., 28, 56 (1850).

THE EARLIER PHYSICAL CHEMISTRY 23

by preparing the sodium-ammonium salt of racemic acid,
and allowing it to crystallize. Salts of dextro- and laevo-
tartaric acids will separate, and can be distinguished by
the difference in crystal forms. Certain right-handed
hemihedral planes appear on the salt of the dextro-acid,
and left-handed planes on the salt of the laevo-acid. There
is also a fourth tartaric acid, which is inactive, but this
can be transformed into the other modifications.

There are several other examples known of a substance
existing in a dextro- and laevo-modification, and also in an
inactive form ; and by combining the active modifications,
the inactive is formed, and from the inactive form the
active may be obtained.

A direct study of the relation between optical activity,
and composition and constitution, will be considered more
in detail. We will deal with the compounds of carbon. It
was observed by the French chemist, Le Bel,^ and a little
later by van't Hoff,^ that every carbon compound which
is optically active can be represented as containing a car-
bon atom in combination with four different atoms or
groups. Take the simplest case, that of lactic acid. We

have : —

CH,

I
H— C— COOH

Le Bel ascribed optical activity to the asymmetrical nature
of such an arrangement, but van*t Hoff went much far-

1 Bull. Soc. Chim. [2], 22, 337 (1874).
a Ibid,, 33, 295 (1875).

24 ELECTROLYTIC DISSOCIATION

ther, and tried to show how the atoms are actually ar«
ranged in space. He represented the central carbon atom
of the system, as placed at the centre of a regular tetrahe-
dron, with its four bonds acting in the directions of the
solid angles. At those angles are placed the four atoms,
or groups, in combination with the central carbon atom.
If these atoms, or groups, are the same, we would have a
perfectly symmetrical arrangement, and every atom would
bear the same relation to the molecule as every other
atom. Take the case of marsh gas, the four hydrogen
atoms should each bear the same relation to the molecule,
and such has been shown to be the case by the elaborate
work of Henry. If either two of the atoms, or groups, at
the corners of the tetrahedron are the same, then it is im-
possible to so arrange them that two tetrahedra, contain-
ing the same four groups at the comers, could not be
completely superimposed. But if all four atoms, or groups,
are different, then two tetrahedra containing these at the
comers can never be superimposed, but bear the relation
to one another of an object and its image in a mirror.

If this asymmetrical arrangement is the cause of optical
activity, then only those carbon compounds could be opti-
cally active which have four different atoms, or groups,
combined with the central carbon atom. Of all the cases
of optical activity known among carbon compounds, there
is only one possible exception. Baeyer ^ has described a
dipentene, which he thinks does not contain an asymmetric
carbon atom, and which is, however, optically active. But
this cannot be cited as a positive exception, since the con-
stitution of this substance is not definitely established.

1 Ber. d. chem. Gesell., 27, 454.

THE EARLIER PHYSICAL CHEMISTRY 2$

Another consequence of the van't Hoff theory is, that
whenever a dextro-rotatory substance appears, a laevo
must also be formed, and such is the fact Of the large
number of cases known, there is no exception to this
rule.

If optical activity is due to the presence of an asymmet-
ric carbon atom, then, whenever we have such a carbon
atom present, we ought to have optical activity. There
are, however, many compounds known, which contain an
asymmetric carbon atom, yet do not show optical activity.
This is explained by assuming that there are present an
equal number of dextro- and laevo-molecules, and optical
inactivity is the result. Similarly, if there are two asym-
metric carbon atoms in the same molecule, these may
exactly neutralize each other's influence on polarized light,
as in the case of the fourth variety of tartaric acid.

It is difficult to overestimate the importance of these
suggestions by Le Bel and van't Hoff. They underlie
all that has been done along the line of stereochemistry,
and this is certainly one of the most important advances
which has been made in organic chemistry in the last
quarter of a century.

This suggestion of the tetrahedron as the spatial ar-
rangement in carbon compounds has been developed much
farther by Wislicenus ^ than was done by van't Hoff. The
former has shown how this arrangement is capable of
accounting satisfactorily for the transformations of maletc
and fumaric acids; of the malic acids; and, what is even
more interesting, it furnishes a beautiful explanation of

^ Monograph, Ueber die r^umliche Anordnung der Atome in organischen
Molekiilen, Leipzig.

26 ELECTROLYTIC DISSOCIATION

the optical behavior of the four tartaric acids; facts
which hitherto had been empirically established, but whose
significance was entirely unknown. While space will not
permit us to enter into a discussion of this monograph by
Wislicenus, yet we should again call attention to its unus-
ual interest and importance for all who are interested in
the philosophy of organic chemistry.

The suggestion by van*t Hoff to account for optical
activity 'has been further extended by Guye.^ If optical
activity is due to the groups being different at the four
corners of the tetrahedron, — to an asymmetrical arrange-
ment, — then by changing the degree of asymmetry, the
degree of optical activity ought also to be changed. If we
have a carbon atom surrounded by four different atoms or
groups, the centre of gravity of the system will lie off of
the planes of symmetry. If now we replace one of the
atoms or groups by one having a greater weight, the centre
of gravity of the system will be moved toward the heavier
substituent. By changing the masses of the atoms or
groups, the centre of gravity of the system can be changed,
first in one and then in another direction.

Guye has shown, in a large number of cases, that as the
centre of gravity of the system is changed, by intro-
ducing lighter or heavier groups, the optical activity of
the substance changes, and in the way that would be ex-
pected. As the asymmetry was increased, optical activity
in general increased.

By introducing groups of the weights desired, the centre
of gravity could often be changed from one side of the
molecule to the other, and in a number of such cases the

1 Compt. rend., no, 714.

THE EARLIER PHYSICAL CHEMISTRY 27

nature of the rotation was changed — a dextro-rotatory
substance becoming laevo-rotatory, and the reverse.

There are some cases known which cannot be entirely
reconciled with the views of Guye. Work of this kind
is undoubtedly of the very highest importance, since it
throws light on the inner arrangement of the atoms and
groups in the molecule.

Another outcome of the stereochemical conception of
van*t Hoff, with respect to carbon, is the recent work
which has been done on the stereochemistry of nitrogen.
Hantzsch and Werner ^ have shown, that if we represent
the nitrogen atom as being placed at one of the angles of
a tetrahedron, we can explain the differences in constitu-
tion which undoubtedly exist between many of the isomeric
substances containing nitrogen ; differences for which it is
impossible to account, in many cases, by the ordinary
methods of representing constitution, which do not take
into account spatial relations.

Although the work of Wislicenus, Guye, and Hantzsch
and Werner was done in the last few years, yet it is the
direct outcome of the suggestion made by van't Hoff in
187s, which is more than ten years before the newer de-
velopments in physical chemistry began. It, therefore,
seems not to be entirely out of place to refer to this recent
work under the head of the earlier physical chemistry, of
which it is the direct consequence.

Magnetic Rotation of the Plane of Polarization. — It was
discovered by Faraday ,2 that substances in general have
the power to rotate the plane of polarization of light, when
placed in a suitable position in a magnetic field. An electro-

1 Ber. d. chem. Gesell., 33. 11, 1243. 3764, 3769. ^ Pogg. Ann., 68, X05.

28 ELECTROLYTIC DISSOCIATION

magnetic field is the most convenient, the current flowing
in a plane at right angles to the direction in which the ray
of light moves. The amount of rotation depends on the
strength of the magnetic field, length of layer of substance,
the temperature, and the nature of the substance. To dis-
cover any relations between magnetic rotation and compo-
sition, every one of the above conditions must be kept
constant, from one substance to another.

The work of BecquereP brought out some relations,

such as that the rotatory power of the alcohols increased
with increase in molecular weight; but by far the most
elaborate investigation of this phenomenon we owe to
W. H. Perkin.^ He chose as his unit the molecular rota-
tion of water, and compared other substances with it. A
few examples are given : —

SuBSTAKCB Molecular Rotation

Methyl alcohol, CH4O . i.64<

.040.
r.ySo^

Ethyl alcohol, CjHeO -w--v

\).988

Propyl alcohol, CsHgO 3.768'^

Formic acid, HaCOj i«6i7s

yo.908
Acetic acid, C2H4O2 ^'5^S\

y>o-937
Propionic acid, CsHeOa 3*462^

^i.oio
Butyric acid, C4H8O2 447^'^

These results, taken from a large number, show, for a
homologous series, a constant difference in the magnetic

^ Ann. Chim. Phys. [4], 22, 5. 2 joum. prakt Chem. [2], 31, 481 ; 33, 523.

THE EARLIER PHYSICAL CHEMISTRY 29

rotation produced by the constant difference in composi-
tion of CHg. The effect of constitution on magnetic rota-
tion can be seen by comparing isomeric compounds.

SUBSTANCB MaGNBTIC ROTATION

r Propyl alcohol, CaHgO 3.768

I Isopropyl alcohol, CsHgO 4.019

J Ethylene chloride, C2H4C12 5485

[EthyUdene chloride, C2H4Cla 5»33S

These examples suffice to bring out the fact, that
isomeric substances have different magnetic rotation,
showing the effect of constitution on this property.

Perkin has continued his work on magnetic rotation up
to the present, and some of his more important com-
munications are referred to below.^

J. W. Rodger and W. Watson ^ have published an inves-
tigation on magnetic rotation, where a stronger magnetic
field was used, and, consequently, the amount of rotation to
be measured was greater. Their paper is devoted mainly
to a description of their apparatus, and contains too few
results to warrant any generalization. It is to be hoped
that this work will be continued, using the stronger mag-
netic field.

Conclusion from the Preceding Work. — On examining
the work thus far described, we are impressed by the large
number of relations which have been pointed out between
physical properties, and composition and constitution.
But we are also impressed by the fact that these relations

J Chem. News, 60, 253 ; 6a, 255 ; 64, 19 ; 65, 284 ; 66, 277 ; 67, 143 ; 68, 302 ; 69, 224 ;
71. 123; 73. 30I' Journ. Chem. Soc, 59, 981 ; 61, 287 ; 61, 800; 65, 815 ; 69, 1025.
Ztschr. phys. Chem.» az, 451 ; 21, 671. ^ Ztschr. phys. Chem., 19, 323.

30 ELECTROLYTIC DISSOCIATION

are only approximations; they are not sharply defined
and rigorous. A relation was often discovered, which, at
first, seemed to be fairly exact, but as the experimental
work became more refined, a larger number of exceptions
appeared. Thus, in many cases, what seemed to be a
quantitative relation was merely a qualitative one.

We feel, throughout this entire work, the purely empir-
ical nature of the generalizations reached, and that they
are very incomplete expressions of the truth. There is a
lack of any definite, mathematical conception, in terms of
which this earlier work can be interpreted.

The Study of Solutions. — The physical properties of
substances may be studied when they are isolated, or when
they are mixed with other substances. Under the latter
condition, one substance is said to be dissolved in the other,
and we have to do with solutions. A number of the prop-
erties of solutions were early investigated. Graham^
studied the phenomenon of diffusion, and Fick^ pointed
out that diffusion depends upon, and is proportional to, the
difference in concentration of the solutions. Blagden^
discovered, more than a hundred years ago, that the lower-
ing of the freezing-point of water by a dissolved substance
is proportional to the amount of substance present. The
same fact was rediscovered by Riidorff,* and, later, Coppet^
showed that the molecular lowering of the freezing-point,
produced by closely allied substances, is very nearly con-
stant.

Raoult ^ studied the freezing-point lowering of solutions

1 Liebig's Ann., 77, 56, 129 ; 80, 197. 8 phil. Trans., 78, 277.

2 Fogg. Ann., 94, 59. * Pogg. Ann., 114, 63 ; 116, 55 ; 145, 599.
6 Ann. Chim. Phys. [4], 23, 366 ; 25, 502; 26, 98.

6 Compt. rend.,$>4, 1517; 95, 188, 1030; Ann. Chim. Phys. [6J, 2, 66w

THE EARLIER PHYSICAL CHEMISTRY 31

in solvents other than water, and arrived at the generali-
zation, that a molecule of any substance, in one hundred
molecules of a solvent, lowers the freezing-point of the
solvent by a nearly constant amount These investigations
by Raoult on freezing-point lowering were very elaborate,
including a large number of solutions in acetic acid, formic
acid, benzene, nitrobenzene, ethylene bromide, etc.

The lowering of the vapor-pressure of a solvent by a
dissolved substance was early investigated. Wiillner^
pointed out that the lowering of the vapor-pressure of
water by dissolved substances is proportional to the
amount of substance, and Raoult ^ studied the influence of
temperature, concentration, and nature of dissolved sub-
stance, on the depression of the vapor-tension of the
solvent. Raoult ^ worked with a number of solvents, and
found that the depression of the vapor-tension produced
by one molecule of substance in one hundred molecules of
solvent was the same for different solvents. Raoult also
showed how the lowering of *the freezing-point of a solvent
by a dissolved substance, and also the lowering of its vapor-
tension, may be used to calculate the molecular weight of
the substance in solution.

Other Lines of Work. — The earlier physical chemists
were not all engaged with problems such as we have been
considering. They measured the heat liberated in chem-
ical reactions. They studied the behavior of substances
when submitted to the action of the electric current. The
velocity with which chemical reactions take place, and the
conditions of equilibrium, were investigated. And the dif-

1 Pogg. Ann., 103, 529 ; 105, 85 ; no, 564. 3 Compt rend., 103, 1125.

• Ibid., 104, 1430; Ann. Chizn. Phys. [6] , 15, 375 ; Ztschr. phys. Chem., 3, 353.

32 ELECTROLYl'IC DISSOCIATION

ferent powers of substances to react, as depending upon
their composition and constitution, were carefully deter-
mined.

This brief account of the nature and condition of phys-
ical chemistry, before the theory of electrolytic dissociation
arose, would be unsatisfactory, and, perhaps, misleading,
without some statement as to the development of thermo-
chemistry, electrochemistry, and chemical affinity. By
knowing the condition of the several branches of physical
chemistry, before the new conceptions arose, we can see
the more clearly what changes have been introduced,
what advances made by them.

THE DEVELOPMENT OF THERMOCHEMISTRY

The quantitative study of the amount of heat liberated
in chemical reactions was begun very early, and has been
continued from the time of Robert Boyle to the present.
The problem, in one form or another, has attracted the
attention of men like Davy, Lavoisier, and Laplace. In-
deed, the very important discovery was made by the last
two,^ that just as much heat is required to decompose a
compound into its constituents as was liberated when the
constituents united to form the compound. But the begin-
ning of modem thermochemistry dates from the time of
G. H. Hess.^

Work of Hess. — Hess discovered the principle which has
come to be known as the " Constancy of the sum of the
heats of reaction." If a chemical transformation takes
place in one stage, a certain amount of heat is liberated,
which we will call a. If the transformation takes place in

i CEuv. de Lav., II, 287. 2 Pogg. Ann., 50, 385 (1840).

THE EARLIER PHYSICAL CHEMISTRY 33

two stages, in which, respectively, h and c amounts of heat
are liberated, we always have, A + ^ = ^. This is perfectly
general, regardless of the number of stages involved in the
transformation. The discovery of this principle makes
it possible to study, thermochemically, a great number of
reactions which are comparatively complex taking place
in more than one stage.

In addition to this important discovery, Hess made
another of very wide significance. He observed that when
solutions of neutral salts are mixed, there is little or no
heat liberated or absorbed. He concluded, that the heat
consumed in decomposing the salts w^s exactly equal to
that liberated in the formation of the new salts with acid
and base interchanged, since it was known that under
the conditions that solutions of two salts are mixed, four
salts are always formed, provided all four are easily solu-
ble and no precipitate is produced. This has come to be
known as Hess's law of the thermoneutrality of salts.
The significance of this law was not understood until it
was fully explained by the theory of electrolytic disso-
ciation.

Favre and Silbermann. — We now come to the beautiful
thermochemical investigations of Favre and Silbermann.^
They greatly improved the apparatus and method used
in thermochemical measurements. The calorimeter which
they devised is the same in principle as every form used
since their time. They carried out elaborate thermo-
chemical investigations, which were undoubtedly the most
accurate up to their time.

Thermochemical investigations since the time of Favre

1 Ann. Chim. Phys. [3] , 34, 357 ; 36, i ; 37, 406.

34 ELECTROLYTIC DISSOCIATION

and Silbermann have centred around two men: Berthelot
in Paris, and Julius Thomsen in Copenhagen. Much
work has also been done by pupils of these men, either
working with them or independently.

Work of Berthelot. — Berthelot^ began his very elaborate
thermochemical investigations in 1865, and these have ex-
tended over a long period. The results of his work are
published in his well-known book, of two volumes, ** Essai
de Mecanique Chimique." The three principles which he
developed in his work are : —

First, the heat liberated in a chemical reaction depends
only on the condition of the system at the beginning and
at the end, and not at all on the intermediate stages.

Second, the heat evolved in a chemical process is a
measure of the corresponding chemical and physical work.

Third, every chemical reaction tends to form those sub-
stances which are formed with the greatest evolution of heat.

This last principle has come to be known as the law of
maximum work, but would better be known as the law of
maximum heat evolution.

The last of the three principles announced by Berthelot
has attracted by far the most attention. As an expression
of a perfectly general truth, it is, of course, not exact.
There are many exceptions known to it, and some of these
were recognized and pointed out by Berthelot himself.
And yet, notwithstanding the exceptions, if one will care-
fully read the "Essai de Mecanique Chimique," the im-
pression is almost sure to be left that here is, at least,
the kernel of a great truth, even if it is expressed in an
imperfect and not sufficiently comprehensive manner.

1 Ann. Chim. Phys. [4], 6, 290; 28, 94,

THE EARLIER PHYSICAL CHEMISTRY 35

Much of the criticism of this third principle, whether its
true discoverer be Berthelot^ or Julius Thomsen,^ is evi-
dently not entirely well founded, if all that Berthelot has
written concerning it is taken into account.

Work of Julius Thomsen. — The thermochemical work
of Julius Thomsen has been collected into four volumes,
and published under the title of " Thermochemische Un-
tersuchungen." This, taken as a whole, undoubtedly con-
tains the most elaborate and accurate thermochemical
measurements which have ever been made.

In order that a reaction may be studied thermochem-
ically, one condition is that it should proceed rapidly to
the end. Many reactions between organic compounds do
not fulfil this condition. Indeed, most organic reactions
are relatively slow. To study such reactions thermo-
chemically, some means must be devised which would
accelerate the velocity of the reaction. Berthelot^ im-
proved the form of apparatus which had already been
suggested for this purpose. A thick-walled, steel cylinder,
lined on the inside with platinum or enamel, is used for
accelerating the velocity of such reactions as organic com-
bustions. The substance to be burned is placed on a
suitable arrangement, and introduced into the "bomb."
This is then tightly closed, and filled with oxygen under
high pressure. The substance is ignited by an electric
current; the combustion proceeds very rapidly, and the
heat set free is measured in some convenient form of
calorimeter. The use of the Berthelot bomb has greatly
widened the field of thermochemical investigation.

1 Ann. Chim. Phys. [5], 4, 6 ; [4], 18, 103. ^ Ber. d. chem. Gesell., 6, 423.

8 Ann. Chim. Phys. [5], 23, 160.

36 ELECTROLYTIC DISSOCIATION

Some of the most accurate thermochemical measure-
ments, in which the bomb has been employed, have been
made by Stohmann,^ in Leipzig (who worked for a time
with Berthelot), and by his assistant, Langbein.

Thermochemical Results. — A few thermochemical re-
sults will suffice to bring out the kind of relations which
have been discovered by such work.

The heat evolved when acids and bases neutralize each
other has been carefully investigated. We will give a few
results for the strong acids and strong bases : —

NaOH + HNOs = 13680 cal.
NaOH + HClOs = 13760 cal.
NaOH -h HBrOg = 13780 cal.
NaOH-+- HIO3 =13810 cal.
NaOH + HCl =13700 cal.
NaOH + HBr =13700 cal.
NaOH + HI = 13700 cal.

In the above table the base is kept constant and the

acid changed ; yet the heat of neutralization of equivalent

quantities is nearly a constant. A few results will be cited

in which a given acid is neutralized with a number of

bases : —

KOH + HCl = 13700 cal.

^Ba (OH) 2 + HCl = 13900 cal.

i Sr (0H)2 -h HCl = 13800 cal.

^Ca (0H)2 H- HCl = 13900 cal.

Here, again, the heat of neutralization is nearly a con-
stant, and the same constant as in the preceding case. It
can, therefore, be stated, that the heat liberated, when-

1 Joum. prakt. Chem., 33, 241; 35,40; 39, 509; 40,341; 42, 367; 43, x; 44,
336; 45.332-

THE EARLIER PHYSICAL CHEMISTRY 37

ever a strong acid is neutralized by a strong base, is a con-
stant, within experimental error, independent of the nature
of the acid and of the base. If either the acid or base is
weak, a different heat of neutralization is found.

The meaning of these facts was entirely unknown at
the time of their discovery. Why should the heats of
neutralization of strong acids and strong bases be a con-
stant, and why should the heats of neutralization of weak
acids and bases be different.? These were questions
whose meaning was not even suspected before the theory
of electrolytic dissociation was proposed. These facts, as
we shall see, are not only explicable in terms of that
theory, but are a necessary consequence of i^ Indeed,
the constancy of the heat of neutralization of strong acids
and strong bases is a very good argument in favor of the
correctness of the new theory, and this argument is even
strengthened by the fact that weak acids and bases have
a different heat of neutralization.

Certain relations between the composition and constitu-
tion of organic compounds and their heats of combustion
have been worked out. Take the marsh-gas series of
hydrocarbons.

SuBSTAMCB Heat op Combustion

Methane, CH4 211 900 cal.v

\i 58500 cal.

Ethane, CjHd 370400 cal.^

^158800 cal.

Propane, CgHg 529200 cal.^

^158000 cal.

Butane, C4H10 687200 cal.^

^159900 cal.

Pentane, QHji 847100 cal.

38 ELECTROLYTIC DISSOCLVTION

A difference of CHj produces very nearly a constant
difference in the heats of combustion of these hydrocar-
bons. The constitution of these compounds seems to have
no effect.

The following results were obtained for the ethylene
hydrocarbons : —

SuBSTANCB Heat of Combustion

Ethylene, C2H4 333400 cal.v

^159300 cal.

Propylene, CsH^ 49 2 700 cal.^

^15790000!.

Isobutylene, C4H8 650600 cal.^

^157000 cal.

Amylene, C5H10 807600 cal.

A constant difference in the heats of combustion is
observed here, also, for the constant difference in compo-
sition of CHg; and this is the same difference as in the
case of saturated hydrocarbons. The heats of combustion
of the two series are not the same, because, in addition
to two hydrogen atoms more in one system than in the
other, we have doubly united carbon atoms. And when-
ever there is double or triple union between the carbon
atoms, the heat of combustion is affected by it.

The halogen substitution products of the marsh-gas
hydrocarbons show, also, constant differences in the heats
of formation: —

Dip. Dip.

CHgCl 22000 cal. CHsBr 14200 cal. 7800 cal. CHsI 2800 cal. 19200 cal.

C2H5Q 29600 cal. QHsBr 21800 cal. 7800 cal. C2H6I 9900 cal. 19700 cal.
C3H7Q 36000 cal. CsHiBr 29100 cal. 6900 cal.

Relations appear for the alcohols which are similar
to those found for the hydrocarbons. The difference

THE EARLIER PHYSICAL CHEMISTRY 39

between the heats of combustion of members of a homolo-
gous series of alcohols is nearly constant, as the following
results will show : —

Substance Heat of Combustion

Methyl alcohol, CH4O 182200 cal.v

\158300 cal.

Ethyl alcohol, CsHeO 340500 cal.^

\i 58100 cal.

Propyl alcohol, CsHgO 498600 cal.

The effect of constitution on heat of combustion is seen
in the fact, that primary alcohols have larger heats of com-
bustion than either secondary or tertiary. An interesting
application of the eflfect of constitution on heat of com-
bustion has been made by Julius Thomsen, in the case of
benzene, to which reference has already been made.

THE DEVELOPMENT OF ELECTROCHEMISTRY

The decomposition of chemical compounds by the elec-
tric current has attracted the attention of physicists and
chemists ever since the discovery of the voltaic element
at the close of the last century. The comparatively insig-
nificant elements which were first constructed sufficed,
however, to effect a number of decompositions, such as the
electrolysis of metal salts, of water to which acid has been
added, etc. But it remained for Sir Humphry Davy ^ to
construct the large voltaic element which effected such
remarkable decompositions, and led to the discovery of the
alkali metals. The current from his element was passed
through the fused oxides of potassium and sodium, when
small globules were seen to rise to the surface of the mol-

^ Qilb. Ann., 7, 114 (1801).

40 ELECTROLYTIC DISSOCIATION

ten mass, and take fire on contact with the air. Thus were
sodium and potassium first separated from their compounds.

Davy's Electrochemical Theory. — The direct decomposi-
tion of the oxides of the alkali metals by the electric cur-
rent, also the decomposition of acidulated water, and a
large number of other chemical substances, pointed to
some close relation between chemical attraction and elec-
trical attraction. As the net result of his very elaborate
electrochemical studies, Davy was led to the electrochem-
ical theory which bears his name. The atoms of sub-
stances, by contact, acquire different electrical charges,
and these atoms then attract one another, because they are
charged, the one positive, and the other negative. These
charges may be so slight, that the attraction between them
will not be sufficient to cause the atoms to change their
former relations, or they may be great enough to effect
such a rearrangement, when a chemical compound will be
formed. Chemical attraction between atoms is, then, but
the electrical attraction between the opposite charges which
have accumulated upon them, due to their contact with
one another.

Electrolysis consists in destroying the difference between
the charges upon the atoms in the compound, the nega-
tively charged atom receiving positive electricity from the
positive pole, to which it is attracted, and becoming neutral ;
the positively charged, attracted and neutralized at the
negative pole. The compound would thus necessarily be
broken down by electrolysis, since the force which held its
constituents together no longer exists.

Berzelius' Electrochemical Theory. — The theory of Ber-
zelius differed fundamentally from that of Davy. Accord-

THE EARLIER PHYSICAL CHEMISTRY 41

ing to Davy, an atom, as such, is electrically neutral, and
becomes charged positively or negatively by contact with
another atom, which takes a charge of the opposite sign.
Berzelius claimed that every atom is electrically charged
with both kinds of electricity. These exist upon the atom,
in polar arrangement, and the electrical character of the
atom depends upon which is present in excess. One is
usually present in large excess, giving the atom a decidedly
positive or negative character. One " pole " is usually
much stronger than the other, so that the atom reacts as if
it was " unipolar." Chemical attraction is but the electri-
cal attraction of these oppositely charged atoms, and the
intensity of the former is conditioned by the magnitude of
the latter.

A negatively charged atom is attracted to and combines
with one which is charged positively. The magnitude of
these opposite charges may not be the same, and the com-
pound formed will itself be electrically positive or nega-
tive, depending upon which charge upon the atoms is the
greater. Two compounds, the one charged positively and
the other negatively, may, then, in turn, combine, forming
a still more complex compound. In this way Berzelius
attempted to account for the more complex substances,
such as the so-called double compounds.

The theory, as put forward by Berzelius, did not Jong
enjoy freedom from adverse criticism. If chemical union is
produced by the electrical attraction of oppositely charged
atoms, then, as soon as these atoms come together, the
electrical differences would disappear, and the compound
must fall apart. As soon, however, as the atoms separated,
they would become oppositely charged, and again reunite.

42 ELECTROLYTIC DISSOCIATION

There would thus result a continued decomposition and
reunion, and a chemical compound would, at best, be in a
state of unstable equilibrium. This would apply to all
chemical compounds.

But the theory was called upon to meet, apparently, a
more serious objection. If chemical union depends only
upon the attraction of the opposite electrical charges upon
the atoms, then the properties of the compound formed
must depend upon the nature of the charges upon the
atoms in the compound. It was, however, found to be
possible to substitute the three hydrogen atoms in acetic
acid by three chlorine atoms, passing from CHgCOOH
to CClgCOOH. And the remarkable fact was discovered,
that the properties of trichloracetic acid were very similar
to those of acetic acid itself.

This, Berzelius himself could not satisfactorily reconcile
with his theory. Each of the three hydrogen atoms car-
ried a positive charge, while the three chlorine atoms each
carried a negative. Yet the three hydrogen atoms, with
their positive charges, could be replaced by the three
chlorine atoms with their negative charges, without ma-
terially changing the properties of the compound. This is
cited, up to the present, as a fatal objection to the electro-
chemical theory of Berzelius.

The very recent work of J. J. Thomson^ has, however,
thrown entirely new light on the above line of argument.
Thomson has shown that the sajne substance may be both
positively and negatively charged. Thus, hydrogen gas^
has been elefctrolyzed by him, with the result that positive
hydrogen went to one pole and negative to the other.

1 Nature, 52. 453. 2 /j;Vf., 52, 451 (1895).

THE EARLIER PHYSICAL CHEMISTRY 43

This was shown from the difference in the spectra of the
hydrogen around the two poles. The molecule of hydro-
gen is, then, very probably made up of a positive and a
negative hydrogen ion.

The important point in this connection, brought out by
the work of Thomson, is that we must not conclude that
because hydrogen is sometimes positively charged, it is
always so. Thomson's own words, in connection with that
portion of hfs paper which bears on the theory of Ber-
zelius, are here given.

" In many organic compounds, atoms of an electroposi-
tive element hydrogen are replaced by atoms of an elec-
tronegative element chlorine, without altering the type of
the compound. Thus, for example, we can replace the 4
hydrogen atoms in CH4, by CI atoms, getting, successively,
the compounds CH3CI, CHgClg, CHClg, and CCI4 : it seemed
of interest to investigate what was the nature of the charge
of electricity on the chlorine atoms in these compounds.
The point is of some historical interest, as the possibility
of substituting an electronegative element in a compound
for an electropositive one was one of the chief objections
against the electrochemical theory of Berzelius. When the
vapor of chloroform was placed in the tube, it was found
that both the H and CI lines were bright on the negative
side of the plate, while they were absent from the positive
side, and that any increase in the brightness of the H
lines was accompanied by ^n increase in the brightness of
those due to CI. . . . The appearance of the H and CI
spectra on the same side of the plate was also observed in
methylene chloride, and in ethylene chloride. Even when
all the H in CH^ was replaced by CI, as in carbon tetra-

44 ELECTROLYTIC DISSOCIATION

chloride CCI4, the CI spectra still clung to the negative
side of the plate."

The same point was tested with SiCl4, and the CI spectra
was brightest on the negative side of the plate. "From
these experiments it would appear that the CI atoms, in
the chlorine derivatives of methane, are charged with elec-
tricity of the same sign as the H atoms they displace."

From this, the argument against the theory of Berzelius
is left without foundation, since the hydrogen atoms in
acetic acid are replaced by chlorine, which has the same
kind of charge. Therefore, the properties of trichloracetic
acid should resemble closely those of acetic acid itself.

Faraday's Law. — The next important advance in elec-
trochemistry was made by Faraday, upon whose investi-
gations too much stress cannot be laid. He showed the
identity of electricity from different sources, whether pro-
duced by friction or by chemical action ; and also investi-
gated the relation between the amount of a compound
decomposed by the current, and the amount of current.
He found that the two were proportional to one another,
and then announced his law.

The amount of chemical decomposition effected by the
passage of the current is proportional to the amount of
electricity which flows through the conductor.

Faraday determined, also, the amounts of different ele-
ments, which would be separated from their compounds,
by passing the same current through solutions of these
compounds. For example, the same current would be
passed through solutions of, say, copper sulphate, zinc
chloride, and silver nitrate, and the amounts of Cu, Zn, and
Ag deposited determined.

THE EARLIER PHYSICAL CHEMISTRY 45

The following generalization was reached by this
work : —

The amounts of the different elements which are sepa-
rated by the same quantity of electricity bear the same
relation to one another as the equivalents of these
elements.

The atoms of all univalent elements carry exactly the
same quantity of electricity, — of bivalent elements twice as
much, of trivalent three times, and so on. In a word, all
atoms have either the same capacity for electricity, or a
simple rational multiple of the capacity of the univalent
atoms.

Faraday is also the author of the system of nomencla-
ture, which we use in electrochemistry up to the present

Electrolysis. — The power of the current to decompose
chemical compounds had been made especially prominent
by the work of Faraday. This he termed electrolysis.

Some of the most interesting and important advances
made in electrochemistry, at that time, were along this line ;
and theories were proposed to account for the facts then
known, which we now recognize to contain the germ of
the theory of electrolytic dissociation. If the two poles
of a voltaic cell are immersed in acidulated water, hydro-
gen is liberated upon the one pole, and oxygen upon the
other. Between the two poles there is a layer of water
particles, which apparently undergo no decomposition.
The question arose, do the hydrogen and oxygen set free,
come from the same or from different water particles ? It
is not a simple matter to answer this question satisfac-
torily, and yet it is fundamental to the solution of the
question of electrolysis.

46 ELECTROL^IC DISSOCIATION

A superficial examination of what took place in electroly-
sis would probably lead to the conclusion that the hydro-
gen and oxygen come from different water particles. Yet
it might be that the water which was decomposed was
that which was exactly halfway between the poles, and
that the hydrogen moved from this point in the one direc-
tion, and the oxygen in the other.

Humphry Davy undertook to answer this question exper-
imentally. He placed the poles of a voltaic cell in sepa-
rate vessels, containing acidulated water, and connected the
two vessels by placing a finger of one hand in the one,
and a finger of the other hand in the other, care being
taken to properly insulate his body from the earth. Elec-
trolysis took place, hydrogen separating at one pole of the
battery, oxygen at the other. In such an arrangement, it
is difficult to see how the oxygen and hydrogen set free
could come from the same particle of water. It is, there-
fore, very probable, that in the electrolysis of acidulated
water, the hydrogen and oxygen which are liberated at
the poles come from different molecules of water.

Theories of Electrolysis. — The first to account at all
satisfactorily for electrolysis was Grotthuss, at the early
date of 1805. At the moment when the hydrogen and
oxygen separate, the one becomes positive and the other
negative. The positively charged hydrogen is attracted
to the negative pole, and repelled'from the positive pole.
The negatively charged oxygen is attracted to the positive
pole, and Repelled from the negative. But since the at-
tracting and repelling forces vary inversely as the square
of the distance from the electrodes, the sum of the forces
which act, respectively, upon the hydrogen and oxygen

THE EARLIER PHYSICAL CHEMISTRY

particles, as they approach the electrodes, is constan':.
This clear and concise idea of Grotthuss is represented
graphically in the accompanying figure.

The atoms marked positive represent hydrogen ; those
marked negative, oxygen. Before the current is passed,
each oxygen atom is combined with a definite hydrogen
atom, forming water. When the current is passed, the
hydrogen atom nearest the negative pole gives up its
positive charge to that pole, becoming electrically neutral,
and separates as hydrogen gas. The oxygen atom which

+ - + - +

Fig. I.

was originally in combination with this hydrogen is now
free, but it combines at once with the hydrogen of the
next molecule of water. This sets another oxygen atom
free, which combines with the hydrogen of the next water
molecule, and so on until the positive pole is reached,
when the last oxygen atom in the chain, not finding any
hydrogen with which to combine, takes up a positive
charge from the positive pole, becomes electrically neutral,
and escapes as gaseous oxygen.

The gases, which escape only at the electrodes, come

48 ELECTROLYTIC DISSOCLVTION

from different molecules of water, as was made probable
by the experiment of Davy. The layers of molecules
between the electrodes are, during the electrolysis, con-
stantly interchanging their constituents.

The distinctive feature of the theory of Grotthuss is,
that before the current is passed, each hydrogen atom is
combined fixedly with a definite oxygen atom, from which
it never parts company. The current must first decom-
pose the water molecules, before any electrolysis can take
place. This theory accounted, satisfactorily, for all the
facts which were known about electrolysis, at the time
when it was proposed.

Clausius' Theory of Electrolysis. — While the theory of
Grotthuss accounted for all the facts which were then
known, new facts were soon brought to light, which could
not be reconciled with it. According to this theory, the
current must first decompose the molecules before it can
effect any electrolysis. If the current used is not capable
of decomposing one molecule of water, it is clear that it
cannot decompose more than one, and no electrolysis
would result. But as the strength of the current in-
creases, it must reach a point where it is capable of
decomposing a molecule of water. At this point many
molecules must be simultaneously decomposed, since they
are all under the effect of the same force, and have almost
exactly the same position to one another. If the con-
ductor conducts only electrolytically, we must conclude
from this theory, that as long as the driving force in the
conductor is below a certain limit, no current will pass ;
but when it has reached this limit, a very strong current
suddenly exists.

THE EARLIER PHYSICAL CHEMISTRY 49

Says Clausius,^ this conclusion from the theory is in
direct opposition to what are now known to be the facts.
The smallest force produces a current by alternate de-
composition and reunion, and the intensity of the current
increases according to Ohm's law, i.e. proportional to
the force. Therefore, the assumption that the part mole-
cules of an electrolyte are combined rigidly to form whole
molecules, and that these have a definite, regular arrahge-
ment, is without foundation.

The assumption, then, that the natural condition of an
electrolytic liquid is one of equilibrium, in which every
positive part molecule is combined rigidly with a negative,
was abandoned by Clausius as untenable, and his own
theory proposed in its place.

An electrolytic solution consists mainly of whole mole-
cules of the electrolyte, but in addition there are some
" part molecules," which have parted company. A posi-
tive part molecule may, during the movements to which
it is subjected, come into a position with respect to the
negative part of another molecule, which is more favor-
able for union with this than with its own negative com-
panion. It would then part company with the latter, and
join the former. This would have, then, a positive and a
negative part molecule, each free to move about through
the solution and combine with other part molecules, or
break down whole molecules already existing as such in
the solution. These movements and decompositions take
place as irregularly as the heat movements which produce
them. The two part molecules, resulting from the break-
ing down of a whole molecule, may combine directly with

1 Pogg. Ann., loi. 338 (1857).

50 ELECTROLYTIC DISSOCIATION

one another, or may be prevented from doing so by the
movements due to heat. The amount of such decompo-
sition in a solution would depend upon the nature of the
solution and upon the temperature.

Allow an electric force to act upon a solution containing
a mixture of whole and of part molecules. The part mole-
cules will no longer move about in all directions, due to
the action of heat alone, but more positive parts will move
in the direction of the negative pole, and negative parts
toward the positive pole, than in the other directions.
This directing influence of the current will also facilitate
the breaking down of the whole molecules into part
molecules.

This assumption of a partial breaking down of the mole-
cules in an electrolytic solution, before the current is
passed, accounts for the fact that a weak current will effect
electrolysis — a fact which could not be brought within the
range of the theory of Grotthuss. The directing influence
which the current exerts would exist for a current of any
strength, and would be proportional to the strength of the
current. In the opinion of Clausius, the action of the
current is primarily a directing one, but, at the same time,
it facilitates the decomposition of the molecules into part
molecules. This theory of Clausius, as will be seen later,
contains the germ of the theory of electrolytic dissociation.

A theory as to the condition of things in solution was
proposed by Williamson ^ in 1851, as the outcome of his
work on the preparation of ether by the action of sulphuric
acid on ethyl alcohol. The reaction which produced the
ether was recognized as proceeding in two stages : —

1 Liebig's Ann., 77, 45 (1851).

THE EARLIER PHYSICAL CHEMISTRY 5 1

.OH yOCsH,

+ HOC2H5 = S02<

X)H \ OH

.OCoH* X)H CoH,

<0H yOCsHfi

+ HOC2H5 = S02< + HjO.

OFT N nw

+ HOC2H5 = S02< + >0.

OH X)H C2H/

The first stage of the reaction consists in the replacement
of a hydrogen atom in the sulphuric acid, by the ethyl
group, with the elimination of a molecule of water; the
second. In the replacement of the ethyl group in ethyl sul-
phuric acid by the hydroxyl hydrogen of the alcohol. The
reaction which takes place as represented in I is then
almost exactly reversed in II, the final result being the
removal of a molecule of water from two molecules of
alcohol, and the formation of a molecule of ether. From
this Williamson concluded, " that in an aggregate of the
molecules of every compound, a constant interchange
between the elements contained in them is taking
place."

He concluded his paper with this statement : " In recent
years chemists have added to the atomic theory an uncer-
tain, and, as I believe, an unsubstantiated hypothesis, that
the atoms are in a condition of rest. I reject this hypothe-
sis, and found my views on the broader basis, the movement
of the atoms.*' ^

Clausius criticised the views of Williamson as being too
broad. His assumption went too far beyond the facts. It
was not necessary to assume that all, or even a large part,
of the molecules in a solution are broken down into part

1 Liebig's Ann., 77, 48.

52 ELECTROLYTIC DISSOCIATION

molecules. The assumption that a few of the molecules
are thus broken down, accounted for all the facts then
known.

Hittorf's Work on the Migration Velocity of Ions.—
The changes in concentration, which take place when
solutions are electrolyzed, could be explained only by
assuming that the positive and negative part molecules,
or, as Faraday called them, ions, move through the solu-
tion with different velocities. The measurement of these
relative .velocities was undertaken by Hittorf,^ and his
investigation of this problem has now become a classic.
He studied the effect of concentration of solution, tempera-
ture, and strength of current, upon the relative velocities
of ions. His work is of importance, not simply as giving
us the relative velocity of ions, but as throwing light on a
number of other problems. What ions are formed from
the given compounds ? which constituents go to make up
the cation, and which the anion ? are questions which come
within the range of the work of Hittorf. Take the com-
pound KaPtClg; does the platinum form part of the ca-
tion, or of the anion ? does it go to the positive or to the
negative pole.? Or take the compound K4Fe(CN)g; when
it is electrolyzed, does the iron go with the potassium to
the cathode, or with the cyanogen to the anode.? The
solution of such problems is of great assistance in deter-
mining the chemical constitution, especially of complex
compounds.

Eohlrausch's Work on the Conductivity of Solutions. —
Solutions of different electrolytes show very different con-
ducting power. A simple and accurate method of meas-

1 Pogg. Ann., 89, 117, 177 ; 98, I ; 103, i ; 106, 337, 513.

THE EARLIER PHYSICAL CHEMISTRY 53

uring the conductivity of solutions has been devised by
Kohlrausch.^ He has applied his method to a large num-
ber of solutions of different concentrations of acids, bases,
and salts; and has furnished us with the most accurate
conductivity measurements which have ever been made.
The results of this work will be considered in a later
chapter, since their bearing upon the theory of electro-
lytic dissociation is direct. Indeed, we shall learn that
the conductivity of solutions of electrolytes furnishes us
with one of the most rigid tests to which the theory of
electrolytic dissociation can be subjected.

THE DEVELOPMENT OF CHEMICAL DYNAMICS AND CHEMICAL

STATICS

The brief sketch which will be given here, of the de-
velopment of this branch of physical chemistry, will not
include the earliest suggestions to account for chemical
action, since many of them are now only of historical
interest. The Swedish chemist, Bergmann, attempted
generalizations which were undoubtedly advances on the
disconnected knowledge before his time; but it was
Wenzel (1777) who first saw clearly the effect of mass
on chemical action, and laid the foundation for the law of
mass action, which has played such a prominent r61e since
his time. He, however, gave only a qualitative expression
to the law; viz., that chemical action is proportional to
the concentration of the substances which are allowed to
react.

Berthollet developed much more fully the effect of

1 Pogg. Ann., 138, 280; 131. I ; 159, 233; Wied. Ann., 6, i ; 11, 653; a6, i6i.

54 ELECTROLYTIC DISSOCIATION

mass in chemical action, and showed by direct experi-
ment how it comes into play. The affinities which exist
between substances are not to be regarded as absolute
forces, but are dependent upon the masses of the sub-
stances which are present. Thus barium sulphate can be
partly decomposed by boiling it with potassium hydroxide.
Calcium oxalate can, similarly, be partly decomposed by
the same reagent. If the potassium hydroxide is present
only in small quantity, no appreciable decomposition takes
place ; but if the quantity is large, and is removed from
time to time, new alkali being added, barium sulphate
can be completely decomposed by boiling potassium hy-
droxide. This was a clear demonstration of the effect of
mass.

Following this same idea, BerthoUet pointed out the
effect of the state of aggregation on chemical activity.
That chemical activity should be greatest, it is necessary
that all the parts should come into action. This is best
effected in the liquid state of aggregation. If a solid is
present, the activity is less, or if a solid is formed as the
result of the reaction, its activity is far less than in the
liquid condition. Similarly, if a gas is formed in the reac-
tion, it quickly escapes from the field of action, and its
chemical activity therefore ceases.

This work of BerthoUet was published in two volumes
as his "Essai de Statique Chimique,'' but was so far in
advance of its day, that it either failed to attract attention
altogether, or only aroused opposition from those who did
not comprehend its full significance.

It was much later before any further evidence was
brought forward, to show the effect of mass in chemical

THE EARLIER PHYSICAL CHEMISTRY 55

activity. Heinrich Rose^ showed that the sulphides of
the alkaline earths are largely decomposed when boiled
with large volumes of water, liberating hydrogen sulphide,
and forming the hydroxide.

He also called attention ^ to a process which is going on
in nature. Over the surface of the earth the weak chemi-
cal reagents, carbon dioxide and water, are continually
decomposing some of the most stable compounds — the
silicates. The geological process known as weathering is
a replacement of silicates by hydroxides and carbonates,
or by basic carbonates. This reaction, in which such
stable compounds are broken down by such a weak acid
as carbonic acid, requires, of course, a long period of time,
and is the result of the mass action of a large amgunt of
carbon dioxide, such as exists in the atmosphere, and in
the soil. Such a reaction is entirely beyond the possi-
bilities of the laboratory, on account of the time and mass
of substance required to effect it.

