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of Physical Chemistry

** ' y



EDITED BY

SIR WILLIAM RAM S AY K.C.B,, F, R.S .



T. P. C.



TEXT-BOOKS OF PHYSICAL
CHEMISTRY

EDITED BY SIR WILLIAM RAMSAY, K.C.B., F.R.S.



TEXT-BOOKS OF PHYSICAL CHEMISTRY,

EDITED BY SIR WILLIAM RAMSAY, K.C.B., F.R.S., D.Sc.



STOICHIOMETRY. By SYDNEY YOUNG, D.Sc., F.R.S., Pro-
fessor of Chemistry in the University of Dublin ; together with an
INTRODUCTION TO THE STUDY OF PHYSICAL CHEMISTRY
by Sir WILLIAM RAMSAY, K.C.B., F.R.S., Editor of the Series.
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AN INTRODUCTION TO THE STUDY OF PHYSICAL
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THERMOCHEMISTRY. By JULIUS THOMSEN, Emeritus
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of Chemistry, University College, London. Crown 8vo. gs.

ELECTRO-CHEMISTRY. PART I. GENERAL THEORY. By
R. A. LEHFELDT, D.Sc., Professor of Physics at the East London
Technical College. Including a Chapter on the Relation of Chemical
Constitution to Conductivity, by T. S. MOORE, B.A., B.Sc., Lecturer in
the University of Birmingham. Crown 8vo. 55.

PART II. APPLICATIONS TO ELECTROLYSIS, PRIMARY AND
SECONDARY BATTERIES, etc. By N. T. M. WILSMORE, D.Sc.

STEREOCHEMISTRY. By A. W. STEWART, D.Sc., Carnegie
Research Fellow, Lecturer on Stereochemistry in University College,
London. With 87 Illustrations. Crown 8vo. los. 6d.

RELATIONS BETWEEN CHEMICAL CONSTITUTION
AND PHYSICAL PROPERTIES. By SAMUEL SMILES, D.Sc.

\In preparation.

THERMODYNAMICS. By F. G. DONNAN, M.A., Ph.D.

\Jn preparation.

ACTINOCHEMISTRY. By C. E. K. MEES, D.Sc., and S. E.
SHEPPARD, D.Sc. \In preparation.

PRACTICAL SPECTROGRAPHIC ANALYSIS. By J. H.
POLLOK, D.Sc. [In preparation.



LONGMANS, GREEN, AND CO.

39 PATERNOSTER ROW, LONDON
NEW YORK, BOMBAY, AND CALCUTTA



ELECTRO-CHEMISTRY

PART I
GENERAL THEORY



BY

R. A. LEHFELDT, D.Sc.

PROFESSOR OF PHYSICS AT THE TRANSVAAL UNIVERSITY COLLEGE



INCLUDING

A CHAPTER ON THE RELATION OF CHEMICAL
CONSTITUTION TO CONDUCTIVITY

BY

T. S. MOORE, B.A., B.Sc.

FELLOW AND LECTURER OF MAGDALEN COLLEGE, OXFORD



SECOND -EDITION r> ; % 5 ''/,



LONGMANS, GREEN, AND CO,

39 PATERNOSTER ROW, LONDON

NEW YORK, BOMBAY, AND CALCUTTA

1908

All rights reserved



L5



PREFACE

THE present volume deals with the general theory of electro-
chemistry. This is divided into two parts, one giving the
relation between quantity of electricity and quantity of chemical
action ; the other and more recent part forms the pendant to
the first by giving the relation between electromotive force and
intensity of chemical action. These subjects are dealt with
in Chapters I. and III. Chapter II. is in the nature of an
appendix to the first chapter, and may be omitted by those
who are not interested in pure chemistry, without detriment
to the continuity of the book.

In a subsequent volume it is hoped to discuss the most
important applications of the theory, to primary and secondary
cells, to electrolysis, and to the solution of chemical problems.

R. A. L.

May t 1904.



257709



CONTENTS

CHAPTER I

By R. A. LEHFELDT, D.Sc.

MECHANISM OF CONDUCTION IN ELECTROLYTES

SECT. PAGE

1. Faraday's Laws : Measurement of Quantity of Electricity . . I

2. Mechanism of Electrolysis 12

3. Phenomena at the Electrodes , 21

4. Migration of Ions . . . , 32

5. Conductivity of Electrolytes 43

6. Equivalent and Ionic Conductivities 58

7. Arrhenius' Theory of Dissociation 69

8. The Law of Dilution 75

9. Conductivity of Mixtures 81

10. Non-aqueous Solutions 84

11. Conduction of Fused Salts 80



CHAPTER II

By T. S. MOORE, B.A., B.Sc.