Rose ® also carried out some investigations on the decom-
position of insoluble salts by soluble salts. It was known,
long before his time, that barium sulphate can be trans-
formed into the carbonate, both by fusion with potassium
carbonate, and also by boiling with an aqueous solution of
potassium carbonate. Rose, however, undertook a quan-
titative study of the conditions under which this transfor-
mation takes place, and the amount of carbonate required
to effect complete decomposition. He found that the sul-
phates of strontium and calcium are more easily decom-
posed by alkaline carbonates than the sulphate of barium,

1 Pogg. Ann., 55, 415. 2 Ibid,, 82, 545.

8 Ibid,, 94, 481 ; 95, 96, 284, 426.

56 ELECTROLYTIC DISSOCIATION

and concluded, correctly, that this was due to the presence
of a reversible reaction between the barium carbonate and
alkaline sulphate formed, resulting in the reformation of
barium sulphate.

The result of this work of Rose, and that of his con-
temporaries, was to call attention to the r61e played by
mass in bringing about chemical reaction. The full im-
portance of the action of mass, as we shall see, was, how-
ever, not recognized until somewhat later.

Wilhelmy's Discovery of the Law of Reaction Velocity. —
Wilhelmy ^ treated cane-sugar with a number of acids, and
studied the velocities with which inversion takes place.
He worked with different acids, with different amounts of
cane-sugar, and at different temperatures. He found that
it was only the sugar which underwent change, the acid
remaining unaltered. The law of mass was found to
obtain ; the amount of sugar transformed in a given time
^ being proportional to the amount present at that time.

Applying the principle of mass, — remembering that it
is only the sugar which undergoes change, the acid being
unaltered, — Wilhelmy deduced the following mathemat-
ical relations, which are taken from his epoch-making
paper : ^ —

" Let dZ be the amount of sugar inverted in unit time

dTy and let us assume that this is determined by the

formula : ^ —

- 41= MZS
dT

in which M is the mean value of the infinitely small quan-
tity of sugar, which is transformed in unit time, by the

1 Pogg. Ann., 8i, 413 (1850). 2 /^^Vj?., 81, 418.

THE EARLIER PHYSICAL CHEMISTRY 57

action of the unit of acid present. (Z is the amount of
the sugar, 5 that of the acid.)

" The above equation gives, on integration : —

"LogZ^-j'MSdT

or since, as already shown, 5 is constant, M is also inde-
pendent of Zf and at the same time of 7*, which should
be proved later by experiment : —

LogZ = - J/5r+C.
For 7^=0,^ = Zq, whence :
Log Zq — logZ = MST, or Z= ZqE.

Since Zq, S, and T are given, and Z is known by experi-
ment, the formula can be used to determine -Af."

This work of Wilhelmy, which must be regarded as the
foundation of chemical dynamics, like most important inves-
tigations, did not receive a just recognition until attention
was called to it much later.^ When we consider that this
was the first successful attempt to express the velocity of
a chemical reaction mathematically, and that this was in
1850, we can form some conception of the rapidity of the
growth of knowledge along this line.

Other contributions to our knowledge of the mechanism
of chemical reactions were made in the next few years.
Lowenthal and Lenssen ^ showed that the amount of sugar
inverted by different acids was proportional to the strength
of the acids. But the next marked advance we owe to the
French chemist Berthelot.

1 Ostwald, Journ. prakt. Chem., 29, 385 (1884).
3 Journ. prakt. Chem., 85, 321 (1B52).

58 ELECTROLYTIC DISSOCLVTION

Work of Berthelot and P^an de St. Gilles. — Berthelot
and P^an de St. Gilles^ made an elaborate investigation
of the conditions of formation and decomposition of ethe-
real salts. The reactions by which these are formed from
acids and alcohols proceed slowly, and tend toward a limit,
the point at which the reaction reaches a condition of
equilibrium depending upon the amount of acid or alcohol
present, upon the temperature, etc. On the other hand,
if an ethereal salt is treated with water, a certain amount
of it is decomposed, the amount depending upon the quan-
tity of water used, and other conditions. A reaction of this
kind is, evidently, well adapted to the study of reaction
velocity, condition of equilibrium, etc.

They determined the effect of temperature on the
velocity of this reaction, and found that to transform 30
per cent of a given mixture of alcohol and acid, at from
6° to 9°, required 95 days, while at loo"^ it required less
than 5 hours to effect the same transformation. Pressure
was found to have no influence on reaction velocity, at
least up to sixty or eighty atmospheres.

Berthelot 2 and St. Gilles, in the course of their study
of ether formation, arrived at the following generalization :
"The amount of ether formed in every moment is pro-
portional to the product of the reacting substances."
This was a beautiful confirmation of the action of mass.

They also determined the relation between chemical
composition and the amount of ether formed. A few of
their results are given, using different alcohols and acids,
and allowing the reaction to proceed until equilibrium was

1 Ann. Chim. Phys. [3] , 65, 385 ; 66,$', 68, 225 (1862-1863).

2 Idld. [3], 68. 225.

THE EARLIER PHYSICAL CHEMISTRY 59

reached, i.e. until the maximum amount of ether was
formed under the conditions. This is indicated in per-
centage of the theoretical amount of ether which might
be formed under the conditions, if the reaction went to
the end.

Limit

CjHeO with CHjCOOH 66.9%

QHeO with CH3 . CHj . CH, . COOH 69.8%

CjHeO with CeHaCOOH 67.0%

CH4O withCHjCOOH 67.5%

CH4O withQHfiCOOH 64.5%

CH4O with CaH4(C00H), 66.1%

C5HiaO with C H3COOH 68.9 %

C^HijO with CHs • CHj . CHj • COOH 70. 7 %

QHuO with CeHftCOOH 70.0%

This is a remarkable result. Neither the chemical com-
position of the acid, nor of the base, has any marked
influence on the amount of ether formed.

The effect of increasing the amount of the alcohol, with
respect to the acid, was also determined.

n is the number of equivalents of ethyl alcohol, to one
equivalent of acetic acid.

n Limit n Limit n Limit

0.2 19.3% 2. 82.8% 12.0 93.2%

0.5 42.0% 4. 88.2% 19.0 95.0%

i.o 66.5% 5.4 90.2% 50.0 100.0%

1-5 77.9%

These results exhibit the effect of mass in a striking
manner ; all the acid being transformed into ethereal salt,
when fifty equivalents of alcohol are present to one of acid.

The action of mass was shown also by the work of

6o ELECTROLYTIC DlSSOCLVTION

Deville^ on dissociation. Many substances are partially
broken down by heat into their constituents — in many
cases into their elements. Thus, water-vapor at a high heat
is partially decomposed into hydrogen and oxygen. The
fact was established, that if either the hydrogen or oxygen
resulting from the decomposition is removed, the dissocia-
tion will proceed farther, and may become complete. If,
on the other hand, an excess of either hydrogen or oxygen
is added to the dissociating water-vapor, the amount of
dissociation is decreased. Deville studied a number of
cases, and concluded that this is general, that an excess
of either of the products of dissociation will diminish
the amount of dissociation of a vapor. An excellent ex-
ample of this is furnished by phosphorus pentachloride.
This compound cannot be volatilized without decomposi-
tion, unless there is an excess of either chlorine or phos-
phorus trichloride present. In the presence of an excess
of one of these, the molecular weight of phosphorus penta-
chloride, as determined, is very close to the theoretical
molecular weight.

This work of Deville is one of the most direct confirma-
tions of the effect of mass, yet it was used by him as an
argument against mass action, being a factor in chemical
activity. Another example of admirable work, but erro-
neous interpretation of results obtained.

Guldberg and Waage's Law of Mass Action. — We have
seen that the effect of mass on chemical activity was
recognized as early as the time of Wenzel. A clearer
expression of its action was furnished by Berthollet. Rose
showed, both from nature, and by direct experiment, what

1 Compt. rend., 45, 857; 56, 195, 729; 59, 873; 60, 317.

THE EARLIER PHYSICAL CHEMISTRY 6 1

a marked influence mass has in effecting chemical reac-
tions. Berthelot and P^an de St. Gilles demonstrated the
effect of mass action on the formation of ethereal salts
from alcohols and acids, and thus made it probable that
the effect of mass on chemical reactions is general.

It was Guldberg and Waage,^ however, who gave a com-
plete mathematical expression to the action of mass. If
two substances react, the action is proportional to the active
masses of each of them. The intensity of the reaction is,
therefore, measured by the product of the active masses.
The reaction is, of course, dependent also upon the nature
of the substances, temperature, etc. These must be taken
into account. If we represent the active masses of two
substances by m and «, and the coefficient depending upon
the nature of the substance, etc., by c, the force of the
chemical reaction is expressed by mnc.

If the reaction is reversible, i.e. if the substances formed
can react and give the original substances, as e.^. in the
formation of ethereal salts, then there will exist a force
which tends to stop the original reaction, and to set up
one in exactly the opposite sense. If we represent the
active masses of the substances formed in the original
reaction by m' and «', and the coefficient depending upon
the nature of the substances by c', the magnitude of the
force opposing the original reaction will be expressed by

When the condition of equilibrium is reached, the two
forces are equal and opposite, and we have : —

fnnc^nJn!<^ (i)

1 ifetudes sur les Affinit^s Chimiques, Cbristiania, 1867 ; Joum. prakt. Chem. [2],
xg, 69 (1879). Ostwald's Lehrb. d. allg. Chemie, II, 2, p. 104.

62 ELECTROLYTIC DISSCOATION

If we bring together equivalents of the four substances
ffty fly m\ n!, they will generally not be in a state of equilib-
rium, but a certain amount of m and n will pass over into
m! and «', and this amount we will call x. The amounts
of the four substances present will then be, w — ;ir, n — ;r,
/«' -{-Xy n! -\- X. The active masses being the amounts in
a given volume v^ we will have : —

m — X n — X m* -{-x ti •\- x
, , , ,

V V V V

where v is the entire volume of the solution. Substituting
these values for niy «, w^', and nJ in (i), we have : —

{m — x){n— x) = -r(w' + x){n^ 4- x).

This equation is perfectly general, applying to all values
of X. If we determine x in any one case, we can calculate

— • Knowing — ,we can calculate the value of x for any
k k

amounts of the original substances brought together. In
a word, we could calculate exactly how the four substances
would react, whatever the quantities brought together, and
how much of each would exist when equilibrium was
reached.

Guldberg and Waage's work also led to a more com-
prehensive conception of the reversibility of many chemi-
cal reactions, equilibrium being the special condition
under which the reactions in the two directions were of
equal velocity. The velocity of any reaction is, in reality,
the difference between the velocity in one direction, and

the velocity in the other. The velocity v is the amount

dx
transformed in unit time, v = —— ; but this is equal to a

THE EARLIER PHYSICAL CHEMISTRY 63

factor 6 times the force acting in one direction, minus the
force acting in the other direction.

V = -— = 0{mnc — fn!n!(^y

If the reaction proceeds only in one direction, ffJn^c^ be-
comes equal to zero, and the equation of reaction velocity
becomes : —

The above relations obtain, only when all of the sub-
stances which enter into the reaction are soluble. If one
or more of the substances is insoluble, the relations are
much simplified. Take the reaction between potassium
carbonate and barium sulphate, in which potassium sul-
phate and barium carbonate are formed.

Let M be the active mass of potassium carbonate.

Let N be the active mass of barium sulphate.

Let M^ be the active mass of potassium sulphate.

Let N* be the active mass of barium carbonate.

Barium sulphate and barium carbonate are insoluble,
and their active masses, N and N\ are, therefore, con-
stant. We have then : —

MC=M'C or ^ = constant

This is a very simple relation, and holds whenever two
of the substances are insoluble. The value of the con-
stants for the insoluble substances depends upon their
degree of insolubility.

The law of mass action has been tested in a large num-
ber of directions, and by a great variety of methods. The

64 ELECTROLYTIC DISSOCIATION

general result has been a thorough confirmation of the
views of Guldberg and Waage.

The Application of Thermodynamics to Chemical Pro-
cesses. — The scope of this work will not permit of more
than a brief reference to the leading investigations bearing
upon this problem. Horstmann ^ was the first to success-
fully apply thermodynamics to chemical processes. He
chose dissociation phenomena, since they are reversible
processes ; and if they take place between solids and gases,
obey the same laws as vaporization. If we represent by
h the heat of combination, and by / the dissociation press-
ure, the following relation between the two obtains : —

in which T is the absolute temperature, and u the volume
of the vapor. Knowing either A or/, we can calculate the
other. He later applied the entropy principle to conditions
of equilibrium, and showed that a system will always
assume that arrangement in which entropy is a maximum.
The condition for equilibrium is then : —

— = o
dx

in which e is the entropy, and x the amount of untrans-
formed substance.

Willard Gibbs's ^ applications of thermodynamics to con-
ditions of chemical equilibrium are so comprehensive and
general, that it is impossible to give any adequate concep-

1 Ber. d. chem. Gesell., 2, 137; 4, 635; Liebig's Ann., 170, 192 (1872-1873).

2 Trans. Conn. Acad., Ill, 1874-1878. Translated into German by Ostwald,
Leipzig, 1892.

THE EARLIER PHYSICAL CHEMISTRY 6$

tion of his epoch-making work in a few paragraphs. The
reader who may desire to follow out Gibbs's mathematical
deductions must be referred to his original communication,
or to the second part of the second volume of Ostwald's
Lehrbuch, where a systematic account of his deduction is
given.

It should, however, be stated here, that the work of
Willard Gibbs has placed the science of chemical equilib-
rium on an entirely new basis, from the theoretical stand-
point, and is ranked as one of the leading contributions to
mathematical chemistry and physics.

The work of van't Hoff ^ is in part theoretical, and in
part experimental. This deals largely with the velocity
of reactions from both standpoints, and also investigates
the influences which affect the velocity of a reaction, such
as temperature, pressure, form of vessel, etc. The con-
ditions of equilibrium were also investigated by van't Hoff
and his pupils, and the temperatures ascertained at which
a large number of transformations take place.

The observations for the different kinds of equilibrium
have led to the following general conclusion : ^ " Every
equilibrium between two different conditions of matter
(systems) is, at constant volume, by a decrease in temper-
ature, displaced in the sense of that system whose forma-
tion liberates heat." This generalization includes all pos-
sible cases of chemical as well as of physical equilibrium.
This principle, termed by van't Hoflf that of "movable
equilibrium," is then applied to both heterogeneous and

1 Etudes de Djmamique Chimique, Amsterdam, 1884. Studien zur Cbemischen
Dynamik, van't Hoff and Cohen.

3 Studien zur Cbemischen Dynamik (van't Hoff and Cohen), p. 223.

66 ELECTROLYTIC DISSOCLVTION

homogeneous equilibria. The concluding chapter of this
important work by van't Hoff and Cohen is devoted to
the subject of chemical affinity. The generalization reached
was,^ that " the work expressed in calories, which affinity
can do in a chemical transformation, at a given tempera-
ture, is equal to the amount of heat which this transforma-
tion produces, divided by the absolute temperature at
which the transformation takes place, and multiplied by
the difference between this, and the temperature at which
the transformation takes place."

If A is the amount of work done, q the amount of heat
produced, T the temperature of the transformation, and
P the absolute temperature of the transformation, we
have : —

which is the mathematical expression of the above gener-
alization. In connection with the study of chemical equi-
librium, the work of Le Chatelier^ must be mentioned.
He arrived at two laws which he stated thus : Law of the
opposition of action and reaction (page 210). "Every
variation of a factor of equilibrium causes a transformation
of the system, which tends to niake the factor in question
undergo a variation of sign opposite to that which we have
given it."

Thus, an elevation of temperature produces a reaction
with absorption of heat, an increase in pressure a reaction
with diminution of volume, etc.

1 Studien zur Chemischen Dynamik, p. 247.

2 Recherches Exp6rimentales et Th6oriques sur les Equilibres Chimiques. Paris,
1888.

THE EARLIER PHYSICAL CHEMISTRY 6/

Le Chatelier termed his second generalization the law
of equivalence of systems in equilibrium, and expressed it
thus : —

"Two equivalent elements in a system in equilibrium,
i.e, which can be substituted for one another without chang-
ing the condition of equilibrium, will be equivalent in every
other system where they can be substituted for one another,
and further, will be mutually in equilibrium if in opposition
to one another."

An example cited is the equality of the vapor-tension of
water and of ice at the melting-point.

Methods of measuring Affinity. — The theoretical deduc-
tions, especially of the last four pieces of work referred to,
have been tested experimentally by a number of methods.
Julius Thomsen ^ determined the way in which a base is
divided between two acids, by means of the amount of heat
liberated. While Ostwald,* utilizing the change in volume
which occurs in chemical reactions, obtained far more
satisfactory and reliable results than Thomsen. Ostwald
showed that the action between acids and bases is condi-
tioned by two coefficients,' the one depending upon the
nature of the acid, the other upon the nature of the base.
The chemical affinity of an acid for a base is then expressed
by the product of these two coefficients. These affinity
coefficients are the numerical expressions of the strength
of the acid or base, and hold, quantitatively, for all actions
in which the acid or base takes part.

In addition to the thermochemical method of J. Thom-
sen, and the simpler and more reliable volume chemical

1 Pogg. Ann., 138, 497 (1869).

2 Journ. prakt. Chem. [2], 16, 385 (1877).

68 ELECTROLYTIC DISSOCIATION

method of Ostwald, a number of other methods of measur-
ing relative affinities have been devised. Ostwald^ pro-
posed the velocity with which substances like zinc sulphide,
or calcium oxalate, are dissolved by different acids, as a
measure of the relative affinities of the acids. He ^ also
used the velocity, with which a reaction like the transfor-
mation of acetamid into ammonium acetate takes place
under the influence of acids, as a measure of the affinities
of the acids. Ostwald has also studied other reactions in
this same connection, such as the catalysis of methyl
acetate, inversion of cane-sugar, etc., and found that the
coefficients for the different acids, as determined by the
different methods, agreed satisfactorily.

A relation was thus discovered, which, as we will see, is
of the very greatest importance, in connection with the
theory of electrolytic dissociation. The affinity coefficients
of acids and bases bear the same quantitative relations to
one another as the conductivities of these acids and bases.

The discussion of this relation belongs to a later chapter
of this work, and it suffices here to merely call attention
tQ its existence.

Conclusions from the Earlier Physical Chemical Work. —
From the preceding sketch of the development of the
several chapters of physical chemistry, we can form a
fairly clear conception of the state of physical chemistry
just before the theory of electrolytic dissociation was
proposed. Much work had been done on the relations
between the various properties, and composition and con-
stitution ; and a great number of generalizations had been
reached, which, however, held only approximately. Much

1 Journ. prakt. Chem. [2], 19, 468 (1879). 2 ibid, [2], 27, i (1883).

THE EARLIER PHYSICAL CHEMISTRY 69

valuable experimental work had also been done on the
amount of heat liberated in chemical reactions, laying
stress upon the energy transformations which take place
in chemical processes, and which are probably the condi-
tioning causes of all chemical action. Here, also, relations
were pointed out, which, however, like the above, have
been shown to be only approximations. Then, the founda-
tions of electrochemistry were laid, early in the century,
and rapidly developed, and theories to refer chemical
action to purely electrical causes were proposed. The
decomposing action of the current was studied, and theo-
ries advanced to explain electrolysis, which lie at the
foundation of our most modem theory. The relation
pointed out here by Faraday, between the amount of
current and the amount of decomposition which it effects,
is one of the most exact with which we have to deal.
Similarly, other electrochemical relations are freer from
exceptions than those which we have just considered.
Some of the more important steps in the development of
chemical dynamics and statics have been taken up, includ-
ing, especially, the law of mass action, which underlies this
entire chapter of physical chemistry.

But, from what has preceded, we can see not only
the state of development, but also the inherent nature
of physical chemistry. What was the chief aim of the
physical chemist in these earlier periods ? It was, plainly,
to discover relations between apparently disconnected
phenomena and disconnected facts. It attempted to con-
nect, and thus systematize, the great masses of isolated
facts, which were yearly being brought to light, and thus
refer them, as far as possible, to common causes.

70 ELECTROLYTIC DISSOCIATION

It has, however, been repeatedly shown, that these earlier
relations were, in many cases, only approximations. The
number of exceptions continued to increase, as more ac-
curate experimental work was done, until, in some cases,
the generalization almost entirely disappeared. Neverthe-
less, the aim of the earlier physical chemist is the aim of
the physical chemist of to-day — to discover generalizations
wherever they exist. It is by this means, and this means
only, that chemistry can be advanced from pure empiri-
cism to the rank of an exact mathematical science.

We will now follow the rise and development of the
widest and most important generalization which has ever
been reached by physical chemistry.

CHAPTER II

THE ORIGIN OF THE THEORY OF ELECTROLYTIC

DISSOCIATION

PFEFFER'S osmotic INVESTIGATIONS

Introdttction* — If we would trace the origin of the
theory of electrolytic dissociation, we must turn neither to
chemistry nor to physics, but to the osmotic investigations
of the botanist, W. Pfefifer.^ It had long been known,
that when a solution of a substance is placed upon one
side of a partition, through which the solvent can pass
but the dissolved substance cannot, and the pure solvent
placed upon the other side, the pure solvent will flow
through the partition into the solution. This phenomenon
is termed osmosis, and the pressure thus produced, osmotic
pressure. We may demonstrate this phenomenon by
filling a bladder with a solution of alcohol in water, and
then immersing it in pure water. Water will flow through
the bladder into the solution of alcohol, and the bladder
will become distended. This is, of course, but a qualita-
tive demonstration ; and were we dependent upon natural
membranes alone to measure osmotic pressure, it is' safe
to say that very little would have been accomplished.
Pfeffer, however, succeeded in devising artificial mem-
branes, with which he could study osmotic pressure
quantitatively.

1 Osmotische Untersuchungen, Leipzig, 1877 ; Harper's Science Series, IV, p. 3

72 ELECTROLYTIC DISSOCIATION

Pfeffer's Method of measuring Osmotic Pressure. — Cer-
tain precipitates have the property of allowing the solvent
to pass through them, but of preventing the dissolved
substance from passing. , Jf . these precipitates are de-
posited at the plane of contact of two solutions, or of a
solution, and a solvent, they act like the animal mem-
brane described above. This important fact was dis-
covered by Traube, who was the first to prepare these
artificial membranes, and use them to study osmotic press-
ure. His methodj however, was far inferior to that
devised by .Pfeffer. :

To make these membranes more resistant, Pfeffer de-
termined to form them upon a support. He states that
the plant cell furnished him with a model. " In these,
the plasma membrane which, in its diosmotic properties, is
similar to the artificially precipitated membranes, is pressed
against the cell wall." Pfeffer caused the precipitate to
be deposited *ih. the walls of very fine-grained, unglazed
porcelaiil cells. The precipitate which gave him the best
results was cOppei* ferrocyanide. A porcelain cell was
filled on the'iftside with a solution of potassium ferrocy-
anide, and immersed in a solution of copper sulphate.
Thfe two solution's penetrated the walls of the porcelain
cell, and. met right in the Walls.

Where they came in contact, there was precipitated
coppeir . f e;rrocyanide as a membrane, which, when the
cell Was broken, appeared as a fine line.

Tbef itieihbranes deposited in this way had many of
the prqpetrties desired. . They were semipermeable, i,e.
allowed the solvent to pass through and prevented the
disspjlved -substance, and were sufficiently resistant to

THEORY OF ELECTROLVTIC DISSOCIATION 73

withstand considerable pressure without breaking - -The
apparatus in its complete form, as used by Pfeffer, is
seen in Fig. 2. ' ■

The porcelain cell, with
semipermeable membrane
deposited in the walls, is
seen at 2. This cell was
about 46 mm. high, 16 mm.
internal diameter, and tbe
walls were from i J to 2 mm,
thick. "The narrow glass
tube V, called the connecting
piece, was fastened into the .
porcelain cell with fused'
sealing-wax, and the closing
piece t was set into the otiier.
end of this tube in the same .
manner. The shape and
purpose of this are shown
in the figure. The glass ring
r was necessary only in.

experiments at higher tem- '"

perature, in which the seal-
ing-wax softened. The ring
was then filled with pitch,
which also held together
firmly the pieces inserted'
into one another." The
manometer m is attached 'c:i,ri^t»i;i^i£iii.*s;si

t -4.1. ^■'°- *

for measunng the pressure.
To give an idea of the precautions which are necessary

74 ELECTROLYTIC DISSOCIATION

to prepare, successfully, such semipermeable membranes
as were used by Pfeffer, a paragraph is quoted from his
monograph : ^ —

** The porcelain cells were first completely injected with
water under the air-pump, and then placed for at least
some hours in a solution containing 3 per cent of copper
sulphate, and the interior was also filled with this solution.
The interior only of the porcelain cell was then once
rinsed out quickly with water, well dried as rapidly as
possible by introducing strips of filter paper, and after
the outside had dried off, it was allowed to stand some
time in the air until it just felt moist. Then a 3 per
cent solution of potassium ferrocyanide was poured into
the cell, and this immediately reintroduced into the solution
of copper sulphate.

" After the cell had stood undisturbed for from twenty-
four to forty-eight hours, it was completely filled with the
solution of potassium ferrocyanide, and closed as shown
in Fig. 2. A certain excess of pressure of the contents
of the cell now gradually manifested itself, since the solu-
tion of potassium ferrocyanide had a greater osmotic press-
ure than the solution of copper sulphate. After another
twenty-four to forty-eight hours the apparatus was again
opened, and generally a solution introduced which con-
tained 3 per cent of potassium ferrocyanide, dnd i J per
cent of potassium nitrate (by weight), and which showed
an excess of osmotic pressure of somewhat more than three
atmospheres."

The osmotic pressure of solutions is measured with
this apparatus as follows : The cell is completely filled

1 Harper's Science Series, IV, p. 6.

THEORY OF ELECTROLYTIC DISSOaATION 75

with the solution and then tightly closed. The solution
also extends into the arm of the manometer attached
to the cell. The whole apparatus is then immersed in
the pure solvent, as
shown in Fig. 3.

The closed cell is
fastened to a glass
rod, and so immersed
in the liquid in the
bath that the entire
manometer is covered.
The temperature of
the bath is read by
thermometers. The
entire apparatus is
placed under a bell-
jar and kept in a
room at uniform tem-
perature. This is
necessary, since con-
siderable time is
required for the mer-
cury to reach the
highest point and
remain perfectly sta-
tionary. Water flows __. „, „ ,. , , „

in through the semi- <*7rtiu,i»^«r^H-P«*B™»«

permeable membrane,

and the pressure produced is finally read off on the ma-
nometer. The water which enters the cell dilutes the solu-
tion and diminishes its osmotic pressure, but the amount

76 ELECTROLYTIC DISSOCIATION

of waiter Which, enters is so slight that the error from this
source is not large.

Some of Pfeffer's Results.. — Pfeffer measured the os-
motic pressure of solutions of a number of substances at
different concentrations, and at different temperatures. A
few of the results which he obtained are given.

Osmotic Pressure for Cane-Sugar of Different Concentration

Pbrcbntagb Concby

Wbight %

Osmotic Prbssukb

I.O

S3S "a«*-

2.0

1016 mm.

2.74

15 18 mm.

4.0

2082 mm.

6.0

3075 mm.

Effect of Temperature on Osmotic Pressure

The following results were obtained with a i per cent
solution pf cane-sugar : —

Tbmpbraturb Prbssurb

(

14.2 C. 510 mm.

32.0** C. 544 mm.

6.8** C. 505 mm.

13.7** C. 525 mm.

.22.0** C. 548 mm.

{

1 5-5** C. 520 mm.

36.0** C. 567 mm.

These are a very few of the results which were recorded
by Pfeffer.

This investigation was undertaken , by Pf eflFer purely
from the standpoint of vegetable physiology, and with no

THEORY OF ELECTROLYTIC DISSOCIATION "^^J

idea of throwing light on any physical-chemical problem.
His work was completed and published in 1877. From
the botanical standpoint it was a contribution of the very
highest value. Pfeffer did not point out any bearing
which his results might have on problems such as those
with which we are now about to deal. Indeed, their sig-
nificance was not seen until nearly ten years later, when
van't Hoff showed that this work of PfefFer marked the
beginning of a new era in physical chemistry. .

RELATIONS BETWEEN OSMOTIC PRESSURE AND GAS PRESSURE

DISCOVERED BY VAN'T HOFF

Historical. — In following up the discovery of a great
generalization, it is always of interest to trace the stages
by which it was reached. We are very fortunate in this
case, since van't Hoff himself has given us an account
of the development of the ideas which' led him to the
discovery of the relations between osmotic pressure and
gas pressure. In the winter of 1894, he was invited by
the German Chemical Society to give a lecture on his
physical chemical investigations. He chose for his theme,
" How the Theory of Solutions Arose," and here we find
a detailed statement of the steps which led to his discov-
ery. This lecture is published in full in the Berichte der
deutschen chemischen Gesellschafty 27, 6 (1894). A few
pages from this lecture are given, since it contains a con-
cise statement of the facts which are of such unusual
interest in this connection.

' " It was when I first began to think on chemical matters,
under the guidance of Kekul^ and Wislicenus, that the ideas
.about the position of atoms in space began to germinate.

78 ELECTROLYTIC DISSOCIATION

" The entire ' Arrangement of Atoms in Space * was, in-
deed, only a structure which depended upon the relation
of a physical property — optical activity — to chemical
constitution.

" Although so young, I wished then to know, also, the
relations between constitution and chemical properties.
The constitution formula should, indeed, be the expression
of the entire chemical behavior.

"Thus arose my * Ansichten iiber die organische Chemie,*
with which, indeed, you are not familiar, and which is
scarcely worth knowing. It had this value, however, for
me, that it pointed out, very clearly, the existence of a gap.

" Let us take an example : —

" It is known that oxygen in organic compbunds has an
accelerating action on almost all transformations. The
oxidation of CH^ is more difficult than of CHgOH, etc.

" To obtain relations of value in this connection, there is
need of accurate knowledge of the velocity with which a
reaction proceeds, and thus I began the study of the
velocity of reactions, and there appeared my * Etudes de
Dynamique Chimique.*

" Reaction velocity was at first the chief aim, but chemi-
cal equilibrium was closely associated with it. Equilibrium
resting, on the one hand, on the equality of two opposite
reactions, and procuring a firm support, on the othier,
through its connection with thermodynamics. You see
how, to obtain my object, I was ever led farther from
it, which often occurs.

"And I must go still farther ; for the question of equilib-
rium borders directly on the problem of affinity, and I was
thus concerned with the very simple affinity phenomenon

THEORY OF ELECTROLYllC DISSOCIATION 79

— at first with that which expresses itself as an attraction
for water.

" Mitscherlich had already raised the question, in his
* Text-book of Chemistry' (4th edition, 1844, 565), as to
the magnitude of the attractive force which holds the
water of crystallization in Glauber salts. He saw a means
of measuring this in the diminished tension of the water of
crystallization.

" * If Glauber salt is brought into the barometric vacuum
at 9°, the mercury falls about 2J lines (5.45 mm.), due to
the liberation of water-vapor. Water itself produces, on
the other hand, a fall of 4 lines (8.72 mm.). The affinity
of the sodium sulphate for its water of crystallization cor-
responds, therefore, to the difference, i J lines (3.27 mm.),
i,e. about ^^ kg. per square inch.'

" This value, 5-J^ of an atmosphere, appeared to me as
small without precedent, for I had the impression that
even the weakest chemical forces are very laige, as
appeared to me to follow also from Helmholtz's Faraday
Lecture. Thus, the question arose, whether it is not pos-
sible, in simpler cases, to measure this attraction for water
in a more direct way; and for this purpose the aqueous
solution is the simplest conceivable — much simpler than
the compound containing water of crystallization.

" Coming from the laboratory with this question vividly in
mind, I met my colleague De Vries and his wife. He was
just at that time carrying out osmotic investigations, and
he told me about Pfeffer's determinations.

" You recognize the apparatus sketched here. The so-
called osmotic pressure is measured with a battery cell,
whose wall is made semipermeable, i,e. permeable only

ELECTROLYTIC DISSOaATlON

to water, but not to the dissolved substance, e,g, sugar — .
by the method of Traube. This is accomplished by deposit-

MITSCH

ERLICH

PFEF

FER

Fig. 4.

ing a membrane of copper f errocyanide within the walls of
the porcelain cell. The osmotic pressure of a one per cent
solution of cane-sugar is two-thirds of an atmosphere.

" This pressure was remarkably large in comparison with
that described by Mitscherlich, and yet a relation exists
between the two.

" Let us consider the sugar solution as placed below, on
the left side, and separated by means of a semipermeable
membrane from water which is on the right side below.
The movement of the water is to the left, into the space
containing vapor with the pressure observed by Mitscher-
lich, into the water with that observed by Pfeffer.

" A calculation can be based directly upon this relation.
The force described by Mitscherlich is very small, because
it acts on the more dilute vapor ; that of Pfeffer is large,
because it acts on the concentrated water. Therefore : —

THEORY OF ELECTROLYTIC DISSOCIATION 8 1

Pfeffer : Mitscherlich = looo : -^0.08056— (i +-^/),

760 2 273 '

and thus Pfeffer's force, calculated from the decrease in
tension (freezing-point) : —

Tbmpbraturb Osmotic Prbssukb 0.00039 T

d.'^'* 0.664 0.668

15.5° 0,684 0.689

22** 0.721 0.704

32** 0.716 0.728

S^"" 0.746 0.737

The above proportiqnality is, however, not perfectly
rigid. The exact formula is obtained, in case the work
which the water attraction can perform is chosen as the
starting-point. This is independent of whether the water
is carried over as such, or as vapor ; and thus we have the
relation (for 18 kgs. water): —

Pi 323

in which p^ and // are, respectively, the tension of the
water and of the solution, P the osmotic pressure in kgs.
per qm., and Fthe volume of 18 kgs. of water in cbm.

" This formula corresponds very accurately with Pf effer's
results, but it can be used for determining pressure only
in case the tension /; is known ; and thus Mitscherlich's
question of water of crystallization is also solved, since
it is evident that this water attraction corresponds to that
of a solution of equal maximum tension. We have then
the following : —

82 ELECTROLYTIC DISSOCIATION

Substance

Tbmpbraturb

PRBSSURK

Na2S04.ioH20

9°

600 atmos.

FeS04. 7H2O

25°

510 atmos.

reS04 . 7 H2O

65°

245 atmos.

CUSO4 . 5 HjO

50°

1 100 atmos.

CUSO4 . 3 H2O

—

1 730 atmos.

" This means that if NajSO^ should be prevented from
taking up its water by pressure, in a suitable manner, —
say in Pf effer's apparatus, — 600 atmospheres at 9° would
be necessary and sufficient.

"We must now turn from Mitscherlich's question of affin-
ity to dilute solutions; since where we are dealing with the
union of water of crystallization. It is obvious that enor-
mous concentrations obtain."

We see from the above paragraphs, the exact stages by
which van't Hofif arrived at the study of dilute solutions
from the standpoint of osmotic pressure. From the posi-
tion of atoms in space, he was led to study reaction velocity,
and from this the conditions of equilibrium. But closely
connected with the problem of equilibrium was that of
affinity. He took up, as an example of affinity, the attrac-
tion of salts for their water of crystallization, and sought
to measure this more directly than had been done. This
led him, through the suggestion of De Vries, directly to
Pfeffer's osmotic investigations. Having dealt with con-
centrated solutions, he then turned to dilute ; and we shall
now learn the nature of the results which he obtained, by
comparing the gas pressure of gases with the osmotic
pressure of dilute solutions.

Boyle's Law for Dilute Solutions. — In 1887 van't Hoff
published a paper in the first volume of the Zeitschrift

THEORY OF ELECTROLYTIC DISSOCIATION 83

fiir physikalische Chemie, under the title, " The R61e of
Osmotic Pressure in the Analogy between Solutions and
Gases." ^ The object of this communication, as its title im-
plies, is to point out certain relations between the gas press-
ure of gases and the osmotic pressure of dilute solutions. To
quote from the translation in Harper's Science Series : —

" The analogy between dilute solutions and gases acquires
at once a more quantitative form, if we consider that in
both cases the change in concentration exerts a similar
influence on the pressure ; and, indeed, the values in ques-
tion are, in both cases, proportional to one another.

" This proportionality, which, for gases, is designated as
Boyle's law, can be showa for osmotic pressure, experi-
mentally from data already at hand, and also theoretically."

Van't Hoff then gives enough of Pfeffer's data to show
experimentally, that there is proportionality between os-
motic pressure and concentration.

" Let us first give the results of Pfeffer's determinations
of osmotic pressure (P), in solutions of sugar, at the same
temperature (13.2® to 16.1*^) and different concentrations

P
C

535 mm.

S35

1016 mm.

508

2.74%

15 18 mm.

554

4% •

2082 mm.

521

3075 mm.

513

p .
"The nearly constant value of— indicates that, in fact, a

proportionality between pressure and concentration exists."^

1 Ztschr. phys. Chem., i, 481. Translated into English by H. C. Jones. Har-
per's Science Series, IV, p. 13.

2 Harper's Science Series, IV, p. 16.

84 ELECTROLYTIC DISSOCIATION

The work of De Vries^ is then cited, as furnishing a
second line of experimental evidence, of the applicability of
Boyle's law to the osmotic pressure of dilute solution. De
Vries compared the osmotic pressure of solutions of sugar,
potassium nitrate, and potassium sulphate, with that of the
contents of a plant cell, whose protoplasmic sac contracts
when the cell is introduced into a solution which has
stronger attraction for water. It was found that equal
changes in concentration of solutions of sugar, potassium
nitrate, and potassium sulphate, exert the same influence
on the osmotic pressure. The experimental evidence was
thus very strongly in favor of the law of Boyle for the
osmotic pressure of solutions.

A theoretical demonstration of this law for solutions was
also given by van't Hoff :^ —

Gay Lussac's Law for Dilute Solutions. — Having found
that the law of Boyle for gases applies to the osmotic
pressure of solutions, one would naturally inquire whether
other gas laws also apply to solutions. Thus, the attempt
was made to apply to the osmotic pressure of solutions
the law of Gay Lussac, which holds for the tempera-
ture coefficient of gas pressure. The law was tested
both experimentally and theoretically on thermodynamic
grounds.

For experimental demonstration, recourse was had again
to the results of Pfeffer's investigations. This investiga-
tor found that the osmotic pressure always increased with
rise in temperature. If from one of two experiments
carried out with the same solution at different tempera-

1 " Eine Methode zur Analyse der Turgorkraft," Pringsheim's Jahrb., 14.
8 See Harper's Science Series, IV, 17.

THEORY OF ELECTROLYTIC DISSOCIATION 85

tures we calculate the result of the other, on the assump-
tion of Gay Lussac's law, and compare it with the value
directly obtained, we have the following relations: —

1. Solution of cane-sugar.^

At 32** a pressure of 544 mm. was observed.
At 14.15*' the calculated pressure is 512 mm., instead of
510 as found by experiment.

2. Solution of cane-sugar.

At 36"* the pressure observed was 567 mm.
At is.s"* the calculated pressure is 529 mm., instead of
520.5 mm. as found experimentally.

3. Solution of sodium tartrate.

At 37.3** the pressure observed was 983 mm.

At 13.3° the calculated pressure is 907 mm., instead of
908 found by experiment.

There is evidently a close approximation, in the above
results, between the observed and calculated values.

The law of Gay Lussac, as applied to the osmotic press-
ure of solutions, received further experimental support
from the work of Bonders and Hamburger.^ They
worked with animal cells (blood corpuscles) in a manner
similar to De Vries. They found that solutions of potas-
sium nitratp, sodium chloride, and sugar, which have the
same osmotic pressure as the contents of the cells in ques-
tion, at o**, and therefore the same as one another, show
exactly the same relation at 34^ i.e. all have the same
osmotic pressure at this higher temperature.

This shows that the temperature coefficient of osmotic

1 Harper's Science Series, IV, p. 19.

3 Onderzoekingen gedaan in het physiologisth, Laboratorium der Utrechtsche
lloogeschool [3],9, 26. '

86 ELECTROLYTIC DISSOCIATION

pressure for solutions of these three substances is the
same; and, taken with Pfeffer's results, is strong evi-
dence in favor of the law of Gay Lussac as applied to
solutions.

Experimental Evidence in Favor of both the Laws of
Boyle and Gay Lussac for Solutions. — It was observed by
Soret,^ that if a homogeneous solution is pla(ied in a tube,
and the top of the tube kept warmer than the bottom,
the solution will not remain homogeneous, but will become
more concentrated in the colder portion. This is exactly
analogous to what would occur with a gas; the colder
portion would become more concentrated. The experi-
ments were made by Soret in vertical tubes, the upper
portions of which were warmed to a constant temperature,
and the lower portions cooled to a constant temperature.
It was soon found, as would be expected, that the time
required to establish equilibrium was much greater for
solutions than for gases.

How does the " Principle of Soret " throw any light on
the applicability of the laws of Boyle and Gay Lussac to
solutions ? A gas will always distribute itself in a space
so that the gas pressure is the same at every point in the
space. If one portion of the space is colder than another,
the gas pressure of any given molecule in this portion
will be less than in the warmer portion ; therefore, more
gas particles must collect in the colder portion, to give the
same pressure as in the warmer portion of the tube.

Similarly, with solutions, the dissolved substance will
distribute itself throughout the solvent, so that the osmotic
pressure is the same at every point in the solution. If

1 Archives des Sciences Phys. et Nat. [3], 2, 48; Ann. Chim. Phys. [5], 22, 293.

THEORY OF ELECTROLYTIC DISSOOATION 87

one part of the solution is colder than another, a dissolved
particle will exert less osmotic pressure where the solution
is colder. It will, therefore, require more particles in the
colder region, to exert a given pressure, than in the warmer
region. We can calculate the change in concentration of
a gas with change in temperature, from the laws of Boyle
and Gay Lussac. Similarly, if the laws of Boyle and Gay
Lussac apply to the osmotic pressure of solutions, we can
calculate the difference in concentrations between the
colder and warmer parts of a solution, for a given differ-
ence in the temperature of these two regions. Then, the
difference in the concentrations of the two parts can be
determined experimentally, and the calculated results com-
pared with the results of experiment.

This has been done for solutions of copper sulphate,
and the following results are given by van*t Hoff : —

1. Solution of copper sulphate.

The part cooled to 20° contained 17.332 per cent. The
concentration calculated for 80°, is 14.3 per cent. That
found experimentally was 14.03 per cent.

2. Solution of copper sulphate.

The part cooled to 20° contained 29.867 per cent. 24.8
per cent was calculated for 80*^, while 23.871 per cent was
found.

It should be observed, that the results found by experi-
ment are slightly lower than those calculated on the basis
of the laws of Boyle and Gay Lussac, yet the difference is
only slight. It must, however, be stated in this connection,
that it has been shown that the time required to establish
equilibrium in a solution is much greater than was formerly
supposed, and in the earlier experiments not enough time

88 ELECTROLYTIC DISSCOATION

was allowed for the final equilibrium to be reached. Con-
sequently, the difference in concentration between the
colder and the warmer portions of the tube, as found by
experiment, was less than the calculated, since the latter
was based on perfect equilibrium having been reached.
More recent experiments, in which the tubes have been
allowed to stand for several months, give results which
agree very closely with the calculated, and thus the " Prin-
ciple of Soret" is a strong experimental support, to the
applicability of the laws of Boyle and Gay Lussac to the
osmotic pressure of dilute solutions.

Avogadro's Law for Dilute Solutions. — It has been
shown, thus far, that the osmotic pressure of solutions is
proportional to the concentration, and, also, that the tem-
perature coefficient of osmotic pressure is the same as that
of gas pressure. In a word, gas pressure and osmotic
pressure are analogous, both obeying the laws of Boyle
and G^y Lussac.

The more important question, however, still remains:
What is the relation between the actual osmotic pressure
exerted by a dissolved particle, and the gas pressure of a
gaseous particle, under the same conditions of temperature
and concentration.? Van't Hoff answered this question
both experimentally and theoretically.

He found in Pfeffer's determinations of the osmotic
pressure of cane-sugar, an experimental solution of this
problem. The osmotic pressure of a sugar solution of
known concentration was compared with the gas pressure
of hydrogen gas, containing the same number of particles
in a given space. A i per cent solution of sugar was
used. Hydrogen of the same concentration would con-

THEORY OF ELECTROLYTIC DISSOCIATION 89

tain ^j X ID grams per litre, i,e, 0.0581 gram per litre.
Since hydrogen at 0° and atmospheric pressure weighs
0.08956 gram per litre, hydrogen under the above condi-
tions would exert a pressure of -^— ^ atmosphere at o^

^ 0.08956 ^ '

qr 0.649 atmosphere; and at t^ of 0.649(1 +0.00367/)
atmosphere.

Comparing this at different temperatures with Pfeffer's
results, we have : — :

PBRATURB

Osmotic Prbrsurb

Gas Prbssurb
0.649(1-1-0.00367/)

6.8

0.664

0.665

137

0.691

0.681

14.2

0.671

0.682

15s

0.684

0.686

22.0

0.721

0.701

32.0

0.716

0.725

36.0

0.746

0.735

These results suffice to bring out the relation, that the
osmotic pressure of a solution of sugar at a given tem-
perature is exactly equal to the gas pressure of a gas, which
contains the same number of molecules in a given volume
as there are sugar molecules in the same volume of the
solution.

This relation has been found to hold for such a large
number of substances, that we are led to the all-important
generalization : that the osmotic pressure of a dissolved
particle is exactly equal to the gas pressure of a gaseous
particle at the same temperature and concentration.

The law of Avogadro, applied to gases, states that equal
volumes of all gases, at the same temperature and pressure,
contain the same number of ultimate particles.

90 ELECTROLYTIC DISSOCIATION

The law of Avogadro, as applied to solutions, states that
solutions which, at the same temperature, have the same
osmotic pressure, contain in a given volume the same num-
ber of dissolved particles.

Van't Hoff has shown that the law of Avogadro, as
applied to solutions, is confirmed also by the lowering of
the vapor-tension, and of the freezing-point of the solvent,
produced by the dissolved substance.

He has also given a thermodynamic demonstration of
the law.^

General Expression of the Laws of Boyle, Oay Lussac,
and Avogadro, for Solutions and Gases. — Having shown
that the three laws of gas pressure apply to the osmotic
pressure of solutions, van't Hoff attempted to furnish a
general expression for these three laws. "The well-
known formula, which expresses for gases the two laws of
Boyle and Gay Lussac : —

PV=RT,

is now, where the laws referred to are also applicable to
liquids, valid also for solutions, if we are dealing with the
osmotic pressure. This holds even with the same limita-
tion, which is also to be considered with gases, that the
dilution shall be sufficiently great to iallow one to disre-
gard the reciprocal action of, and the space taken by, the
dissolved particles.

"If we wish to include in the above expression also the
third, the law of Avogadro, this can be done in an exceed-
ingly simple manner, following the suggestion of Horst-
mann,^ considering always kilogram molecules of the

1 See Harper's Science Series, IV, 22. 2 Bar. d. chem. GeselL, 14, 1243.

THEORY OF ELECTROLYTIC DISSOCIATION 91

substance in question; thus, 2 k. hydrogen, 44 k. carbon
dioxide, etc. Then R in the above equation has the same
value for all gases, since, at the same temperature and
pressure, the quantities mentioned occupy also the same
volume. If this value is calculated, and the volume taken
in Mr^y the pressure in A'® per Mr\ and if, for example,
hydrogen at 0° and atmospheric pressure is chosen: —

^= '°333. v= ^^, r= 273. R = 845.05.

The combined expression of the laws of Boyle, Gay
Lussac, and Avogadro is then : —

p F= 84s r,

and, in this form, it refers not only to gases, but to all solu-
tions, P being then always taken as osmotic pressure."^
The conclusion from what has thus far been given of
van't Hoff's paper is that the three laws of gas pressure
apply directly to the osmotic pressure of solutions, and
this is perfectly general for solutions such as we have been
considering. But there are many exceptions, and these
are of even more interest than the cases which conform to
the laws of gas pressure.

Exceptions to the General Applicability of the Gas Laws
to Osmotic Pressure. — While the osmotic pressures of
solutions of compounds like cane-sugar conform to the
gas laws, the osmotic pressures of large classes of chemical
substances do not conform to these laws. The excep-
tions include all the acidSy all the bases^ and all the salts.
If we will consider the number of compounds contained in

1 Harper's Science Series, IV, 24.

92 ELECTROLYTIC DISSOCIATION

these three classes, it is a question whether the exceptions
will not outnumber the cases which conform to rule.

All of these compounds give an osmotic pressure y which
is greater than would be expected from the gas laws.

The expression PV—RT no longer applies to the
osmotic pressure of these substances, and, therefore, a
coefficient was introduced by van't Hoff ; when the expres-
sion became : —

PV^iRT.

This coefficient, which for acids, bases, and salts is always
greater than unity, has come to be known as the " van't
Hoff iy What was the real physical or chemical signifi-
cance of these exceptions? Why does a large class of
compounds show an osmotic pressure which conforms to
the gas laws, and yet a very large class give an osmotic
pressure which is always too great ?

Van't Hoff saw clearly the discrepancy which existed
here, as will be seen from his own words: " If we are still
considering * ideal solutions,' a class of phenomena must be
dealt with which, from the now clearly demonstrated
analogy between solutions and gases, are to be classed
with the earlier so-called deviations from Avogadro's law.
As the pressure of the vapor of ammonium chloride, for
example, was too great in terms of this law, so, also, in a
large number of cases, the osmotic pressure is abnormally
large, and in the first case, as was afterwards shown, there
is a breaking down into hydrochloric acid and ammonia, so,
also, with solutions, we would naturally conjecture that, in
such cases, a similar decomposition had taken place. Yet
it must be conceded that anomalies of this kind, existing

THEORY OF ELECTROLYTIC DISSOCIATION 93

in solutions, are much more numerous, and appear with
substances which it is difficult to assume break down in
the usual way. Examples in aqueous solutions are most of
the salts, the strong acids, and the strong bases. ... It
may then have appeared daring to give Avogadro's law
for solutions such a prominent place, and I should not
have done so, had not Arrhenius pointed out to me, by
letter, the probability that salts and analogous substances,
when in solution, break down into ions." ^

The last sentence gives us the connecting link between
the generalization reached by van't Hoff, and the discovery
of the theory of electrolytic dissociation. The latter we
owe to the Swedish physicist, Arrhenius, to whose work we
will now turn.

ON THE DISSOCIATION OF SUBSTANCES DISSOLVED IN WATER

BY SVANTE ARRHENIUS

A paper,^ under the above title, appeared in the same
volume of the Zeitschrift fur physikalische Chemicy as the
paper by van*t Hoff which we have just considered.
Arrhenius was impressed by the generalizations reached
by van*t Hoff, and especially by the large number of
exceptions. This will be seen best by quoting the words
with which Arrhenius began his paper.

"In a paper submitted to the Swedish Academy of
Sciences, on the 14th of October, 1885, van't Hoff proved
experimentally, as well as theoretically, the following un-
usually significant generalization of Avogadro's law : —

1 Harper's Science Series, IV, 34.

2 Ztschr. phys. Chem., i, 631 (1887). Translated into English by H. C. Jones.
Harper's Science Series, IV, 47.

94 ELECTROLYTIC DISSOCIATION

"The pressure which a gas exerts at a given temperature,
if a definite number of molecules is contained in a definite
volume, is equal to the osmotic pressure which is produced
by most substances under the same conditions, if they are
dissolved in any given liquid." ^

"Van't Hoff has proved this law in a manner which
scarcely leaves any doubt as to its absolute correctness.
But a difficulty which still remains to be overcome, is that
the law in question holds only for *most substances,' a
very considerable number of the aqueous solutions investi-
gated furnishing exceptions; and in the sense that they
exert a much greater osmotic pressure than would be
required from the law referred to."

The above are the words with which Arrhenius stated
the problem; we will now follow the line of thought which
led him to its solution.

" If a gas shows such a deviation from the law of Avo-
gadro, it is explained by assuming that the gas is in a state
of dissociation. The conduct of chlorine, bromine, and
iodine, at higher temperatures, is a very well-known
example. We regard these substances, under such con-
ditions, as broken down into simple atoms.

"The same expedient may, of course, be made use of to
explain the exceptions to van*t Hoff*s law; but it has not
been put forward up to the present, probably on account
of the newness of the subject, the many exceptions known,
and the vigorous objections which would be raised from
the chemical side to such an explanation. The purpose
of the following lines is to show that such an assumption,

1 Van't Hoff, Unc propri6t6 g6n6rale de la matifere dilute, p. 43. Sv. Vet-ak-s
Handlingar, 21, Nr. 17, 1886.

THEORY OF ELECTROLYTIC DISSOCIATION 95

of the dissociation of certain substances dissolved in water,
is strongly supported by the conclusions drawn from the
electrical properties of the same substances, and that, also,
the objections to it from the chemical side are diminished
on more careful examination." ^

Arrhenius then offers his explanation of the exceptions
to van't Hoff's generalization. As we shall see, he goes
back to the theory put forward by Clausius to account for
electrolysis, and which has already been considered, in con-
nection with the development of electrochemistry (p. 48).

" In order to explain the electrical phenomena, we must
assume with Clausius,^ that some of the molecules of an
electrolyte are dissociated into their ions, which move inde-
pendent of one another. But since the * osmotic pressure *
which a substance dissolved in a liquid exerts against the
walls of the confining vessel must be regarded, in accord-
ance with the modem kinetic view, as produced by the
impacts of the smallest parts of this substance, as they
move against the walls of the vessel, we must therefore
assume, in accordance with this view, that a molecule dis-
sociated in the manner given above, exercises as great a
pressure against the walls of the vessel as its ions would do
in the free condition. If, then, we could calculate what
fraction of the molecules of an electrolyte is dissociated
into ions, we should be able to calculate the osmotic press-
ure from van*t HofFs law.'* ^

We see from the above, that the simple qualitative sug-
gestion, that some molecules are broken down into parts or

1 Harper's Science Series. IV, 48.

* Pogg. Ann., loi, 347 ; Wied. Elektr., 2, 941.

s Harper's Science Series, IV. 48.

96 ELECTROLYTIC DISSOCIATION

ions, is not new with Arrhenius. This theory, as already
stated, had been advanced some thirty years before by
Clausius. The new feature, which was introduced by
Arrhenius, was to point out a method of determining just
what per cent of the molecules are broken down into ions.
The merely qualitative suggestion of Clausius was thus
converted into a definite theory, which could be tested
experimentally. The method of calculating the amount of
dissociation into ions, as worked out by Arrhenius, will
now be given in his own words.

"In a former communication, *0n the Electrical Con-
ductivity of Electrolytes,' I have designated those mole-
cules, whose ions are independent of one another in their
movements, as active; the remaining molecules, whose ions
are firmly combined with one another, as inactive. I have
also maintained it as probable, that in extreme dilution, all
the inactive molecules of an electrolyte are transformed
into active.^ This assumption I will make the basis of the
calculations now to be carried out. I have designated the
relation between the number of active molecules, and the
sum of the active and inactive molecules, as the activity
coefficient.^ The activity coefficient of an electrolyte at
infinite dilution is therefore taken as unity. For smaller
dilution it is less than onCy and from the principles estab-
lished in my work already cited, it can be regarded as equal
to the ratio of the actual molecular conductivity of the
solution, to the maximum limiting value which the mo-
lecular conductivity of the same solution approaches with

^Bihang der Stockholmer Akadtmie^ 8, Nr. 13 and 14, d TL, pp. 5 and 13;
I Tl., p. 6.

a Loc, cU., 2 Tl., p. 5.

THEORY OF ELECTROLYTIC DISSOCIATION 97

increasing dilution. This obtains for solutions which are
not too concentrated {i.e, for solutions in which disturbing
conditions, such as internal friction, etc., can be disre-
garded). If this activity coefficient (a) is known, we can
calculate, as follows, the values of the' coefficient /, tabu-
lated by van't Hoff •: i is the relation between the osmotic
pressure actually exerted by a substance, and the osmotic
pressure which it would e^ert, if it consisted only of inac-
tive (undissociated) molecules, i is evidently equal to the
sum of the number of inactive molecules, plus the number
of ions, divided by the sum of the inactive and active
molecules. If, then, m represents the number of inactive,
and n the number of active, molecules, and k the number
of ions into which every active molecule dissociates {e.g.^
k = 2 ior KCl, i.e. K and CI ; ^ = 3 f or BaClg and KjSO^,
i.e, Ba, CI, CI, and K, K, SO4), then we have : —

m -{• kn

t =

m -{• n

" But since the activity coefficient (a) can, evidently, be
n

wntten

Arrhenius thus shows how it is possible to calculate the
value of the van*t Hoff coefficient /, knowing the activity
coefficient (a), which can be determined directly from the
conductivity of the solution.

He then shows how the value of i can be calculated also
from the lowering of the freezing-point of water produced
by the dissolved substance.

1 Harper's Science Series, IV, 48,
H

98 ELECTROLYTIC DISSOCIATION

" On the other hand, i can be calculated as follows, from
the results of Raoult*s experiments on the freezing-point
of solutions, making use of the principles stated by van't
Hoff. The lowering (/) of the freezing-point of water (in
degrees Celsius), produced by dissolving a gram-mole-
cule of the given substance in one litre of water, is divided

by 18.5:— ^ „j

^ = -- —

18.5

Arrhenius then compared the values of /, calculated
from the conductivity of solution, with the values calcu-
lated from the freezing-point lowerings, to see whether the
two series would agree with one another. He made the
comparison for a large number of bases, acids, and salts,
and also for a number of organic compounds, where the
value of i is unity. A few examples from each class of
compounds will be given, since it is a matter of the very
greatest importance to determine whether the two values
of / agree. If they do, the theory just advanced is made
quite probable. If they do not, it is almost a conclusive
argument against the correctness of the theory.

Basks

Substance

X8.5

/«x+(*-i)«

Barium hydroxide,

Ba(OH)a

2.69

2.67

Strontium hydroxide,

Sr(OH),

2.61

2.72

Calcium hydroxide,

Ca(0H)8

2.59

2-59

Sodium hydroxide.

NaOH

1.96

1.88

Potassium hydroxide.

KOH

1.91

1-93

Ammonia,

NH3

1.03

1. 01

Methylamine,

CHsNHa

1. 00

1.03

Trimethylamine,

(CH3)3N

1.09

1.03

Ethylamine,

C2H5NH,

1. 00

1.04

Aniline,

CeH^NH,

0.83

I.OO

1 Harper's Science Series, IV, 49.

THEORY OF ELECTROLYTIC DISSOCIATION

Acros

Hydrochloric acid,

HCl

1.98

1.90

Hydrobromic acid,

HBr

2.03

1.94

Nitric acid.

HNO3

1.94

1.92

Chloric acid,

HCIO,

1.97

1.91

Sulphuric acid.

H2SO4

2.06

2.19

Sulphurous acid.

HjSOs

1.03

1.28

Formic acid,

HCOOH

1.04

1.03

Acetic acid,

CHsCOOH

1.03

1. 01

Tartanc acid.

C4HeO«

1.05

I. II

Malic acid.

C4He05

1.08

1.07

Lactic acid.

CsHeOa

1. 01

1.03

Salts

SUBSTAMCB

Potassium chloride,
Sodium chloride,
Ammonium chloride.
Potassium cyanide.
Potassium nitrate.
Potassium acetate,
Silver nitrate,
Potassium sulphate.
Ammonium sulphate.
Barium chloride,
Strontium chloride.
Calcium chloride,
Barium nitrate,
Strontium nitrate,
Calcium nitrate,
Mercuric chloride,
Cadmium nitrate.

'■J.,

««!+(*- i)a

1.82

1.86

NaCl

1.90

1.82

NH4CI

1.88

1.84

KCN

1.74

1.88

KNO,

1.67

1.81

CHjCOOK

1.86

1.83

AgNO,

1.60

1.86

K^,

2. II

2-33

(NH4)^4

2.00

2.17

BaCl,

2.63

2.54

SrCl,

2.76

2.50

CaCIj

2.70

2.50

Ba(NO,),

2.19

2-13

Sr(N03).

2.23

Ca(NO,),

2.02

2-33

HgCl,

I. II

1.05

Cd(NO,),

2.32

2.46

* ' • •

* • ••• ••• •• *«

* • • •• *• *':••

* • • • • • •

100 ELECTROLYTIC DISSOCL^TION

Organic Compounds

Methyl alcohol,

CH4O

0.94

1. 00

Ethyl alcohol,

CjHeO

0.94

I.OO

Butyl alcohol,

C4Hm,0

0-93

1. 00

Mannite,

C6H14O6

0.97

1. 00

Invert sugar,

CeH^Oe

1.04

1. 00

Cane-sugar,

C12H21O11

1. 00

Phenol,

CeHeO

0.84

1. 00

Acetone,

CsHeO

0.92

1. 00

That there is a general agreement between the two val-
ues of i, in the above tables, is evident. That there are
some discrepancies, is just what would be expected, from
the experimental errors contained in both the freezing-
point and the conductivity methods. It must be further
borne in mind, that the freezing-point method was very
imperfectly developed when the above determinations were
made. :

Another cause of these discrepancies was pointed out
by Arrhenius, as follows : —

" There is one condition which interferes, possibly very
seriously, with directly comparing the figures in the last
two columns ; namely, that the values really hold for differ-
ent temperatures. All the figures in next to the last col-
umn hold, indeed, for temperatures only a very little below
0° C, since they were obtained from experiments on in-
considerable lowerings of the freezing-point of water. On
the other hand, the figures of the last column for acids and
bases (Ostwald's experiments) hold at 2$^, the others at
18°. The figures of the last column for non-coaductors
hold, of course, also at 0° C, since these substances, at this

• • • * " **
• • • * *

THEORY OF ELECTROLYTIC DISSOCIATION lOI

temperature, do not consist, to any appreciable extent, of
dissociated (active) molecules.*' ^

Arrhenius then refers to the general agreement between
the two sets of values in the following terms : —

"An especially marked parallelism appears, beyond
doubt, on comparing the figures in the last two columns.
This shows a posteriori^ that in all probability the assump-
tions on which I have based the calculation of these figures
are, in the main, correct. These assumptions were.: —

"I. That van't Hoff's law holds not only for most, but
for ally substances, even for those which have hitherto been
regarded as exceptions (electrolytes in aqueous solution).

" 2. That every electrolyte (in aqueous solution) consists
partly of active, (in chemical and electrical relation) and
partly of inactive, molecules, the latter passing into active
molecules on increasing the dilution, so that in infinitely
dilute solutions only active molecules exist. Arrhenius
then calls attention to the difference between the kind of
dissociation indicated here, and that shown when a vapor-
like ammonium chloride dissociates by heat.

" Although the dissolved substance exercises an osmotic
pressure against the wall of the vessel, just as if it were
partly dissociated into its ions, yet the dissociation with
which we are here dealing is not exactly the same as that
which exists when, e,g,y an ammonium salt is decomposed
at a higher temperature. The products of dissociation in
the first case (the ions) are charged with very large quan-
tities of electricity, of opposite kind, whence certain condi-
tions appear (the incompressibility of electricity), from
which it follows that the ions cannot be separated from

l.Harper's Science Series, IV, 54.

102 ELECTROLYTIC DISSOCIATION

one another to any great extent without a large expendi-
ture of energy. On the contrary, in ordinary dissociation,
where no such conditions exist, the products of dissociation
can, in general, be separated from one another.*' ^

Although Arrhenius pointed out, so clearly, the charac-
teristic feature of the dissociation which he believed elec-
trolytes to undergo in the presence of water, namely, that
the products of dissociation were charged, the one always
positively, the other always negatively, yet this has often
been overlooked.

Summary. — In concluding this chapter, we will briefly
recall the steps which led to the theory of electrolytic dis-
sociation. The stages by which van't Hoff passed from
the study of the position of atoms in space to Pfeffer's
work on osmotic pressure have been followed in detail.
Van't Hoff showed, from Pfeffer's results, and also theoreti-
cally, that the laws of Boyle, Gay Lussac, and Avogadro,
for gas pressure, apply to the osmotic pressure of solutions.

But these apply only to solutions of non-electrolytes, i,e,
substances which, when in the presence of water, do not
conduct the current. All electrolytes, i,e, the acids, bases,
and salts, are exceptions, showing greater osmotic pressure
than would accord with the laws of gas pressure. To what
was this discrepancy due.? Since osmotic pressure is
proportional to the number of parts present, too great
osmotic pressure means more parts present than would
be expected.

In order that we might have more parts present than

' the molecules, it is necessary that the molecules should

undergo decomposition. How is it possible to think of

1 Harper's Science Series, IV, 54.

THEORY OF ELECTROLYTIC DISSOCIATION 103

stable molecules, such as hydrochloric acid, potassium
hydroxide, potassium chloride, suffering decomposition?
Arrhenius furnished the answer. He had resort to the
old theory proposed by Clausius, to account for electrol-
ysis, that in the presence of water the molecules are
broken down into ions. Arrhenius pointed out two ways
of calculating the amount of this dissociation, the one
based on conductivity, the other on freezing-point lower-
ing, and showed that the results from the two methods
agreed.

All of the compounds which give abnormally great
osmotic pressure, and are therefore dissociated into ions,
conduct the current when in solution in water, and are
therefore electrolytes. This kind of dissociation has come
to be known as electrolytic^ and the theory advanced by
Arrhenius as the Theory of Electrolytic Dissociation,

It is one thing to propose a theory, and another to pro-
pose a theory which is true. In the next chapter we will
consider some of the lines of evidence bearing upon the
theory of electrolytic dissociation.

CHAPTER III

£VU)BNCE BEARING UPON THE THEORY OF ELECTROLYTIC

DISSOCIATION

THE PHYSICAL PROPERTIES OF COMPLETELY DISSOCIATED

SOLUTIONS SHOULD BE ADDITIVE

A theory in science must, first of all, be capable of
experimental test. If it cannot be shown to be either true
or false, it is of little value as a scientific generalization.

Arrhenius pointed out in his first paper, that evidence
bearing upon his theory could be obtained from a study of
the physical properties of solutions, whose dissociation, in
terms of the theory, was supposed to be complete. " If a
salt (in aqueous solution) is completely broken down into
its ions, most of the properties of this salt can, of course,
be expressed as the sum of the properties of the ions; since
the ions are independent of one another in most cases, and
since every ion has therefore a characteristic property,
independent of the nature of the opposite ion with which
it occurs."

He also observed that we rarely have to do with com-
pletely dissociated solutions. Those of the salts, strong
acids, and strong bases, are dissociated only from 80 to 90
per cent, at ordinary dilutions, 2^nd the additive nature of
the properties of even such solutions would be only ap-
proximate. Another class of substances, such as mercuric

104

EVIDENCE FOR THE THEORY I OS

chloride, cadmium iodide, and all of the weak acids
and bases, organic and inorganic, are comparatively lit-
tle dissociated by water at moderate dilutions, and the
physical properties of solutions of these substances are
not those of the ions alone, but of both ions and
molecules.

The point/ in a word, is this : The physical properties of
completely dissociated solutions must be a function of the
physical properties of the ions, as there are no mole-
cules: present. Since each ion has its own specific prop-
erties, independent of the nature of the other ioni with
which it is associated, the physical properties of com-
pletely dissociated solutions must be the sum of the
physical properties of the ions in those solutions. If the
solutions are not completely dissociated, their properties
are those both of the ions and of the molecules.

We must now study the physical properties of com-
pletely dissociated solutions, and see what relations exist
between these and the physical properties of the ions which
they contain. We will take solutions of salts.

Specific Gravity of Salt Solutions. — If a salt is added
to water, the volume of the solution is different from that
of the pure solvent, and also from the sum of the volumes
of the liquid and the solid. If the resulting solution is
very dilute, the salt is completely dissociated 'into its ions.
Nernst^ has shown, from the results of J. Traube,^ that
the change in volume under such conditions is an additive
property of the ions. Given a solution containing a
gram-molecular weight of a salt whose molecular weight
is M, in m grams of water. Let the specific gravity of

1 Theoretische Chemie, p. 317. 2 Ztschr. anorg. Chem., 3, i.

toS

ELECTROLYTIC DISSOCIATION

the solution be 6", the specific gravity of water s. The
change in volume Az/, on dissolving the salt, will be: —

S s'

The following results are given : —

KCl = 26.7
KBr = 35.1
KI =45-4

JKBr -KCl =8.4 1
I NaBr - NaCl = 9.0 J

[KI -KCl =18.71
t Nal - NaCl = 18.4 J

NaCl= 17.7
NaBr = 26.7
Nal = 36.1

r KI - KBr = 10.3 1
1 Nal- NaBr = 9.4/

KCl - NaCl = 9.0
KBr - NaBr = 8.4
KI -Nal =9.3 J

These results show the additive nature of the specific
gravity of salt solutions. The difference between the
chlorine and the bromine ions is about S,y; between
chlorine and iodine 18.5; between bromine and iodine
9.8 ; while between potassium and sodium it is about 9.0.

The additive nature of the specific gravity of salt solu-
tions had, indeed, been pointed out much earlier by
Valson.^ He had shown exactly what is brought out
above: Given salt solutions of comparable concentration,
i.e. containing say a gram-molecule of the salt per litre,
the difference between the specific gravities of solutions
containing two metals combined with the same acid is
constant, whatever the nature of the acid. Similarly, the
difference between the specific gravities of two salts of
the same acid with any metal is constant, regardless of

1 Compt. rend., 73, 441 (1874).

EVIDENCE FOR THE THEORY I07

the nature of the metal. The specific gravity of a salt
solution is, then, obtained by adding to a constant number
two values, — the one for the acid, the other for the

metal. These values Valson termed " moduli " ; and he
worked out their values for a large number of elements.

Valson ^ concluded from his work, that the molecules of
salts must be completely broken down in solution. But
the evidence in favor of such a view was not strong
enough at that time to bring it into favor.

Change of Volume in Neutralization. — The change of
volume produced by neutralizing acids with bases has
been extensively studied by Ostwald.^ The solutions
contained a gram-equivalent of the acid or base, in
a kilogram, and were, therefore, not completely disso-
ciated ; so that, if the change in volume was addi
tive, it would be shown only approximately by- such
solutions.

Ostwald^ worked with nineteen acids, including the
strongest mineral acids, and some of the more strongly
dissociated organic acids. He neutralized these with the
three bases, potassium, sodium, and ammonium. A few
of his results are given, the change in volume being ex-
pressed in cubic centimetres. The differences in the hori-
zontal lines are the differences between potassium, sodium,
and ammonium, in combination with the same acid. The
differences in the vertical columns are the differences
between the different acids in combination with the same
bases, obtained by subtracting the value for the acid from
the value for nitric acid.

1 Compt. rend., 73, 441 ; 74, 103 ; 75, 1033. a Joum. prakt. Chem. [2] , 18, 353.

< Lehrb. d. allg. Chem. I, p. 788.

108 ELECTROLYTIC DISSOCIATION

Potassium Sodium Ammonium

Hydkoxidb Hydroxidb Hydroxidb

Nitric acid, 20.05 (0.28) 19.77 (26.21) — 6.44 (26.49)

(o-53) (o-53) (0-13)

Hydrochloric acid, 19.52 (0.28) 19.24 (25.81) — 6.57 (26.09)

(7.69) (7.61) (7.15)

Formic acid, 12.36 (0.20) 12.16 (25.75) —13.59 (25-95)

(10.53) (10.49) (9-82)

Acetic acid, 9.52 (0.24) 9.28 (25.54) — 16.26 (25.78)

(8.15) (8.29) (7.91)

Sulphuric acid, 11.90 (0.42) 11.48 (25.83) — 14.35 (26.25)

(11.82) ("•84) (ii«i9)

Succinic acid, 8.23 (0.30) 7.93 (25.56) — 17.63 (25.86)

•

If we take the perpendicular rows in parentheses, we find
very nearly a constant difference for the strong acids and
bases. Similarly, if we take the horizontal rows in paren-
theses, we find very nearly a constant difference. This
means that the difference of change in volume, produced
by neutralizing two different bases by a given acid, is a
constant, independent of the nature of the acid; and,
similarly, the difference of the change in volume on neu-
tralizing two different acids by a given base, is independent
of the nature of the base.

The change in volume, when acids and bases neutralize
each other, like the specific gravity of salt solutions, is,
then, an additive property, depending both upon the nature
of the acid and of the base ; and we could work out here,
as Valson has done in the case of specific gravities, the
numerical values of the constants for each constituent.

Specific Refractive Power of Salt Solutions. — Gladstone
calculated the refraction equivalents 7?, of a number of ele-
ments, from the formula : —

EVIDENCE FOR THE THEORY IO9

in which P is the weight of the substance, n the index of
refraction, and d the density. He also showed that the
refraction coefficients of salts were the sum of the refrac-
tion equivalents of the elements.

That this is true is seen from the following table of re-
sults, taken by Arrhenius ^ from the Lehrbuch of Ostwald.^
Only a few examples are given here.

HVDROGBN

Potassium

Sodium

Chloride,

14.44

(4.00)

18.44

(3.3)

15.11

(6.2)

(6.9)

{6.6)

Bromide,

20.63

(4.7)

«5-34

(3.6)

21.70

(34)

(3-5)

(3.0)

Nitrate,

17.24

(4.6)

21.80

(3.1)

i8;66

(4.0)

(S-8)

(5-4)

Acetate,

21.20

(6.4)

27.65

(3.6)

24.05

(24.0)

(300)

(26.4)

Tartrate,

45.18

(12.4)

57.60

(7-2)

50.39

The differences, both horizontally and vertically, are as
constant as could be expected, except for the two organic
acids which, at the dilutions employed, are only slightly
dissociated. This means that the different effect of potas-
sium and hydrogen, on the refraction equivalent, is con-
stant, whatever the acid with which they are combined, and
the same holds for potassium and sodium. Also, that chlo-
rine, bromine, etc., have a constant effect on the refractive
power, whether they are combined with hydrogen, potas-
sium, or sodium. In a word, the refractive power of salt

1 Ztschr. phys. Chem., i, 645. Harper's Science Series, IV, 62.

2 Lehrb. d. allg. Chem., II, p. 446.

ilO ELECTROLYTIC DISSCOATION

solutions is distinctively an additive property of the con-
stituents.

Rotatory Power of Salt Solutions. — The power possessed
by solutions of some salts to rotate the plane of polariza-
tion of light, must be a property of the optically active con-
stituent of the salt, or, if both constituents are optically
active, it must be the sum of the activities of the two.
Oudemans^ has shown that optically active bases, such as
the monacid alkaloids^ produce the same rotation, regard-
less of the nature of the optically inactive acid with which
they are combined. And optically active acids rotate the
plane of polarization, independent of the nature of the inac-
tive base combined with them. This is very well shown
by the work of Hartmann,^ on the salts of camphoric acid.

lAf

(NH,),

Na,

37-S

395

38-4

39- »

36-0

36.1

365

The rotatory power of salts of this acid is practically
constant, independent of the nature of the base combined
with it.

The Color of Salt Solutions. — The absorption which light
undergoes, in passing through a solution of a completely
dissociated substance must, in terms of our theory, be the
sum of the absorption of the cation, plus that of the anion.
If one of the ions is colorless, the absorption must be
entirely that of the other ion.

That this is qualitatively true is a matter of common
experience. We utilize the color of solutions to determine
the nature of their constituents. Thus, cupric salts in di-
lute aqueous solutions are blue, or bluish green, regardless

1 Beibl., 0, 635. > Ber. d. chem. Gesell. (1888), 221.

EVIDENCE FOR THE THEORY III

of the chemical nature of the anion with which the copper
is combined, provided that it is colorless. Likewise, the
chromates are yellow, and the salts of nickel green.

A method for determining, quantitatively, whether the
absorption of light is additive, is to prepare a number of
salts of an acid whose anion is colored, the cation being
always colorless. Then determine whether all of the salts
have the same absorption spectrum. The metallic salts
of permanganic acid are particularly well adapted to this
purpose, and they have been thoroughly studied by
Ostwald^ in this connection. These salts show five
absorption bands in the yellow and green, and four of
these have been measured by Ostwald for thirteen salts
of permanganic acid. The results are so striking, that
they are given in the following table : —

Permanganates. Absorption Bands.

i ii iii iv

Hydrogen, 2601 ± 0.5 2698 ± 0.8 • 2804 ± 0.7 2913 ± 1.7

Potassium, 2600 ± 1.3 2697 ± o.i 2803 ± 0.9 2913 ± i.i

Sodium, 2602 ± 1.2 2698 ±0.8 2803 ±0.7 2913 ±0.8

Ammonium, 2601 ± 1.3 2698 ± 1.4 2802 ± o.i 2913 ± o.i

Lithium, 2602 ± 0.2 2700 ±0.2 2804 ± 0.8 2914 ± 1.7

Barium, 2600 ± 0.9 2699 ± 0.8 2804 ± 0.6 2914 ± 1.3

Magnesium, 2602 ± 0.8 2700 ± 0.6 2802 ±0.7 2912 ± 1.8

Aluminium, 2603 ± 0.4 2699 ± 0.9 2804 ± 0.9 2914 ±0.7

Zinc, 2602 ± 0.5 2699 ± 0.7 2802 ± 1.2 2912 ± I.I

Cobalt, 2601 ±0.2 2698 ±0.1 2803 ± 0.9 2912 ±1.7

Nickel, 2603 ±0.5 2700 ±0.7 2804 ±0.7 2913 ±1.8

Cadmium, 2600 ± 0.1 2700 ± 0.2 2803 ± 0.8 2913 ± 1.4

Copper, 2602 ± 1.2 2699 ±0.1 2803 ±0.9 2913 ±0.8

1 Ztschr. phys. Chem., 9, 584.

112 ELECTROLYTIC DISSOCIATION

From these results, Ostwald concluded that the absorp-
tion spectra of the thirteen permanganates are just the
same.

A large number of other compounds were investigated/
including ten salts of fluorescein, ten of eosin yellow, ten
of eosin blue, ten of iodoeosin, ten of dinitrofluorescein,
rosolic acid, and a number of other substances. Also a
large number of cases were studied, where a colored cation
was combined with a number of colorless anions. Thus,
the salts of pararosaniline with twenty colorless acids,
and an equal number of the salts of aniline violet, were
investigated.

Ostwald studied, in all, about three hundred cases, to
determine whether the color of a solution with one colored
ion is effected at all by the presence of the colorless ion.
He concluded that salts with one and the same colored ion,
in dilute solution, always show exactly the same absorp-
tion spectra.

The elaborate investigation just considered shows con-
clusively, that the color of salt solutions is exactly the color
of the colored ion, and from this it follows, that if both
ions were colored, the color of the solution would be the
sum of the colors of the two ions. The color of salt
solutions is, therefore, an additive property.

The use of indicators in quantitative analysis is based
upon this fact. That a substance may be used as an
indicator for acids and bases, it is necessary that one of
the ions should have a different color from the molecule.
Take the case of phenolphthalem. Its alcoholic solution
is nearly colorless, and since it does not conduct the

1 Loc, cU,

EVIDENCE FOR THE THEORY 1 13

current, it is undissociated. The molecules of phenol-
phthalern are, therefore, colorless. If we add an alkali, say
sodium hydroxide, to phenolphthalelfn, the sodium salt is
formed ; but this dissociates at once into the cation sodium,
and the complex organic anion, which is deeply colored.
The characteristic color of phenolphthaleln, acting as an
indicator for an alkali, is, then, always the color of the
complex anion. If to the colored solution a little acid is
added, the original phenolphthalern is formed, and is
colorless.

Take, on the other hand, the basic indicator, cyanine;
the molecules of the free base are blue. It is a weak
base, and, therefore, but little dissociated. Add acid ; the
salt is formed, which at once dissociates. The complex
organic cation is colorless, and, hence, on adding acid, the
color due to the molecules of the free base disappears.
This is exactly the opposite of the case first considered.

Finally, take methyl orange, where the molecules are red.
Add a base, the salt is formed, and this breaks down at
once into ions. The color of the complex organic anion
is, in this case, yellow. The addition of acid, therefore,
brings out the characteristic red color of this indicator.

A number of other cases might be taken up, where the
molecule is either colorless, or has a different color from
one of its ions, but the cases considered are typical, and
suflSce to make the point clear.

A Demonstration of the Dissociating Action of Water. —
Jones and Allen ^ have worked out a color demonstration
of the dissociating action of water, which is based upon
the principle of indicators just considered. If, to an

1 Amer. Chem. Joum., 18, 377.

114 ELECTROLYTIC DISSOaATION

alcoholic solution of phenolphthaleln, a few drops of
aqueous ammonia are added, there is no sign of the red
color of the indicator. If water is now added to the
alcoholic solution, the red color appears. When potassium
or sodium hydroxide is substituted for ammonia, the red
color appears at once, without the addition of water.
There is, thus, a marked . difference between potassium
and sodium hydroxide and ammonium hydroxide.

It would be difficult to interpret these facts without the
aid of the theory of electrolytic disspciation. In the light
of this theory they are perfectly intelligible.

When a few drops of aqueous ammonia are added to
several cubic centimetres of alcohol, little or no dissociation
of the ammonium hydroxide is effected. The addition of
water dissociates the base, the degree of dissociation de-
pending upon the amount of water present with respect to

+ -

alcohol. The presence of the ions NH^ and OH would
cause the phenolphthaleYn to dissociate. The complex
anion gives its characteristic color to the solution in
which it is present. The hydrogen and hydroxyl ions
would then combine and form water.

It is possible that the actual course of the reaction is
somewhat different from that just described. It may be
that the ammonium group first combines with the phenol-
phthaleln in the alcoholic solution. The addition of water
would then dissociate this compound, giving the colored
anion referred to above.

The dissociation theory furnishes this explanation. It
remains to determine whether the explanation is true.'

If it is, then a solution, formed by adding a little aqueous
ammonia to a considerable volume of alcohol, should show

EVIDENCE FOR THE THEORY 1 15

little or no dissociation, and the amount of the dissociation
should increase with the addition of water. Solutions of
potassium or sodium hydroxide, in mixtures of alcohol
and water, should be more dissociated than corresponding
solutions of ammonium hydroxide. Indeed, a solution of
sodium or potassium hydroxide, in alcohol alone, should
manifest some dissociation, since, as stated above, it gives
the color reaction with phenolphthalern.

All of these points were tested, experimentally, by the
conductivity method, with the result that the theory of
electrolytic dissociation was entirely confirmed.

This experiment furnishes a satisfactory lecture demon-
stration of the dissociating action of water. A few drops
of an alcoholic solution of phenolphthaleYn are placed in a
glass cylinder, and diluted to, say, 50 cc. by the addition of
alcohol. A few drops of an aqueous solution of ammonia
are then added. A red color may appear where the
aqueous ammonia first comes in contact with the alcoholic
solution of phenolphthalern, but this will disappear, in-
stantly, on shaking the cylinder, leaving the solution with
a yellowish tint, possibly due to the formation of the
ammonium salt of phenolphthaleYn. Water is then gradu-
ally added to the cylinder, when the red color will appear,
at first faint, then stronger, as the amount of water
increases. When the red color has become intense,
add a considerable volume of alcohol, and the entire
color will disappear, leaving the solution slightly yellow
again.

The experiment serves, then, not only to illustrate the
dissociating action of water, but the driving back of the
ions into molecules by alcohol.

Il6 ELECTROLYTIC DISSOCLVTION

Conductivity is Additive. The Law of Eohlrausch. —

It has been shown by Kohb*ausch, that the conductivity of
solutions of electrolytes is an additive property of the ions
which take part in carrying the current. Indeed, the law
of Kohlrausch, of the independent migration velocity of
the ions, is but another expression of this fact. It is well
known that the law, in the form stated by Kohlrausch,
holds only for great dilutions, in which dissociation is com-
plete. Ostwald^ has pointed out that the law holds for any
dilution, provided that we take into account the amount of
the dissociation at that dilution. This is obviously neces-
sary, since it is only the dissociated molecules which take
part in the conductivity. If we represent the percentage
of dissociation, or the activity coefficient, by a, the law of
Kohlrausch becomes : —

u depending upon the cation, v upon the anion. The law
in this form is applicable to all solutions of electrolytes,
and illustrates, also, the additive property of conduc-
tivity.

A number of other properties could be adduced in
evidence of the general principle, that the properties of
completely dissociated solutions are additive, being the
sum of the properties of the ions ; but those already con-
sidered are quite sufficient. The theory of electrolytic
dissociation is here entirely substantiated by the facts.
And these facts would be very difficult to explain without
some such conception as that with which we are now
dealing.

1 Lehrb. d. allg. Chem. II, p. 673.

EVIDENCE FOR THE THEORY I17

PROPERTIES OF. COMPLETELY DISSOCIATED, AND OF UNDIS-

SOCIATED MIXTURES

Mixture of Two Completely Dissociated Compounds. —

The theory of electrolytic dissociation leads to some inter-
esting conclusions, in the case of mixtures of completely
dissociated substances, and these conclusions can be tested
experimentally. Let us take the case of two salts which
are completely dissociated at moderate dilutions, say,
sodium chloride and potassium bromide. We would have
in the solution only the ions into which these compounds
had dissociated : —

NaCl = Na + Cl;
KBr = K + Br.

We would have sodium and potassium cations, and chlorine
and bromine anions. All the properties of such a mixture
would be a function of the properties of these ions.

Suppose we were now to prepare a mixture of potassium
chloride and sodium bromide, which was completely dis-
sociated. We would have in the solution : —

KCl = K +Clj

+ -
NaBr = Na 4- Br,

potassium and sodium cations, and chlorine and bromine
anions. But these are exactly the same ions which we
had in our first mixture.
We are led to the conclusion, that if we use gram-

Il8 ELECTROLYTIC DISSOCIATION

molecular weights of both substances in each case, we
will have exactly the same number of the same kinds of
ions in the two solutions. And since the properties of a
completely dissociated solution depend only upon the
properties of the ions present, the properties of these two
mixtures must be the same. If, then, we mix a gram-
molecular weight of sodium chloride with a gram-molecu-
lar weight of potassium bromide, and dilute the solution of
the two until both are completely dissociated, this mix-
ture must have exactly the same properties as that pre-
pared by mixing a gram-molecular weight of potassium
chloride with a gram-molecular weight of sodium bro-
mide, and diluting the solution to the same point as the
first. This is the conclusion to which we are led by our
theory. What are the facts.** The facts confirm this
conclusion absolutely. All of the properties of the two
mixtures have been found to be exactly the same. The
two solutions resemble one another as closely as the two
halves of the same solution.

Mixture of Two Completely Undissociated Compounds. —
The conclusion to which we are led in the case of com-
pletely dissociated compounds does not obtain at all for
undissociated substances. Indeed, in the latter case, we
are led by the theory to exactly the opposite conclusion.
Take two undissociated substances — say methyl chloride
and ethyl bromine — and dissolve the mixture; we will
have only molecules of the two substances present. The
properties of this mixture will be a function of the
properties of these two kinds of molecules.

Then, mix methyl bromide and ethyl chloride, we will
have only these two kinds of molecules present, and

EVIDENCE FOR THE THEORY 119

the properties of the mixture will be a function of the
properties of the molecules which are in the mixture.

But in the first mixture we have molecules of methyl
chloride and ethyl bromide, in the second, of methyl bro-
mide and ethyl chloride. And since we have different
kinds of molecules in the two mixtures, the properties of
the two must be different.

If, then, we mix gram-molecular weights of methyl
chloride and ethyl bromide, the mixture must have differ-
ent properties from a corresponding mixture of gram-
molecular weights of methyl bromide and ethyl chloride.

This is the conclusion to which we are led by the theory
of electrolytic dissociation, and here again the facts are
in perfect accord with the theory. It has been found,
experimentally, that a mixture of methyl chloride and
ethyl bromide has properties quite different from a corre-
sponding mixture of methyl bromide and ethyl chloride.

Fact and theory thus agree, both when the constituents
of the mixture are completely dissociated, and when they
are not at all dissociated.

HEAT OF NEUTRALIZATION IN DILUTE SOLUTIONS

If the theory of electrolytic dissociation is true, a dilute
aqueous solution of a strongly dissociated compound con-
tains only ions, as has been stated. A solution of a base
contains the hydroxyl anion, and a cation whose nature
depends upon the particular base used. A solution of an
acid contains the hydrogen cation and an anion whose
nature depends upon the acid chosen. Similarly, a solu-
tion of a salt is but a solution of anions and cations. In
terms of the theory of electrolytic dissociation, the pro-

I20 ELECTROLYTIC DISSOCIATION

cess of neutralizing an acid by a base consists in the
union of the hydroxyl anion of the base with the hydro-
gen cation of the acid, forming a. molecule of water. The
cation of the base and the anion of the acid remain in
exactly the same condition after neutralization as before.
Let us take an example.

A solution of hydrochloric acid is a solution of hydro-
gen cations and chlorine anions: —

HCl = H + Ci.

A solution of potassium hydroxide is a solution of
potassium cations and hydroxyl anions: —

KOH = K + OH.
When the two solutions are brought together we have: —

K + OH + H + CI = K -h CI 4- H2O.

The potassium and chlorine are in exactly the same
condition after neutralization as before, Le, both are ions ;
while the hydrogen and hydroxyl are united, forming a
molecule of water.

Neutralization of acids and bases is, then, in terms of
the theory of electrolytic dissociation, nothing more than
the union of the cation hydrogen and the anion hydroxyl
to form a molecule of water.

How can this be tested experimentally i

If neutralization consists only in the formation of a mole-
dule of water, then the neutralization of any acid by any
base is the same process as the neutralization of any other

EVIDENCE FOR THE THEORY 121

acid by any other base. Therefore, the heat liberated by

neutralizing an equivalent of any acid by an equivalent of

any base must always be the same, since it is the heat of

formation of the same amount of water from the ions

+ -

H and OH. This can be tested directly by experiment.

It is only necessary to measure the heat liberated when

acids and bases are neutralized, and see whether this is

the same for the different compounds.

The following tables of heats of neutralization will test

this point: —

Strong Acms and Bases

HCl +NaOH = 13700 cal. HCl4- LiOH = 13700 cal.

HBr -f NaOH =13700 cal. HCl + KOH =13700 cal.

HNOa + NaOH = 13700 cal. HCl -f i Ba(0H)2 = 13800 cal.

HI + NaOH = 1 3800 caL HCl + ^ Ca(0H)2 = 1 3900 cal.