RELATION OF CHEMICAL CONSTITUTION TO * CONDUCTIVITY

1. Relation of Charge carried to Constitution 93

2. Relation of Mobility to Constitution 94

3. Relation of Number of Ions in Solution to Constitution . t .98

4. Double and Complex Salts 133

5. Pseudo Acids and Bases 140

6. Amphoteric Electrolytes 143



PAOE



Vlll CONTENTS

CHAPTER III

By R. A. LEHFELDT, D.Sc.

THEORY OF CHEMI-ELECTROMOTIVE FORCE

SECT -

1. Voltaic and Electrolytic Cells .......... I4 6

2. Electromotive Force ............. l ^

3. Electrode Potential ............. I5 6

4. Influence of Concentration ..... . ..... !6i

5. Concentration Polarisation . . . . . . . . . . . X 68

6. Chemical Polarisation . ........... jyj

7. Thermodynamic Theory (i) ..... ...... !77

(ii) The Gibbs-Helmholtz Equation ........ 185

(iii) Single Potential Differences at Electrodes ..... 194

(iv) Potential Differences between Liquids ...... 205

(v) Concentration Cells . . ......... 210

(vi) Chemical Cells ............ 220

Transition Cells ........... 220

Cells with Reaction in a Homogeneous System . . 223

8. Methods of Measurement

A. Measurement of Electromotive Force ...... 225

B. Measurement of Single Potential Differences .... 236

9. Standard Cells ............ ... 241

TABLES .................. 255

INDEX ............... . . 2 6i



SYMBOLS

C = Concentration (gram-equivalents per litre).
E = Electromotive force.

E = Electro-affinity, or electrolytic potential (see p. 158),
F = Faraday (see p. 3).

K = Reaction (or ionisation) constant (see p. 76).
L = Latent heat (see p. 178).
Q = Heat of reaction (see pp. 154 and 1/9).
R = Gas constant (8*316 joules per mol).
T = Absolute temperature.

UA U c = Mobility of anion and cation (see p. 43).
W = Work (see p. 179).
A = Equivalent conductivity (see p. 58).

//TT

= Temperature coefficient of electromotive force.
a i

i = van't Hoffs factor (see p. 70).

/A /c = Ionic conductivity of anion and cation (see p. 62).
r = Valency.

t Temperature (Centigrade).
A c = Velocity of anion and cation.

v = Dilution (c.c. per gram -equivalent).

x = Migration ratio of anion (see p. 35).

y = Degree of Ionisation (see p. 71).

f] = Concentration (gram-equivalents per c.c.).

K = Electric conductivity.



ELECTRO-CHEMISTRY



CHAPTER I

MECHANISM OF CONDUCTION IN ELECTROLYTES

i. FARADAY'S LAWS : MEASUREMENT OF
QUANTITY OF ELECTRICITY

THERE is a group of substances which, when an electric
current is passed through them, suffer chemical decomposition.
These substances are called electrolytes ; the process of decom-
position electrolysis ; and reactions occurring in electrolysis may
be described as electro-chemical. It is the study of such
electro-chemical reactions that forms the subject of the present
book.

As a typical process of electrolysis we may take the decom-
position of dilute sulphuric acid between platinum plates.
Imagine, then, this arrangement of
apparatus (Fig. i) Place some dilute -f-
sulphuric acid in a beaker ; insert into ""^2
it two plates of platinum, so as to be
partially immersed, taking care that
they do not touch each other; con-
nect the upper parts of the plates by
wires to a source of electric current
(battery, dynamo, thermopile, etc.).
Such an arrangement is known as an
electrolytic cell. The platinum plates
serve to convey the current into and out of the liquid, and are
called electrodes ; that by which the current is led in, the anode^
T. P. c. B



FIG. i.



that by which



ELECTRO-CHEMISTRY
it is led 'but the cathode. The liquid is the



electrolyte, and the reaction that occurs when a current is
passed through is the decomposition of water into its elements,
oxygen and hydrogen.

Now, the leading peculiarity of this, as of all electro-chemical
as distinguished from ordinary chemical reactions, lies in the
appearance of the products of reaction at the electrodes only ;
not, as usual, throughout the mass of the reacting material. In
the case chosen as example, all the oxygen appears at the
surface of the anode, all the hydrogen at that of the cathode.
It is therefore convenient to consider the amount of material
evolved, or in the case of a solid deposited, at either electrode,
and in order to arrive at the true nature of electrolysis, it is first
necessary to find on what this amount depends. This was
accomplished by Faraday, and the laws in which he formulated
his observations are commonly known by his name. They
are

(i.) The amount of any substance deposited is proportional
to the quantity of electricity which flows through the electrolyte.

(ii.) The amounts of different substances deposited by the
same quantity of electricity are proportional to their chemical
equivalent weights.