Weak Acid and Strong Base

CHsCOOH -f NaOH = 13400 cal.
CHCI2COOH + NaOH = 14830 cal.
H3PO4 4- NaOH = 14830 cal.

HF 4- NaOH = 16270 cal.

The agreement between the heats of neutralization of
the strong acids with the strong bases is striking, when we
consider the necessary errors involved in thermochemical
measurements.

The heats of neutralization of weak acids with a strong
base differ very greatly from the constant obtained when
both compounds are strongly dissociated.

122 ELECTROLYTIC DISSOCIATION

In the application of the theory to the phenomenon of
neutralization, it was assumed above, that both the acid
and the base were completely dissociated. If, on the
other hand, either acid or base is incompletely dissociated,
then the heat set free when the two are brought together
is .not simply the heat liberated by the union of hydrogen
and hydroxyl ions to form water, but this quantity, plus
the heat of dissociation of that part of the acid or base
which is undissociated.

This explains the difference between the amounts of
heat liberated, when both the acids and bases are strong,
and when either the acid or base is weak.

The theory of electrolytic dissociation is, then, strictly in
accord with the facts, as far as the heat of neutralization is
concerned. This applies not simply to the strong acids
and bases, but to the apparently exceptional cases of the
weakly dissociated compounds.

It will be observed, that in the above interpretation of
the process of neutralization, it is assumed that all of the
hydrogen and hydroxyl ions combine to form water. It
has been shown by six separate lines of work, that when-
ever hydrogen and hydroxyl ions come together they
combine and form water. This is the same as to say
that water is undissociated. The apparent assumption is,
therefore, well supported by the experimental facts.

Hess's Law of the Thermoneutrality of Salt Solutions. —
A dilute aqueous solution of a salt is, in terms of our theory,
a solution of ions. Thus, a dilute aqueous solution of
potassium chloride contains only potassium and chlorine
ions. Similarly, a dilute solution of sodium chloride is but
a solution of sodium and chlorine ions. When the solutions

EVIDENCE FOR THE THEORY 1 23

of the two salts are mixed, the mixture contains only po-
tassium, sodium, and chlorine ions.

+ —
KCl in dilute aqueous solution = K + CL

+ -
NaCl in dilute aqueous solution = Na + CI.

When the two solutions are mixed, we have : —

K + Na + CI + CI,

and there should be no thermal change produced on mix-
ing such solutions. It has long been known, that if com-
pletely dissociated solutions of neutral salts are mixed,
there is neither evolution nor absorption of heat, provided
that none of the ions unite to form molecules, or to form
new complexes of ions. These facts are usually stated as
Hess's law of the thermoneutrality of salt solutions, which
but names them, without attempting an explanation.

The theory of electrolytic dissociation not only furnishes
a reason for the law of the thermoneutrality of salt solu- .
tions, but makes it a necessary consequence of its own
validity.

OSMOTIC PRESSURE — LOWERING OF FREEZING-POINT —
RISE IN BOILING-POINT — CONDUCTIVITY

It will be remembered that Arrhenius proposes the
theory of electrolytic dissociation, to account for the abnor-
mally large osmotic pressure shown by certain classes of
substances. We may divide chemical compounds into two
classes, with respect to their power to exert osmotic press-
ure : First, substances like the carbohydrates, alcohols,
etc., i,e, the chemically inactive organic compounds, which
exert an osmotic pressure that obeys the gas laws, and

124 ELECTROLYTIC DISSOCIATION

will be called normal ; second, the acids, bases, and salts
which exert a much greater osmotic pressure.

If we determine the freezing-point lowering produced by
these substances, when dissolved in water, we will find that
they again divide themselves into two classes ; the organic
compounds giving freezing-point lowerings which we will
call normal, and the acids, bases, and salts, giving a
greater depression of the freezing-point. All of those
compounds, and only those, which show too great osmotic
pressure, give too great lowerings of the freezing-point of
water.

Furthermore, if we study the rise in the boiling-point of
solvents produced by dissolved substances, we will find,
again, that the organic compounds above referred to pro-
duce a certain rise in the boiling-point, while all the acids,
bases, and salts produce a greater rise in boiling-point.
Substances divide themselves here, as in the last two cases,
into two classes, and it is exactly the same division as
shown both by osmotic pressure, and lowering of freezing-
point.

Finally, if we study the conductivity of solutions of
chemical compounds, we will find that solutions of the neu-
tral organic compounds do not conduct the current, while
solutions of all acids, bases, and salts, do conduct. If we
were to divide all chemical substances with respect to their
power to conduct the electric current, they would again
fall into two classes, and exactly the same two classes as
were furnished by each of the above three properties.
Substances which conduct the current are termed electro-
lytes, and those which do not conduct, non-electrolytes ; so
that we will now refer to these two classes of chemi-

EVIDENCE FOR THE THEORY 125

cal compounds as, respectively, electrolytes and non-
electrolytes.

We have, then, this very remarkable relation. All of
those substances, and only those, which show abnormally
great osmotic pressure, show abnormally great lowering of
the freezing-point, rise in boiling-point, and conduct the
current. These electrolytes, as we will see later, are also
the most active chemically.

The converse is also true, that all of those substances,
and only those, which show normal osmotic pressures,
show normal lowering of freezing-point, rise in boiling-
point, and do not conduct the current. These non-electro-
lytes, as we will also see, are the least active of chemical
substances.

Having found this qualitative relation, it remains to see
whether it is quantitative, — whether a substance which
shows too great osmotic pressure produces a lowering of
freezing-point, and rise in boiling-point, which is too great,
by the same amount.

If the abnormally great osmotic pressure is explained by
the dissociation of molecules into ions, so, also, must the
abnormally great lowering of freezing-point, and rise in
boiling-poinjt, produced by electrolytes, as well as their
conductivity, be due to the same cause. If the theory of
electrolytic dissociation is true, there must be a quantitative
relation between abnormal osmotic pressure, lowering of
freezing-point, rise in boiling-point, and conductivity. If
such a quantitative relation can be shown to exist, it
would be a strong argument in favor of the theory we
are considering. We will show that such a relation does
exist.

126 ELECTROLYTIC DISSCXIATION

Relation between Osmotic Pressure and Lowering of Freez-
ing-point. — The relations between the four properties
here considered will be pointed out, first experimentally,
and then in part, theoretically.

De Vries^ has measured the relative osmotic pressures
of a number of solutions, using vegetable cells. Without
going into the details of this method, the principle can be
concisely stated. When some vegetable c^Us, containing
colored protoplasm surrounded by a semipermeable mem-
brane, are immersed in solutions which have a greater
osmotic pressure than the contents of the cell, we can
see the contents of the cell contracted to one side, due to
the loss of water to the solution. If the solution in which
the cell is immersed has the same osmotic pressure as the
contents of the cell, no water will pass into or out of the
cell, and it will present a normal appearance. If the solu-
tion has a smaller osmotic pressure than the contents of
the cell, water will pass in, and the cell will be distended.
By studying the behavior of the cell in the solution, under
the microscope, we can determine whether the solution has
a greater, less, or the same osmotic pressure as the con-
tents of the cell. By starting with a solution which has
a greater osmotic pressure than the contents of the cell,
and diluting it gradually, we can determine, from the
behavior of the cell, when its osmotic pressure is just equal
to that of the contents of the cell. We can thus pre-
pare solutions of different substances, having each the
same osmotic pressure as the cell contents, and, therefore,
all having the same osmotic pressure. Such solutions,
which have the same osmotic pressure, were termed isos-

1 Ztschr. phys. Chem., 2, 415.

EVIDENCE FOR THE THEORY 1 27

motic. When these concentrations were expressed in
molecular quantities, their reciprocal values were termed
isotonic coefficients. These show, directly, the relative
osmotic pressures of solutions of equal molecular concen-
tration. The coefficients for a number of compounds, as
compared with the molecular lowerings of the freezing-
point, are given in the following table, taken directly
from the work of De Vries.^

SUBSTAMCB

Isotonic Coefficients

MOLBC.

Low. OF Frebziw

MULTI^IED BY XOO

POINT MULTIPUED BY XO

CcHuOe

181

185

C12H22OU

188

193

MgS04

196

192

KNOj

300

308

KaSO*

391

390

NaCl

305

351

These are just a few of the many cases given by De
Vries. But they are sufficient to show the proportionality
between isotonic coefficients and molecular lowering of the
freezing-point for a number of classes of substances.

Relation between Osmotic Pressure and Lowering of
Vapor-tension. Rise in Boiling-point. — In the same table
in which the above relation is pointed out, De Vries also
shows that a proportionality exists between the isotonic
coefficients of a number of substances, and the molecular
lowering of the vapor-tension; lowering of vapor-tension
being used here, instead of rise in boiling-point, which is
proportional to it. A few results taken from the table
are given: —

1 Ztschr. phys. Chem., 2, 427.

128 ELECTROLYTIC DISSOCIATION

Isotonic CoBrnasNTS

LOWBMNG

i OP Vapor-tbnsion

SUBSTANCC

MULTIFUCD BY

zoo

MULTIPUBD BY 1000

C^HiO,

198

178

C«IV),

202

188

NaNO,

300

296

KjCfit

393

37«

KSOt

391

351

CaCl,

433

517

Js^Cffijfjj

SOI

499

The proportionality between osmotic pressure and low-
ering of vapor-tension, or rise in boiling-point, is at once
apparent.

Relation between Osmotic Pressure and Conductivity. —
De Vries also compared the osmotic pressure of solutions
and their conductivity. He calculated the sum of the
molecules and ions, on the one hand from osmotic press-
ure, on the other from conductivity, and then compared
the two values to see how they agfreed. He obtained the
following results : ^ —

Sum op Molbculbs and Ions calculatbd —

>BPPiaBNTS From Conductivity

100
100
100

135
180

187

182

234

SUBSTANCB

From Isotonic

Non-conductors

CjHgO,

100

CeHxjOg

106

CijHjjOu

lOI

Conductors

MgS04

KNO,

176

KCl

181

NaCl

179

NH4CI

182

K^«

230

1 Ztschr. ph3rs. Chem., 3, 109 ; also loc, cit.

EVIDENCE FOR THE THEORY 129

The agreement between osmotic pressure and lowering
of freezing-point, rise in boiling-point, and conductivity, is
as close as could be expected, when we consider the large
experimental error involved in determining osmotic press-
ure, directly, by any method, and even in determining the
relative osmotic pressure of solutions by the method of
De Vries.

Relation between Lowering of Freezing-point and Rise
in Boiling-point. — Raoult ^ has shown, purely empirically,
that the lowerings of the freezing-point, produced by some
eighteen salts, stand in the same relation to one another
as the rise in boiling-point produced by these same com-
pounds. The results are not tabulated, and, therefore,
will not be given here.

Relation between Lowering of Freezing-point and Con-
ductivity. — That a quantitative relation exists between
these quantities, for any given substance, was shown by
Arrhenius, when he proposed the theory of electrolytic
dissociation. Some of the data which he brought forward
to prove this point have already been given (p. 98). The
agreement between the values of /, as calculated from freez-
ing-point lowering and from conductivity, was only fairly
close, because the freezing-point method at that time was
in a crude state, and gave only approximate results.

The freezing-point method has now been greatly im-
proved,^ — a number of sources of error having been elimi-
nated, — until it can be used to measure the value of the
coefficient of dissociation, as it is termed, with considerable

1 Compt. rend., 70, 1349 (1870).

3 Jones, Ztschr. phys. Cbem., zx, no and 529; Z2, 633. Loomis, Wied. Ann.,
5if 500; 57, 495 ; 60, 523. Raoult, Ztschr. phys. Chem., 27, 617.

I30 ELECTROLYTIC DISSOCIATION

accuracy. The values of a have been determined by Jones,^
for a large number of dilutions of different substances,
using the freezing-point method. These have been com-
pared with the values of a for the same dilutions of the
same substances, using the conductivity method. The fol-
lowing results are taken from the paper of Jones: —

CoMPOinfDS

CONCBNTRATION

a FROM

Conductivity

a PROM Frbbzing-

POINT LOWBRING

NaCl
NaCl
NaCl

0.001
0.0 1

O.I

98.0

93-5
84.1

98.4

90.5
84.1

BaCla
BaCl,
BaCl,

O.OOI

0.005

0.05

93-9
87.9

75-3

94.2
87.6

77-7

HCl

0.002

lOO.O

98.4

HCl
HCl

O.OI
O.I

98.9

93-9

95*8

H2SO4
HaS04
HaS04

0.003
0.005

0.05

89.8

35-4
62.3

86.0
83.8
60.7

KOH

0.002

1 00.0

98.4

KOH
KOH

O.OI
O.I

99.2
92.8

93-7
83.1

KaCOa
KsCOs
KjCOs

0.003
0.005

92.0
88.6
71.9

96.6
96.0

77.5

The percentage of dissociation a, as measured by the
freezing-point method, agrees surprisingly well with the
values obtained from conductivity. The slight differences
which exist are probably due to the different temperatures

1 Phil. Mag., 36. 483.

EVIDENCE FOR THE THEORY 131

at which the two sets of measurements were made — con-
ductivity being determined at 18°, and freezing-point
lowering a little below o®.

We have now demonstrated, by experiment, the quan-
titative relation which exists between osmotic pressure,
lowering of freezing-point, rise in boiling-point, and con-
ductivity. We will now give a mathematical demonstration
of one or two of these relations.

Connection between Osmotic Pressure and Lowering of
Freezing-point, established by Thermodynamics. — The con-
nection between osmotic pressure and lowering of the
freezing-point was deduced thermodynamically by van't
Hoff,^ in the paper to which reference has so often been
made.

Van't Hoff showed that solutions in the same solvent,
having the same freezing-point, are isotonic at that tem-
perature. He applied this to dilute solutions, and was led
to the conclusion that solutions which contain the same
number of molecules in the same volume, and, therefore,
from Avogadro^s law, are isotonic, have also the same
freezing-point. This was discovered experimentally by
Raoult, and led to the expression " normal molecular lower-
ing of the freezing-point.*' This means the lowering in
degrees, produced by a gram-molecular weight of the sub-
stance in 100 grams of the solvent. This normal molecular
lowering of the freezing-point, which we will term the
freezing-point constant for the solvent, van't Hoff then
derived from the latent heat of fusion of the solvent.
This deduction has been developed more fully by Ostwald,^

1 Harper's Science Series, IV, 29. Ztschr. phys. Cham, i, 481.

2 Lehrb. allg. Chem., I, p. 759.

132 ELECTROLYTIC DISSOCIATION

and it will be given here essentially as worked out by him,
with some changes ^ which seem to make the steps a little
clearer.

Let us take a solution consisting of n gram-molecules of
the dissolved substance and N gram-molecules of the sol-
vent. Let T be the temperature of solidification of the
solvent, and A the lowering of the freezing-point. Here
as much of the solvent is allowed to solidify as would
serve for the solution of one gram-molecule of the sub-

tance, =— molecules.
n

Let X be the latent heat of fusion of a gram-molecule of

N
the solvent ; the amount of heat liberated would be — \. If,

now, the ice is separated from the solution, warmed to tem-
perature 7^, and melted, and finally allowed to mix with the
solution by passing through a semipermeable membrane, it

will exert an osmotic pressure /. If v is the volume of the

N
solvent which solidified, the work =/z/, the heat — X ; from "^

NX T
But pv^ RTy and R=^2 cal. Substituting, we have : —

A n 2 7^

A =

N X
Let M be the molecular weight of the solvent, and sub-
stituting A^= -jrjTy we have : —

A = ^^' (I)

ICO X ^ ^

1 Jones, Phil. Mag., 36, 493.

EVIDENCE FOR THE THEORY .133

In the Raoult formula m^-^itn is the molecular weight

of the dissolved substance, K is the freezing-point constant,

and A the specific lowering of the freezing-point ^ = — ,

where A is the lowering of the freezing-point observed, and
/ the percentage concentration of the solution.

fit = — r— .

Let n be the number Df molecules of the dissolved sub-
stance in icx) g. of the solvent.

m
substituting, mL = Kmn ;

L^kn (2)

From (i) and (2) K^— ^.

If L is the heat of fusion of i g. of the solvent,

Substituting, iSr= -,

lOoZ

From this equation van't Hoff has calculated the value
of the freezing-point constant for a number of solvents,
and compared these values with those found experimentally.

Sot.v«rr Constant CAi^m^TBD Constant found

OOLYBMT FROM JT— 2_£_ ExPBRIMBNTALLT

ZOOJ^

Water 18.9 18.5

Acetic acid 38.8 38.6

Formic acid 28.4 27.7

Benzene 53.0 50.0

Nitrobenzene 69.5 70.7

134

ELECTROLYTIC DISSOCIATION

The values of the freezing-point constant, as calculated
from the van*t Hoff formula, agree very satisfactorily with
those found by experiment.

Relation between Osmotic Pressure and Lowering of
Vapor-tension (Rise in Boiling-point). Theoretical Demon-
stration. — The relation between osmotic pressure and
lowering of vapor-pressure has been derived in a simple
manner by Arrhenius.^ The line of reasoning is as fol-
lows : Given a vessel of the form shown in Fig. 5,

closed at the bottom by a semiperme-
able wall. Let this vessel be filled with
a solution 5, and dip into a vessel con-
taining the pure solvent D, The whole
is covered with a bell-jar, and exhausted.

Equilibrium will be established when the
pressure of the columi\ of liquid, from
the surface of the solvent up to A, is
equal to the osmotic pressure, and the
free space is saturated by the vapor
Z?'. When equilibrium is established,
the vapor-pressure of the solution at
- h must be just equal to the pressure
of the vapor of the solvent at this point.
If it were less, liquid would condense in A, if more, it
would distil out of A, and there would not be equilibrium,
since liquid would flow either out or in through the mem-
brane. If /' is the tension of the vapor of the solution at
A, / the vapor-tension of the solvent, h the height of the
column of liquid, and d the density of the vapor in the
bell-jar, we have : — f =y _ ^d^

^ Ztschr. phys. Chem., 3, 115.

'D5

Fig. s.

EVIDENCE FOR THE THEORY 1 35

The value of k, — Let us have a very dilute solution, in
which n gram-molecules of substance are contained in
g grams of solvent. From van't Hoflf's law of osmotic
pressure we would have : —

PV^RTxin,

in which P is the osmotic pressure of the solution, and V

its volume. Let s be the specific gravity of both solution

and solvent ; they are practically the same for very dilute

solutions.

P==Axs;

= ^=

Substituting, PV^ nRT^'^^^hg\

Ag-==i nRT ,\ A = .

The value of d, — Let v be the volume of a gram-
molecule of the vapor of the solvent Z>, and /the pressure
of this vapor : —

fv^RT,

RT
If M is the molecular weight of the solvent

M RT
d- f '

— ^

136 ELECTROLYTIC DISSCX3ATION

Substituting the values, h = and d = -^ in the

g KT

equation f =/— Ad, we have: —

^ g

f g

which is essentially Raoult's fundamental equation for the
lowering of the vapor-pressure of a solvent by a dissolved
substance. Raoult's equation, which has been amply veri-
fied by experiment, is usually written : —

f ~N

where N is the number of gram-molecules of the solvent.

It is evident that iV=^ when the two equations become
identical.

Theoretical demonstrations of other relations between
the four properties of solutions, which we are considering,
have been furnished. Thus, Guldberg ^ has proved a direct
connection between lowering of freezing-point and lower-
ing of vapoV-tension. Arrhenius ^ has shown how freezing-
point lowering and conductivity are connected, by cal-
culating the value of the coefficient i from both, and then
showed, experimentally, that the two values agreed with

1 Compt. rend., 70, 1349. > Li>c. eit,

EVIDENCE FOR THE THEORY 1 37

one another (see p. 98). A number of other demonstra-
tions of relations between these properties could be given,
did space permit, but quite enough has been developed to
show, both experimentally and theoretically, that they are
quantitatively connected. Whatever causes electrolytes to
exert a greater osmotic pressure than non-electrotytes, also
causes them to produce a greater lowering of the freezing-
point, rise of boiling-point, and enables them to conduct
the current.

Arrhenius showed that his theory explains all of the
facts concerning osmotic pressure. From the above rela-
tions alone it must, therefore, accord with the facts con-
nected with the other three properties. We have, however,
an abundance of independent evidence, were this neces-
sary, that the theory of electrolytic dissociation is in per-
fect harmony, not only with what is known of the osmotic
pressure of dilute solutions, but with every other property
possessed by them.

EXPERIMENT TO SHOW THE PRESENCE OF FREE IONS

If only ions conduct, then, whenever a current is passed
through a solution of an electrolyte, a movement of the
ions is necessarily involved. The same applies to a
solution of an electrolyte charged electrostatically. If
the charging body is negative, it will attract the ions
which carry the positive electricity in the solution, i,e,
the cations, and will repel the anions. If the solution
could then be separated into two parts, the one would
contain an excess of cations, and the other an excess of
anions.

138 ELECTROLYTIG DISSOCIATION

illustration of a Solution charged Electrostatically. —

Let two vessels, A and B, be filled with a solution of an

electrolyte, say potassium

^ chloride, and let the two

■~~"^ B

be connected with a si-
FiG 6 ^^"" ' phon filled with the same

liquid. Let a negatively
charged body K be brought near to ,^4 ; it will act by in-
duction upon the system AHB, A will become positive
and B negative. If now the siphon H is removed, and
then the body K^ A will remain positive and B negative.

But, from the law of Faraday, electricity can move in
solutions only by a movement of the ions. That A should
be positive, it is necessary that it should contain an excess
of the potassium ions which carry the positive charge.
Similarly, B must contain an excess of chlorine ions. The
number of these free ions in the solution must depend,
of course, upon the intensity of the inducing action. To
discharge Ay introduce a platinum wire connected with the
earth. The potassium ions give up their positive charge
to the wire, and become atoms. These now act upon the
water, forming potassium hydroxide, and hydrogen which
escapes from the solution.

This experiment was proposed by Ostwald,^ simply as
an illustration. It is obvious to any one that, under condi-
tions such as those described, the amount of hydrogen set
free would be far too small to be seen. On account of the
very great charge carried by an ion, the number of ions
which would be induced from one vessel to the other, by
the above arrangement, would be relatively small.

1 Ztschr. phys. Chem.; 2, 272.

EVIDENCE FOR THE THEORY 139

The above experiment illustrates another point, as
Ostwald has shown. That electrostatic charging of elec-
trolytes takes place with enormous velocity, as with con-
ductors of the first class. But Kohlrausch has shown
that the ions move very slowly. If the above induction
phenomenon takes place very rapidly in the solution, then
the potassium ion, which brings the positive charge closest
to K^ could not have been connected with the chlorine
ion, which takes the negative charge to the region most
remote from K, Free ions must, therefore, be present
in the solution at all times, or the electrolyte must be
dissociated.

Experiment of Ostwald and Nemst.— The experiment
described above, while theoretically correct, must be re-
garded as only an illustration. Ostwald and Nernst^
have, however, devised an experiment, which they claim
demonstrates to the eye the effect described by Ostwald,
To be able to see the hydrogen liberated by induction,
unusual precautions must be taken, because of the very
small quantity of gas which will be set free. To liberate
a milligram of hydrogen would require a condenser of
about one square kilometre. But one milligram of hydro-
gen will fill 12 to 13 cubic centimetres, under ordinary
conditions.

By means of a microscope, it is possible to see a bub-
ble of gas 0.0 1 mm. in diameter, and this amount could
be liberated, using a condenser of ordinary dimensions.
The gas was collected in the capillary of a Lippmann
electrometer, since a small quantity could be easily recog-
nized in this way.

1 Ztschr. phys. Chem., 3, a/i (1888).

I40 ELECTROLYTIC DISSOCIATION

The experiment of Ostwald and Nemst will now be
described in detail.

A glass tube 30 to 40 cm. in length, provided with a
stop-cock, was drawn out at one end to a fine capillary.
The diameter of the capillary was such that, when the
tube was filled with mercury, it would begin to flow out of
the fine point. The tube was fastened upright, and its
tip allowed to dip in dilute sulphuric acid. The mercury
was then drawn up into the capillary, and the acid drawn
in after it. By means of the stop-cock, the surface of
contact between the mercury and the acid could be kept
about the middle of the capillary. A platinum wire,
fused into the glass tube, connected with the mercury.

A large glass flask was filled with dilute sulphuric acid.
Its outer surface was covered, with tinfoil, and its neck
varnished with shellac. The contents of the flask were
connected with the sulphuric acid into which the capillary
tube dipped, by means of a moist cord. The glass flask
was insulated, by placing it upon a plate of hard rubber.
The outer coating on the flask was connected with the pos-
itive pole of a small machine for generating electricity ; the
mercury in the tube connected with the earth. When the
machine was set in motion, the meniscus in the capillary
rushed up with violence, and at the same time, several
bubbles of gas separated, which broke the thread of mer-
cury in a number of places. This is nearly the verbatim
account of what happened, as given by the experimenters
themselves.

They explain the facts as follows: "By charging the
coating on the outside of the flask with positive electricity,
the negative electricity in the interior is attracted and held.

EVIDENCE FOR THE THEORY I41

while the positive is repelled. The latter passes through
the thread, into the capillary electrode, and through the
platinum wire in the latter to the earth. There is no
closed current present ; the entire movement of electricity
which is produced is the result of induction." ^

As the outer coating of the flask becomes charged with
positive electricity, the ions SO4, which carry the nega-
tive charge, are attracted, the positive ions, hydrogen, are
repelled, pass over the moist cord to the mercury, give up
their charge, and appear as ordinary hydrogen gas.

The objection could be raised to this experiment, that
a movement of electricity takes place, electrolytically,
through the glass, and that this causes the separation of
the hydrogen. The authors performed a number of ex-
periments to test this point, and convinced themselves
that this is strictly an induction phenomenon.

They worked quantitatively, as far as possible, determin-
ing the amount of hydrogen which separated and the
amount of the electricity induced, and found that the
amount of gas liberated corresponded to that calculated
from Faraday's law to within the limit of experimental
error. They concluded that movement of electricity in
electrolytes, corresponding to Faraday's law, can take
place only with a simultaneous movement of the ions, and
that in electrostatically charged electrolytes a number of
ions, corresponding to the amount of electricity, are free.

The question still remains, whether the ions are not set
free at the moment of the electrostatic charging, so that
the separation of the electricities is accompanied by a kind
of electrolysis in the interior of the liquid. Ostwald and

^ Ztschr. phys. Chem., 3, 132.

• • • •:• !••!

142 ELECTROLYTIC DISSOCIATION

Nernst point out, that Clausius^ has shown, that the
movement of electricity in electrolytes obeys the weakest
electromotive impulses, which would not be possible if
the electricity must first perform an appreciable amount
of work. They then show that such an assumption is
against the laws of thermodynamics.

If we consider all of the precautions which Ostwald and
Nernst have taken, it seems that they have conclusively
proved the point, that free ions exist in electrostatically
charged electrolytes, and these are not set free at the
moment of charging.

THE OSTWALD DILUTION LAW

Conductivity and Dilution. — It is well known, that the
power of solutions of electrolytes to conduct the current
increases with the dilution. If we always deal with
molecular quantities, and express the conducting power
of solutions in terms of moleculaf conductivity, we will
see at a glance, that this is always larger (with a very few
exceptions)^ the greater the dilution. The rate of increase |

with the dilution is comparatively slow for the good con- j

ductors, but much more rapid for the poorer conducting
substances, such as the organic acids. The difference
between the molecular conductivities of the good and poor
conductors thus becomes less as the dilution increases. i

This agrees with the view of Arrhenius, that the strength
of all acids which, as we shall see later, depends only upon
the number of hydrogen ions present, is the same at infi-
nite dilution, since at this dilution all acids are completely ,
dissociated. j

1 Pogg. Ann., 101, 338. ^ Kablukofif, Ztschr. phys. Chem., 4, 429.

: * ! - « • • •

EVIDENCE FOR THE THEORY 143

Ostwald ^ found from his own work, that the molecular
conductivity of all monobasic acids passes through the
same series of values, and if acids A and B have the same
conductivities at dilutions v and v^y they will have the same
conductivities at av and av^.

Having found such a general relation between the con-
ductivities of solutions of different substances, it remains
to discover the mathematical expression connecting dilu-
tion and conductivity. And since dissociation and con-
ductivity are proportional, we would then have connected
dilution and dissociation.

Ostwald's Deduction. — Ostwald ^ has pointed out, that
since the laws of gas pressure apply to the osmotic press-
ure of dilute solutions of non-electrolytes, if Arrhenius's
theory of electrolytic dissociation to account for the excep-
tions shown by electrolytes is true, we ought to be able
to apply the formula for a partly dissociated gas to a partly
dissociated solution.^

For the homogeneous system of one volume of a gas
dissociating into two volumes of gaseous products, Ost-
wald * deduced the formula : —

^ log-^ = ^+ const.

/, Ply and P2 ^^^ ^^^ pressures of the original gas and of
the decomposition products, respectively, ^ is the heat of
decomposition, R is the gas constant, and T the abso-
lute temperature.

1 Joum. prakt. Chem., 31, 433 ; Lehrb. allg. Chem., II, p. 653.

* Ztschr. phys. Chem., 2, 136, 276; 3, 170,

* See also Planck, Wied. Ann., 34, 147.

4 Ztschr. phys. Chem., 2, 36; Lehrb. allg. Chem., II, p. 723 (ist edition).

144 ELECTROLYTIC DISSOCIATION

If the temperature is constant, and neither of the de-
composition products is present in excess, the above
expression becomes: —

•^s= constant (i)

in which / is the pressure of the original gas, and p^
that of the decomposition products.

Turning now to solutions, we must deal with osmotic
pressure instead of gas pressure. The osmotic pressure
is proportional to the amount of substance present, and
inversely proportional to the volume. Let u be the mass
of the undecomposed electrolyte, and u^ the mass of the
decomposition products; v is the volume: —

/ = -7, and py = — ^•

Substituting these values in (i), we have: —

= constant • . (2)

The amount of the dissociation products u^ is equal to
the relation between the conductivity at volume v (/*„),
and the conductivity at infinite dilution (/a«,): —

Uy =

^ Moo

The amount of the undissociated substance u is the
complement of Uii —

U=s I .

Moo

Substituting these values of u and Ui in (2) we have : —

t^J"

z/ = constant .... (3)

EVIDENCE FOR THE THEORY 145

and this is the dilution law of Ostwald. This can, how-
ever, be simplified. If we represent the activity co-
efficient, or the amount of dissociation, by a : —

a =3 — •

» 00

Substituting this value in (3) and taking the reciprocal,
we have: —

r — — ^^ — = constant (4)

(i — a) z;

Ostwald^ proceeded at once to test his formula by
experiment The conductivity of a number of acids at
different dilutions was measured, and the values of a
calculated for these dilutions. These values of «, to-
gether with the volumes of the different solutions z/,
(volume is the number of litres which contains a gram-
molecular weight of the electrolyte), were inserted in
equation (4), to ascertain whether c came out a constant,
over a fairly wide range of concentration.

Acetic Acn>

1*193

0.00180

1-673

0.00179

2.38

0.00182

3-33

0.00179

128

4.68

0.00179

256

6.56

0.00180

512

9.14

0.00180

1024

12.66

0.00177

1 Ztschr. phys. Chem., 3, 170, 241, 369.

146 ELECTROLYTIC DISSOCIATION

O-AMIDOBENZOIC

Acid

2.03

0.00066

128

3.02

0.00074

256

4.54

0.00084

6.62

0.00092

1024

9.44

0.00096

The values obtained for c, for most of the acids in-
vestigated, approached a constant. Ostwald studied be-
tween two and three hundred organic acids, and while
there are a number of cases where c did not come out
very constant, yet it can. be said, in general, that the law
holds approximately for this class of substances. It
should be said, that the organic acids are weakly dis-
sociated compounds.

Bredig,^ in studying the conductivity of ammonia, the
amines, and other weakly dissociated bases, applied the
Ostwald formula to somewhat more than thirty of these
compounds.

Ammonia

Triphenylmethane

PiPERIDINE

V c

8 0.0023

0.0069

8 0.157

32 0.0023

0.0075

32 0.162

64 0.0023

0.0076

64 0.150

256 0.0024

256

0.0074

256 0.152

The values of c (for each compound) are more nearly
constant in the work of Bredig on the weak bases, than
in that of Ostwald on the weak acids.

I Ztschr. phys. Chem., 13, 289.

EVIDENCE FOR THE THEORY ' 147

While the dilution law of Ostwald holds fairly well for
the weakly dissociated acids and bases, it does not apply
at all satisfactorily to the strongly dissociated electrolytes
— the strong acids and bases, and salts of these acids
and bases. The reason for this failure on the part of
Ostwald's law is yet to be discovered.

Rudolphi's Dilution Law, — Rudolphi,^ from a study of
the conductivity of solutions of silver nitrate of varying
concentrations, discovered a new relation, which obtains
for the strongly dissociated compounds. If we represent
the volume by z/, and the constant by r, as above, he found
that when he applied the Ostwald equation to solutions of
silver nitrate, he obtained the following .values : —

For t/ = 16, ^ = 0.26.
For z/ = 64, ^ = 0.13.
For z/ = 256, ^ = 0.065.

A glance at these figures will show that a real constant
would be obtained, if the values of c were multiplied by
the square root of v in each case; thus: —

0.26 X V16 = 0.13 X V64 = 0.065 V256.

We must, then, substitute for v^ in the Ostwald expres-
sion, the square root of Vy when it becomes: —

(i-a)Vz/

= constant.

Rudolphi applied his equation to between fifty and
sixty strongly dissociated compounds, and the values
found for c approached a constant. While marked devia-

1 Ztschr. phys. Chem., 17, 385.

148 ELECTROLYTIC DISSOCIATION

tions are not wanting, yet Rudolphi's expression applies
as well to the strongly dissociated electrolytes, as that of
Ostwald to those which are less strongly dissociated, as
the organic acids and bases. This will be seen from the
following examples: —

Hydrochloric Aod

Potassium Sulphitb

Potassium Acetate

4.36

0.453

1.24

445

0.454

100

1. 19

513

0.455

1,000

1. 18

5-13

128

0.544

10,000

1.03

The Rudolphi expression is, of course, purely empirical.
The physical significance of the V2; is thus far entirely
unexplained. One or two modifications ^ of the Rudolphi
formula have been proposed, but these are also empirical,
and cannot be regarded as essentially in advance of the
original. - '

We thus have two expressions for the relation between
the dissociation of electrolytes and the dilution of the
solution : That of Ostwald, which has a mathematical
basis, and whose physical significance is known, apply-
ing to the weakly dissociated electrolytes; and that of
Rudolphi, which is purely empirical, and whose physical
meaning is unknown, applying to the strongly dissociated
electrolytes. The relation between gaseous and electrolytic
dissociation is thus established, as far as the less strongly
dissociated electrolytes are concerned ; but when the dis-
sociation is nearly complete at moderate dilutions, there
exists a discrepancy which still remains to be explained.

1 Van't Hoff, Ztschr. phys. Chem., i8, 300; Kohlrausch, ibid., 18, 662.

EVIDENCE FOR THE THEORY 149

EFFECT OF AN EXCESS OF ONE OF THE PRODUCTS OF

DISSOCIATION

Further Relation between Dissociation by Heat and Elec-
trolytic Dissociation. — It is well known that the dissocia-
tion of a vapor by heat is diminished by the presence of
an excess of any of the products of dissociation. Thus,
the vapor of ammonium chloride is more stable in the
presence of an excess of ammonia, or of hydrochloric
acid. And the vapor-density of phosphorus pentachlo-
ride, which breaks down by heat into phosphorus trichlo-
ride and chlorine, when determined in an atmosphere of
chlorine, agrees very nearly with the theoretical density.
Many such examples have been brought to light by the
work of Deville and others.

It would be an interesting analogy, if we could find a
similar effect in the case of electrolytic dissociation.

It has long been known, that when a saturated solution
of sodium chloride is treated with gaseous hydrochloric
acid, the gas dissolves and sodium chloride separates. A
saturated solution of the salt contains sodium chloride
molecules, sodium ions, and chlorine ions. When gaseous
hydrochloric acid dissolves in the solution, it dissociates
into hydrogen ions and chlorine ions. We have thus
added one of the products of dissociation of the original
compound, — chlorine ions. The dissociation of the so-
dium chloride is diminished, which is shown by the fact
that some of the ions combine to form molecules, and
these are precipitated from the solution.

The same relation is shown by Nernst ^ in the case of

1 Ztschr. phys. Chem., 4, 375.

I50 ELECTROLYTIC DISSOCIATION

potassium chlorate. If to a saturated solution of potas-
sium chlorate, either potassium or CIO3 ions are added,
some of the potassium chlorate will be precipitated.
Thus, if to a saturated solution of potassium chlorate,
either potassium chloride or potassium hydroxide is
added, there will soon result a precipitation of potassium
chlorate. If, on the other hand, sodium chlorate is added
to a saturated solution of potassium chlorate, some of the
potassium chlorate will be precipitated. This is at least
qualitatively analogous to what takes place in the dissocia-
tion of a vapor by heat. It remains to study this effect
quantitatively.

The theory of the mutual effect of salts on each other's
solubility was developed by Nernst,^ from the theory of
electrolytic dissociation and the law of mass action. If
the electrolyte is completely dissociated into two ions,
the product of the active masses must be constant, and
equal to the square of the solubility of the salt before any
second compound is added. If w is the solubility of the
salt after a second salt with a common ion is added, x the
amount added, and m^ the solubility of the salt alone, we
have : —

mini +;r)= m^.

But since the solutions are only partly dissociated, we
must take into account the amounts of dissociation. Let
(Xq be the dissociation of the original substance in a saturated
solution, «! the dissociation of this substance in the presence
of the substance added, and a the dissociation of the added
substance ; the above expression then becomes : — •

1 Ztschr. phys. Chem., 4, 379.

EVIDENCE FOR THE THEORY 15 1

ma(ma + xai) = ni^a^.

The effect of one salt on the solubility of another with a
common ion was tested experimentally by A. A. Noyes.^
He worked with eleven pairs of substances, determined
the solubility of the one with which the solution was satu-
rated, added the second, and determined the change pro-
duced in the solubility. He then calculated the solubility
of the first salt, after the second was added, from the
formula of Nernst, and compared the solubility found with
that deduced theoretically. There is a general agreement
between the two sets of values, but some discrepancies
appeared, which are larger than could be accounted for by
experimental error.

In calculating solubility from the equation of Nernst, we
must know a, aj, and oq, or the dissociations of all the solu-
tions involved. Noyes concluded from his work that the
deduction of Nernst is perfectly correct, and that the appa-
rent differences are due to errors in the determination of
the dissociation values. The relation between dissociation
by heat and electrolytic dissociation, as effected by an
excess of either of the products of dissociation, is, there-
fore, established.

Determination of Electrolytic Dissociation by Change in
Solubility. — The slight differences between the solubilities
found experimentally and calculated, led Noyes to suspect
that the conductivity method of measuring dissociation was
not accurate. He, therefore, reversed the above procedure,
and used solubility measurements to determine dissoci-
ation. Knowing the dissociation of the substance in the

^ Ztschr. phys. Chem., 6, 241.

152 ELECTROLYTIC DISSOCIATION

saturated solution, and the change in the solubility of
this substance produced by adding a given amount of the
second substance, he could calculate the dissociation of the
second substance.

A condition which must be fulfilled is, that the salt with
which the solution is saturated is not very soluble, since
we would then be dealing with a concentrated solution, to
which the laws here involved do not apply.

Noyes first used thallous chloride with which to saturate
his solvent, since it is not very soluble ; and then added
to this a number of soluble chlorides, as potassium,
sodium, and ammonium, and calculated the dissociation
of the latter, from the change which he found produced
by them in the solubility of the thallous chloride. He ^ at
first obtained dissociation values for the alkaline chlorides
and other compounds, which differed considerably from
that calculated from conductivity.

Agreement between Dissociation determined by Conduc-
tivity, Freezing-point Lowering, and Solubility. — We had,
then, two methods of measuring electrolytic dissociation,
conductivity, and change in solubility, and the two gave
values which did not agree. The question arose, which
is correct, or are both methods to be discarded?

At this time H. C. Jones ^ undertook, at the suggestion
of Ostwald, to so improve the freezing-point method of
Beckmann, that it could be applied to the measurement
of electrolytic dissociation. A thermometer divided into
thousandths of a degree was made, and carefully standard-
ized. The apparatus to contain the liquid was enlarged

1 Ztschr. phys. Chem., 9, 603 ; 13, 162; 13, 412.
a IHd., II, no, 529; 12, 623.

EVIDENCE FOR THE THEORY 153

SO as to hold a litre. The air-bath around the liquid
was enlarged, and a number of precautions taken to
secure more accurate determinations of the temperatures
at which both solvent and solution froze. The dissociation
of a number of acids, bases, and salts was worked out by
this improved freezing-point method, over a considerable
range of concentration. The result was, as has already
been seen (p. 1 30), a satisfactory agreement between the
dissociation calculated from freezing-point lowering and
that calculated from conductivity.

In calculating dissociation from solubility, Noyes had
assumed that the thallous chloride was dissociated to the
same extent as potassium and sodium chlorides. He
afterwards found ^ that this assumption was not correct.
He determined the dissociation of thallous chloride,
and when he introduced the correct values for this com-
pound into the calculation, he found that the dissociation
of the second compound, as determined by solubility,
agreed very satisfactorily with the results of the other two
methods.

The three most general methods of measuring electro-
lytic dissociation give, then, values which agree very well
with one another. This fact should be carefully borne in
mind, in considering the evidence bearing upon the theory
of electrolytic dissociation.

The Relation between the Two Kinds of Dissociation
an Analogy. — The relation which has just been pointed
out, between the dissociation of a vapor by heat and elec-
trolytic dissociation, is only an analogy. The processes
are not at all identical, as is shown by the fact that the

1 Ztschr. phys. Chem., 16, 125.

154 ELECTROLYTIC DISSOCIATION

end products are very different. Take the compound
ammonium chloride; it is broken down by heat into
ammonia and hydrochloric acid: —

NH4Cl = NH8 + HCl.

Both of these are in the molecular condition, and can
be isolated.

When ammonium chloride is dissociated electrolytically
by water, it breaks down thus : —

NH4C1 = NH4 + C1-

The composition of the products is not only different
from the first case, but both the ammonium and chlorine
exist as ions, the one charged positively and the other
negatively, and neither can be isolated as such. That
there is some deep-seated connection between the two
processes is probable. Fused salts often conduct the
current just as they would do if dissolved in water. But
we must leave it for the future to show the exact nature of
the connection between the two kinds of dissociation.

DISSOCIATION AND CHEMICAL ACTIVITY

Perhaps the most interesting test of the theory of elec-
trolytic dissociation yet remains. If the properties of
dilute solutions of electrolytes are, in general, properties
of the ions, what must be said in reference to the property
of such solutions to react chemically. If there are only
ions present in the solutions, it is clear that any chemical
reaction which may take place is a reaction between ions
only. If the solution contains molecules as well as ions.

EVIDENCE FOR THE THEORY I55

the chemical reactivity may be due to the molecules, or it
may be due to the ions, or it may be due to both. The
problem is not only of interest from the physical chemical,
but is of the very highest importance from the purely
chemical, standpoint.

The number of possible cases by which the relation
between dissociation and chemical activity can be investi-
gated is very large. We will take several acids, inorganic
and organic, and a few bases which have been worked
out thoroughly in this connection. The method of attack-
ing the problem is comparatively simple. The dissocia-
tion of substances must be determined, also their power
to react chemically. Then the two must be compared.

Conductivity and Reaction Velocity. — Here, again, we
are indebted for our knowledge chiefly to Ostwald. In a
paper on the catalysis of methyl acetate,^ he expressed the
opinion that the velocity with which acids would invert
cane-sugar, like other reactions of acids, depends only on
their affinity. In a later paper ,2 describing work along
this line, this view was substantiated. It then remained
to determine whether there was any relation between these
two reactions produced by different acids, and the disso-
ciation of the acids themselves. The following table, taken
from Ostwald's Lehrbuch,^ gives a direct comparison of the
conductivities of a number of acids, with their power to
saponify methyl acetate, and to invert cane-sugar.

Column I gives the conductivities of the acids referred
to hydrochloric acid as 100; column II, the velocities with
which they effect the catalysis of methyl acetate; and

1 Joum. prakt. Chem. [2], 38, 495. * Ibid.^ 29, 385.

• Lehrb. allg. Chem., II, p. 650.

156 ELECTROLYTIC DISSOCL^TION

column III, the velocities with which they invert cane-
sugar.

b* .

Hydrochloric acid,

lOO.OO

100.00

Hydrobromic acid,

lOI.OO

98.00

III.OO

Nitric acid,

99.60

92.00

100.00

Sulphuric acid.

65.10

73-90

73.20

Formic acid.

1.68

I-3I

1-53

Acetic acid,

0.42

0.34

0.40

Monochloracetic acid.

4.90

4.30

4.84

Dichloracetic acid,

25-30

23.00

27.10

Trichloracetic acid.

62.30

68.20

75-40

Oxalic acid.

19.70

17.60

18.60

Malonic acid.

3.10

2.87

3-o8

Succinic acid.

0.58

0.50

0.55

Malic acid,

1.34

1.18

1.27

Tartaric acid.

2.28

2.30

—

Racemic acid.

2.63

2.30

—

Ostwald adds, that when we consider that neither the
temperature, nor the dilution, is the same in the three
series, the agreement is satisfactory.