What is implied by the first of these is, essentially, that the
rate at which the electricity flows is of no consequence, provided
the total quantity be the same. I-f we follow the usual exposi-
tion of electrical science, and regard the current defined by
means of its magnetic action as fundamental, we may say that
the total quantity of electricity is measured by the product of
the current into the time that it flows. Current is measured in
amperes, and the meaning of Faraday's first law is illustrated by
saying that five amperes will in two minutes effect exactly the
same amount of electro-chemical reaction as ten amperes in
one minute.

It is consequently more natural for our purpose to look
upon quantity of electricity as fundamental ; the unit in which
this is measured is called the coulomb, the connection between
the two being that (a) a coulomb is the quantity of electricity
conveyed by a current of one ampere in a second, or (b) an



MECHANISM OF CONDUCTION IN ELECTROL YTES 3

ampere is a flow of electricity at the rate of one coulomb per
second.

The most exact measurements on the mass of substance
deposited by the current have been made on silver, and it
appears that one coulomb deposits o'ooni75 grm. of that
metal. This quantity is known as the electro- chemical equiva-
lent of silver, and by means of Faraday's second law we may
calculate from it the electro-chemical equivalent of any other
substance, eg: that of oxygen. The atomic weight of silver is
107*93, and its equivalent weight the same; the atomic weight
of oxygen is 16, but, being a divalent substance, its equiva-
lent weight is 8. Hence the weights of silver and of oxygen
liberated by the same quantity of electricity are in the ratio
107*93 : 8, and the electro-chemical equivalent of oxygen is
ToT^u x 0.0011175 = 0*00008283 grm. per coulomb. For
other numbers, see table, p. 255.

Faraday's two laws may be conveniently summed up in
one statement. In accordance with the second law a gram-
equivalent (the chemical equivalent weight taken in grams) of
any substance must require the same quantity of electricity to
deposit it. This quantity may be calculated from the data for
silver just given ; to deposit one gram-equivalent of silver will
require Q^OOIIIT'S = 9^5 80 coulombs. (As the fourth significant
figure has not been settled with certainty we shall adopt the
approximate value 96600.) Therefore

96600 coulombs are required for the deposition of one gram
equivalent of any substance.

This fundamental quantity of electricity, which occurs con-
stantly in all writings on electro-chemistry, is called by the
Germans a "foraday" 1 a term which we in England may very
well adopt.

Faraday's laws have been found to hold exactly in all cases
that have been satisfactorily measured that is to say, the pas-
sage of one faraday through an electrolyte is always accom-
panied by the appearance at the anode of one gram-equivalent
of new material, and at the cathode of one gram-equivalent ;

1 To be carefully distinguished from the unit of electrostatic capacity
known as a " farad."



4 ELECTRO-CHEMISTRY

for instance, in the electrolytic cell of Fig. i by the appearance
of 8 grms. of oxygen at the anode and 1*0075 grms. of
hydrogen at the cathode. But it often happens that more
than one reaction occur simultaneously : in this case the laws
must be taken as meaning that the total amount of material
deposited at the anode makes up one gram-equivalent, and the
same at the cathode. Thus, if current were passed through a
solution containing copper and nickel under such conditions
that they come down together, one faraday might deposit (on
the cathode) x equivalents of copper and y of nickel \ but it
would be found that x + y = i.

Substances deposited on the anode are called anions, those
deposited on the cathode cations, the term ion being given by
Faraday to the particles that he assumed to travel through the .
electrolyte. Accordingly, a cation travels in the nominal direc-
tion of the electric current (Fig. i), while an anion travels
against it. Cations include all the metals and hydrogen ;
anions, chlorine, bromine, iodine, fluorine, groups such as
NO 3 , SO 4 , and acid radicles generally (as well as OH).

It will be seen from the above classification that electrolytes
are very commonly salts. Solutions of acids, bases, and salts
in water are, indeed, the electrolytes most commonly dealt
with; but similar solutions in pyridine, liquid ammonia, and
various other solvents are also electrolytes ; so are fused salts,
and even a certain number of solids, to a slight degree ; while
electrolytic decomposition of gases has also been observed.

When a process of electrolysis does occur in an unam-
biguous way, it may be used to determine the quantity of elec-
tricity flowing. A cell arranged for this purpose is known as a
voltameter? The chief forms of voltameter are the following :

i. The Water Voltameter. In nearly all cases it is the
volume of gas evolved that is measured. The oxygen and
hydrogen may be collected separately, but that is unnecessary
for voltametric purposes, and the instrument takes a simpler
form when they are allowed to mix. As electrolyte, dilute
sulphuric acid has been much used, but caustic soda is better.

1 To avoid confusion with the word " voltmeter " (p. 227), T.W. Richards
proposes to replace "voltameter" by " coulometer" (= coulomb-meter).