Ostwald studied also other reactions in which acids are
involved, such as the velocity with which they dissolve
calcium oxalate, or the way in which they divide a base
between them. He found, in all of these cases, exactly the
same order of avidity as given above.

A little later he carried out an investigation strictly
analogous to the above, using a number of bases. The
reaction studied was the velocity with which bases sapon-
ify ethyl acetate. The relative reaction velocities and
conductivities are given in the following table. Column I
gives the reaction velocities; column II, the conductivities.

EVIDENCE FOR THE THEORY 1 57

Potassium hydroxide,

161.00

Sodium hydroxide,

162.00

149.00

Lithium hydroxide,

165.00

142.00

Ammonium hydroxide,

3.00

4.08

Methylamine,

19.00

20.02

Ethylamine,

19.00

20.05

Propylamine,

18.06

18.04

Amylamine,

4.00

6.09

Dimethylamine,

22.00

2305

Diethylamine,

26.00

28.03

Trimethylamine,

7.03

9.07

Triethylamine,

22.00

20.02

Tetraethyl ammonium hydroxide,

131.00

128.00

The agreement is as satisfactory as the conditions of
work would allow us to expect.

Dissociation measured by Chemical Activity. — We have
just seen that there is proportionality between dissociation
and chemical activity, and that, therefore, the amount of
dissociation may be used as a measure of the chemical
activity of electrolytes.

This process can, on the other hand, be reversed, and
the chemical activity of substances be used as a measure
of their electrolytic dissociation. The conductivity and
freezing-point are the most convenient and general methods'
for measuring electrolytic dissociation, but there are cases
to which neither of these can be applied. It is sometimes
desired to know the amount of the dissociation of some
acid, in the presence of other electrolytes like the salts.
Since all of the electrolytes present would take part in the
conductivity, and in the lowering of the freezing-point of
the solvent, it would be difficult, if not impossible, to deter-

158 ELECTROLYTIC DISSOCIATION

mine the amount of the dissociation of the acid by means
of either of these methods.

Some method must be employed which will detect one
kind of ions in the presence of others. The chemical
reactivity of the hydrogen ion has been made use of to
solve the above problem. The rate at which cane-sugar
is inverted by hydrogen ions can be determined very
easily, and this reaction has been used by Trevor/ and
others, to measure the number of hydrogen ions present.

Similarly, the specific chemical reactions of other ions
have been used to determine the amount of these which
are present, when more direct methods are not applicable.
Thus, the dissociation of bases can be measured by the rate
at which the hydroxyl ions saponify an ethereal salt. These
examples suffice to show the proportionality between dis-
sociation and chemical activity, and that either may be
used as a measure of the other.

Chemical Reactions usually take place between Ions. —
The facts just pointed out show that chemical reactions, in
which acids and bases are involved, are reactions effected
by ions. The number of reactions in which ions are
known to take part is very great, including by far the
majority of the cases with which we have to deal.

It has been supposed that gases do not conduct
electricity, and are, therefore, undissociated. Reactions
between gases could not be ionic, if this were true. The
recent work of J. J. Thomson ^ has made it very probable
that gases are dissociated, to some extent, and reactions
between gases may be reactions between ions only. Thom-
son ^ has also shown that atoms of elementary hydrogen

1 Ztscbr. phys. Chem., lo, 321. ^ Nature, /oc. cit. « Ibid,

EVIDENCE FOR THE THEORY 159

gas behave as if they were both positive and negative, so
that it is not improbable that reactions between the parts
of elementary gases are ionic, but this is far from proved.
It is not safe to conclude, at present, that all chemical
reactions take place between ions. There are cases known
of substances which conduct very little, or do not conduct
at all, and yet react chemically. We have well character-
ized chemical compounds, formed by the union of two parts
of the same general electrical character. Thus, phos-
phorus and chlorine, sulphur arid chlorine, chlorine and
bromine, chlorine and iodine, iodine and bromine, combine ;
and we are accustomed to regard all of these ions as
carrying a negative charge. But in this connection the
question arises, whether anion and cation are not, after
all, only relative, one ion being charged more or less
positive, or negative, than another.

Reactions between organic compounds, in general, take
place much more slowly than between inorganic, and the
former are much less dissociated. This is probably due to
a slow progressive dissociation of the organic substances,
as the ions already present enter into chemical combina-
tion. This raises the question, whether in those reactions
between apparently undissociated substances, there are
not a few ions present which react, and as these take part
in the reaction, more and more ions are slowly formed,
which then in turn react.

Whatever may be the final decision as to whether mole-
cules can take part in chemical reaction, we are now justi-
fied in stating, that most of the chemical reactions with
which we have to do are not reactions between molecules,
but between ions.

l60 ELECTROLYTIC DISSOCIATION

Dissociating Power of Different Solvents. — Different
solvents have very different powers of breaking down
electrolytes into ions. Water is the strongest dissociant
known. Of the more common solvents, formic acid stands
next to water in its ionizing power. Then come methyl
alcohol and ethyl alcohol, respectively, then acetone, and
finally the ethereal salts and hydrocarbon, which have very
slight dissociating power.

J. J. Thomson^ has worked out an ingenious theory,
which will be considered later, connecting the dissociating
power of solvents with their dielectric constants. Experi-
ment has shown, that there is undoubtedly a qualitative
relation between the two, but there does' not seem to be a
proportionality. This is shown by recent work on the
dissociating power of formic acid,^ and of methyl and
ethyl alcohols.^ While the dissociating powers are in
general in the same order as the dielectric constants, they
are not proportional to them.

If water has such remarkable dissociating power, and as
chemical activity is due chiefly to ions, water should play
a very prominent rdle in bringing about chemical reaction.
We will now examine a number of cases which will show
whether this is true.

EFFECT OF WATER ON CHEMICAL ACTIVITY

Unless very special precautions are taken to exclude
moisture, every chemical reaction takes place in the pres-
ence of water. This is largely due to the presence of
water-vapor in the air, which permeates everything with

1 Phil. Mag., 36, 320. 2 Zanninowich-Tessarin, Ztschr. phys. Chem., 19, 251.

8 Jones, Zt«chr. phys. Chem. Jubelband.

EVIDENCE FOR THE THEORY l6l

•

which it comes in contact. Further, when a solvent other
than water is used, water is often formed as one of the
products of the many reactions. If there was a trace of
water-vapor present to start the reaction, the quantity
would increase rapidly as the reaction progressed.

To study the effect of water on chemical activity, we
must exclude all traces of moisture at the outset, and
choose reactions in which no water is formed. We must
see how the reaction progresses in the absence of water,
then admit water, and see what difference is produced.
This is the method which has been employed, and it has
led to some highly interesting and surprising results.
Some of these will now be taken up.

Action of Dry Chlorine on Metals. — Wanklyn^ passed
dry chlorine over fused metallic sodium, and found that no
action resulted. The melted sodium was shaken in contact
with the chlorine, so as to expose a fresh surface of the
metal. Still there was no chemical action between the
two. This explains the frequent failure of the lecture
experiment, where sodium chloride is formed by the direct
union of sodium and chlorine. If the lecturer is careful to
dry the chlorine gas which is passed over the molten
metal, he usually observes the sodium l)dng in the same
condition after the experiment as before. But if moisture
in any way is admitted^ the reaction takes place with
violence.

Comper^ studied the action of dry chlorine on a number
of metals. He found that metallic zinc was not acted on
by the chlorine at first, but the thin zinc-foil was attacked
after a time. Metallic magnesium was not acted upon at

1 Chem. News, ao, 271 (1869). * Journ. Chero, Soc, 43, 153 (1883),

l62 ELECTROLYTIC DISSCXIATION

all, and metallic silver very slowly. Bismuth was appar-
ently unacted upon, but tin was rapidly attacked. Anti-
mony and arsenic were rapidly acted upon, while mercury
was acted upon as rapidly as by moist chlorine.

In these experiments the chlorine was dried over calcium
chloride for some days. This was, evidently, not sufficient
to remove the last traces of moisture, so that the chlorine
used by Comper was only partly freed from water-vapor.
It would be of interest to repeat these experiments with
perfectly dry chlorine.

Comparative Inactivity of Dry Oxygen. — H. B. Baker ^
carried out a number of experiments with carefully dried
oxygen, which led to results of very considerable impor-
tance. The gas was dried by allowing it to stand for
a long time in the presence of phosphorus pentoxide.
Moist carbon, in the presence of oxygen, burned with the
scintillation characteristic of this reaction. A certain
amount of the dried carbon was burned in dry oxygen, but
much less than of the moist, and there was no scintillation
in the dry oxygen. Baker concluded from a number of
experiments, that pure charcoal, heated in oxygen dried
over phosphorus pentoxide, does not bum with a flame;
partial combustion, however, goes on, both carbon monox-
ide and carbon dioxide being formed. Sulphur, boron,
amorphous and ordinary phosphorus, do not bum in dry
oxygen. Selenium, tellurium, arsenic, and antimony show
no difference in their combustion, whether the oxygen be
moist or dry.

Dixon 2 studied the action of dry oxygen on carbon
monoxide, under the influence of the spark. He mixed

1 Phil. Trans. (1888), 571. « Ibid. (1884), 617.

EVIDENCE FOR THE THEORY 163

three volumes of carbon monoxide and one volume of dry
oxygen, and passed a spark through the mixture. There
was no explosion. More oxygen was then added, and
again the spark passed without explosion.

A fresh charge of carbon monoxide was then prepared
from oxalic acid, and an excess of dry oxygen mixed with
it. The spark passed through this, also, without any explo-
sion. A drop of water was then added to the mixture, the
spark passed and there resulted the usual explosion.

Experiments were then carried out to determine the
velocity of the reaction, as affected by the amount of steam
present. By the addition of steam it was found that the
velocity of the reaction increased very rapidly. The con-
clusions from this work were : The drier the carbon mon-
oxide and the oxygen, the less the tendency to unite ; a trace
of aqueous vapor causes the mixture to become inflam-
mable, and the velocity of the reaction increased with the
amount of water present.

Dry Hydrochloric Acid does not decompose Carbonates. —
After Wanklyn had showed that dry chlorine would not act
on fused sodium, and Baker, that dry oxygen is com-
paratively inactive, it was of interest to test the chemical
behavior of other substances when free from moisture.
One of the most vigorous of chemical reactions is the
decomposition of carbonates by strong acids. Hughes^
studied the behavior of dry hydrochloric acid toward
carbonates, to see what influence moisture would have in
such a reaction.

Hydrochloric acid gas was dried, by passing it over
sulphuric acid and then over phosphorus pentoxide. It

1 Phil. Mag., 34, 117 (1892).

1 64 ELECTROLYTIC DISSOCIATION

was then brought in contact with carefully dried calcium
carbonate. A few results will show the amount of car-
bonate decomposed. In one experiment: —

Amount of carbonate used 0.8705 g.

Weight of carbonate after treating with dried

hydrochloric acid 0.8712 g.

Increase in weight' 0.0007 g«

Percentage increase 0.08

In a second experiment the percentage increase in
weight was o.i. The theoretical increase in weight for
complete transformation is 29 per cent.

Moist hydrochloric acid gas was then passed over cal-
cium carbonate for the same length of time, when more
than one hundred times as much carbonate was decom-

posed as when dry hydrochloric acid gas was used. The
experiment was then performed just as above, using
witherite (BaCOg) instead of calcite. The result of one
experiment is given : —

Amount of witherite used 0.9976 g.

Weight after treating with dried hydrochloric

acid gas 0.9984 g.

Increase in weight 0.0008 g.

Percentage increase 0.08

The theoretical increase in weight, if all of the carbonate
is transformed into chloride, is 14.7 per cent.

Hughes concluded from his work, that the increase in
the weight of the carbonate, after passing a stream of dry
hydrochloric acid over it, was so small, that no definite
proof was furnished of any action having taken place.

EVIDENCE FOR THE THEORY 1 65

The slight variations observed may be due to experimental
errors, or to the imprisonment or entanglement of the
molecules of hydrochloric acid gas amongst the finely
powdered particles of Iceland spar, or witherite.

Dry Acids exert no Action on Litmus and do not form
Salts. — Blue litmus is not changed to red in a stream of
dry hydrochloric acid gas. Gore has shown that dry
liquefied hydrochloric acid has no action on litmus. Marsh
has proved that glacial acetic acid, which is perfectly free
from moisture, has no action on litmus. Marsh ^ has also
shown that pure sulphuric acid, free from every trace of
moisture, does not act on blue litmus, and, further, is
probably incapable of forming salts. And Veley^ has
proved that nitric acid, free from moisture and from nitrous
acid, is probably incapable of forming salts.

Dry Hydrochloric Acid does not precipitate Silver Nitrate
in Ether or in Benzene. — Silver nitrate was dissolved in
anhydrous ether, and in benzene. A current of dried
hydrochloric acid gas was passed through these solutions
for an hour. There was no precipitate formed, though the
solution became slightly turbid. When the silver nitrate
was dissolved in absolute alcohol, a more decided precip-
itate was formed in the course of an hour, but the decom-
position was far from complete. This remarkable result
was also obtained by Hughes.

Comparative Inactivity of Dry Hydrogen Sulphide. —
Veley ® found that dry hydrogen sulphide does not act on
quicklime, and this led Hughes to investigate the action
of dry hydrogen sulphide upon metallic oxides.

1 Chem. News, 61, 2. 2 phil. Trans. (1891), 279.

sjourn, Chem. Soc. (1885), 484; Phil. Mag., 33, 471 (1892).

1 66 ELECTROLYTIC DISSOCIATION

Magnesium oxide was used. Dry hydrogen sulphide
was passed over this, and the increase in weight ascertained.
One or two results will show what took place : —

First

Weight of magnesium oxide used 0-7597 g-

Weight after passing dry hydrogen sulphide . 0.7600 g.
Increase in weight 0.0003 g.

Second

Weight of magnesium oxide used 0.6360 g.

Weight after passing dry hydrogen sulphide . 0.6368 g.
Increase in weight 0.0008 g.

In both cases the increase in weight is within the limit
of experimental error. The change from the oxide to the
sulphide, which is exothermic and would, therefore, be
expected to take place, does not occur.

A drop of water was then added to the magnesium oxide,
and dry hydrogen sulphide passed over it as before.
The white oxide quickly became greenish yellow, and the
following result will show the increase in weight pro-
duced.

Weight of magnesium oxide and water . . . 0.7235 g.

Weight after passing the hydrogen sulphide gas 0.8435 g-

Gain in weight 0.1200 g.

The gain in weight, which expresses the amount of oxide
transformed into sulphide, is from 200 to 400 times as great
as when all moisture is excluded.

Similar results have been obtained with barium oxide.

EVIDENCE FOR THE TPIEORY 167

Dry hydrogen sulphide has no action upon barium oxide,
from IS"" to 90*^.

Ferric oxide showed a slight increase in weight when
dry hydrogen sulphide was passed over it. But this was
probably due to the incomplete drying of the oxide of iron.

When dry hydrogen sulphide was passed over paper
which had been moistened with lead acetate and afterwards
thoroughly dried, there was no action whatever. Moist
paper containing lead acetate was, of course, acted upon
at once. By passing the dried gas first over dry paper,
and then over moist, the difference in the action is very
striking.

The same experiment was performed, using antimony
trichloride instead of lead acetate. The dry paper was
unaltered by the dried hydrogen sulphide, while the moist
paper was immediately turned yellow. The same experi-
ment was performed with salts of tin, cadmium, bismuth,
silver, copper, mercury, and cobalt, and exactly the same
results were obtained in all cases.

We may conclude, in general, that dry hydrogen sul-
phide has no action on the dry soluble salts of the metals,
but if moisture is present a change takes place at once.

Hughes ^ found that when mercuric chloride is dissolved
in absolute alcohol, a current of dry hydrogen sulphide
can be passed for fifteen minutes, without producing any
change. Afterwards the solution became slightly turbid,
then pale yellow, dark yellow, and finally greenish yellow.
No further change took place when the current was passed
an hour and a half. The addition of a small amount of
water changed the green to a black precipitate.

1 Phil. Mag., 35, 531 (1893).

1 68 ELECTROLYTIC DISSOCIATION

Other Reactions which do not take place without Water.
— According to Baker,^ sulphur trioxide does not combine
with dry lime, or dry copper oxide.

Dry ammonium chloride may be sublimed from a mix-
ture of this salt with dried lime, without ammonia being
liberated.

Dry hydrogen and chlorine may be exposed to the
sunlight for two days, without anything like complete
reaction taking place.

Dry ammonia and hydrochloric acid can be partially
separated from a mixture of these gases, when oppositely
charged plates are placed in the mixture, the ammonia pass-
ing to'the negative plate, the hydrochloric acid to the positive.

Dry Hydrochloric Acid does not act on Dry Ammonia. —
The heading of this paragraph must be a surprise to any
one who is familiar with the properties of these gases, and
is not acquainted with the experimental work which has
been done to establish this fact.

Hughes 2 stated, that when ammonia is dried over lime,
and hydrochloric acid is dried by phosphorus pentoxide,
the two would remain in the presence of one another for
24 hours, without any deposit being formed, even upon the
sides of the containing tube.

H. B. Baker ^ published a very careful investigation of
this point, in which the ammonia and hydrochloric acid
gases were dried over phosphorus pentoxide, and brought
together in such a manner that any change in volume
could be readily observed. He concluded, that perfectly
dry ammonia and perfectly dry hydrochloric acid gas are
entirely without action upon one another.

1 Journ. Chem. Soc, 6j, 611. 2 Lqc^ qit. 3 Journ. Chem, Soc, 65, 611,

EVIDENCE FOR THE THEORY 1 69

The conclusion of Baker was called in question by
Gutmann.^ The latter claimed that ammonia and hydro-
chloric acid cannot be dried over phosphorus pentoxide,
since the gases are absorbed.

Baker,^ in reply, shows that the phosphorus pentoxide
used by Gutmann must have contained metaphosphoric
acid. And, further, that Gutmann did not take sufficient
care in drying the gases. The glass apparatus must be
carefully heated to remove the moisture, which, as is well
known, clings to it so tenaciously, and is held by it so
persistently. Baker repeated his earlier experiments,
working with .tHe greatest care, and found that his original
conclusion was confirmed in every respect. Dry hydro-
chloric acid gas does not combine with dry ammonia gas.

If this fact creates surprise, the following will be almost
beyond belief.

Dry Sulphuric Acid does not act on Dry Metallic
Sodium. — An experiment was performed before the
Chemical Society of London,^ in which a piece of metallic
sodium was plunged into concentrated sulphuric acid.
When the sodium, wrapped with a piece of wire which
served as a handle, was immersed in the acid, there was a
flash of light, showing incipient reaction ; then there was
perfect quiescence, the sodium remaining freely suspended
in the sulphuric acid. The reaction at first was due to the
presence of a few sodium ions on the surface of the metal,
produced by the moisture in the air, to which it was
exposed for an instant.

No one should repeat this experiment, unless the greatest

1 Liebig's Ann., 299, 3. 2 journ. Chem. Soc. (1898), 422.

8 Proceed. Chem. Soc. (1894), p. 86.

170 ELECTROLVnC DISSOCIATION

precautions Ire taken in drying both the sodium and the
sulphuric acid. It is quite evident that ordinary methods
of drying would not suffice.

The facts which have been cited in this section show
conclusively the necessity of the presence of water in
many chemical reactions. The question still remains, why
is water essential.? We believe we have the answer, in
that water has a very high dissociating power, breaking
down the molecules into ions, which then react. These
facts are just what would be predicted, if the theory of
electrolytic dissociation is true.

Conclusion. — Some of the lines of evidence bearing
upon the theory of electrolytic dissociation have been
presented in this chapter. There are many more which
might be adduced; but it seems that what has been
presented suffices to show how strong the evidence is in
favor of the truth of this generalization. It has already
been mentioned, and stress should be laid upon it, that
there are facts to which the theory, as we now conceive it,
does not seem to apply. But the evidence in favor of
the theory is so overwhelming, in comparison with the few
apparent exceptions, that we should examine the latter
very closely before concluding finally that they are real
exceptions. Without for a moment ignoring the facts for
which the theory does hot seem to entirely account, the
writer believes that the evidence in favor of a great
generalization being expressed by the theory of electro-
lytic dissociation is as strong as in the case of many of
our so-called laws of nature. For how many of these
apply under all conditions, and are entirely free from
exceptions ?

CHAPTER IV

SOME APPLICATIONS OF THE THEORY OF ELECTROLYTIC

DISSOCIATION

In the last two chapters we have attempted to answer
the questions, how did the theory of electrolytic dissocia-
tion arise, and what are some of the reasons for believing
that it is true ? There still remains the question, of what
scientific use is this theory? And this brings us to the
subject of our last chapter.

Few theories have ever been advanced in science which,
in a dozen years, have found wider application than the
theory which we are considering. It has already been
applied not only to chemical problems, but also to physical,
and to biological in the broadest sense. A few of these
applications will now be taken up.

APPLICATION OF THE THEORY OF ELECTROLYTIC DIS-
SOCIATION TO CHEMICAL PROBLEMS

This theory has never directly exercised any marked
influence on the study of the relations between the com-
position and constitution of pure substances, and their
properties. This is obviously true, since pure substances
are undissociated.

The theory has, however, had an indirect influence in
this direction. It has opened up such a number of

^7*

172 ELECTROLYTIC DISSOCIATION

entirely new fields of research, that it has detracted from
work along these lines. The number of investigations of
relations, such as the above, has become less in the last
few years ; and although an elaborate piece of work has
appeared from time to time, the physical chemist of to-day
finds more promising lines of work suggested to him by
the newer conceptions. Without detracting for a moment
from the value of the enormous amount of labor spent in
studying the properties of pure substances, yet it should
be stated, that the great advances in the last few years
have resulted from the study of one substance in the
presence of another.

THE THEORY OF ELECTROLYTIC DISSOCIATION AS APPLIED

TO SOLUTIONS

It will be remembered that van't Hoff showed that
solutions behave, in certain respects, like gases. There is
an analogy between the gas particles distributed in space
and the dissolved particles distributed throughout the
solvent, — space bearing a similar relation to the gas that
the solvent does to the solution. It has also been shown,
as stated above, that it is in solutions, chiefly, that we have
molecules broken down into ions. Further, the impor-
tance of a thorough study of solutions becomes at once
apparent, when we consider that most chemical reactions
take place in solution. This is especially true of inorganic
reactions, most of them taking place in what has come
to be known as the wet way. And, indeed, in organic
chemistry, also, some solvent is often employed which has
the property of dissociating to some extent one or more of
the substances present.

APPLICATIONS OF THE THEORY 1 73

We know matter in three states of aggregation, solid,
liquid, and gas, and have, therefore, nine classes of
solutions : —

Gas in gas Gas in liquid Gas*in solid

Liquid in gas Liquid in liquid Liquid in solid

Solid in gas Solid in liquid Solid in solid

Examples of all of these nine classes are known. We
can, however, from the standpoint of the dissociation
theory, deal best with solutions in liquids as solvents,
and we will, therefore, limit ourselves to solutions of this
kind.

Osmotic Pressure. — Since van't Hoff^ pointed out the
analogy between the osmotic pressure of dissolved sub-
stances and the gas pressure of gases, much work has
been done on methods of measuring osmotic pressure.
Osmotic pressure, as has already been shown, is a very
difficult quantity to measure directly, and a number of
comparative methods have been devised. These aim to
measure the relative osmotic pressures exerted by different
substances. If we, then, know the absolute osmotic press-
ure of any one of these substances, we can calculate the
absolute osmotic pressure of all the others. The rel-
ative method of De Vries^ has already been considered.
Those of Tammann,^ Bonders and Hamburger,* Wladimi-
roff,^ and Lob® should be mentioned, in order that they
may be examined, if desired. These methods have been
applied, not only to non-electrolytes, but also to electro-

1 Loc. cit, * Loc, cit, * Wied. Ann., 34, 299.

* Onders Physiol. Lab., Utrecht (3), 9, 26; Ztschr. phys. Chem., 6, 319.
6 Ztschr. phys. Chem., 7, 529. • /did., 14, 424.

174 ' ELECTROLYTIC DISSOCIATION

lytes. Since an ion exerts exactly the same osmotic
pressure as a molecule, when we determine the osmotic
pressure of a partly dissociated solution, we can calculate
the amount ,to which that solution is dissociated. We
know,, from the study of non-electrolytes, the osmotic
pressure which would be exerted if there was no dissocia-
tion ; we know that if the electrolytes break down into
two ions, that the solution when completely dissociated
would give twice this osmotic pressure. Knowing the
actual osmotic pressure exerted, we can calculate the
amount of dissociation at once. Although we have more
accurate methods of measuring dissociation than the
above, yet this serves to confirm the results of other
methods.

Diffusion. — Our knowledge of the osmotic pressure of
solutions has thrown light on the way in which salts diffuse
in solution. It is well known that a salt always diffuses
from the solution into the. pure solvent, or from a more
concentrated to a more dilute solution ; and this continues
until the whole has become homogeneous. The law of
diffusion was discovered by Fick.^ "The amount of salt
which diffuses through a given cross-section is propor-
tional to the difference in concentrations of two cross-
sections lying very close to one another." Diffusion
depends, then, upon difference in concentration.

The fundamental question of diffusion is, however, still
unanswered. What causes it? What is the force in
operation which drives the dissolved substance from one
region to another quite remote, if the solution is allowed
to come in contact with the pure solvent, or if a more

1 Pogg. Ann., $4, 59 (1855).

APPLICATIONS OF THE THEORY 175

concentrated is brought in contact with a more dilute
solution ?

We see at once a connection between the law of diffu-
sion and that of osmotic pressure. Diffusion depends
upon difference in concentration. Osmotic pressure de-
pends also upon difference in concentration, and a quan-
titative study of both the diffusion and osmotic pressure of
non-electrolytes and electrolytes has shown that osmotic
pressure is the cause of diffusion. Wherever there is a
difference in the osmotic pressure of two solutions, diffu-
sion will take place from the region of greater into that
of less pressure, if the two solutions are brought in con-
tact. This is analogous to the diffusion of gases, which
always takes place from the region where the gas exerts
a greater pressure to the one where the pressure is smaller.

But there exists a marked difference between the two
kinds of diffusion. With gases this takes place very
rapidly, and equilibrium is usually established in a short
time. But diffusion in solution proceeds very slowly, and
it may require weeks and months for a condition of equi-
librium to be reached, if the column of liquid has any
considerable length.

Nernst^ has worked out a theory of diffusion based
upon osmotic pressure, first for non-electrolytes, which are
simpler because there is no dissociation, and then for elec-
trolytes, taking into account their dissociation. This leads
to the conclusion, that the forces required to drive dis-
solved particles through the solvent at any appreciable
velocity are enormous. Ostwald^ has calculated that the
force required to drive 60 grams of urea through water,

1 Ztschr. phys. Chem., 2, 613. 2 Lehrb. allg. Chem., I, p. 697.

176 ELECTROLYTIC DISSOCIATION

with the velocity of i cm. per second, has the value of '
2500 million kilograms. He suggests that the cause of
this is the very fine state of division of the dissolved sub-
stance. The force required to throw a small stone with a
considerable velocity is not great. But powder the stone
very finely, and an enormous force would be required to
project the particles of dust with the same velocity. Now
let this process of division be continued until the mole-
cules were reached, and forces of the above order of
magnitude would be required.

The principle of Soret,^ which has already been con-
sidered, as furnishing evidence for the applicability of the
law of Gay Lussac to the osmotic pressure of solutions,
should be referred to again in this connection. The
change in the concentration of a homogeneous solution,
produced by keeping the different parts at different tem-
peratures, has been shown to agree with that calculated
from the above law. This principle applies as well to
solutions which are dissociated as to those which are not,
since an ion exerts the same osmotic pressure as a mole-
cule, and is, therefore, subject to the same law of diffusion.

Lowering of Freezing-point. — The theory of electro-
lytic dissociation has been applied to the lowering of the
freezing-point of the solvent produced by the dissolved
substance. Reference has already been made . to this
fact, in connection with the evidence bearing upon the
theory. It was there shown that Arrhenius proved that
the values of the coefficient " /,'* calculated from freez-
ing-point lowering, agreed with those calculated from
conductivity.

1 Loc, cit, see p. 86.

APPLICATIONS OF THE THEORY 1 77 '

The freezing-point method was used for a long time,
chiefly to determine the molecular weights of substances
in solvents which do not dissociate them. The applicabil-
ity of the freezing-point method to the problem of molec-
ular weights was pointed out by Raoult,^ several years
before the theory of electrolytic dissociation was proposed.
By working with solvents other than water, such as formic
and acetic acids, benzene, and nitrobenzene, he was able
to discover certain general laws of the freezing-point low-
ering of solvents. When water was used as a solvent,
so-called abnormal values were obtained. The freezing-
point lowerings were usually much greater than would be
expected from what was found in other solvents.

The experimental method used at first by Raoult was
necessarily crude, as it had just been devised by him.
This has since been very greatly improved by Beckmann.^
And the method of Beckmann has been enlarged and
improved by Jones,^ Loomis,* Lewis,^ Ponsot,® and others.
The most refined of all is probably the method described
very recently by Raoult,^ in which he has utilized the best
points in all of the above-described methods. However
this may be, the freezing-point method has * now been
developed to a fair degree of perfection.

The direct object in improving the freezing-point method
was not the determination of molecular weights, — the
method of Beckmann would suffice for this purpose, — but
to measure the electrolytic dissociation of acids, bases, and

1 Ann. Chim. Phys. [6], 2, 66; Harper's Science Series, IV, 71.

2 Ztschr. phys. Chem., 2, 638, 715 ; 7; 323. 5 Ztschr. phys. Chem., 15, 365.
« Ibid., II, no, 529 ; I2, 623 ; 18, 283. « Ann. Chim. Phys. [7] , 10, 79.
* V^ied. Ann., 51, 500; 57, 495 ; 60, 523. 7 Ztschr. phys. Chem., 27, 617.

178 ELECTROLYTIC DISSOCLVTION

salts in water. There were also certain theoretical questions
involved, in connection with the freezing-point constant.

The freezing-point method has already been applied
extensively to the measurement of electrolytic dissocia-
tion, and is now to be regarded as one of the most gen-
eral methods for this purpose. The results obtained by
Jones, compared with those of Kohlrausch from conduc-
tivity, have already been given.

Ions lower the freezing-point of a solvent exactly the
same amount as molecules, so that with a partly disso-
ciated electrolyte we have the sum of the lowering of the
molecules plus that of the ions. We know, however, from
non-electrolytes, how much lowering the molecules alone
would produce, and we can calculate from the lowering
found, what percentage of the molecules is broken down
into ions.

The application of the freezing-point method to the prob-
lem of molecular weights in solution has helped to solve
a large number of questions, especially in organic chem-
istry. But from a physical chemical point of view, the
newer application of the freezing-point method to the de-
termination of electrolytic dissociation is by far the more
important.

Lowering of Vapor-tension, Rise in Boiling-point. —
What has been said in reference to the lowering of the
freezing-point of solvents, can be applied directly to the
lowering of their vapor-tension by substances dissolved in
them. Here, again, Raoult ^ did much of the pioneer work.
The laws of the lowering of vapor-tension, or rise in boiling-

1 Ann. Chim. Phys. [6] , 15, 375 ; Compt. rend., 104, 1430 ; Harper's Science
Series, IV, 97, 125.

APPLICATIONS OF THE THEORY 179

point, had not been discovered, mainly because dissociat-
ing solvents had been used. Raoult worked with solutions
in ether, and discovered the general law of the lowering
of vapor-tension : One molecule of any undissociated sub-
stance, dissolved in one hundred molecules of any volatile
liquid, lowers the vapor-pressure of this liquid by a nearly
constant fraction of its value.

He showed how the lowering of vapor-tension, like the
lowering of the freezing-point, can be used, to determine
the molecular weight of the dissolved substance.

Beckmann ^ improved this method of Raoult, as he had
improved the freezing-point method. Instead of measur-
ing the depression of the vapor-tension, he determined the
rise in boiling-point, — a quantity which could be much more
easily and accurately ascertained. The Beckmann method
of determining molecular weights has been modified by a
number of investigators. The more important of these
improvements are those introduced by Hite,^ Jones,^ and
Landsberger.*

The boiling-point method, like the freezing-point, has
been applied also to the measurement of the dissociation
of electrolytes. The freezing-point method can be used in
this connection, with only a few solvents, since many of the
solvents with high dissociating power freeze at a tempera-
ture which is too low to deal with successfully in this con-
nection. Indeed, the freezing-point method, as a measure
of dissociation, has been applied mainly to aqueous solu-
tions. The boiling-point method for measuring electrolytic

1 Ztschr, phys. Chem., 4, 532 ; 6, 437 ; 8, 223 ; 15, 656 ; 17, 107 ; 18, 473 ; 21, 239.

2 Amer. Chem. Journ., 17, 507.

8 Results will appear in Ztschr. phys. Chem. Jubelband.
* Ber. d. chem. Gesell., 31, 4^8.

l80 ELECTROLYTIC DISSOCIATION

dissociation admits of much wider application. It can be
employed with formic acid, methyl alcohol, ethyl alcohol,
acetone, etc., solvents which have a fairly great dissociating
power.

This application of the boiling-point method is of very
considerable importance, since it is the only method avail-
able for measuring accurately the dissociation of electro-
lytes in these solvents. The conductivity method cannot
give very close results, because of the difficulty of deter-
mining the value of the molecular conductivity (fioo) at
complete dissociation. These solvents all dissociate so
much less than water, that, with the exception, of formic
acid, the dilution at which the dissociation is complete is
so great that the conductivity method does not give accu-
rate results. The impurities in the solvents, at these very
high dilutions, also render the results imperfect.

The importance of measuring dissociation in solvents
other than water will be evident, when we consider that
this is the first step toward a physical chemistry in other
than aqueous solutions. And, in addition, there is in-
volved a theoretical question of interest and importance.
J. J. Thomson ^ has shown, as already mentioned, that if
the molecules are held together by the attraction of oppo-
sitely charged parts, and if the. molecules are broken down
into these parts by solvents, the dissociating power of sol-
vents should stand in the same relation as their dielectric
constants.

Jones 2 has measured the dissociation of a number of
salts in methyl and ethyl alcohol, using his modification

1 Phil. Mag., 36, 320.

2 Results will be published in Ztschr. phys. Chem. Jubelband.

APPLICATIONS OF THE THEORY l8l

of the Beckmann boiling-point apparatus. While he found
a qualitative relation between the dielectric constants of
these solvents and their dissociating power, compared with
water, a proportionality between dielectric constants and
dissociating power does not exist, as has already been
stated.

^ The application of the boiling-point method to the prob-
lem of electrolytic dissociation has been made only in the
last year or two, and much of value will undoubtedly
result from further work with this method. It would,
doubtless, have been applied much earlier, but for the
experimental difficulties involved. The method at first
was, of course, imperfect, containing a large number of
errors, and, further, the boiling-point constants of solvents
are small, and therefore the quantity to be measured was
always small. A number of sources of error have now
been removed from the boiling-point method, and when
all the details are carefully observed,, and the entire work
carried out with the greatest care and precaution, results
can be obtained for the electrolytic dissociation in the
alcohols, which should be accurate to within about i per
cent.

The rise in the boiling-point, like the lowering of the
freezing-point, is that produced by both molecules and
ions, — an ion lowering the boiling-point to the same
extent as a molecule. But in partly dissociated solutions
we know, from a study of non-electrolytes, the rise produced
by the molecules. We know, further, that if the mole-
cules of the electrolyte were completely broken down into
two ions each, the rise in the boiling-point would be twice
as great a§ if there was no dissociation, Frgm the rise

1 82 ELECTROLYTIC DISSOCIATION

actually found, we can calculate, at once, the percentage
of dissociation of the solution in question.

The theory of electrolytic dissociation has been applied
to solutions, in a much wider sense than would be inferred
from the foregoing. The additive nature of the properties
of completely dissociated solutions has already been dis-
cussed. It is not necessary to deal, moreover, with solutions
of only one electrolyte in a solvent. Two or more electro-
lytes can be brought simultaneously into the solvent, and
the resulting solution studied. The effect of one dis-
sociated substance on another with a common ion has
already been indicated. Some interesting properties of
solutions, which, when mixed, do not reciprocally affect
each other's properties, have been worked out by Arrhe-
nius^ and others. Arrhenius^ worked with solutions of
acids, and termed those which fulfil this condition^ "iso-
hydric." The study of such solutions from the standpoint
of his theory, brought out much of interest.

Then, again, we are not limited to one or more electro-
lytes in one solvent. We can have one or several electro-
lytes, in one or more solvents ; and such cases have been
studied. The electrolytes may, or may not, have a common
ion, or the solvents may, or may not, be mixable with each
other. The number of possibilities is very great, and
some have already been studied. But the scope of this
work will not allow further detail.

The Theory of Electrolytic Dissociation as applied to
Electrochemistry. — New light has been thrown upon this
entire field, by the theory of electrolytic dissociation.
Many facts which were discovered before the theory was

1 Wied. Ann., 30, 51. 2 Ztschr. phys. Chera., 2, 284.

APPLICATIONS OF THE THEORY 1 83

proposed, have now, by means of it, been correlated, and
rationally explained.

Electrolysis. — We can now interpret much more clearly
the phenomenon of electrolysis. A dilute solution of an
electrolyte is completely dissociated; there are no mole-
cules present, all of them having been broken down into
ions. When the current is passed through such a solu-
tion, it directs the ions, the one to the cathode, the other
to the anode, where they give up their charges and sepa-
rate in the atomic or molecular condition. There appears
to be a marked difference between the* way in which
metallic conductors carry the current, and the manner
in which it passes through a solution of an electrolyte.
A metal wire carrying a current apparently undergoes
no change except in temperature, while a solution con-
ducts only by undergoing simultaneous decomposition, —
the positively charged parts moving in one direction, the
negatively charged in the other. Although there is appar-
ently such a marked difference in the way in which the
two classes of conductors carry the current, a closer study
of the two processes brings out relations between them
which do not appear on the surface. Indeed, the work
of J. J. Thomson has made it probable that there is a
close relation between metallic and electrolytic conduction.
The view seems to be gaining ground that conduction in
metals is also ionic, the ions here being, of course, very
much more restricted in their movements.

The ions into which electrolytes dissociate all carry the
same amount of electricity, or a simple rational multiple of
this unit quantity. This was discovered early in the cen-
tury by Faraday, and is now the well-known Faraday's

1 84 ELECTROLYTIC DISSOCIATION

law. All univalent ions carry the same amount of electric-
ity.' This we will call the unit. All bivalent ions carry
twice, all trivalent ions three times this amount, and
so on.

This was proved by the fact, that when a current is
passed through solutions of metallic salts containing uni-
valent, bivalent, trivalent, etc., metallic ions, the quantities
of the metals which separate stand in the same relations
as their chemical equivalents. Univalent metals separate
in the ratios of their atomic weights, bivalent in the
ratios of one-half their atomic weights, trivalent metals
in the ratios of one-third of their atomic weights, and
so on.

This connects, directly, the charges carried by the ions
with their valence. The combining power of ions is condi-
tioned by the amount of electricity which they carry. If
they carry one unit of electricity, they have the smallest
valence or combining power. If two units, they have
twice the combining power ; if three units, three times the
power to combine, and so on.

This is exactly what would be expected, if the power
to enter into chemical combination was the attraction
between oppositely charged parts. The larger the charge
carried by the ion, the greater its combining power. We
may now say that chemical valence is conditioned by the
amount of electricity carried by the ion, and we thus give
a more definite and precise meaning to a term which has
hitherto been characterized chiefly by vagueness and
obscurity.

The law of Faraday, which applies to the amount of
electrical energy carried by the ions, has its analogue in

APPLICATIONS OF THE THEORY 185

the law of Dulong and Petit, which says, that the capacity
for heat energy is the same for all atoms.

After the law of Faraday had been shown to be a true
expression of the amount of electricity carried by ions, it
became a matter of importance to determine the amount
of electricity carried by some unit quantity of ions. The
most convenient quantity to use was the atomic weight of
the element in grams. The problem, then, was to deter-
mine the amount of electricity which would electrolyze
a gram-atomic weight of a univalent metal, or half a
gram-atomic weight of a bivalent metal. This quantity,
termed the " electrochemical equivalent,'* has been worked
out with great care, and with the following result: To
separate a gram-atomic weight of a univalent element
like silver, requires, in round numbers, 96,540 coulombs of
electricity — more accurately 96,537 coulombs. This value
is given to show the enormous charges carried by the ions,
and also for future reference.

The large amount of electrical energy carried by the ions
explains the great difference between the properties of
atoms or molecules, and ions. Potassium, sodium, and such
substances, when present in the metallic or molecular con-
dition, act upon water with great vigor, while potassium and
sodium ions are perfectly inactive toward water. The same
distinction applies to a large number of other substances.

The failure to recognize the distinction between atoms
or molecules, and ions, that the one is charged and the
other not, led to confusion in the early days of the theory
of electrolytic dissociation. This distinction, however, has
so often been insisted upon, that it is now pretty generally
understood.

1 86 ELECTROLYTIC DISSOCIATION

When electrolytes are decomposed by the current, the
ions may give up their charges and separate on the elec-
trodes as metallic ions do, yielding the free metal. Or the
ion may be of such a nature that when it loses its charge,
and passes over into the atom, or group of atoms, this
may act chemically upon the water present, and decom-
pose it. Thus, when a sodium salt is electrolyzed, the
sodium ion gives up its charge to the cathode and becomes
an atom. But, of course, free sodium cannot exist as such
in the presence of water. It decomposes water, forming
sodium hydroxide, and hydrogen gas separates from the

cathode : —

Na + HOH = NaOH + H.

This is true of a large number of ions. When they lose
their charge, they act upon the water present. When an
acid is electrolyzed the hydrogen ion passes to the cathode,
gives up its positive charge to this, and escapes as hydro-
gen gas. The anion, whose nature depends upon the acid
used, passes to the anode, and gives up its negative charge
(in reality takes up a positive charge). The anion, after it
becomes electrically neutral, decomposes the water pres-
ent. If the acid is hydrochloric, the free chlorinq around
the anode decomposes water, forming hydrochloric acid,
and sets oxygen free : —

2 CI + H2O = 2 HCl + O.

When an acid is electrolyzed, we thus have hydrogen
set free at one pole and oxygen at the other.

It may be said, in general, that anions, after they have
lost their charge, are incapable of existing in the presence

APPLICATIONS OF THE THEORY 1 87

of water, but decompose it chemically, setting oxygen
free. A current can, then, be passed through a solu-
tion of an electrolyte in only one way. The ions must
carry the electricity, and must separate at the electrodes
after losing their charge. The cation may separate
directly, as the metals do, or it may act upon water,
liberating hydrogen. The anion, after losing its charge,
usually decomposes water, liberating oxygen at the
anode.

The decomposing action of the current has often been
used to determine what part of a compound forms the
cation, and what part the anion. The principle is
simple. The electrolyte is dissolved in water, and the
current passed. The cation moves to the cathode, the
anion to the anode. After electrolysis, determine what
constituents have collected around the two electrodes;
that around the cathode is the cation, that around the
anode is the anion. In all acids hydrogen is the cation,
and the remainder of the molecule, whatever its nature,
forms the anion. In the case of some of the organic
acids the anion is very complex. The metal in salts forms
the cation, the remainder the anion. Bases dissociate into
a hydroxyl anion, and the remainder forms the cation.
The characteristic ion of acids is hydrogen, of bases is
hydroxyl. This same method of determining how a
molecule will dissociate has been applied also to very
complex cases. How will compounds like K4Fe(CN)g,
K2PtCle, KMnO^, dissociate; what will be the cation,
and what the anion.? This has been determined by
electrolyzing solutions of these salts. We would expect
that all of the metals would go to the cathode, and the

1 88 ELECTROLYTIC DISSCOATION

remainder of the compounds to the anode. These com-
pounds, however, dissociate as follows: —

++++

K^FeCCN)^ = K^ -h F<CN)e.

K2Pt(Cl)e =K^-h PtClg.
KMnO^ = K + MnO^.

These examples serve to show the relative nature of
cation and anion. What is a cation under one condition,
may be a part of an anion under other conditions. Take
the above cases, iron in iron salts is always the cation,
and this applies, also, to platinum and manganese. But
in these complex salts, where there is a more positive ion
present, such as potassium, these three metals become,
respectively, a part of the anion. A number of other
cases, similar to these, have been worked out, and many
interesting results have been found.

A fact of unusual interest in connection with the
charge which ions may carry has been pointed out by
Ostwald.^ An ion having exactly the same chemical com-
position may carry different charges under different con-
ditions. The ion (FeCNg) may carry four charges, as it
does if it comes from the compound K4Fe(CN)g, or it may
have only three charges, if it is a product of the dissociation
of KgFe(CN)g. Similarly, the ion MnO^ is univalent, if it
comes from the compound KMnO^, and bivalent if from
K2Mn04. As Ostwald points out, these are especially
interesting cases of isomerism, since it cannot be referred
to a different "position of the atoms." The only diflfer-

1 Lehrb. allg. Chem., II, p. 588.

APPLICATIONS OF THE THEORY 1 89

ence here is in the charges which the ions carry. The

properties of Mn04 are very different from Mn04.
Trivalent iron, manganese, cobalt, etc., have very different
properties from bivalent, and there is no more reason to
expect them to have the same properties, than to expect
that red phosphorus would have the same properties as
yellow. In both cases there is a different amount of
energy present. This is proved by electrolysis for iron,
manganese, etc., compounds. Only two-thirds as- much
ferric iron will separate for a given current as ferrous, and
the same applies to the other compounds. That there are
different amounts of energy in the two modifications of
phosphorus, is shown by their heats of combustion, which
are very different.

The ions with the larger charge usually tend to lose
some of it, and pass over into the condition where they
carry less electricity. Many of the phenomena which we
describe as oxidation and reduction are due only to the in-
crease and decrease, respectively, of the electrical charges
upon the ions, — a ferrous ion passes over into a ferric by
taking up one positive charge ; a cupric ion becomes a
cuprous ion by losing one positive charge.

Modes of Ion Formation. — We have spoken of molecules
dissociating directly into two, three, and more ions, and
have, perhaps, left the impression that electrolytic dissocia-
tion can take place in. only one way. There are, however,
a number of ways in which molecules can break down
iiito ions. The following have been pointed out by Ost-
wald :^ —

(i) A molecule may break down directly into an equiva-

^ Lehrb. allg. Chem., II, p. 786.

I go ELECTROLYTIC DISSOCIATION

lent number of positive and negative ions. This is the
case when acids, bases, and salts are dissolved in water.
The amount of dissociation depends upon the dilution.
Strong acids, strong bases, and salts are completely dis-
sociated in about one one-thousandth normal solutions;
while weak acids and bases are completely dissociated
only at much greater dilutions.

(2) An electrically neutral substance may take the
charge from an ion and become itself an ion, while the
original ion, having lost its charge, becomes electrically
neutral. The example given by Ostwald is that of one
metal displacing another from its salts. When a bar of
zinc is immersed in a solution of copper sulphate, the zinc
takes the positive charge from the copper, becoming zinc
ions, while the copper ions, having lost their charge,
separate as metallic copper.

(3) One neutral substance may pass over into positive
ions, while another neutral substance may pass over into
an equivalent of negative ions. Metallic gold is electri-
cally neutral. Chlorine, when dissolved in water, does not
pass over into the ionic condition. But when metallic gold
is brought into the presence of chlorine water, the gold
passes over into cations, and the chlorine into an equivalent
of anions.

It should have been stated earlier, that when gold dis-
solves in chlorine water auric chloride is formed, and,
indeed, this compound is obtained if the solution is
evaporated. If the solution is dilute, we have only gold
ions and chlorine ions present, and no molecules what-
ever of gold chloride.

Neither the gold nor the chlorine can pass into ions

APPLICATIONS OF THE THEORY 191

when alone, but in the presence of each other they both
become ions.

(4) An ion may take up a larger charge than it already
carries, converting a neutral substance into an ion with the
opposite charge. Thus, a ferrous ion in the presence of
chlorine becomes a ferric ion, the chlorine passing from
the molecular into the ionic condition. This is an example
of a large number of reactions, which are usually termed
processes of oxidation.

But, on the other hand, an ion may lose a part of the
charge which it already carries, converting a neutral sub-
stance into an ion of the same electrical character. Thus,
when a solution of potassium manganate is treated with

chlorine, the Mn04 ions, carrying two charges, pass 6ver

into the MnO^ ions carrying one charge, the negative
charge which it has lost going to the chlorine, converting
this into an ion. The processes where ions lose part of the
charge which they already carry are processes of reduction.

These methods of ion formation have all been described
by Ostwald,^ as already stated, and the above examples
are those which he has chosen to illustrate the several
processes.

Velocity of Ions. — Whenever a current is passed
through a solution of an electrolyte, there is a mechanical
movement of the ions toward the electrodes. To under-
stand the electrochemical behavior of ions, we must study
the velocities with which they move through solutions.

If we pass a current through a solution of copper
sulphate, using copper electrodes, copper will be deposited

I Loc, cii.

192 ELECTROLYTIC DISSOCIATION

on the cathode, and exactly an equal amount will pass into
solution from the anode. The total amount of copper in
solution will thus remain constant, but the color of the
solution in the neighborhood of the anode will become
deeper, while in the neighborhood of the cathode it gradu-
ally becomes less intense. The solution becomes more
concentrated in copper around the anode, and less concen-
trated around the cathode.

If platinum electrodes were used in this experiment,
copper would separate at the cathode, and since there is no
metallic copper present to pass into solution, the amount
in solution would become constantly less. In this case the
color would disappear more rapidly around the cathode.

Relative Velocity of Ions, — Hittorf ^ was the first to cor-
rectly explain this phenomenon. He suggested that it
was due to the different velocities with which the anions
and cations move. How this explanation can account for
the facts, we can see from the following diagram, which we
owe in principle to Ostwald.^

In the following figure, / represents the condition in
the solution of the electrolyte before the current has
been passed through it. The black circles represent the
anions, and the white circles the cations. For each anion
present in the solution there is a corresponding cation, and
neither anions nor cations have separated at the electrodes.

Let us take a case where the velocity of the anion dif-
fers greatly from that of the cation, and for simplicity, let
us say that the velocity of the anion is twice as great as

^ Pogg, Ann., 89, 177; 98, i; 103, i; 106, 337, 513. Ueber die Wanderungea
der lonen, Ostwald Klassiker, 21 and 22.
a Lehrb. allg. Chem., II, p. 595.

o
o

Hi g

o
o
o

o
o

194 ELECTROLYTIC DISSOCIATION

that of the cation. Pass a Current through the solution
until three molecules have been decomposed, and the con-
dition represented in II will exist. Three anions will have
separated at the anode, ahd three cations at the cathode.,
But the solution will have become, relatively, more con-
centrated on the anode side of the middle layer marked m.
Of the three molecules which have separated from the

V solution, two have come from the cathode (C) side of the
middle layer m, and one from the anode side {A), If we

/divide the loss around the cathode by the total number of
molecules electrolyzed, we will obtain the valjue f. If, on
the other hand, we divide the loss around the anode by

(the total number of molecules electrolyzed, the result is J.
But these two values stand to one another in exactly the
same relation as the relative velocities of our anion and
cation. From this we can make two general statements.
First, to find the relative velocity of the cation, divide the
loss around the anode by the tota,! amount of electrolyte
decomposed. Second, to find the relative velocity of the
anion, divide the loss around the cathode by the total

V amount of electrolyte decomposed.

There are thus three quantities which can be deter-
mined experimentally : the change in concentration around
the cathode, the change in concentration around the anode^
and the total amount of the electrolyte decomposed. It is
necessary to determine only two of these, the third being
obtained by difference.

The total amount decomposed is, from Faraday's law,
proportional to the amount of current passed through the
solution ; and this is ascertained by measuring the latter
by means of a voltameter.

APPLICATIONS OF THE THEORY I95

A number of methods, based upon the above principles,
have been devised for measuring the relative velocity of
ions. The solution must be electrolyzed in part, and the
apparatus so constructed that the change in concentration
can be measured. To accomplish this, the parts of the
solution around the two electrodes must not be allowed
to mix after the current is passed, or even while the cur-
rent is passing.

A number of forms of apparatus were devised, and used,
by Hittorf, in which a membrane was interposed to pre-
vent the parts of the solution from mixing again, but it
has been found that the membrane affects the results
obtained.

Kistiakowsky ^ has devised and used a form of apparatus
without any membrane, and thus removed this source of
error. Loeb and Nernst ^ have used a form of apparatus
which is essentially a Gay Lussac burette. The electrode
around which the solution becomes more concentrated is
placed below, and the electrolysis is interrupted while there
is still an unaltered layer of solution between the two
electrodes. This method is not capable of any very high
degree of accuracy, since there is no means by which the
solutions of different concentrations can be completely
separated from one another, removed, and analyzed. The
method of blowing out the solution around the anode,
together with enough of the unaltered middle layer to
wash out the heavier solution, is not in keeping with the
most refined work. From work oh this problem, which
has been carried out in this University, it seems to be far
better to measure the amount of current directly, by means

1 Ztschr. phys. Chem., 6, 97. ' Ibid,, 2, 952.

196 ELECTROLYTIC DISSOCIATION

of a voltameter, than by an indirect method, such as that
used by Loeb and Nernst. The work of Bein,^ on the
relative velocity of ions, has extended over a number of
years, and very recently an elaborate investigation* has
been published by him on this problem. The forms of
apparatus used by him are modifications of burettes, some
of them very elaborate and complex. The work of Bein,
taken as a whole, is probably the best which has ever been
done on the relative velocity of ions. The objection, how-
ever, to the apparatus of Loeb and Nernst, seems to
apply here with some force. There does not seem to be
any means of completely separating the solutions, after
the electrolysis is brought to an end.

At the suggestion of the writer, W. T. Mather,* working
in this University, undertook to devise a form of apparatus
for determining the relative velocity of ions which would
be free from the above-mentioned objection.

The form of apparatus which he constructed, and ap-
plied successfully in a few cases, consists, essentially, of
two upright tubes connected by a U tube, which joins the
upright tubes near the top. In the centre of the U tube a
stop-cock of large bore is introduced. When the electrol-
ysis has proceeded as far as desired, the stop-cock is
closed, and then the solutions in the two arms removed
and analyzed. The two parts of the solution are thus
completely separated, which is not possible in any form
hitherto described.

The methods just described have to do only with the

1 Wied. Ann., 46, 38.

« Ztschr. phys. Chem., 27, 32 ; 28, 439.

' Dissertation. Johns Hopkins University.

APPLICATIONS OF THE THEORY 197

relative velocities with which the ions move, and con-
siderable stress has been laid upon this point, because
of a generalization which has been reached in connection
with these velocities.

KohlrauscKs Law of the Independent Migration Velocity
of Ions. — F. Kohlrausch ^ carried out a beautiful investi-
gation on the power of solutions of electrolytes to conduct
the current, which will be referred to again. The con-
ductivity of a solution, referred to molecular quantities, he
termed its " molecular conductivity.*' He studied the con-
ductivity of solutions at different dilutions, and found that
the molecular conductivity increased with the dilution, up
to a certain point, and then remained constant, no matter
how far the dilution was carried beyond this point. This
maximum constant value of the molecular conductivity we
will call7x«.

Kohlrausch observed that the difference between the
values of /*„, for two electrolytes with a common anion
and different cations (say, KCl and NaCl), is the same as
the difference when there is another common anion and
the same cations as before, thus, KNOs and NaNOg. This
will be seen from the following examples : —

DiPPBRBNCB

KCl fi«o= 140^

NaCl fi»= 120'^

KNOs /^= i35-7\
NaNOs M«,= 113-7''^

1 Wied. Ann., 26, z6a

198 ELECTROLYTIC DISSOCIATION

Kohlrausch concluded, from a large number of such
facts, that the value of /*« for any electrolyte is the sum
of two constants, the one depending upon the anion, the
other upon the cation. And these constants are the same
for any given ion, regardless of the nature of the other ion
which is present in the solution.

These constants are, moreover, the velocities of the
anions and cations respectively, and thus Kohlrausch was
led to his law of the independent migration velocities of ions.

If we represent the velocity of the cation by c^ and of
the anion hy a: —

From the method of determining the relative velocities,

just discussed, we determine the value of -. Knowing

c
c + a and -, we can calculate, at once, the values of c

a
and a.

The absolute velocity of ions can be calculated from the
law of Kohlrausch, for a definite fall in potential. The
absolute velocity of at least one ion can be determined
directly by experiment; and should the calculated value
agree with the value found, it would argue very strongly
in favor of the law with which we are dealing.

According to Kohlrausch, the absolute velocities of
cation and anion {c and a respectively) are obtained from
the relative velocities {c and ^), by multiplying by a factor.
For a fall in potential of one volt per centimetre along the
tube, or a potential gradient of one volt per centimetre,
the value of the factor is no. 10^^. The absolute velocity
of hydrogen, as calculated by Kohlrausch for the above
potential gradient, is 0.0032 cm. per second.

APPLICATIONS OF THE THEORY 199

The absolute velocity of the hydrogen ion has been
measured directly by the beautiful experiment of Lodge.^

A glass tube 8 cm. wide and 40 cm. long was carefully
graduated. The ends were bent down at right angles.
The tube, placed horizontally, was filled with gelatine in
which sodium chloride was dissolved. This material was
colored red by a little phenolphthalein, to which just
enough sodium hydroxide had been added to bring out the
color. The ends of the glass tube were dipped into vessels
filled with dilute sulphuric acid. The apparatus was then
allowed to stand, and the rate ascertained at which the
acid diffused into the jelly. The current was then passed
from one vessel containing the acid, through the horizontal
tube, to the other vessel. The hydrogen ions of the sul-
phuric acid move with the current, displace the sodium
ions from the salt, and form hydrochloric acid. This
decolorizes the phenolphthalein in the jelly, and the move-
ment of the hydrogen ions can thus be traced. When the
proper correction is introduced for diffusion, we have at
once the velocity of the hydrogen ion for the potential
gradient used.

Lodge found, in three experiments, that under a fall of
potential of one volt per centimetre, the hydrogen ion has
a velocity of 0.0029, 0.0026, and 0.0024 cm. per second.
This value agrees very closely with that calculated by
Kohlrausch, from his law of the independent migration
velocity of ions.

Whetham ^ has measured the absolute velocity of a few
ions, using a somewhat different method, which is, how-
ever, the same in principle as that of Lodge. The ve-

^ a A. Report (1886), 393. 2 Phil. Trans. (1893), A. p. 337.

r200 ELECTROLYTIC DISSOCIATION

locities of the copper ion, and the €1307 ion, found by
Whetham, agree closely with those calculated from the law
of Kohlrausch.

It would be difficult to interpret the law of Kohlrausch,
if molecules existed as such in very dilute solutions. The
law is, however, not. only explained by the theory of elec-
trolytic dissociation, but is a necessary consequence of it.
In dilute solutions, the molecules are completely broken
down into ions, and each of these moves through the
solution with a velocity which is definite for a given fall

. in potential.

The law of Kohlrausch applies to very dilute solutions
of strongly dissociated compounds. It holds, at medium
dilution, for comparatively few substances, and does not
hold at all for the weak acids and bases. How are these
facts to be explained .^

The theory of electrolytic dissociation furnishes not only

t an explanation of the law, but an equally satisfactory
explanation of the exceptions.

Those solutions to which the law applies are completely
dissociated. All of the molecules are completely broken
down into ions, and all of the ions take part in conducting
the current. The conductivity is, then, a maximum, and

. gives the true value of fi^. In those cases, however, where
the law of Kohlrausch does not apply, the solutions are
not completely dissociated. Some of the molecules are not
broken down into ions, and these, therefore, take no part
in conducting the current. The molecular conductivity of
such solutions is not the maximum conductivity — is not
the true value of /Aoo, but is always less. This applies to
the fairly concentrated solutions of the most strongly dis-

APPLICATIONS OF THE THEORY gQi

sociated electrolytes, and even to the very dilute solutions
of the weakly dissociated electrolytes, such as the organic
acids and bases.

In all such cases, where the solutions are not com-
pletely dissociated, we must take into account the amount
of the dissociation^ When this is done, the law of
Kohlrausch becomes much more general, and can be
applied, as Ostwald^ has shown, to partially dissociated
solutions.

If we represent the degree of dissociation by a, the law
becomes : —

which holds for completely dissociated solutions, where
a =3 I, and also for solutions in which the dissociation is
not complete.

The relation between the migration velocity of the ions
and conductivity is thus completely accounted for by
our theory.

The Conductivity of Solutions. — The conducting power
of a solution is evidently closely connected with its dis-
sociation, since only ions carry the current. We can then
obtain new light on the dissociation of solutions by study-
ing their conductivity.

The conductivity of any conductor of electricity is the
reciprocal of the resistance of that conductor. The resist-
ance r, from Ohm's law, is expressed thus : —

1 Lehrb. allg. Chem., 11, p. 673.

202 ELECTROLYTIC DISSOCIATION

in' which ir is the difference in potential at the two ends of
the conductor, and c is the strength of current. The con-
ductivity C is therefore : — *

The unit of resistance most generally used is that of a
column of pure mercury io6 cm. in length and i sq. mm.
in section, at oP C.

Specific Conductivity, — The resistance of conductors
depends upon their form as well as upon their chemical
nature. In order, therefore, that the resistances of
different substances may be measured so as to be com-
parable, it is necessary that the conductors should have
the same or comparable forms. The dimensions usually
chosen are a cylinder i m. in length and i sq. mm. in sec-
tion. The resistance offered by substances of these
dimensions^ is known as their specific resistance.

The term "specific resistance" is, sometimes, applied
also to the resistance offered by a cube whose edge is
I cm. in length. This is ^^^^^^ of the former.

The term "specific resistance,*' or its reciprocal, "spe-
cific conductivity," can be applied to conductors of the
second as well as to those of the first class. In this case,
the specific conductivity would be the conductivity of a
cylinder of the liquid i m. in length and i sq. mm. in
cross-section.

Conductors of the second class are, however, generally
solutions of some electrolyte in some solvent, and their con-
ductivity is conditioned by the presence of the electrolyte.
That the resistances of such solutions should be com-
parable, it is clear that we must deal with comparable

APPLICATIONS OF THE THEORY 203

quantities of the dissolved substances. The most con-
venient quantities are gram-molecular weights of the
different substances.

Given a normal solution, which contains a gram-molecu-
lar weight of the electrolyte in a litre. Let us place the
litre of solution between two electrodes which are i cm.
apart. The cross-section of this solution would be 1000
sq. cm.

If we represent by v the number of cubic centimetres
61 any solution which contains a gram-molecular weight of
the dissolved substance, and by s the specific conductivity
of a cube of the solution whose edge is i cm. in length, the
molecular conductivity^ fi, is the product of these two : —

11^ vs.

But if we represent by s the specific conductivity of a
prism of the solution, i m. in length and i sq. mm. in cross-
section, the molecular conductivity is expressed thus : —

A general expression for the molecular conductivity,
where g- gram-molecular weights are contained in a litre of

the solution, is : —

sxio^ ^^ sx 10^
/i = or /A = f

g S

depending upon our definition ' of specific resistance,
whether it is referred to a cube of the solution whose edge
is I cm. long, or to a cylinder of it i m. long and i sq. mm.
in cross-section.

Method of Measuring the Conductivity of Solutions, —
If a continuous current is passed through an aqueous
solution of an electrolyte from, say, platinum electrodes,

204

ELECTROLYTIC DISSOCIATIOK

the electrodes will become covered with gas. The resist-
ance! of the solution cannot then be measured as such,
since this polarization of the electrodes will introduce a
new source of resistance into the circuit. The effect of
polarization must be overcome by some means. Kohl-
rausch has accomplished this by using an alternating
current. His method consists in passing an alternating
current from a very small induction coil between platinum

plates immersed in the solution. The resistance of the
solution is balanced against a rheostat, using a Wheatstone
.bridge and telephone. A dynamometer may, be used
instead of the telephone, for determining the reading on
the bridge. A galvanometer cannot, of course, be used
with an alternating current.

The Kohlrausch apparatus is sketched diagrammatically
in Fig. 8. y is a small induction coil, tuned to a very high
pitch, and should be placed at some distance from the

APPLICATIONS OF THE THEORY 2^0$^

bridge, or enclosed in a box lined with cotton, to deaden ^
the sound. It is driven by a storage cell. AB is a metre
stick divided accurately into millimetres. Over this is
stretched a wire of platinum, or,, better, of manganine,
(an alloy containing manganese) or nickelic, which have
a very small temperature coefficient of resistance. W is b,
rheostat. R is the vessel containing the solution and elec-.
trodes. The electrodes are cut from thick sheet platinum,
and into each plate a piece of stbilt platinum wire, about an

inch in length, i? welded. The wire is sealed into a glass

-','•■■■■ ■ I'

tube which is filled with mercury, and electrical connection
thus established between the plate and the copper wife
which is immersed in the mercury. Oiie arm of the tele-
phone T is thrown into the circuit between the rheostat
and the resistance vessel, and the other arm is connected
with the bridge wire by means, of a slider. This is moved
along the wire until that point is found at which the hum
of the induction coil ceases to be audible in the telephone.
If this is some point C, and we represent AC hy a, BC by ^,'
the resistance in W by z£/, and the resistance, of the solu-
tion in the vessel by r, then from the principle of .the

bridge we have : —

ra = wby

_wb
a'

But the conductivity of a solution c is the reciprocal of the
resistance r; therefore: —

The conductivities of solutions determined from this
expression would not be comparable with one another, !

206 ELECTROLYTIC DISSOCIATION

since there is nothing in this expression which takes into
account the concentration of the solution. It is most con-
venient to refer all concentrations to molecular normal,
which contains a gram-molecular weight of the electro-
lyte in a litre. If we represent by v the number of litres
of the solution which contains a gram-molecular weight
of the electrolyte, the above expression becomes: —

_ va
wb'

Instead of c^ we now write for the molecular conduc-
tivity the letter fi. And to indicate the concentration at
which the fi is determined, we write /i».

_ va
wo

Even this expression does not take into account the
dimensions of the cell used. A cell constant k must be
introduced and determined for each cell, before it can be
employed for conductivity measurements. The complete
expression for calculating the molecular conductivity ^^ is
then : *—

Canying out a Conductiyity Measurement. — To carry
out a conductivity measurement, the constant k for the
cell must first be determined. For this purpose a solution
must be used whose value of /i„ is known. The value of
/i« for a one-fiftieth normal solution of potassium chloride
at 25° is 129.7.

The platinum plates are covered with platinum black,
by electrolyzing, in the cell, a dilute solution of platinic

APPLICATIONS OF THE THEORY 207

chloride. The — solution of potassium chloride is placed

in the cell, the latter introduced into a thermostat which
is exactly at 25**, and the values of ^, b, and w ascertained ;
V and ^^ are known, and k can be calculated at once.

Having determined the cell constant, the measurement
of the conductivity of a solution is comparatively simple.
The solution of known concentration is placed in the cell,
warmed accurately to the temperature desired, and then
the values of ^, b, and w ascertained; k and v being
known, /i^ is calculated at once.

Conductivity of Water. — The conductivity of the water
used is very important. When we determine the conduc-
tivity of an aqueous solution, what we actually measure is
the sum of the conductivities of the electrolyte and of
the water used in preparing the solution. For this reason
very pure water must be used in such work, and a number
of methods for purifying water for conductivity measure-
ments have been devised.

It is quite certain that perfectly pure water has never
been prepared. The purest has undoubtedly been obtained
by Kohlrausch and Heydweiller.^ They distilled in a
vacuum the purest water obtainable by other methods, and
determined its conductivity without allowing it to come in
contact with the air. A millimetre of this water, at zero
degrees, has a resistance equal to that of a copper wire
I mm. in diameter, extending one thousand times around
the earth.

It is, of course, not practicable to prepare water of this
degree of purity for ordinary conductivity measurements.

1 Ztschr. phys. Chem., 14, 317.

208 ELECTROLYTIC DISSOCIATION

A number of methods are, however, available for purifying
water sufficiently for such measurements.

Nernst^ suggests fractional crystallization. Hulett^ dis-
tilled water first from potassium bichromate and sulphuric
acid, and then redistilled it from a solution of barium
hydroxide.

Jones and Mackay^ distilled ordinary distilled water
from potassium bichromate and sulphuric acid, and then
passed the vapor directly into a boiling alkaline solution
of potassium permanganate. Two distillations Were thus
effected at once.

Any of the above methods will yield water of sufficient
purity for ordinary conductivity work.

The fact that pure water does not conduct the current,
means that it is practically undissociated. This same fact
has been shown by a number of independent investiga-
tions, in which widely different methods have been used.
Space will not permit of a discussion of these exceedingly
interesting pieces of work. Reference only can be made
to that of Wijs,* Arrhenius,^ Ostwald,® Bredig,^ Nernst,®
and Kohlrausch.® The reader is urgently advised to care-
fully examine these investigations, which all agree in
showing that water is very slightly dissociated.

The fact that water is undissociated is of great im-
portance. It means that hydrogen and hydroxyl ions
cannot remain in the presence of each other uncombined.
This has already been referred to (p. 122), in connection

1 Ztschr. phys. Chem., 8, Ida • Ibid., ii, 521.

2 Ibid., 21, 297. 7 Ibid., 11, 829.
8 Ibid., 22, 237 ; Amer. Chem. Journ., 19, 91. • Ibid., 14, 155.
* Ibid., II, 492. » Ibid., 14. 317.
» Ibid,, 5, 16.

APPLICATIONS OF THE THEORY 209

with the explanation of the phenomenon of neutralization
of acids and bases. The great tendency of hydrogen and
hydroxyl ions to unite is, undoubtedly, the conditioning
cause of a large number of chemical reactions. This will
become apparent, when we recall how many chemical reac-
tions there are in which a molecule of water is formed.

Calculation of Dissociation. — The calculation of disso-
ciation from conductivity is comparatively simple. The
molecular conductivity of strong acids and bases and salts
increases from any moderate dilution up to a dilution of
about 1000 litres, where it becomes constant. This maxi-
mum constant value of the molecular conductivity means
complete dissociation. If the solution is not dissociated at
all, the conductivity, and, consequently, the molecular con-
ductivity, is zero. To calculate the dissociation of any
partially dissociated solution, it is only necessary to deter-
mine the ratio between the molecular conductivity of the
solution in question and the molecular conductivity of the
substance when completely dissociated.

Representing the molecular conductivity of the solution
of volume v by /x„, and the molecular conductivity when
the substance is completely dissociated by ^«„ the per-
centage of dissociation a is calculated thus: —

The value of ft^ for any dilution of any substance can
be ascertained at once by means of the conductivity
method. The value of /too for the strongly dissociated
electrolytes can also be determined directly by the con-
ductivity method. It is only necessary to increase the

2IO ELECTROLYTIC DISSOCIATION

dilution of the solution until the molecular conductivity
attains a constant maximum value. This is usually reached
at about looo litres. If the electrolyte is not strongly
dissociated, as in the case of the organic acids and bases,
resort must be had to an indirect method of determining
the value of ii^. This, again, can only be referred to,^
since space will not allow it to be more fully discussed.

It will be seen at once from Kohlrausch*s law, that the
conductivity method can also be used to determine the
velocity of ions. In terms of this law the value of /ttoo,
for any compound, is the sum of two constants, the one
depending upon the anion, and the other upon the cation.
These constants represent, further, the relative velocities
of the two ions.

Given a compound like hydrochloric acid ; we determine
the value of /x« for the compound, by the conductivity
method. This is the sum of the velocities of the hydrogen
and chlorine ions. We know the velocity of the hydro-
gen ion. If we subtract this from the value of ii^ for
hydrochloric acid, we obtain the velocity of the chlorine
ion.

This principle has been used extensively, especially by
Ostwald 2 and Bredig,^ for determining the relative velocity
of ions. The work of Ostwald is typical. He wished
to determine the relative velocities of the anions of a
number of organic acids. He prepared the sodium salts
of each of these acids, and determined the value of
/ioo for these sodium salts, by the conductivity method.
The value of ii^ for the sodium salts is, from Kohlrausch's

1 Ostwald, Lehrb. d. allg. Chem., II, p. 69a.

2 Ztscbr. phys. Chem., 2, 840. 8 /^id.

APPLICATIONS OF THE THEORY 211

law, the sum of the velocities of the sodium cation and
of the organic anion of the acid. Knowing the velocity
of sodium to be 44.5 in terms of the units used, he had
but to subtract this number from the /i* for the acid, to
obtain the velocity of the anion of the acid.

Bredig ^ worked on a very large number of organic
bases. Here, it was necessary to prepare a salt of the
base which would be strongly dissociated, and would give
the value of ftoo at moderate dilutions. If the hydro-
chloric acid salt was used, the velocity of chlorine must
be subtracted from the /i* found, and the difference
would be the velocity of the organic cation.

It is thus a very simple matter to determine the
relative velocities of cations and anions, since Kohlrausch
discovered the law to which these conform.

A number of stoichiometric relations between the com-
position and constitution of ions, and their velocities, have
been pointed out by Ostwald and Bredig. In general, the
more complex the ion the slower it moves. Isomeric
anions have very nearly the same velocity, while con^
stitution has a marked influence on the velocity of cations.
The effect of certain atoms, and also of the symmetry of
the molecule, have been worked out by Bredig.^ For
details in this connection, his original communication must
be consulted.

The conductivity of solutions in the different solvents
varies very greatly. Solutions in water were thought to
have the greatest conductivity, until it was recently
shown that solutions in liquid ammonia conduct better
than in water. This fact has been confirmed by Goodwin

1 Loc, cit, 2 Ij)c, cit.

212 ELECTROLYTIC DISSOCLVTION

an4 Thompson, in their work on the dielectric constant
of liquid ammonia. Next to these solvents, in dissociat-
ing power, come formic acid, methyl alcohol, ethyl alcohol,
acetone, and finally the oils, hydrocarbons, and ethereal
salts. When substances which conduct well in water are
dissolved in the last-named solvents, the solutions, as has
already been mentioned, show very little conductivity, and
are, therefore, very slightly dissociated.

The dissociation in solvents whose solutions conduct
but little cannot be measured accurately by the con-
ductivity method, on account of the difficulty of deter-
mining the value of /i*. The most strongly dissociated
electrolytes are not completely dissociated by these sol-
vents, at dilutions which come within the range of the
conductivity method. Thus, it is impossible to determine
the value of /a«, for any substance in ethyl alcohol, by the
conductivity method. The values of /i^, for any dilution,
can be determined in these solvents as well as in water.
Some assumption, however, must be made in calculating
the value of /*«, which may introduce considerable error.

The freezing-point method can be used with only a few
solvents, because most substances freeze at temperatures
which are too far removed from the ordinary to secure
accurate measurements.

The boiling-point method is, at least theoretically, the
freest from objections in such cases, and could be used
to measure dissociation, if the experimental difficulties
could be overcome.

This has been accomplished, in part, by H. C. Jones.^
He has devised a boiling-point apparatus which diminishes

1 Amer. Chem. Joum., 19, 581.

APPLICATIONS OF THE THEORY 213

some of the sources of error inherent in other forms, and
he has applied this to the measurement of electrolytic
dissociation in methyl and ethyl alcohols.^ The results
obtained are fairly satisfactory. A comparison of the dis-
sociation of a few salts, by water, methyl alcohol, and ethyl
alcohol, taken from the paper of Jones, is given in the
following table : —

SUBSTANCB

DiLimoN

NOKMAL

Dissociation
IN Water

Dissociation

IN Mbtkyl

Alcohol

DlSSOOATION

IN Ethyl
Alcohol

KI,

O.I

88%

5«% -

*5%

Nal,

O.I

84%

60% 1

33%

NHJ,

0.1

50%

KBr,

0.1

86%

50%

"■

NaBr,

0.1

86%

60%

24%

NH4Br,

0.2

49%

21%

CHsCOOK,

O.I

83%

36%

16%

CHjCOONa,

O.I

38%

14%

The dissociation in methyl alcohol is more than half of
that in water. The dissociation in ethyl alcohol is less
than one-third of that in water.

This method can also be applied to the investigation of
solutions in other solvents.

Thomson's Theory. — Reference has already been made
to a theory proposed by J. J. Thomson,^ which connects
the dissociating power of solvents with their dielectric con-
stants. This theory will now be given, in Thomson's own
words. *' If we take the view that the forces which hold
the atoms in the molecules together are electrical in their
origin, it is evident that these forces will be very much
diminished when the molecule is close to the surface of, or

1 Ztschr. phys. Chem., Jubelband, van't HoS,

2 Phil. Mag., 36, 32a

214 ELECTROLYTIC DISSOCLVTION

surrounded by, a conductor, or a substance like water, pos-
sessing a very large specific inductive capacity (dielectric
constant).

"Thus, let A, B represent two atoms in a molecule,
placed near a conducting sphere, then the efifect of the

electricity induced
on the sphere by
A will be repre-
sented by an oppo-
site charge placed
at A\ the image
of A in the sphere.
If A is very near
the surface of the
sphere, then the

Fig, 9*

negative charge at
A^ will be very nearly equal to that at A, Thus, the
effect of the sphere will be practically to neutralize the
electric effects ol A\ as one of these effects is to hold
the atom B in combination, the affinity between the atoms
A and B will be almost annulled by the presence o£
the sphere. Molecules condensed on the surface of the
sphere will thus be practically dissociated.

" The same effect would be produced, if the molecules
were surrounded by a substance possessing a very large
specific inductive capacity. Since water is such a sub-
stance, it follows, if we accept the view that the forces
between the atoms are electrical in their origin, that when
the molecules of a substance are in aqueous solution, the
forces between them are very much less than they are
when the molecule is free, and in a gaseous state."

APPLICATIONS OF THE THEORY 21$

The above results show that the solvent with the higher
dielectric constant has the higher dissociating power, but
that the two are not proportional is seen by comparing the
above values for dissociation, with the dielectric constants
of these three solvents.

DiBLBCTRTC CONSTANT

Water, 76 to 78

Methyl alcohol, 32.5 to 34

Ethyl alcohol, 25.7 to 26

We have not yet sufficient data to fairly test the value
of Thomson's theory. It is so beautiful and simple, and
is such a welcome application of the theory of electrolytic
dissociation, that we are inclined to hope that it may be of
wide-reaching significance.

Conductivity at Elevated Temperatures. — We have,
thus far, dealt with the conductivity of solutions — of one
substance in the presence of another. The question still
remains: Do any substances conduct by undergoing de-
composition when alone ? Pure substances conduct with-
out undergoing decomposition, such as the metals, carbon,
etc., which belong to conductors of the first class. But
substances which undergo decomposition when they con-
duct are called conductors of the second class. Do
any pure homogeneous substances belong to the second
class ?

At elevated temperatures, a number of pure substances
are known to conduct like conductors of the second class,
or electrolytes. Substances which are liquid at ordinary
temperatures do not conduct, and are, therefore, non-
electrolytes.

It thus seems that heat acts, to a certain extent, like

2l6 ELECTROLYTIC DISSOCIATION

a solvent, converting a substance which does not conduct
into one which has the power to carry the current.

Electromotiye Force. — The theory of electrolytic dis-
sociation has also been applied, with beautiful results, to
the problem of the source of the electromotive force in
primary cells. This could properly be dealt with under
the head of electrochemistry, but is so distinctly physical
in its nature, that it will be taken up as an example of
the application of this theory to physical problems.

Strength of Acids and Bases. — The applications of the
theory of electrolytic dissociation, described in this sec-
tion, we owe almost entirely to Ostwald. Reference has
already been made to his extensive investigations of the
conducting power of electrolytes, and especially of the
organic acids. His law connecting dissociation with dilu-
tion has already been deduced. It will be remembered
that, if we represent the percentage of dissociation by a,
and the dilution of the solution, or number of litres which
contains a gram-molecular weight of the electrolyte, by v^
the Ostwald dilution law is :

= constant.

(l — a)v

It has already been pointed out, that this law does not
hold for the strongly dissociated electrolytes, the strong
acids and bases, and the salts; but does apply to the
more weakly dissociated compounds, such as the organic
acids and bases.

Ostwald has shown that the value of the constant for
a substance is a characteristic of that substance, and an
expression of its chemical activity.

APPLICATIONS OF THE THEORY 2l7

The constant for any substance is determined by meas-
uring the conductivity of the substance at several dilutions,
calculating the dissociation from these measurements, by

means of the formula a = -^, already considered ; and

knowing a and v, the constant c is calculated from the
Ostwald dilution law, just given. An example, taken
from the work of Ostwald,^ will make this clear.

Formic Acid (HCOOH). /i« = 376

M«

^x 100

15.22

4.05

0.0214

21.19

6.63

0.0210

29.31

7-79

0.0206

40-50

10.78

0.0203

128

55-54

14.76

0.0200

256

75.66

20.12

0.0198

102. 1

27.10

0.0197

1024

134.7

35.80

0.019s

The constants of other acids and bases were deter-
mined in exactly the same manner. In this investigation,
Ostwald studied between two and three hundred organic
acids, and brought out some interesting and important facts
in connection with the strength of these acids, and pointed
out certain relations between the strength of the acids and
their composition and constitution.

In the preceding chapter, it was shown that the strength
of acids thus determined by conductivity, agreed with
that found by other methods, such as the velocity with
which they inverted cane-sugar, saponified methyl acetate,

1 Ztschr. phys. Chem., 3, 170, 241, 369,

2l8 ELECTROLYTIC DISSOCIATION

etc. We can, then, regard conductivity as the true meas-
ure of the strength of acids.

But conductivity is proportional to dissociation, since only
ions conduct the current. Therefore, the strength of an
acid is conditioned by the amount to which it is dissociated.

All acids dissociate into a hydrogen cation, and into the
remainder of the molecule which forms the anion. The
anion may be simple, consisting of the halogen alone, as
with the halogen acids, or it may be very complex, as with
the higher members of the homologous series of organic
acids. The anion differs in its nature with every acid.
The cation of all acids, however, is hydrogen, and, there-
fore, the acidity of these compounds is due to this common
constituent into which all acids dissociate.

The strength of acids, then, resolves itself into the num-
ber of hydrogen ions present in their solutions. When
we say an acid is strong, we mean that it is largely disr
sociated in solution, or that its solution contains a large
number of hydrogen ions. And this leads us to an inter-
esting conclusion pointed out by Ostwald. All acids are
completely dissociated at infinite dilution ; therefore, at
infinite dilution all acids have the same strength. Exactly
the same remarks apply to bases. Bases dissociate into a
hydroxyl anion, and the remainder of the compound forms
the cation. The latter may be simple, as with the alkalies,
or may be very complex, as in the organic bases.

The common constituent of bases is, then, the hydroxyl
anion, and basicity is due to the presence of this ion. A
strong base means one which is largely dissociated, or
in whose solution there is a large number of hydroxyl
ions. But all bases, like all acids, are completely disso-

APPLICATIONS OF THE THEORY 219

ciated at infinite dilution. Therefore, all bases have the
same strength at infinite dilution.

These generalizations for acids and bases are of very
wide significance, and greatly simplify and correlate phe-
nomena, which have been hitherto regarded as more or
less disconnected.

Relations between Acidity and Composition and Constitu-
tion. — Some of the relations between acidity and com-
position and constitution will be considered.

Hydrochloric, hydrobromic, and hydriodic acids are to
be ranked among the strongest acids. They have very
nearly the same strength, as is shown by the fact that they
conduct to just about the same extent. Hydrofluoric acid
is much weaker, as is shown by its comparatively small
conductivity. These facts are established by the following
results ; —

%^ •

HBr

331

341

—

343

354

353

27.8

355

361

360

33-6

369

373

372

55.8

4096

376

372

373

—

Hydrocyanic acid conducts but little better than pure
water, and is, therefore, one of the weakest acids. When
sulphur is introduced into this acid, we have, in sulpho-
cyanic, one of the strongest acids.

HCN

HCNS

326

0.33

337

0.38

—

0.46

358

220 ELECTROLYTIC DISSOCL^TION

Hydrocyanic acid, judged by its conductivity, can, there
fore, scarcely be regarded as an acid, while sulphocyanic
acid is nearly as strong as hydrochloric acid.

The introduction of oxygen usually increases the acidity,
that is to say, forms a compound which is more dissociated
by the solvent. This is by no means general. Take the
acids of phosphorus; the more oxygen there is present
the weaker the acid, as is seen in the following results : —

H,P0,

H,PO,

H,P04

At»

131

121

194

175

293

274

183

356

330

316

262

1024

344

336

320

The order of strength of some of the more common
mineral acids is as follows, expressed in terms of hydro-
chloric acid = 100 : —

HCl

100

HB)r

lOI

HNO,

99.6

H^04

65.1

H3PO4

Turning to the organic acids, we find a number of rela-
tions established. The introduction of chlorine into the
fatty acids increases the acidity. Take the chlorine sub-
stitution products of acetic acid : —

CHjCOOH

CH,aCOOH

CHCljCOOH

CQaCOOH

/«•

/*•

-- -^

21.2

109

245

8.65

73-4

256

327

128

16.99

126.0

308

336

024

46.00

236.0

342

339

APPLICATIONS OF THE THEORY

221

The introduction of oxygen into an acid, forming the
hydroxyl group, increases the acidity. This is seen from
the following example : —

Succinic Aao

Mauc Acid

Tartaric AaD

C,H4(COOH),

QH,(0H)(C00H),

CH,(OH),(COOH),

th,

f*.

3-73

8.45

—

iS-7

26.6

58.1

» 64

22.1

50.8

79-4

58.6

126.0

183.0

4096

142.0

255.0

341.0

The effect of introducing one and two hydroxyl groups
is shown in these examples.

In the aromatic series we have to take into account not
simply the nature of the group, but the position which it
takes, whether ortho, meta, or para. The introduction of
oxygen into benzoic acid, forming a hydroxy acid, has a
very different influence on the acidity, depending upon the
position occupied by the oxygen.

Benzoic Aao

Saucyuc Acii>

^-OXYBBMZOlC

7>-0XYBENW)IC

(0)

Acid

CbHbCOOH

C8H4(OH)COOH

€eH4(OH)COOH

CeH4(OH)COOH

/*»

/«•

22.1

81.2

25.5

14.3

256

42.3

137.0

47.7

28.3

2048

104.0

255.0

1 14.0

73-0

Hydroxyl in the ortho position increases the acidity very
markedly. In the meta position it has but a slight effect,
while in the para position it actually lessens the acidity.

The introduction of the nitro group has a very different
influence, depending upon its position.

222 ELECTROLYTIC DISSOCUTION

Benzoic Acid C-Nitrobbnzoic ilf-NiTROBBNZoic T'oNitrobbhzoic

Acid

AaD

M»

P-9

A<*

/«»

22.1

159

47-5

57.9

263

1 1 7.0

123

2048

104.0

301

190.0

195

The nitro group in the ortho position has the greatest
acidifying power, while in the para position it has some-
what greater power than in the meta.

The introduction of more and more nitro groups, in
general, increases the acidity. Thus, take phenol, which
is a very weak acid. Introduce one nitro group, we have
its acidity increased. Introduce a second nitro group,
and its acidity is still further increased. Introduce the
third nitro group, and we have picric acid, which is nearly
as strong as the mineral acids.

As the unsaturated acids contain less and less hydro-
gen, the affinity increases. Thus, acrylic acid, C3H4O2, is
stronger than propionic, CgHgOg. The effect of constitu-
tion can be seen by studying the acidity of maletc and
fumaric acids, which have the same composition.

Malbic Acid

Fumaric Acid

/A»

A*»

166

58.8

305

179.0

2048

333

275.0

8192

339

337-0

Maleic is much stronger for the greater concentrations,
but never has a molecular conductivity greater than a
monobasic acid. Fumaric, at high dilution, has a greater
conductivity than a monobasic acid. The second hydro-

APPLICATIONS OF THE THEORY 223

gen takes part in the conductivity, before the first has
reached a maximum.

Take citraconic acid and two of its isomeres: —

ClTRACX>MIC

Itaconic

Mbsaconic

M«

A(«

56.4

II.7

25-5

250.0

84.7

162.0

4096

322.0

186.0

291.0

From its conductivity, citraconic acts like a monobasic
acid. In itaconic one carboxyl is weaker than the other,
while mesaconic conducts itself like a dibasic acid, whose
hydrogen atoms are nearly or quite equivalent. By a
careful study of the conductivity of acids, as Ostwald has
shown, some light can be thrown on their constitution.

The introduction of the amido group weakens the acid
properties, as would be expected from the basic nature
of this group.

Bases. — Some work has been done on strength of bases
by Ostwald,^ Bredig,^ and others. But these have not
been worked up as thoroughly as the organic acids.

The conductivities of the strong bases, like those of
the strong acids, reach a maximum at a dilution of about
one thousand litres. The value of /*« for the bases is
less than for the acids, since the velocity of the. hydroxyl
ion is only about 170, while the velocity of the hydrogen
ion is about 325 at 2S*^C. The strong bases include the
hydroxides of the alkalies and alkaline earths. Ammonia
is sometimes regarded as a strong base, but it is not

1 Journ. prakt. Chem. (2), 33, 35a.
s Ztchr. phys. Chem., 13, 289.

224 ELECTROLYTIC DISSOCIATION

It was found that the conductivity of ammonia is slight,
compared with that of, say, potassium hydroxide. Other
reactions with ammonia were also studied, such as the
velocity with which it would effect reactions, and these
results confirmed those from conductivity. Ammonia is,
then, a comparatively weak base.

We will now compare the strength of ammonia with
that of the substituted ammonias: —

NH, NHjCH, NHjCjH, NH,C»Ht NHjCHg

/K*

/x*

1.46

6.41

6.06

—

6.13

26.4

26.8

23-7

19s

256

17.8

64.8

66.9

59-2

49.2

1024

370

108.0

1 1 2.0

97-7

82.3

Thus, all monamines are stronger than ammonia.
We will examine some of the di- and triamines.

NH(CH,),

NH(C,H,),

N(CHa),

N(C,H^,

M»

6.SS

—

2.63

4.76

128

55-9

65.8

23-7

49-7

XO24

120.7

130.3

56.8

11.6

Dimethylamine is only a little stronger than methyl
amine, and, similarly, diethylamine is but little stronger
than ethylamine.

The triamines are not as strong as the diamines. The
results for one of the tetramines are given : —

(C,H«)4N0H

/*v

176.2

128

186.4

1024

182.6

APPLICATIONS OF THE THEORY 22$

and these show that the compound is a fairly strong base ;
indeed, much stronger than either of the other amines.

The effect of introducing two amido groups into a
compound can be seen from ethylene diamine.

C,H4(NH,),

S.go

256

23.16

1024

40.91

It is surprising that the ethylene diamine is much
weaker than the ethylamine, since two amido groups
should increase the basic property. This suggests the
acids of phosphorus, where the weaker acid is the one
containing the greater number of oxygen atoms.

A large number of relations between composition and
constitution and chemical activity have been worked out,
but those already given suffice to show the nature of the
relations which have been discovered. No generalization
of very wide significance has been reached, and exceptions
are usually present to any general statement which may
be made. This work resembles, in many respects, the
earlier physical chemical investigations, which had to do
with problems of this same general type.

Although many exceptions appear in work of this kind,
nevertheless, its value is great, since it is only step by step
that we arrive at the truth, and a great many steps are
required to arrive at truth in its broader relations. We
will leave here the chemical side of modem physical
chemistry, and turn to the application of the theory of
electrolytic dissociation to a physical problem.

226 ELECTROLYTIC DISSOaATION

APPLICATION OF THE THEORY OF ELECTROLYTIC DISSOCIA-
TION TO A PHYSICAL PROBLEM

The theory of electrolytic dissociation has not been
applied as widely to physics as it has been to chemistry.
This, from the nature of the case, was to be expected.
Ions are the main, if not the sole factors in chemical
activity; while molecules are generally the units with
which the physicist has to deal.

That chapter of physics, which is most concerned with
ions, is the one which has to do with electrical phenomena,
and, especially, with electricity as generated in primary
cells. Here, one of the essential agents is a solution of
some electrolyte, or solutions of more than one electrolyte,
and these solutions are always more or less dissociated.
The ions are, thus, essential to the action of such cells, and
here our theory bears directly upon a problem which is,
indeed, a physical one.

THE SEAT OF THE ELECTROMOTIVE FORCE IN PRIMARY

CELLS

The question as to the origin of the electromotive force
in primary cells is as old as the cell itself. Volta con-
cluded that the main source of the electromotive force was
at the point of contact of the two metals. Others have
supposed that the contact of the two solutions was the
chief source of the electromotive force. Others, again,
sought for the electromotive force of such elements, at the
points of contact of the electrodes with the electrolytes.
The question was unsettled when the theory of electro-
Ijrtic dissociation was proposed. We shall see that this

APPLICATIONS OF THE THEORY 22^

theory has furnished us with a solution to this problem,
and we now have a pretty clear conception of what takes
place in the primary cell.

The application of the van't HofI laws of osmotic press-
ure, and the Arrhenius theory of electrolytic dissociation,
to explain the action of the cell, we owe to Nemst,^ who
did this epoch-making work while in the laboratory of
Ostwald in Leipzig.

It will be assumed that the reader is familiar with the
method of measuring the electromotive force of elements.
The method, in general, is to balance the cell in ques-
tion against one of standard electromotive force, such
as the Clarke. element, by means of a convenient resistance
box, and using the Lippmann electrometer to determine
the point of equilibrium. We will not spend more time
upon this experimental side of the problem, but proceed
at once to the calculation of the electromotive force of
elements.

Calculation of Electromotive Force from Osmotic Press^
ure. — The method of calculating electromotive force
from osmotic pressure is given essentially as deduced by
Ostwald* from the work of Nemst.

If we allow a substance to pass, isothermally, from
one condition to another, the maximum amount of ex-
ternal work is always the same, regardless of how this
takes place, whether osmotically, or electrically, or in any
other way. If we know the maximum external work
which is obtainable from a process, we know the amount
of electrical energy; and, as we shall see, the electro-
motive force is calculated directly from the electrical

1 Ztschr. phys. Chem., 4, 199. 2 Lehr. d. allg. Chem., H, p. 825.

228 ELECTROLYTIC DISSOCIATION

energy. The first step is, then, to determine the maximum
external work which is obtainable in a given process.
This can be done by allowing the substance to pass, at
constant temperature, in a reversible manner, from one
condition over to the other.

Given a gas under a pressure /j, and volume v, and
allow it to expand isothermally to a pressure /j. When a
gas expands isothermally it takes up heat, and gives it up
as volume energy. The energy set free under these con-
ditions is : —

— Cvdp.

But pv^RT, where R is the gas constant and T the
absolute temperature, whence the above expression be-
comes for gram-molecular weights : —

-RTJ

-=-1

which expresses the volume energy obtained under the
condition.
This becomes on integration : —

RT\si*fy
P%

This amount of energy, which is converted into work by
an ideal gas in passing from pressure /j to pressure /g* ^s
exactly equal to the work obtained from an ideal solution

* In is natural logarithm.

APPLICATIONS OF THE THEORY 229

under the same conditions. That is, a solution of volume
V passing, isothermally, from an osmotic pressure /^ to an
osmotic pressure /j.

But with the movements of the ions, we have the move-
ments of the electrical charges which they carry. And,
from what has been s^d, the amounts of work correspond-
ing to the movements of the ions can be transformed into
electrical energy.

We have, then, shown, thus far, how to calculate the
maximum external work obtainable, when a solution of
osmotic pressure p^ passes isothermally and reversibly
over to osmotic pressure p^ and the relation between this
work and the electrical energy obtainable.

But knowing the electrical energy, how can we deter-
mine the electromotive force } Electrical energy, like every
other manifestation of energy, can be factored into an
intensity and a capacity factor. The intensity factor of
electrical energy is the electromotive force, or potential,
and the capacity factor the amount of electricity. If we
call the former tt, and the latter e^y we have the energy
electric e^ = tt^q. If we know e^y we can calculate tt at
once, since e^ is known from Faraday's law. Knowing
the quantity of ions which pass from one osmotic pressure
over to the other, we know the amount of electricity e^ ;
knowing e^y we calculate tt.

Let us deal with a gram-molecular weight of univalent
ions. These will carry 96,540 coulombs of electricity, and
this quantity we will now designate by e^. If the ions are
bivalent they will carry twice as much ; if trivalent three
times, and so on. Let us represent the valence of the
ions by v\ then a gram-molecular weight will carry ve^

230 ELECTROLYTIC DISSOCLVTION

amount of electricity. Suppose a gram-molecular weight
of these ions is charged ir potential. The amount of
electrical energy required to eflfect this charge is: —

But this electrical energy is equal to the osmotic, calcu-
lated above, where a gram-molecular weight was taken
into accoimt We have: —

irve^

= RT\n

A
A'

RT\a

Pi.

This is the fundamental equation for calculating the
electromotive force of elements, from the osmotic pressures
of the electrolytes around the electrodes.

This equation has been very much simplified by
Ostwald,^ by introducing numerical values wherever it
is possible.

R^2 calories, and i calorie = 4.18 x 10^ ergs. 7) the

absolute temperature, can be taken as 290^*0. for the aver-

RT
age conditions. The constant = 0.0251 volt, since

volt X coul =10^ ergs.

The above equation then becomes: —

0.0251. /i
nr = ^— In ^

or in case the ions are univalent : —

7r = 0.0251 In^-

^ Lehrb. d. allg. Chem., II, p. 827.

APPLICATIONS OF THE THEORY 23 1

Thus far we have been using the natural logarithm
obtained in the process of integration, which we have writ-
ten In. It is far more convenient in practice to use the
Briggsian. To pass from the former to the latter we must
divide the above constant by 0.4343, when we obtain
0.058.

The final expression of the general formula for calcu-
lating the electromotive force of an element, from the
osmotic pressure of the electrolytes around the electrodes,
is then : —

7r = 0.058 log =^»

where log is the Briggsian logarithm. If the valence of
the ion is greater than one, this must be divided by the
valence. Before attempting to apply this expression to
any concrete cases, we must examine another conception
introduced by Nernst,

Electrolytic Solution-tension. — We are perfectly famil-
iar with the fact that when a solid or liquid is evaporated,
the molecules pass into the space above the liquid; and
equilibrium is established, for a given temperature, when
the vapor exerts a certain definite pressure. This press-
ure is designated as the vapor-tension, or vapor-pressure,
of the substance in question.

Says Nernst:^ "If, in accordance with van*t Hoff's
theory, we assume that the molecules of a substance in
solution exist also under a definite pressure, we must ascribe
to a dissolving substance in contact with a solvent, simi-
larly, a power of expansion, for here, also, the molecules
are driven into a space, in which they exist under a certain

1 Ztschr. phys. Chem., 4, 150.

232 ELECTROLYTIC DISSOaATION

pressure. It is evident that every substance will pass into
solution until the osmotic partial pressure of the molecules
in the solution is equal to the 'solution-tension' of the
substance."

Nernst thus introduced the conception of solution-ten-
sion ; and, at the same time, called attention to the close
analogy between evaporation and solution, which can be
seen only through a knowledge of the osmotic pressure of
solutions. The metals, like many other substances, have
the possibility of passing into solution as ions. Every
metal, in water, has, then, a certain solution-tension pecul-
iar to itself, and we will designate this by P,

If we dip a metal into pure water, let us see what will
take place. In consequence of the solution-tension of the
metal, some ions will pass into solution. When metallic
atoms pass over into ions, they must secure positive electric-
ity from something. They take it from the metal itself,
which thus becomes negative. The solution becomes
positive, because of the positive ions which it has received.
At the plane of contact of the metal and solution, there is
formed the so-called electrical double layer, whose exist-
ence was much earlier recognized by Helmholtz.^ The
positively charged ions in the solution and the negatively
charged metal attract one another, and a difference in
potential arises. The solution-tension of the metal tends
to force more ions into solution, while the electrostatic
attraction of the double layer is in opposition to this.
Equilibrium is established when these two forces are
equal. Since the ions carry such enormous charges, the
number which will pass into solution before equilibrium is

1 Wied. Ann.. 7, 337 (1879).

APPLICATIONS OF THE THEORY 233

established is so small that they cannot be detected by
any ordinary method. When we are dealing with a metal
immersed in pure water, it is evident that the difference in
potential which obtains in the double layer is conditioned
only by the magnitude of the solution-tension of the metal
in question.

If we dip a metal of solution-tension P, into a solution
of one of its salts, the case is not quite as simple. Let
the osmotic pressure of the metallic ions in the solution
of the salt be /, then either of three conditions may exist.
The solution-tension may be greater than the osmotic
pressure, less than the osmotic pressure, or just equal to it.
We may have : —

p>p- (I)

p<p. (2)

p^p' (3)

Let us first take case No. i, where a metal of solution-
tension P is immersed in a solution of one of its salts, in
which the osmotic pressure / of the metallic ions is less
than its own solution-tension.

At the moment the metal touches the solution, a number
of metallic ions, which always carry a positive charge, will
pass into solution. These ions have carried positive elec-
tricity from the metal into the solution, and the metal
has thus become negative, the solution positive. At the
places where the metal and solution come in contact, the
double layer is formed, due to the attraction of the opposite
charges.

"This double layer has a component of force, which
acts at right angles to the plane of contact of the metal

234 ELECTROLYTIC DISSCOATION

and solution, and tends to drive back the metallic ions from
thje electrolytes to the metal. It acts in direct opposition
to the electrolytic solution-tension." ^

The condition of equilibrium is reached when these two
opposing forces just equalize one another; and the final
result is the existence of an electromotive force between
the metal and the solution, the metal being negative, the
solution positive.

It is clear that a metal cannot throw as many ions into
a solution of its salt, as into pure water, because the
osmotic pressure of the metallic ions already in the solu-
tion acts against the solution-tension of the metal.

Let us now take the second case ; where the solution-
tension of the metal is less than the osmotic pressure of
the metallic ions in the solution. Metallic ions will separate
from the solution upon the metal. When a metallic ion
passes over into an atom it gives up its positive charge,
and in this case it gives it up to the metal, which becomes
positive. The solution, having lost some of its positively
charged ions, becomes negative. At the points of contact
of solution and metal, we have again the electrical double
layer, but this time the metal is positive and the solution
negative, which is exactly the reverse of the case first con-
sidered. Metal ions will separate from the solution until
the electrostatic component of force of the double layer, at
right angles to the plane of contact of metal and solution,
is just equal to the excess of the osmotic pressure over the
solution-tension. Equilibrium is established when the sum
of the solution-tension of the metal and this component of
force is just equal to the osmotic pressure of the metallic

1 Ztschr. phys. Chem., 4, 151.

APPLICATIONS OF THE THEORY 235

ions in the solution. An electromotive force exists here,
also, between the metal and the solution, but in the reverse
direction from the case first considered.

The third case is where the solution-tension of the
metal is just equal to the osmotic pressure of the metallic
ions in the solution. Just as soon as the metal touches
the solution, equilibrium is established. Ions neither dis-
solve from the metal, nor separate from the solution.
There is no double electrical layer formed, and there
is no difference in potential between the metal and the
solution.

If now we inquire which metals have high, and which
low solution-tensions, we will find that magnesium, zinc,
aluminium, cadmium, iron, cobalt, nickel, and the like,
are always negative when immersed in solutions of their
own salts. This means that the solution-tension of the
metal is always greater than the osmotic pressure of
the metal ion, in any solution of their salts which can be
prepared. If, on the other hand, we take gold, silver,
mercury, copper, etc., we usually find the metal positive
when immersed in a solution of its salt. This means that
the solution-tension of the metal is so small, that it is less
than the osmotic pressure of the metallic ion in the solu-
tion. When a very dilute solution of salts of these metals
is prepared, the osmotic pressure of the metallic ion may
become less than the very slight solution-tension of these
metals ; and then the metal would be negative with respect
to its solution.

We have, thus far, spoken chiefly of the solution-tension
of metals, which tends to drive the metal over into cations.
Substances which can pass over into anions have also a

236 ELECTROLYTIC DISSOCIATION

solution-tension, as is pointed out by Le Blanc.^ If the
chlorine ions in a solution had an osmotic pressure which
was gfreater than the solution-tension of chlorine, the chlo-
rine ions would pass over into ordinary chlorine. But
Le Blanc adds, that, as far as we know, all substances
which can yield negative ions have a high solution-tension.

Constancy of Solution-tension. — It was supposed for a
time, that the solution-tension of a metal is a characteristic
constant for the substance. This view was held by Ostwald
and developed in his Lehrbuch. On page 852 it is stated
that "the value P^ of the electrolytic solution-pressure, is
a constant peculiar to the metal, which deptnds upon the
temperature only, and generally increases with increasing
temperature."

So far as we know, this holds for a given solvent, but
does not apply to different solvents.^ Jones has found
that the solution-tension of metallic silver, when immersed
in an alcoholic solution of silver nitrate, is only about one-
twentieth of that in an aqueous solution. We can, there-
fore, regard solution-tension as a constant only for any
given solvent in which the salts of the metal are dissolved.
Indeed, this is what we would expect, when we consider
that nearly every substance dissolves differently in, or has
a specific solution-tension towards, every solvent. If the
substances which dissolve readily in solvents, vary so
greatly from solvent to solvent, as we know they do, why
should not substances which are only slightly soluble, such
as the metals, show this same difference t

Calculation of the Difference in Potential between Metal

1 Lehrb. der Elektrochemie, p. 121.

2 Ztschr. phys. Chem., 14, 346 ; Phys. Rev,, 2, 8z.

APPLICATIONS OF THE THEORY 237

and Solution. — The difference in potential between a
metal of solution-tension P^ and a solution of one of its
salts in which the metal ion has an osmotic pressure/, can
be calculated as follows.

When a substance of solution-tension P is converted
into ions of osmotic pressure P, no work is done. There-
fore, to convert a substance of solution-tension P into ions
of osmotic pressure /, the maximum work to be obtained
is the same as that obtained by transferring the ions from
osmotic pressure P to osmotic pressure /. Now we have
seen that the gas laws apply to the osmotic pressure of
solutions, and the amount of work can be calculated from
a gas in passing from gas pressure P to gas pressure /.
If we deal with a gram-molecular weight, we have seen
(p. 228) this to be: —

We have seen that this osmotic work is equal to the
electrical work for an isothermal transformation. The
electrical work is the potential times the amount of elec-
tricity. If we are dealing with gram-molecular quantities,
it is irve^.

Equating these two values, we have : —

irve^ = RT In— >

or, if the ions are univalent, z; = i, when we have: —

RT. P
w s= In —

^0 P

238 ELECTROLYTIC DISSOCIATION

RT
Now we know, from page 230, that = 0.0251 volt

Passing from natural to Briggsian logarithms, this becomes
0.058 volt.

The potential between metal and solution is, then, when
r=290^:— ^

7r = 0.058 log—

We have learned, thus far, how to calculate the electro-
motive force of elements from the osmotic pressures of
the solutions around the electrodes ; and also how to cal-
culate the potential between a metal and the solution of
one of its salts in which the metal is immersed. With
these two conceptions in mind, we will now study a few
elements to see how these principles are applied.

Types of Cells. — If the chemical process in the cell
remains the same during the time it is closed, the cell
is constant. If the chemical process changes, it is
inconstant.

Constant elements differ among themselves. Through
some of these we can send a current in the opposite direc-
tion without changing their electromotive force. This class
of constant elements is termed reversible. This applies to
elements in which the electrodes are immersed in solutions
of their salts. Take as an example the Daniell element.
This consists of a bar of zinc immersed in a solution of
zinc sulphate, and a bar of copper in a solution of copper
sulphate. When the current is passed in the opposite
direction through this cell, its nature is not changed.
The normal action is that the zinc dissolves and copper
separates. When a current is passed in the opposite

APPLICATIONS OF THE THEORY 239

direction, copper dissolves and zinc separates. But neither
process changes the nature of the cell.

Concentration Elements of the First Type. — We will
first consider a very simple type of a reversible element,
the two electrodes being of the same metal, and are
immersed in solutions of the same salt of that metal, the
solutions having different concentrations. To take a con-
crete example : Two bars of metallic zinc are immersed in
solutions of zinc chloride, the one bar in a tenth-normal
solution of the salt, the other in a hundredth-normal solu-
tion. The two solutions are connected by a tube filled
with either solution. When the two zinc bars, which are
the electrodes, are connected externally, the current flows,
and we have an element. Ostwald defines a cell or element
as any device in which chemical energy is converted into
electrical.

The only difference between the two sides of this element
is in the concentration of the electrolytic solutions. The
element is, therefore, termed a "concentration element."
Further, since the salt of the metal is soluble^ this is termed
a ** concentration element of the first class," to distinguish
it from other concentration elements which will be taken
up later.

Take the example given above, of two bars of zinc in
two solutions of zinc chloride of different concentrations.
The action of the cell is such as to make the two solutions
become more and more nearly of the same concentration.
The more dilute solution becomes more concentrated, and
the more concentrated more dilute, until when the two
become equal the element ceases to act. Zinc then passes
into solution in the more dilute solution, and zinc ions

240 ELECTROLYTIC DISSOCIATION

separate as metal on the bar from the more concentrated
solution. The electrode in the more concentrated solution
is always positive, since metallic ions are giving up their
positive charges to it, and separating as metal upon it.
The electrode in the more dilute solution is negative,
because ions are passing from it into the solution, and
carrying with them positive charges, which come from
the electrode. In an element of this kind, the current
always flows on the outside, from the electrode which is
immersed in the more concentrated solution.

The action of this cell is just what we would expect
The solution-tension of the zinc is the same on both sides
of the cell. The osmotic pressure of the zinc ions is, of
course, greater in the more concentrated solution. The
osmotic pressure, which works directly against the solu-
tion-tension, will cause the ions to separate from the
solution in which this pressure is the greater. The
electromotive force of such an element would be the
difference in the potential upon the two sides of the cell.

RT , P RT ^ P RT ^ p.

IT = m In — = In ^-^'

ve^ /j ve^ /i ve^ p^

Here v is the valence of the cation, p^ and p^ the
osmotic pressures of the zinc ions in the two solutions.
This, however, does not take into account the changes in
the concentrations of the solutions, which are taking place
while the current is passing.

If e^ electricity passes from the electrode into the
electrolyte, a gram-molecular weight of univalent cations
separates from the electrode, dissolves, and increases by
unity the concentration around this electrode. But, at

APPLICATIONS OF THE THEORY 24 1

the same time, cations are moving from this electrode,
with the current, over towards the other electrode. The
amount depends upon the relative velocities of anion and
cation. If we represent the relative velocity of cation by
Cy and of anion by a, the number of the cations which will

move over with the current is . The increase in the

c -\- a

concentration, due to a gram-molecular weight of cations
passing into solution, is then : —

c a
I = .

This factor is to be multiplied into the former equation
to obtain the osmotic work, which can then be equated to
its equal, the electrical energy. Let «, represent the number
of ions in the electrolyte. Taking into account both sides
of the cell, we have : —

2 a fiiR T . p^
ir = In ^-^:

or, 7r = ? 0.0002 riog^-

According to this ,f ormula, the only variables are /j
and /2» ^^ osmotic pressures of the cation in the two
solutions around the electrodes. The electromotive force
of such elements should depend only upon the relative
osmotic pressures of the solutions, and not upon the
absolute osmotic pressures. This has been found to be
true. The electromotive force should also be independent
of the kind of zinc salt used, provided the salt is soluble,
and yields the same number of zinc ions in each solu-
tion as the salt in question. Thus the chloride could be
replaced by the bromide, iodide, nitrate, etc., of such

242 ELECTROLYTIC DISSOCIATION

concentration that the osmotic pressure of the zinc ions
remained the same, and the electromotive force of the
element should remain unchanged, and such again is the
fact. The reason for this will be seen at once by examin-
ing the last equation; since it is only the osmotic pressure
of the cations which comes into play — the anion having
nothing whatever to do with the electromotive force of
the element.

The electromotive force of a number of elements of
the type we are considering has been measured, and to
within the limits which could reasonably be expected has
been found to agree with that calculated from the above
equation. To calculate the electromotive force, a number
of quantities must be measured, c and ^, the relative
velocities of cation and anion, must be determined ; simi-
larly, /i and /2» ^^ osmotic pressures of the cations in
the solutions, must be ascertained by indirect methods,
which involve the measurement of the dissociation of these
solutions. Since each of these processes introduces an
error of greater or less magnitude, we could not expect a
very close agreement between the electromotive force as
measured and as calculated. When we take all of these
facts into account the agreement is often surprisingly
close.

The following results, obtained by Moser, for solutions
of copper sulphate, with copper electrodes, are cited by
Ostwald.^ The concentrations of solutions, I and II, are
the number of parts of water to one part of copper
sulphate, ir is the electromotive force expressed in
thousandths of a Daniell cell. The unit is o.ooi i volt.

1 Lehrb. d. allg. Chem., II, p. 833.

APPLICATIONS OF THE THEORY 243

ir Obsbrvbd V {

Calcuu

12S.5

4.208

27.4

6.352

23.8

8.496

21.4

17.07

15.8

34.22

10.3

The concentration of one solution was maintained con-
stant throughout, and that of the other varied at will.
The agreement in these cases is very satisfactory.

Concentration Elements of the Second Type. — The char-
acteristic of the element which we have just been consid-
ering is that the metal is surrounded by one of its soluble
salts. We may also have concentration elements in which
the metal is surrounded by one of its insoluble salts ;
thus, silver surrounded by silver chloride. In the latter
case we must have present, in addition, a soluble chloride ;
and the soluble chloride must be of different concentra-
tions on the two sides of the cell. The element would
consist then of a bar of silver, surrounded by solid silver
chloride, and over this a solution of some chloride, say
potassium chloride; and on the other side, a bar of silver
surrounded by solid silver chloride, and over this a solu-
tion of potassium chloride, of different concentration from
that used on the side first described.

This element is termed a concentration element of the
second class.

The action of this cell will be such as to dilute the
more concentrated solution of potassium chloride, and to
concentrate the more dilute solution. Silver dissolves
from the electrode surrounded by the more concentrated
potassium chloride, and the ions of silver unite with the

244 ELECTROLYTIC DISSOCIATION

chlorine ions, and solid silver chloride is formed. The
potassium ions move with the current over to the other
side of the element, and form potassium chloride with some
of the chlorine which was there in combination with silver
as silver chloride. This silver then separates as metal
upon the electrode. In this way the more concentrated
potassium chloride becomes more dilute, and the more
dilute becomes more concentrated.

The electrode immersed in the more concentrated po-
tassium chloride is the one from which silver ions separate ;
therefore, this is the negative pole. The pole in the
more dilute solution of potassium chloride, receiving silver
ions, is positive. The current then flows upon the outside,
from the pole in the more dilute potassium chloride, to
the pole in the more concentrated.

This is exactly the reverse of what takes place in a

concentration element of the first type. There, as we
have seen, the current flows on the outside, from the
pole surrounded by the more concentrated electrolyte.

The electromotive force of a concentration element of the
second type is calculated in a manner perfectly analogous
to that employed with concentration elements of the first
type. The electromotive force tt is equal to the dif-
ference in the potential at the two poles : —

RT , P RT , P RT , p.
TT = m in — = In ^-^^

As in the case of the concentration element of the first
class, this does not take into account the changes in the
concentrations of the electrolytes which are taking place.
At the anode the metallic silver is passing into solution.

APPLICATIONS OF THE THEORY 245

and when e^ electricity is allowed to flow, a gram-
molecular weight of the silver will pass over into ions —
will dissolve. This will change the concentration of the
potassium chloride around this pole by — i. But at the
same time potassium is moving with the current, and
chlorine in the opposite direction, and this further changes

the concentration. If we represent the relative migration

+ -

velocities of K and 67, respectively, by c and a, the total
change in concentration around the anode will be: —

a c

-I +

C'\'a c + a

The change in concentration around the cathode would

be, of course : -^

This factor : —

c + a

must be multiplied into the above expression for electro-
motive force ; when taking into account both sides of the

cell, we have : —

2 c ftiR T . px

TT = ; '- In =^;

c + a vcq /2

^ s= 0.0002 T log^;

c + a.v /j

where «, is, as before, the number of ions yielded by
th« electrolyte, and v the valence of the cation. The
electromotive force of a number of such elements has
been measured by Nernst.^ Mercury was used as the
metal, since it could easily be obtained in pure condition.

1 ^tschr. phys. Chem., 4, 1^9.

246 ELECTROLYTIC DISSOCIATION

It was covered with an insoluble salt of mercury, and the
sibluble electrolyte then added. The chloride, bromide,
acetate, and hydroxide of mercury were used, and the
soluble electrolyte on both sides of the cell must con-
tain the same anion as the salt of mercury which was
employed. If the chloride was used, the soluble elec-
trolyte must be a chloride. If the hydroxide of mercury
was employed, a soluble hydroxide must be used, and so
on.

Some of the combinations which were made and meas-
ured by Nemst are given in the following table. The first
column contains the soluble electrolyte which was em-
ployed. Columns II and III give the concentrations of
the solutions of this electrolyte on the two sides of the cell.
" TT calculated " is the electromotive force calculated from
the preceding formula, and " ir found " is the electromotive
force of the combination, as measured by Nemst.

SOLUBLB

III

Elbctrolytb

CONCBMTRATION X

Concentration a

Calculatkd

Found

HCl

0.105

0.018

0.0717

0.0710

HCl

O.I

0.0 1

0.0939

0.0926

HBr

0.126

0.0132

0.0917

0.0932

KCl

0.125

0.0125

0.0542

0.0532

NaCl

0.125

0.0125

0.0408

0.0402

LiCl

0.1

O.OI

0.0336

0.0354

NH4CI

0.1

O.OI

0.0531

0.0546

NaBr

0.125

0.0125

0.0404

0.0417

CHaCOONa

0.125

* ' 0.0125

0.0604

0.0660

NaOH

0-235

0.030

0.0183

0.0178

KOH

0.1

O.OI

0.0298

0.0348

NH4OH

0.305

0.032

0.0188

0.024

APPLICATIONS OF THE THEORY 247

Liquid Elements. — It has long been known that there
may be differences in potential at the contact of two solu-
tions of electrolytes. Tljiis can be shown by constructing
an element in which the two electrodes are of the same
metal, and immersed in the same solution of the same
electrolyte. There can, therefore, be no difference in po-
tential between the two metals, nor between the metals
and electrolytes, for the tensions between the metals and
electrolytes are the same on the two sides, and act in direct
opposition to one another. If two solutions of electrolytes
of different concentrations are introduced into the circuit
between the solutions in which the electrodes are im-
mersed, we will have an element with a certain definite
electromotive force. A typical liquid element would be
the following : —

Mercury-mercurous chloride.

— potassium chloride.
10

potassium chloride.

100

hydrochloric acid.

— hydrochloric acid.

— potassium chloride.
10

Mercurous chloride-mercury.

Theory of the Liquid Element. — The first satisfactory
theory of the liquid element we owe to Nemst.^ What is the

^ Ztschr. phys. Chem., 4, 140.

248 ELECTROLYTIC DISSOCIATION

source of the differences in potential in liquid elements ?
That differences in potential should exist in electrolytes
there must be a lack of uniform distribution of ions. The
region which is positive must contain an excess of cations,
and that which is negative, an excess of anions. The cause
of this lack of uniform distribution of ions is to be found
in the different velocities with which the different ions
diffuse.

Take the case of a solution of hydrochloric acid in con-
tact with pure water. The hydrogen and chlorine ions
in the solution of the acid are present in the same number.
They are, therefore, under the same osmotic pressure, and
are driven with the same force into the water. But they
move with very different velocities, from regions of higher
to those of lower osmotic pressure. Hydrogen is, as we
have seen, the swiftest of all ions, and moves very much
faster than chlorine. It will thus diffuse into the water
more rapidly than chlorine, and will tend to separate from
the chlorine. But the positive ions cannot separate from
the negative ions, without producing a separation of the
two kinds of electricity. There will result, therefore, elec-
trostatic attractions between the layers, which will retard
the hydrogen ions and accelerate the chlorine ions, until
the two have the same velocity.

Differences in potential will result ; and always in the
sense, that the water or the more dilute solution will have
the sign of the swifter ion. Hydrogen being the swiftest
of all ions, water, or the more dilute solution of acid, is
always positive with respect to the more concentrated.
Next to hydrogen, in order of velocity, comes hydroxyl.
Water, or the more dilute solution of a base, must, there-

APPLICATIONS OF THE THEORY 249

fore, always be negative with respect to the more con-
centrated.

Nemst has shown not only how it is possible to account,
qualitatively, for the differences in potential between elec-
trolytes, but has furnished us also with a method of calcu-
lating these differences quantitatively.

Given two solutions of different concentrations of an
electrolyte like hydrochloric acid, which is composed of a
univalent cation and a univalent anion. Let the velocity
of the cation be Cy and that of the anion a. Let p^ be the
osmotic pressure of both ions in the more concentrated
solution, and p^ the osmotic pressure in the more dilute.
If e^ electricity is passed from the more concentrated to

the more dilute solution, of a gram-equivalent of

c -\- a

cations will move with the current, and of a gram-

c -V a

equivalent of anions will move against the current.

of cations have moved from a region of greater to

c + a
one of less osmotic pressure. The work is : —

RTlvi

c + a p2

But of anions have moved from a resrion of lower

c + a

into one of higher osmotic pressure. The work done upon
them is : —

-JL-.RT In^.
c + a /j

The total gain is the difference between these two: —

i—?.RT]T.^-
c + a /,

250 ELECTROLYTIC DISSCX:iATION

Equating this against the electrical energy ire^^ we
have:— c^a RT , p.

c-Va e^ /,

or, IT = ^^i^ 0.0002 T log 4^.

If c is greater than a^ the more dilute solution is positive,
as already stated, and the current flows on the outside,
from the more dilute solution to the more concentrated.
If ^x is greater than c^ the more dilute solution is negative,
and the current flows in the opposite direction.

If the velocities of the two ions are equal {c = a)^ the
right member of the above equation becomes zero, and there
is no electromotive force. It is, therefore, impossible to
construct a liquid element from solutions of an electrolyte
whose cation and anion have the same velocities. If the
valence of either ion is greater than unity, this must be
taken into account. If we represent the valence of the
cation by ^, and that of the anion by z/j, the above ex-
pression becomes : —

IT =

; i O.OCX)2 T log ^^•

Nernst prepared liquid elements and determined their
electromotive force. He then calculated the electromotive
force from the above equation, and compared the values
found experimentally with those from calculation.

The following element already referred to was con-
structed: — 12^4
Hg-HgCl-KCl-KCl-HCl-HCl-KCl-HgCl-Hg.

lOO

APPLICATIONS OF THE THEORY 25 1

The potential differences at the ends are equal and
opposite, and therefore equalize one another. The four
differences in potential which must be taken into account
are indicated above. But the potential differences are
dependent upon the relative not upon the absolute osmotic
pressures. The potentials at 2 and 4 are, therefore, equal
and opposite, and can also be left out of account. This
leaves the potentials at i and 3, and these can be calcu-
lated by the method already given. Let c^ and a^ be the
relative velocities of potassium and chlorine ions, and c^
and ^3 the relative velocities of hydrogen and chlorine
ions; the electromotive force of this element would be
calculated as follows, from the equation just deduced.
The electromotive force would be the difference between
these two -potentials : —

^1 + ^1 ^0 A ^2 + ^2 ^0 /i

p and /i are the osmotic pressures of the potassium and
chlorine ions in the more concentrated and more dilute
solutions, respectively; />' and/^' the osmotic pressures of
the hydrogen and chlorine ions in the solutions of hydrp
chloric acid.

Pi Px
Introducing this into the last equation, we have : —

V^l + ^1 ^2 + ^2/ ^0 P\

or, IT = [^1—-^ — f2_^2\ 0.0002 Tlog ~

Vi + ^1 ^2 + V P\

252 ELECTROLYTIC DISSOCIATION

This is the expression for calculating the electromotive
force in liquid elements, like the above, where the valence
of the cation is the same as that of the anion. If they are
different, we will represent the valence of the cations by
V and z;', and that of the anions by v^ and v^ ; the equa-
tion for the electromotive force would then become : —

7r =

^ — ^ ^2 ^2

C-i + ^1 ^o -f- d

0.0002 T'log —

The electromotive force of the liquid elements which
have been studied, as calculated from the above equation,
agrees with that measured, to within the limits of experi-
mental error.

It should be observed, that the expression deduced
above holds only for the potential at the contact of solu-
tions of the same electrolyte, the solutions being of dif-
ferent concentrations. If different electrolytes are used,
we have no general means of calculating the potential at
their surface of contact.

It should be stated before leaving the subject of liquid
elements, that the potential at the contact of two solutions
is usually not great, and that the electromotive force of
liquid elements is in general not large.

Sources of Potential in a Concentration Element. — We
may now analyze, more closely, the electromotive force in
a concentration element, in the light of what we have
learned about the liquid element. Thus far, we have dealt
with the concentration element as if the only sources of
the potential were at the points of contact of the electrodes
and the solutions. And indeed this is practically true in

APPLICATIONS OF THE THEORY 253

the cases of the concentration element which we have
studied.

We have learned from the study of the liquid ele-
ment, that the plane of contact of two solutions of an
electrolyte is also a seat of potential. In the concentra-
tion element there is always such a contact between two
solutions of the electrolyte, and this must be a source of
potential. In the concentration element which we have
studied, this potential is so small that it can practically be
neglected. While the potential between solutions is usually
small, it may, however, easily assume proportions which
must be taken into account. We must now see how it is
possible to calculate the potential at the contact of the
two solutions in the concentration element. We can then
analyze the electromotive force of a concentration element
into its three constituents, and calculate the magnitude of
the potential at each electrode, and also at the surface of
contact of the electrolytes.

Let the potential at one electrode be tt', at the other

electrode tt", and at the contact of the two electrolytes

tt"'. The values of these potentials are calculated by

means of the following formulas: —

p
w' = 0.0002 riog — ;

p
ir^^ = — 0.0002 r log — ;

tt'" = 0.0002 T — - — log ~

c + a ^ /a

These equations obtain for univalent ions. If the
valence of the ion is greater than one, this must be taken

254 ELECTROLYTIC DISSOCIATION

into account in the way already described. The sum of
the three potentials must then be the potential of the con-
centration element.

tt' + tt" = - 0.0002 riog ^ ;

(tt' + Tt") + Tt'" = 0.0002 T -^ log ^

This must be the same as the equation already deduced
(p. 241) for the concentration element. It will be seen to
be the case, if we consider that «, = 2, and v for univalent
ions equals i.

We can thus calculate the magnitude of the three
sources of potential in a concentration element of the first
class. An element of this class has been chosen, since
the relations are somewhat simpler. The main sources of
potential are at the contact of electrode and electrolyte,
while a very small potential exists at the contact of the
two electrolytes. In elements of this kind, it is perfectly
clear that there is no potential where the two electrodes
come in contact, because these are of the same metal.

The Electromotive Force of the Daniell Element. — The
elements which we have considered thus far have both
electrodes of the same metal. The solution-tension of the
metal was, therefore, the same upon both sides of the cell,
and being of equal value and opposite sign, it disappeared
from the equation for the electromotive force of the
element.

In most of our common elements, however, two metals
are used as electrodes, or a metal and carbon. It is evi-
dent that in these cases the solution-tension of the electrode

APPLICATIONS OF THE THEORY 255

must be taken into account, since it is different for different
metals.

The Daniell element is taken as a type of the two metal
elements with which we are so familiar. The application
of our fundamental equation to this element will serve as
an example of the way in which it may be applied to
other well-known elements.

The Daniell element consists of zinc in zinc sulphate,
and copper in copper sulphate. Zinc dissolves and copper
separates from the solution. The zinc electrode is there-
fore negative, and the copper positive, the current passing
on the outside from the copper to the zinc. The electro-
motive force is equal to the difference in potential at the
two electrodes, since the potential at the contact of the
zinc sulphate and copper sulphate is so slight that we can
practically disregard it.

Representing the potential at the two electrodes by
Wj and TTj, we have: —

2<fo

•

9r,

2^0

Pi.

in which P and P-^ are the solution-tensions of the two

metals.

RT , P RT , P.

^ 2^0/2^0/1

In the light of this example, the application of the con-
ceptions here developed, to other special cases, should be
a simple matter.

256 ELECTROLYTIC DISSOCIATION

The Gas-tMittery. — The typical gas-battery consists of
an electrolyte, two gases which can act chemically upon
one another, and two platinum electrodes which are partly
surrounded by the electrolyte, and partly by the gases.

Take as a simple example, hydrogen over one electrode
and chlorine over the other, the electrolyte hydrochloric
acid, and the electrodes platinum. Hydrogen and chlorine
will pass into solution at the two poles until there is an
equilibrium between the force driving these substances
into solution (solution-tension), and the osmotic pressure
of the hydrochloric acid solution, which acts against the
above-named force. The hydrogen pole is negative, since
the solution-tension of the hydrogen is gpreater than the
osmotic pressure of the solution; the hydrogen atoms
becoming ions by taking positive electricity from the
platinum electrode, which thus becomes negative. Exactly
the opposite result is obtained at the other electrode,
chlorine atoms becoming ions by taking negative electric-
ity from the electrode, which therefore becomes positive.

Ostwald ^ has shown that the theory of Nernst can be
applied also to the electromotive force of the gas-battery.
He has worked out even a simpler case than the one
given above. We will take up first the simplest possible
case, where we have the same gas, say hydrogen, over
both electrodes, the hydrogen upon the two sides being
at different pressures.

The action of such an arrangement would be, as Ost-
wald shows, to equalize the pressure of the gas upon the
two sides of the cell. Hydrogen must pass into solution
as ions upon the side where it is under the greater

^ Lehrb. d. allg. Chem., II, p. 895.

.«

APPLICATIONS OF THE THEORY 257

pressure, and ions of hydrogen must separate as gas upon
the other side of the cell. Upon the side where hydrogen
atoms are becoming ions, they take positive electricity
from the electrode, which becomes negative, and the other
electrode positive, because positive hydrogen ions are
giving their charges up to it. We have here an analogue
of the concentration element, and the electromotive force
can be calculated in a similar manner.

The electromotive force of this element also is the
difference in the potential upon the two sides: —

RT , P RT, P,

IT = In In — ;

where P is the solution-tension of hydrogen, and/j and/j
the pressures of the hydrogen gas upon the two sides.
The solution-tension, being the same upon both sides of
the cell, disappears, as in the concentration element, and

then we have: —

0.0002 T , /,
TT = log ^

Since for hydrogen, z;=2, we have: —

TT = 0.0290 log ^

Ostwald * has also calculated the electromotive force for
a gas-battery consisting of two gases. But as this has
been worked out much more fully by Smale,^ we will turn
to his work.

Take the case of oxygen at one pole and hydrogen at
the other.

1 Loc, cii. s Ztschr. phys. Chem., 14, 577, and z6, 563.

258 ELECTROLYTIC DISSOCIATION

Let P^ be the solution-tension of hydrogen.
Let P^ be the solution-tension of oxygen.
Let T be the absolute temperature.
The potential at the hydrogen pole is: —

p
IT. = O.00O2 T log— i

A
Since the solution-tension of oxygen is negative: —

ir^ =5 0.0002 T log^ ;

vj — TTj = TT = 0.0002 y log -^ — 0.0002 T'log^;

P P

TT = 0.0002 T log — ^ -f 0.0002 T log — ^'

The theoretical consequences of this equation are very
interesting. P^ and Pj, the solution-tensions of the gases,
are independent of the nature and concentration of the
electrolyte used on the two sides of the element; and
/i and /2 arc practically constant for solutions of nearly
the same dissociation.

Smale^ has tested this point, using seven acids, three
bases, and seven salts. The concentrations for the same
electrolyte vary in most cases from o.i to o.ooi normal.
He found that the electromotive force of the hydrogen-
oxygen battery was practically constant, independent of
both the nature and concentration of the electrolytes used
beneath the gases.

A few results taken from the work of Smale will bring
out this fact

1 Loc, cit.

APPLICATIONS OF THE THEORY 259

Elbctrolytb Usbd

Concentration Normal

E.M.F.

HCl

O.I

0.998

HCl

0.01

1.036

HCl

0.00 1

1-055

KOH

O.I

1.098

KOH

O.OI

1.095

KOH

0.00 1

1.093

KjSOi

O.I

1.074

KjSO*

O.OI

1.069

K^4

0.00 1

1.069

The results thus agree satisfactorily with the deduction
from theory.

If, instead of oxygen, other gases, as chlorine, are used,
the electromotive force depends upon the concentration of
the electrolyte, which also agrees with theory, as is shown
by Smale.

But the theory admits of still further experimental test.

If the electrodes are of two different metals, say plati-
num and palladium, and are surrounded by the same
gas which does not attack them, and are immersed in the
same electrolytes, the electromotive force at each electrode
is in terms of the theory formulated thus : —

p
TT. = 0.0002 T log— ;

TTj = 0.0002 T log --^.

Pj and P^ are the solution-tensions of the gas in plati-
num and palladium, respectively ; p^ and p^ the osmotic
pressures at the electrodes ; which are equal in this case,

260 ELECTROLYTIC DISSOCLVTION

since the same electrolyte is used on both sides. There-
fore, we have: —

p
'H'^-- w^zstr^i O.CXX)2 T log -=i volts.

The metal electrodes then play only this r61e, they offer
a large surface to the gas, which facilitates its solution in
them. The electromotive force of such an element should,
therefore, be independent of the nature of the electrode
usedf since solution-tension is a constant for any given
metal, according to the theory. It should, further, be inde-
pendent of the size of the electrode.

Both of these points were tested experimentally by
Smale. The nature of the electrode, whether platinum,,
palladium, or gold, had no influence on the electromotive
force. The size of the electrode, beyond a certain point,
had no influence. A certain amount of surface is, how-
ever, necessary in order that the electrode should reach its
full tension.

This work of Smale furnishes then another beautiful
experimental confirmation of the consequences of that
theory, which has enabled us to calculate the electromotive
force of concentration elements, liquid elements, etc.

A number of other types of elements might be taken
up, and their electromotive force calculated from the
method of Nemst, which, as we have already seen, is
based upon van't Hoff's laws of osmotic pressure, and
Arrhenius's theory of electrolytic dissociation. This is,
however, not necessary, since the application to special
cases is simple, if the fundamental principles are once
grasped.

APPLICATIONS OF THE THEORY 26 1

Chemical Action at a Distance. — Before concluding this
section, we will diescribe a phenomenon of unusual inter-
est. On account of its close relation to solution-tension,
it should appear in this connection.

In 1 89 1, a paper was published by Ostwald,^ under the
surprising title ** Chemische Femewirkung." It was sur-
prising, because chemical action, as ordinarily understood,
takes place only between substances which are close to one
another. Ostwald begins his paper by calling attention
to the fact that amalgamated zinc is not dissolved by
dilute acids, but if the zinc is surrounded by a platinum
wire, it is dissolved by the acid. It is not even necessary
for the platinum wire to surround the zinc, for if the wire
touches the zinc at any one point, solution will take place.

Ostwald suggests that the zinc and platinum wire be
joined at one place, and then the free ends of both im-
mersed in a vessel containing, say, potassium sulpha,te.
Let a screen of some porous material be placed between
these free ends of the platinum and zinc, so that the salt
solution around the one is separated from that around the
other. He then asks the question : To which metal must
sulphuric acid be added, in order that the zinc may be
dissolved by the acid.?

" The question seems at first sight to be absurd ; since,
in order that the zinc should dissolve, it appears to be self-
evident that the acid should be added to the zinc. If we
carry out the experiment we find exactly the reverse to be
true. The zinc does not dissolve rapidly, if acid is added
to the solution of potassium sulphate around the zinc. If,
on the contrary, the acid is added to the solution around

1 Ztschr. phys. Chem., 9, 54a

262 ELECTROLYTIC DISSOCIATION

the platinum, the zinc dissolves with a copious evolution of
hydrogen gas. The hydrogen appears on the platinum, as
is always the case when zinc is in combination with plati-
num. To dissolve the zinc under the conditions described,
the solvents must not be allowed to act on the metal to be
dissolved, but on the platinum which is in contact with the
zinc."

A number of other cases are cited.

Zinc in sodium chloride behaves in the same manner,
when hydrochloric acid is added to the platinum. Cad-
mium also behaves like zinc. Tin, surrounded by sodium
chloride, dissolves when hydrochloric acid is added to
the platinum. Aluminium behaves like tin. Silver con-
nected with platinum dissolves in sulphuric acid when a
few drops of chromic acid are added to the platinum.
Gold dissolves in sodium chloride, if chlorine is brought
in contact with the platinum.

Experiment to demonstrate Chemical Action at a Distance.
Fill a beaker with a solution of potassium sulphate. Take
a piece of glass tubing about lo cm. long and 2 cm. wide,
and close the lower end with vegetable parchment. Fit
a bar of pure zinc, about 10 cm. long, tightly into a cork
which just closes the top of this glass tube. Fill the
glass tube with some of the same solution of potassium
sulphate, and insert the bar of zinc — the cork closing
the top of the glass tube. Around the top of the zinc
bar above the cork wrap a piece of platinum wire of
sufficient length to reach nearly to the bottom of the
beaker, when the glass tube is introduced into the beaker
in the manner to be hereafter described. The free end
of the platinum wire should be coiled upon itself a num-

APPLICATIONS OF THE THEORY 263

ber of times, or it is better if it is connected with a piece
of platinum foil a few centimetres square, so as to expose
a larger surface.

The glass tube is now immersed in the beaker until the
surface of the solution in the tube is only a centimetre or
two above the surface of the solution in the beaker, the
free end of the platinum wire, or the platinum foil, being
allowed to rest on the bottom of ^ the beaker.

If a few drops of sulphuric a,cid are introduced into the
potassium sulphate just around the bar of zinc, the zinc
will be very slightly affected. But if a few drops of sul-
phuric acid are poured upon the coiled end of the platinum
wire, or upon the platinum foil, the zinc will dissolve
rapidly in the neutral potassium sulphate which surrounds
it, and a copious evolution of hydrogen will take place
from the platinum, where it is in contact with the sulphuric
acid. After a few moments the presence of zinc can be
demonstrated in the inner tube, by any of the well-known
reactions for zinc.

As Ostwald states, similar phenomena have long been
known. Nearly forty years ago Thomsen^ described a
galvanic element, which consists of copper in dilute sul-
phuric acid, and carbon in a chromate mixture. When the
carbon and copper were connected, the metal dissolved as
the sulphate, in sulphuric acid, in which copper alone is
not soluble. While similar facts were known, there was
no rational explanation offered to account for them, until
Arrhenius proposed the Theory of Free Ions,

It is almost self-evident that the phenomenon is closely
connected with electrical changes. Ostwald demonstrated

1 Pogg. Ann.*, Ill, 192 (i860).

264 ELECTROLYTIC DISSOCIATION

this, by introducing between the metal and the platinum a
fairly sensitive galvanoscope. When the acid was added to
the platinum, the presence of a current was shown by the
throw of the instrument.

The explanation of this phenomenon is perfectly simple,
now that we have the theory of electrolytic dissociation,
and are familiar with its application to the primary cell.

When metallic zinc is immersed in a solution of a neutral
salt, like potassium sulphate, it sends, in consequence of
its own solution-tension, a certain number of zinc ions into
the solution. The zinc is thus made negative, and the
solution, which has received the positive ions, positive.
This continues until a definite difference in potential be-
tween metal and solution is established. The amount of
metal required to effect this condition is, as we have seen,
so small that it cannot be detected by any chemical means.

The zinc cannot dissolve further, because of the excess
of positive ions in the solution. In order that more zinc
may pass into solution, some of these positive ions must
be removed. If the zinc is in combination with another
metal, such as platinum, the latter takes the same nega-
tive charge as the zinc. When the platinum is immersed
in the solution, it attracts the excess of positive ions in
the solution, and these collect upon the platinum.

We would expect the excess of positive ions in the
solution to give up their charge to the negative platinum,
and separate from the solution, or, in case of potSssium,
decompose the water which is present. This depends
both upon the nature of the ion and of the electrode. If
the positive ion is the potassium of potassium sulphate,
the difference in potential produced by introducing the

APPLICATIONS OF THE THEORY 265

zinc is not sufficient to cause this ion to lose its charge
to the platinum. If sulphuric acid is added to the
platinum, the difference in potential, produced by 'intro-
ducing the bar of zinc, is sufficient to compel the
hydrogen to give up its positive charge tOxthe platinum,
and separate as ordinary hydrogen. The platinum, having
received positive electricity from the hydrogen ions, con-
ducts this over to the zinc. The zinc becomes less nega-
tive than before the hydrogen separated at the platinum,
and the difference in potential between the zinc and
the surrounding solution is less than before. More zinc
dissolves or passes over into ions, more hydrogen ions
give up their charge to the platinum and separate as
gas ; and this continues until all of the zinc has dissolved,
or all of the hydrogen ions have separated as gas.

As Ostwald observes, this explanation shows not only
why the acid must be added to the platinum and not
to the zinc, but throws light also on the problem of the
solution of metals in general. A word or two on this
subject. It has long been known that pure zinc does
not dissolve in acids, while impure zinc readily dissolves.
It is quite evident that the zinc in the two cases has
the same tendency to dissolve. Pure zinc dissolves readily
when in contact with a metal, such as platinum, which has
a small solution-tension. As we have seen from the fore-
going explanation, the difference is not in the solution
of the zinc, but in the ease with which the hydrogen
can escape from the solution. The presence of a metal
with small solution-tension allows this to take place more
readily, and this is the reason that impure zinc dissolvc:^^
in acids.

266 ELECTROLYTIC DISSOOATION

The reason why pure zinc does not dissolve in acids is
because this metal has a strong positive solution-tension ;
it sends positively charged ions into solution under a
high solution-tension, and, therefore, opposes the separa-
tion of any other positive ion, like hydrogen, upon it.
Pure zinc, therefore, does not dissolve in acids, because the
hydrogen ions cannot give up their positive charges and
escape.

When a metal like platinum, which has a small solution-
tension, is present, the hydrogen can easily give up its
charge to this metal and escape as gas. The zinc, because
of its high solution-tension, and because the hydrogen
cations can so easily escape, then dissolves.

To repeat the essential steps in the explanation of the
experiment described above: Pure zinc immersed in po-
tassium (or any soluble) sulphate, to which sulphuric
acid is added, or in a solution of pure sulphuric acid
itself, does not dissolve, because the zinc has such a high
solution-tension that the hydrogen ions cannot give up
their charge to it and escape. The zinc, however, throws
a few ions into solution, and becomes negatively charged.
If now the zinc is connected with platinum, which has
a small solution-tension, and the acid added to the plati-
num, the hydrogen ions can easily give up their charge
to the platinum and escape as gas. The platinum, which
was at the potential of the zinc with which it is in com-
bination, now becomes positive with respect to the zinc,
and a positive charge, therefore, flows from the platinum
to the zinc. The zinc, having received positive electricity,
can begin dissolving anew, and continue to pass into
solution as long as it receives positive electricity from

APPLICATIONS OF THE THEORY 267

the platinum — as long, therefore, as there are any hydro-
gen ions in the solution to furnish positive electricity to
the platinum. Or, as we are accustomed to express
it, as long as there is any acid in contact with the
platinum.

This subject will be concluded with a paragraph from
this fascinating paper by Ostwald: "We see that the
usual explanation, that solution takes place because of
galvanic currents between the zinc and the other metals,
is not in strict accord with the facts. ^ The galvanic
currents are inseparably connected with the process
of solution, but they are not the primary causes of the
solution. They are set up, rather, by the process of solu-
tion, which they must necessarily accompany, since solu-
tion is a question of ion formation and disappearance.
If it is possible for the positive ions present to separate
in any way from the solvent, solution takes place."

Ostwald then goes on to show that it is not necessary
for the ion to separate from the solution. The positive ion
may be destroyed in the solution, or a negative ion pro-
duced; and in either case the nietal will dissolve. But
for these and similar facts the original paper must be
consulted.

Conclusion. — In concluding this chapter on the calcula-
tion of the electromotive force of elements, attention should
again be called to the fact, that the method worked out by
Nernst was based directly upon van't Hoff*s laws of
osmotic pressure, and the theory of electrolytic dissocia-
tion. Without either of these conceptions the work of
Nernst would have been absolutely impossible. With
them, he has thrown entirely new light on the whole ques^

268 ELECTROLYTIC DISSOCIATION

tion of the electromotive force of elements, and has fur-
nished us, for the first time, with a satisfactory theory of
the action of the primary cell.

APPLICATION OF THE THEORY OF ELECTROLYTIC DISSOCIA-
TION TO BIOLOGICAL PROBLEMS

The application of a theory of solution to biological
problems is not so evident as to chemical, where solutions
are always involved. Solutions are, however, very fre-
quently used by the physiologist, and any theory of
solution must, therefore, bear upon many physiological
problems.

It is only in the last few years that the theory of electro-
lytic dissociation has found its way into physiology, and
work along this line may be said to have just been begun.
A few examples of the application of the theory in this
direction will be given.

Toxic Action and Electrolytic Dissociation. — Kahlenberg
and True^ published a paper in 1896 on "The Toxic
Action of Dissolved Salts and their Electrolytic Dissocia-
tion,'* which was the pioneer work along this line.

It had been thought that the physiological action of any
substance was due to its chemical nature. In the case of
a solution, all of the chemical and physical properties are
a function of the properties of the ions, plus those of the
undissociated molecules which it contains. It would, there-
fore, seem probable, that the physiological action of such
solutions was due to the same cause. Many investigations
on the physiological action of aqueous solutions on bacteria
and higher forms of plant life, as well as on animals, have

1 Botan. Gazette, 23, 81.

APPLICATIONS OF THE THEORY 269

been made. In work of this kind, percentage concentra-
tion has been dealt with, and this obscures any general
relations which might exist.

If a dilute solution of sodium chloride differs from a
dilute solution of hydrochloric acid, in that the former
contains sodium ions and the latter hydrogen ions, then
tlie poisonous character of the latter must be due to
the hydrogen ions.

Since a very dilute solution is completely dissociated,
the poisonous properties of such a solution must be due to
one or both of the ions which it contains, since there are
no molecules present. If the toxic action of acids on
plants is due only to the hydrogen ion, then solutions bf
different acids containing the same number of hydrogen
ions should be equally poisonous. Solutions of hydro-
chloric acid, nitric acid, and sulphuric acid are completely
dissociated at a volume of about one thousand litres;
hence, solutions of these acids which are of this strength,
or more dilute, should have the same toxic action ; since the

ions CI, NOg, SO4, have none.

This has been tested, experimentally, for the higher
plants, by finding the strength of the solution of the acid
in which the root of the plant will just live. Seedlings of
Lupinus albus L. were employed. They have a straight,
clean radicle, and are well adapted to this work. The
root was suspended in the acid solution, and its condition
determined by the rate of growth. It was a simple matter
to determine when the root was dead, since it lost its satiny
lustre and acquired a dead-white color. Its appearance
may be described as coagulated. The root was immersed
in the solution for fifteen to twenty-four hours, which was

2/0 ELECTROLYTIC DISSOCIATION

the time chosen for an experiment. The root of the plant
was first placed in a more concentrated solution of the
acid. If this was found to kill it, another root was placed
in a more dilute solution, and so on, until a dilution was
reached in which the root just lived. In the case of strong
acids, the root would just live in a solution which contained
a gram-molecular weight of the acid in 6400 litres of solu-
tion; expressed in ordinary terms, the solution had a
volume of 6400 litres. This expresses the toxic action of
the hydrogen ion, and it is the same for all strong acids.
The hydroxyl ion was studied, and found to be far less
poisonous than the hydrogen ion. The root would just
live when the solution contained a gram-molecular weight
of the base in 400 litres of solution. The effect of the
ions of certain salts was also studied. The copper ion
was especially toxic. The roots would just survive in a
solution which contained a gram-molecular weight of
copper ions in 51,200 litres of solution.

Whenever copper forms part of an ion, and is not the
whole ion, the result is very different. Thus, in Fehling's
solution copper forms part of the ion. it being in com-
bination with an organic complex. We would expect it,
therefore, to have a different action, under these condi-
tions, than when alone. This was tested by experiment.
In preparing the Fehling's solution, cane-sugar was used
instead of Rochelle' salt, in order to avoid the excess of
other ions in the solution. An excess of caustic alkali
was avoided, in order to keep out hydroxyl ions, which
are known to be poisonous. The roots would grow in a
solution of this salt, which contained a gram-atomic weight
of copper in 400 litres. Copper, when alone as an ion, is,

APPLICATIONS OF THE THEORY 27 1

thus, far more poisonous than when in combination with
this complex.

Iron in its ionic state has. very different toxic action
than when the iron atom is combined with other things to
form an ion. Thus the iron in a ferric salt has very
different effect from the iron in potassium ferrocyanide.
It would be indeed surprising if this were not true, since
iron in a ferric salt forms a cation, while iron in potassium
ferrocyanide is combined with the 6 CN groups, forming a
part of the complex anion.

Cobalt and nickel have the same toxic action as iron.
The question is raised, whether there is any connection
between this action and the fact that the three elements
have very nearly the same atomic weights. The experi-
mental data are yet far too meagre to answer this ques-
tion. Cadmium and silver also are found to be very
poisonous.

The Cu ion is about as toxic as the hydrogen ion.
Hydrocyanic acid is almost completely undissociated, yet
it is very poisonous. The plant will stand only y^^l^nr ^^ ^
gram-molecule per litre. This is an excellent example of
how molecules as well as ions may be poisonous.

The investigation was extended to the organic acids, and
these, with some exceptions, fell in line with the above
relations.

This investigation has shown that the toxic action of
solutions of electrolytes, which are completely dissociated,
is due to the ions present. When the electrolyte is only
partly dissociated, the undissociated portion may exert a
toxic action. We have here a recognition of the theory of
electrolytic dissociation in the organic world. The paper

2/2 ELECTROLYTIC DISSOCIATION

of Kahlenberg and True contains the following significan:
passage : —

"It will be seen that a wide field for research along
physiological lines opens up, by applying to the field of
biology the dissociation theory which has proved so fertile
in chemistry and physics. Further work in, this direction,
using the latest and best that the new physical chemistry
has to offer, it is to be hoped, will place our knowledge of
the physiological action of solutions of electrolytes on a
better basis than the purely empirical one on which it has
thus far rested. It does not seem too much to expect that
the effect of such study will soon be felt in agriculture and
therapeutics, while bacteriological study, pursued from the
standpoint of the new theory, will yield important additions
to our knowledge of antiseptics."

Another investigation in the same field has been carried

out by F. D. Heald.^ He studied the toxic action of

acids and salts upon different plants. He used the three

plants: —

Ptsunt sativum^

Zea Mais,

Cucurbita Pepo. ,

The conclusions of Kahlenberg were all confirmed by
this work, in which more than one plant was used. Says
the author, "The theory of electrolytic dissociation has
thus thrown light upon the physiological action of different
substances, and the theory has, itself, been strengthened
by these experiments upon living things.'*

Toxic Action of the Phenols and their Dissociation. —
The work begun by Kahlenberg and True has since been

1 Botan. Gazette, 22, 125.

APPLICATIONS OF THE THEORY 2/3

extended by True and Hunkle^ to the phenols. They
investigated a number of phenols, using different con-
centrations, and determined the greatest concentration
in which the roots of Lupinus albus would just live and
grow. The conductivity of the solutions of the different
phenols was also measured. They conclude that, except in
isolated instances, the electrolytic dissociation plays but a
subordinate r61e in determining the toxic properties of
phenylic compounds. Picric and salicylic acids are strongly
dissociated, and are very poisonous because of the large
number of hydrogen ions in their solutions. Electrolytic
dissociation exerts a pronounced influence in the cresols
and mononitrophenols.

Dissociation and Disinfecting Action. — In 1896 a paper
appeared by Paul and Kronig,^ describing the action of a
large number of reagents on bacteria. The work was done
chiefly with the bacillus antkracis, and the staphylococcus
pyogenes aureus. As will be seen, the problem is one of
disinfection, the toxic action of the various substances
being investigated. The bacteria were distributed^ over
the surfaces of carefully washed and completely disin-
fected garnets of equal size. That approximately the
same number of bacteria should be used in each experi-
ment, the same number of garnets was employed, and
the mean of six results was taken. The garnets were
placed in vessels made of platinum gauze, and introduced
into the solution, which was kept at a constant tempera-
ture. After the action had taken place as long as desired,
it was instantly brought to an end by adding some sub-

1 Botan. Centralb., 76, 289, 321, 361, 391 (1898).
3 Ztschr. phys. Chem., 21, 414.

274 ELECTROLYTIC DISSOCIATION

Stance which destroyed the disinfecting property of the
solution. The spores were then washed from the garnets
by shaking in water, and agar-agar jelly added to the
water containing the spores. This mixture was poured
into convenient dishes, and kept at a constant temperature.
The bacteria, which were still alive, began to form dis-
tinctly visible colonies in twenty-four hours, and could
easily be counted. The number of colonies was found to
depend upon the time during which the toxic reagent
acted, a.nd upon the concentration of the solution. In
general, the more dilute the solution the less the dis-
infecting action. The nature of the solvent was found to
efiFect the relative toxic action of compounds.

Some of the more important results obtained by Paul
and Kronig are: —

The disinfecting action of metallic salts depends, not
only on the concentration of the metal in the solution, but
also on the specific properties of the salt and the solvent

The action of a salt of a metal depends not only on the
specific action of the metallic ion, but also on that of the
anion, and of the undissociated part of the salt.

Solutions of metallic salts, in which the metal forms part
of a complex ion, are only weakly disinfecting.

The strong acids are toxic, not only in proportion to the
concentration of the hydrogen ions, but the specific prop-
erties of the anions come into play. The bases which are
equally dissociated, such as potassium, sodium, and lithium
hydroxides, have the same disinfecting action. The
weakly dissociated base, ammonium hydroxide, disinfects
much less.

The disinfecting action of the halogens, CI, Br, I, like

APPLICATIONS OF THE THEORY 275

their chemical action, decreases with increasing atomic
weight.

Solutions of substances in absolute alcohol and ether
are almost without action on bacillus anthracis.

The disinfecting action of mercuric chloride and silver
nitrate in alcohol is increased by the addition of more
and more water.

These results are very interesting, as being an applica-
tion of the theory of electrolytic dissociation in an entirely
new direction. We have here a clear recognition of dis-
sociation in the field of bacteriology.

Toxic Action of Substances on Certain Fungi. — We have
seen the relation between the dissociation of solutions and
their toxic action on certain phanerogams, as brought out
by the work of Kahlenberg, True, and Heald; also the
same relation when lower forms of life, the bacteria, were
used. We must refer, in this connection, to the very recent
investigation of Clark, in which the toxic action of sub-
stances on certain fungi was studied, and this action com-
pared with the dissociation of the substance. Five fungi
were used, and all were found to be much more resistant to
injurious agents than the higher plants. The spores of
moulds require, to inhibit germination, from two to four
hundred times the strength of acid which is fatal to the
higher plants. The hydroxyl ion was found to be more
toxic to moulds than the hydrogen ion. The toxic value of
the ions, CI, Br, I, increases with increasing atomic weight.
It was found that in the case of several acids dissociation
lessens their activity, the molecule being more active than
the ions. Of the eight acids investigated,' six were more
active in the molecular than in the ionic form. The toxic

2/6 ELECTROLYTIC DISSOCIATION

action of the molecule, in the case of hydrocyanic acid,
was as much as 76.6 times that of the hydrogen ion. The
anions of hydrochloric, nitric, and sulphuric acids are only
slightly toxic to fungi.

These results, like those previously described, show that
both molecules and ions may be poisonous to certain forms
of life, just as both molecules and ions may be colored.
The poisonous nature of the molecule or ion depends
greatly upon the nature of the plant on which it acts.

Application of the Dissociation Theory to Animal Phys-
iology. — The theory of electrolytic dissociation has been
applied not only to vegetable, but has already found its
way into animal physiology. The work of Loeb^ was
the first of importance in this field. He studied
the action of certain electrolytes on the muscle of a
frog. When the muscle from the leg of a frog is placed
in a 0.7 per cent solution of sodium chloride, and a
small amount of acid or base added to the solution, the
muscle, by taking up water, undergoes an appreciable
increase in weight. Loeb determined the increase in the
weight of the muscle, produced by hydrochloric acid,
nitric acid, and sulphuric acid, of known concentrations,
and was led to this interesting conclusion. Solutions of
these three acids, which contain the same number of
hydrogen atoms in equal volumes, produce the same in-
crease in the weight of the muscle. He showed that it is
only the hydrogen cation which is active, the anion having
little or no effect; and that when the same number of
hydrogen ions is contained in equal volumes of their solu-
tions, all of these acids produce exactly the same effect.

1 Pfltiger's Archiv f. Physiologic, 69, 1.

APPLICATIONS OF THE THEORY 277

This does not hold for the weakly dissociated organic
acids, since, in these cases, the anions as well as the mole-
cules exert an influence. Loeb then studied the action
of the following bases: lithium hydroxide, sodium hy-
droxide, potassium hydroxide, strontium hydroxide, and
barium hydroxide, and found that they all had the same
influence in causing the muscle to take up water, when
they are used at such concentrations that an equal number
of hydroxyl groups is contained in equal volumes of each
of the solutions. The action of all these alkalies was
found to depend entirely upon the anion of the base, i.e.
hydroxyl; just as the action of the strong mineral acids
depended entirely upon the cation hydrogen. The hy-
droxyl ions have, however, a stronger influence than an
equal number of hydrogen ions. Solutions of potassium
and sodium carbonate also cause the muscle to take up
water. This is due to the hydroxyl ions in their solutions,
formed by the hydrolysis of the salt and the subsequent
dissociation of the base.

That the theory of osmotic pressure, deduced by van*t
Hoff, applies to this phenomenon, is shown by the fact
that solutions of lithium, potassium, rhubidium, caesium,
magnesium, calcium, barium, and strontium chlorides,
produce the same change in the weight of the muscle
as a solution of sodium chloride of equal osmotic
pressure.

Loeb also studied the toxic action of a number of ions

+ +
on muscle, and found that for any given group, as Li, Na,

+ + +

K, Rb, Cs, the relative toxic action is proportional to the

migration velocity of these ions, and not to their atomic

2/8 ELECTROLYTIC DISSOCIATION

++ + +

weights. The same relation obtains for the ions, Be, Mg,

++ ++ ++

Ca, Ba, Sr, but does not extend from one natural group of

the elements to another.

A second investigation was carried out by Loeb,^ which
is an extension of the one just considered. While the
physiological action of the inorganic acids is conditioned
by the number of hydrogen ions present, there is an
apparent exception presented by the organic acids. The
physiological activity of the fatty acids is not proportional
to their dissociation. Thus, lactic acid, which, at the dilu-
tion employed is only eleven per cent dissociated, causes
the muscle to take up as much water as trichloracetic acid
and oxalic acid, in which nearly all of the molecules are
dissociated. Similarly, mandelic acid causes the muscle to
take up as much water as the more strongly dissociated
organic acids, although, at the dilution used, it is only nine-
teen per cent dissociated. Loeb does not offer any final
explanation of this phenomenon, but suggests that since
the difference in the action of the different acids is so
much less than the difference in their dissociation, it
seems probable that those acids which are very slightly
dissociated are transformed in the muscle into products
with stronger dissociation. The author offers this as a
possible explanation, and promises further investigation,
especially with the aromatic acids.

PhTsical Chemical Methods applied to Animal Physi-
ology. — Physical chemical methods have been applied by
Bugarszky and TangP to a very different physiological
problem. They have been employed to determine the con-

1 Pfluger's Archiv f. Physiologic, 71, 457. Ibid,, 72, 531.

APPLICATIONS OF THE THEORY 279

centration of the dissolved substances in the blood serum,
and also the relation between the electrolytes and non-
electrolytes contained in it.

The freezing-point method was used to determine the
molecular concentration of the dissolved substances. The
freezing-point of the serum was first determined, then
the freezing-point of pure water. Since blood serum is
practically water containing electrolytes and non-electro-
lytes, the difference between the two freezing-points is the
lowering of the freezing-point of water produced by the
substances present in the blood serum. A gram-molecular
solution of a non-electrolyte freezes 1.87** lower than pure
water. To determine, therefore, the number of gram-
molecular concentrations to which the substances in blood
serum are equivalent, the difference between the freezing-
point of water and of blood serum must be divided by
1.87. In this calculation the ions which result from the
dissociation of any electrolytes present are treated as if
they were molecules, since an ion produces the same low-
ering of the freezing-point as a molecule.

The above method shows the total concentration of elec-
trolytes and non-electrolytes present in blood serum, but
does not enable us to determine the amount of each. To
accomplish this, some method must be employed which will
enable us to discriminate between undissociated molecules
and ions. Molecules in solution do not conduct the elec-
trie current ; only ions conduct. We can, therefore, use the
conductivity method to determine the amount of electro-
lytes present in the serum. This was done by Bugarszky
and Tangl. The electrolytes present in blood serum are,
almost all, salts. The alkaline reaction of the blood comes

280 ELECTROLYTIC DISSOCIATIOx\

from a few hydroxyl ions, which result from the hydra

lysis of carbonates in the blood. Further, the salts in the

blood are nearly all inorganic ; organic salts being present

only in very small quantity. The conductivity method

is used as an approximate measure of the inorganic

salts present, and is regarded as more accurate than the

method of determining the amount of ash obtained from

+ +
the serum. While the serum contains the cations, Na, K,

Ca, Mg, and the anions CI, COg, HCOg, HPO4, SO^, OH ;

+ - =

the main ions are Na, CI, and some CO3.

The determination of the concentration of the electrolytes
in the blood serum, by the conductivity method, is some-
what complicated by the presence of the non-electrolytes
in the serum, as the authors point out. The conductivity
of an electrolyte is diminished by the presence of a non-
electrolyte, and the magnitude of the effect depends both
upon the nature of the electrolyte and the non-electrolyte.
The non-electrolytes in the blood serum consist chiefly
of albumens, with traces of a number of other substances.
The albumens were isolated, and their effect on the con-
ductivity determined. One gram of albumen in 100 cubic
centimetres of blood serum, diminished the conductivity
2.5 per cent. By applying this correction to the observed
conductivity of the serum, we obtain its true conductivity.
The corrected conductivity can be used for calculating the
concentration of the electrolytes dissolved in the serum.
Knowing the amount of the electrolytes in the serum, it
is a very simple matter to determine the amount of the
non-electrolytes. The freezing-point method gives the sum
of the two, as already stated. By subtracting from the

APPLICATIONS OF THE THEORY 28 1

sum the amount of the electrolytes, we have at once the
quantity of the non-electrolytes.

A number of conclusions of interest and importance
were reached through this work, but since these lie almost
wholly in the field of physiology, they do not come within
the scope of this book. The authors point out that
these same methods can, and should be applied to other
liquids in the animal body.

Application of Osmotic Pressure and Dissociation to the
Mechanics of Secretion. — The work of Dreser ^ illustrates
the application of van't^ Hoff's laws of osmotic pressure
and the theory of electrolytic dissociation, to the mechanics
of secretion. The problem is to calculate the work done
by the kidneys in secreting urine. This is accomplished
by determining the osmotic pressure of the blood serum,
and also that of the urine. There is no direct method of
measuring osmotic pressure, which is of general applica-
bility, so that an indirect method must be employed. The
well-known freezing-point method was used, and from the
difference in the freezing-point of the serum and of the
urine, the difference in their osmotic pressures was cair
culated. If the volume secreted by the kidneys is taken
into account, the osmotic work done by the kidneys is
ascertained. And if we note the time during which the
secretion takes place, the osmotic work done by the kidneys
can be expressed in C.G.S. units.

A number of other investigations have already been
carried out, in which the theory of electrolytic dissociation
and the van't Hofif laws of osmotic pressure have been
applied to biologica^l problems.^ We should mention es-

1 Archiv f. experimentelle Pathologic, 29, 301.

2 I' or a fuller discussion of this question see the admirable book by Hamburger,
Osmotischer Druck und lonenlehre (1902).

282 ELECTROLYTIC DISSOCIATION

pecially the work of Dreser,^ Hamburger,* Hedin,' Heiden-
hain,* van Kardnyi,*^ and van Limbeck.® But the investi-
gations already referred to, suffice to show the nature of
the biological questions upon which modem physical
chemistry is throwing light

It would seem that the theory of electrolytic dissocia-
tion must find wide application in pharmacology. If
chemical action is due mainly to ions, it is very probable
that the pharmacological action of many chemical sub-
stances is largely ionic. This probability is increased,
when we consider how many electrolytes are used in
medicine, and that they are either taken in solution, or
pass into solution in the fluids of the body. It is quite
safe to predict, that many interesting and important results
await the investigation of the relation between the dis-
sociation of drugs, and their action upon the human body.

CONCLUSION

By following a few of the many applications of the
theory of electrolytic dissociation to problems in chemistry,
physics, and biology, we can form some conception of its
wide-reaching significance. The examples which have
been taken up and studied are, in each case, a few chosen
from the many. And if so much has been done in the
short time which has elapsed since the theory was pro-

1 Ztschr. phys. Chem., 21, 108.

2 Du Bois* Archiv, 1886, 476; Virchow's Archiv, 140, 539; Centralb. t Physi-
ologic, 1893-94, 24.

8 Skandinav. Archiv f. Physiologic, 5, 238, 385 ; Pfliiger's Archiv £ Physiologic,
68, 248.

* Pfliiger's Archiv, 56, 600.

6 Centralb. f. Physiologic, 1893, Heft 3 ; Ungar. Archiv £ Med., 1895.

• Archiv f. exper. Pathologic, 25, 64.

APPLICATIONS OF THE THEORY 283

posed, what may we not reasonably expect from the
future ? Since so many substances are broken down into
ions, by water and similar solvents, it is almost certain that
our theory will find application wherever aqueous solutions
of electrolytes are employed. A moment's reflection will
show that comparatively few branches of natural science
lie wholly without its scope.

A careful study of the applications of the theory, which
have already been made, will bring out a fact of pro-
found significance. The theory coordinates and corre-
lates heterogeneous masses of facts, which apparently
bore little or no relation to one another, and refers them
to a common cause. As an illustration, take the neutrali-
zation of acids and bases, or the strength of acids and
bases in general. But this is just what the physical
chemistry of to-day has done, and is doing for several
branches of science, and especially for the science of chem-
istry. Physical chemistry is furnishing us, largely with
the aid of the theory of electrolytic dissociation, with
rational explanations of chemical processes whose mean-
ing was entirely concealed, and is rapidly placing chem-
istry upon that exact mathematical basis which physics
has so long enjoyed.

INDEX

Acids and bases, strength of, 216.

Acids, dry, do not act on litmus, 165.

Acidity, relations between, and composi-
tion and constitution, 319.

Additive nature of conductivity. Law of
Kohlrausch, 116.

Additive property of salt solutions, 104.

Affinity, methods of measuring, 67.

Ammonia, dry, no action, on dry hydro-
chloric acid, 168.

Animal physiology, application of physi-
cal chemical methods to, 278.

Animal physiology, application of the dis-
sociation theory to, 276.

Arrhenius, dissociation of substances in
water, 93.

Arrhenius explains exceptions to gas
laws, 94.

Asymmetric carbon atom, 25.

Atomic and molecular volumes, 11.

Avogadro's law for dilute solutions, 87.

Baeyer describes an exception to van't

HofTs hypothesis, 24.
Bases and acids, strength of, 216.
Bases, strength of, and composition, and

constitution, 223.
Benzene, constitution determined by a

thermal method, 21.
Benzene, constitution determined by re-

fractivity, 20.
Bergmann, work of, 53.
Berthelot and P6an de St Gilles, work

of,. 58.
Berthelot, thermochemical work of, 34.
Berthollet, work of, 54.
Berzelius, electrochemical theory of, 40.
Biological problems, application of the

theory of electrolytic dissociation to,

268.
Blagden, on freezing-point lowering, 30.
Boiling-points and composition, 5.

Boiling-points and constitution, 5.
Boiling-points of liquids, 4.
Boiling-point rise, 178.
Boyle and Gay Lussac's laws applied to
solutions. Experimental evidence for,

85.

Boyle's Law confirmed by Pfeffer's re-
sults, 83.

Boyle's Law confirmed by results of De
Vries, 83.

Boyle's Law for dilute solutions, 82.

Briihl, on refractive power of liquids, 19.

Calculation of dissociation from conduc-
tivity, 209.

Cell for measuring osmotic pressure, 74.

Cells, types of, 238.

Chatelier, Le, chemical equilibrium, 66.

Chemical action at a distance, 261.

Chemical action at a distance, demon-
strated by experiment, 262.

Chemical activity as a measure of disso-
ciation, 157.

Chemical dynamics and statics, develop-
ment of, S3.

Chemical problems, electrolytic dissocia-
tion applied to, 171.

Chemical reactions between ions, 158.

Chlorine, dry, action on metals, 161.

Clausius, theory of electrolysis, 48.

Cohen and van't Hoff, 66.

Color of salt solutions, no.

Composition and acidity, 219.

Composition and boiling-points, 5.

Composition and heat of combustion, 37.

Composition and magnetic rotation, 28.

Composition and molecular heats, 8.

Composition and refractivity, 18.

Composition and strength of bases, 223.

Concentration and osmotic pressure, 75.

Concentration element of the first type,
239.

285

286

INDEX

Concentration element of the second

type. 243-

Concentration element, sources of poten-
tial, 252.

Conductivity and dilution, 14a.

Conductivity and lowering of freezing-
point, 199.

Conductivity and osmotic pressure, 128.

Conductivity and reaction velocity, 155.

Conductivity at high temperatures, 215.

Conductivi^ in different solvents, 211.

Conductivity, molecular, 203.

Conductivity of solutions, 201.

Conductivity of solutions, Kohlrausch, 52.

Conductivity of solutions, method of
measuring, 203.

Conductivity of water, 207.

Conductivity, specific, 202.

Constancy of solution-tension, 236.

Constitution and acidity, 219.

Constitution and boiling-points, 5, 7.

Constitution and heat of combustion, 37.

Constitution and molecular heats, 9.

Constitution and molecular volume, 12.

Constitution and refractivity, 18.

Dale and Gladstone, refraction formula,

17.
Daniell elements, electromotive force o(

254-
Davy, electrochemical theory of, 40.

Deville, on dissociation, 6a

Diffusion, 174.

Dilution Law of Ostwald, 143.

Dilution Law of Rudolphi, 147.

Disinfection and dissociation, 273.

Dissociating action of water, demonstra-
tion of, 113.

Dissociating power of different solvents,
160.

Dissociation and chemical activity, 154.

Dissociation by heat and electrolytic dis-
sociation, 149.

Dissociation calculated from conduc-
tivity, 209.

Dissociation measured by boiling-point
method, 213.

Dissociation measured by different
methods, 152.

Dissociation of substances in water, 93.

Distance, chemical action at a, 261.

Distance, chemical action at a, demoft

strated by experiment, 262.
Dittmar, on boiling-points of metameric

compounds, 6.

Earlier ph3rsical chemistry, i^

Earlier physical chemicad work, conclu-
sions from, 69.

Edwards, refraction formula, 17.

Electrochemical Theories of Davy and
Berzelius, 40.

Electrochemistry and electrolytic disso-
ciation, 182.

Electrochemistry, the development of, 39.

Electrolysis, 45, 183.

Electrolysis, theories of, 46.

Electrolytic dissociation and dissociation
by heat, 149.

Electrolytic dissociation and toxic action,
268.

Electrolytic dissociation, origin of the
theory, 71.

Electrolytic dissociation, theory of, 94.

Electrolytic solution-tension, 231.

Electromotive force, 216.

Electromotive force, calculated from
osmotic pressure, 227.

Electromotive force, seat of in primary
cells, 226.

Electrostatically charging a solution, 138.

Elements, concentration, first type, 239-

Elements, concentration, second type,

243-
Elements, liquid, 247.

Evidence for the theory of electrolytic
dissociation, 104.

Exceptions to laws of gas pressure being
applicable to osmotic pressure, 91.

Excess of one of the products of disso-
ciation, effect of, 149.

Faraday's Law, 44.

Favre and Silbermann, thermochemical

investigations, 33.
Fick's Law of diffusion, 30.
Freezing-point, lowering of, 176.
Fungi, toxic action of substances on, 375.

Gas-battery, 256.

Gas pressure and osmotic pressure, rela-
tions, 76.

INDEX

287

Gay Lussac's Law and Boyle's Law, ex-
perimental evidence for, 85.

Gay Lussac's Law and Pfeffer's results, 84.

Gay Lussac's Law for dilute solutions, 84.

Gibbs, application of thermodynamics to
chemical equilibrium, 64.

Gladstone and Dale, refraction formula,

17-
Goodwin and Thompson, the dielectric

constant of liquid ammonia, 211.
Graham, work on diffusion, 3a
Grotthuss, theory of electrolysis, 46.
Guldberg and Waage, law of mass

action, 60.
Guye, hypothesis of, 26.

Hantzsch and Werner, stereochemistry
of nitrogen, 27.

Heat of combustion, and composition
and constitution, 37.

Heat of neutralization in dilute solutions,
119.

Heat of neutralization of acids and bases,
a constant, 36.

Hess, G. H., work of, 32.

Hess's law of thermoneutrality of salts, 33.

Hess's law of thermoneutrality of salt so>
lutions, 122.

History of van't Hoff's laws, 76.

Hittorf, work on migration velocity of
ions, 52.

Horstmann, application of thermody-
namics to chemistry, 64.

Hydrochloric acid, dry, does not decom-
pose carbonates, 163.

Hydrochloric acid, dry, doas not precipi-
tate silver nitrate in ether or benzene,
165.

Hydrochloric acid, dry, no action on dry
ammonia, 168.

Hydrogen sulphide, dry, inactivity of, 165.

Indicators, theory of, 112.

Ion formation, modes of, 189.

Ions, experiment to demonstrate the

presence of, 137.
Ions the cause of chemical reaction, 158.
Ions, velocity of, 191.

Jones and Allen, experiment to demon-
strate the dissociating action of water,

113.

Jones* measurement of dissociation by
freezing-point lowering, compared with
dissociation from conductivity, 130.

Jones, measurement of dissociation by
the boiling-point method, 213.

Kohlrausch's Law of independent migra-
tion velocity of ions, 197.
Kohlrausch, on conductivity of solutions,

52.
Kopp's work on atomic volumes, 12.

Kopp's work on boiling-points of liquids.
4.

Law of Avogadro, for dilute solutions,
87.

Law of Faraday, 44.

Law of Hess, 122.

Law of Kohlrausch, 116.

Law of mass action, Guldbei^ and
Waage, 60.

Law of reaction velocity, discovery of, 56,

Laws of Boyle and Gay Lussac, applied
to solutions, 82.

Laws of Boyle, Gay Lussac, and Avo-
gadro for solutions and gases, general
expression of, 89.

Laws of gas pressure not always applica-
ble to osmotic pressure, 91.

Le Bel's h3rpothesis, 23.

Liquid elements, 247 ; theory of, 247.

Lodge, experiment on absolute velocity
of ions, 199.

Lorenz-Lorentz, refraction formula, 17.

Lossen, on molecular volume, 13.

Lowering of freezing-point and conduc-
tivity, relation between, 129.

Lowering of freezing-point, and osmotic
pressure, relation between, 126, 131.

Lowering of freezing-point and rise in
boiling-point, 129,

Lowering of vapor-tension and osmotic
pressure, relation between, 127.

Magnetic rotation and composition and
constitution, 28.

Magnetic rotation of plane of polariza-
tion, 27.

Marignac, specific heat of aqueous solu-
tions, II.

Measurement of conductivity, 206.

288

INDEX

Metamerism and properties, x

Mixtures of completely dissociated com-
pounds, 117.

Mixtures of completely undissociated
compounds, 118.

Molecular conductivity, 203.

Molecular heats and composition, 8.

Molecular heats and constitution, 9.

Molecular rotatory power, 2a.

Molecular volume and composition, 11.

Molecular volumes, 11.

Molecular volumes and constitution,
12.

Nemst and Ostwald, experiment to de-
monstrate free ions, 139.

Nemst, calculation of electromotive force,
from osmotic pressure, 227.

Nemst, effect of an access of one of the
ions on dissociation, 149.

Neutralization, change of volume in, 107.

Neutralization, heat of, in dilute solu-
tions, 119.

Neutralization of acids and bases, con-
stant heat of, 36.

Noyes, dissociation measured by change
in solubility, 151.

Optical activity and composition and
constitution, 23.

Optically inactive and optically active
substances, 22.

Origin of the theory of electrolytic dis-
sociation, 71.

Osmotic investigations of Pfeffer, 71.

Osmotic pressure and conductivity, re-
lations between, 128.

Osmotic pressure and gas pressure, re-
lations between, 76.

Osmotic pressure and lowering of freez-
ing-point, relations between, 126, 131.

Osmotic pressure and lowering of vapor-
tension, relations between, 127, 134.

Osmotic pressure, electromotive force
calculated from, 227.

Osmotic pressure, results of Pfeffer, 75.

Ostwald and Nemst, experiment to de-
monstrate the presence of free ions,

139-
Ostwald, change in volume in neutral-
ization, 107.

Ostwald, dilution law, 143.

Ostwald, method of measuring affinity,

67.
Oxygen, inactivity of dry, 162.

P6an de St Gilles, work of, 58.

Perkin, W. H., work on magnetic rota-
tion. 28.

Pfeffer's apparatus for measuring osmotic
pressure, 73.

Pfeffer's method of measuring osmotic
pressure, 72.

Pfeffer's osmotic pressure results, 75.

Phenols, toxic action of, and their dis-
sociation, 272.

Physical problem, electrolytic dissocia-
tion applied to, 226.

Physiology, animal, application of physi-
cal chemical methods to, 278.

Physiology, animal, application of the
dissociation theory to, 276.

Polarized light, rotation of plane of, 21.

Potential difference between metal and
solution, 236.

Potential, sources of, in concentration
element, 252.

Raoult, on freezing-point lowering and
lowering of vapor-tension, 30.

Refraction of light, 16.

Refraction values of the elements, 2a

Refractive power of salt solutions, specific,
108.

Rise in boiling-point, and osmotic press-
ure, relation between, 127.

Rodger and Thorj)e, on viscosity, 14.

Rose, work of, 55.

Rotation of plane of polarized light, 21.

Rotatory power of salt solutions, no.

Rudolphi's dilution law, 147.

Salt solutions, properties are additive,
105.

Schiff, specific heat and composition,
10.

Schorlemmer, boiling-point results, 6.

Secretion, application of osmotic press-
ure and dissociation to, 281. .

Semipermeable membranes, 72.

Silbermann and Favre, thermochemical
work, 33.

INDEX

289

Solubility, change in, as a measure of

dissociation, 151.
Solutions and electrolytic dissociation,

172.
Solutions, the study of, 30.
Solution-tension, constancy of, 236.
Solution-tension, electrolytic 231.
Solvents, different dissociating power of,

i6a
Soret, principle of, 86.
Specific conductivity, 202.
Specific gravity of salt solutions, 105.
Specific heats of liquids, 8.
Specific refractive power of salt solutions,

108.
Stereochemistry of carbon, 23.
Stereochemistry of nitrogen, 27.
Stohmann, thermochemical work of, 36.
Strength of acids and bases, 216.
Sulphuric acid, dry, no action on dry

metallic sodium, 169.

Temperature and osmotic pressure, 76.
Temperatures, conductivity at high, 215.
Theories of electrolysis, Grotthuss, Clau-

sius, and Williamson, 46.
Thermochemical results, 36.
Thermochemistry, the development of,

32-
Thermodynamics applied to chemistry,

64.

Thomsen, J., method of measuring affin-
ity, 67.

Thomsen, J., thermochemical work of, 35.

Thomson, J. J., overthrows argument
against the Berzelius chemical theory,
42.

Thomson's, J. J., theory, 213.

Thorpe and Rodger on viscosity, 14.

Thorpe's work on molecular volumes, 13.

Toxic action and electrolytic dissocia-
tion, 268.

Toxic action of phenols and their disso-
ciation, 272.

Toxic action of substances on fungi, 275.

Valson's " moduli," 107. •

Van't Hofifs coefficient ">',*' calculation
of, 96.

Van't Hoff's coefficient **i" from freez-
ing-point lowering and conductivity,

98.
Van't HofTs Laws, history of, 76.
Van't HofF's Lecture, 77.
Van't Hoff, the asymmetric carbon atom,

23.
Van*t HofT, velocity of reactions, 65.

Vapor-tension, lowering of, 178.

Vapor-tension, lowering of, and osmotic

pressure, relation between, 134.

Velocity, absolute, of ions, 198.

Velocity of ions, Hittorf, 52.

Velocity of ions, 191.

Velocity, relative, of ions, 192.

Viscosity, 14.

Water, conductivity of, 207.

Water, r61e of, in chemical activity, i6a

Wenzel, work of, 53.

Whetham, experiment on absolute veloc-
ity of ions, 199.

Williamson, theory of solution, 50.

Wislicenus, application and extension of
van't Hoff's hypothesis of the asym-
metric carbon atom, 25.

Willlner, lowering of vapor-pressure, 31,

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