MECHANISM OF CONDUCTION IN ELECTROLYTES 5




A very practical form of the apparatus is that of Oettel, shown

in Fig. 2. It consists of a glass jar, some 15 cm. high by 5 in

diameter, containing two cylin-

drical nickel electrodes. The

leads to these are passed air-

tight through an indiarubber

stopper, which also carries the

gas delivery tube ; the latter,

conveniently with a rubber

joint in it, is bent down to

deliver into a gas-measuring

tube standing over water. The

solution used is 15 per cent.

NaOH free from chlorine, and

should nearly fill the jar.

The reaction at both anode
and cathode is quantitatively
exact, so that one faraday
evolves 8 grms. of O and
1*0075 of H. In order to
calculate the weight of gas from the volume, corrections must
be made for

(i.) Barometric pressure b (in millimetres).

(ii.) Temperature of the gas /.

(iii.) Difference in pressure between the gas and the external
air, due to the column of water (height h] left in the gas tube
at the time of measuring. This is equivalent to a mercury

column of height ^.

(iv.) The aqueous vapour with which the gas is saturated.
The pressure of this/ can be found from table, p. 255.

The actual pressure in the gas tube is b - ^ ; that of the

dry gas contained b - -^ -/; and one-third of this is oxygen.

Hence, according to the laws of gases, if v is the measured
volume of the mixed gas, the volume of oxygen reduced to
normal temperature and pressure is



FIG. 2.



ELECTRO-CHEMISTRY



b-



13-6



-P



273



3 7 6o ^273 + '

The specific volume of oxygen is 700*3 c.c. per gram (at
N.T.P.) and 0*00008283 gm. corresponds to one coulomb, so
that the quantity of electricity is

k - P

273 i



- i3'6

3 X "~ 76o



273 + '
h



700-3 X 0*00008283



X 1*8373 coulombs



r~ coulombs



273 + '
The calculation may, of course, be made in a similar way

by means of the hydrogen.

At the average temperature and pressure of the laboratory
this comes to about 5^ coulombs per
cubic centimetre of the mixed gases.
Hence a 100 c.c. gas tube does con-
veniently for an experiment in which 500
coulombs of electricity are used; and
further, it is easy to reckon roughly the
strength of current flowing by observing
how much gas is given off in 20 or 30
seconds.

Another common form of the water
voltameter is Hofmann's apparatus for
the decomposition of water (Fig. 3). In
this the electrodes are of platinum, and
are sealed through the glass ; carbon is
not available on account of its power of
absorbing gases largely. The gases are
collected separately in the graduated
tubes at the sides, and may be run off
from time to time by the taps at the top.
The volume of oxygen and hydrogen
collected may be compared as a test of

the accuracy of the voltameter. The mode of reduction of the




FIG. 3.



MECHANISM OF CONDUCTION IN ELECTROLYTES 7



gas volume is similar to that with Oettel's form, but it must be
remembered (i.) that as the liquid stands higher in the middle
than the side tubes, the pressure in the latter will be greater
than atmospheric ; (ii.) the height //, representing this differ-
ence of level, is no longer of water if the electrolyte be of

density d the equivalent column of mercury is - ^ ; (iii.) the

saturation pressure of water vapour is less over a solution than
over pure water : as a rough rule in the matter, it may be taken
that over 15 per cent NaOH it is 82 per cent., over 30 per
cent. H 2 SO 4 , 84 per cent, of the values
given in table, p. 255.

Since the electrodes are of platinum,
sulphuric acid may be used instead of
soda. It will be found, however, that
while the volume of hydrogen is exact,
that of the oxygen is too low especially
if the acid be strong, on account of for-
mation of ozone and persulphuric acid.

The chief disadvantage of Hof-
mann's form is its considerable electrical
resistance.

Both forms of voltameter work better
after they have been running for a short
time, as the electrolyte is then saturated
with the gases.

For large currents the weight volt-
ameter (Fig. 4) may be used. The
mixed gases are passed through a small
chamber full of strong sulphuric acid, to
dry them, and allowed to escape. The
apparatus is weighed before and after.

The water voltameter has been used
as a meter for domestic electric supply.
In this case, as readings are only taken
at comparatively long intervals, the mea-
surement is by the volume of liquid
electrolysed away. As a meter, the instrument has the serious





FIG. 4.



8 ELECTRO-CHEMISTRY

disadvantage of requiring nearly two volts to work it, and so
absorbing an appreciable fraction of the electric energy it
measures.

If a water voltameter be provided with a capillary tube,
through which the gases have to escape, the pressure in the
tube will be roughly proportional to the rate at which the gas
is flowing, and may therefore be taken as a measure of the rate
of flow of the electricity, i.e. of the current. Such an instrument,
called an ampere-manometer, 1 has occasionally been used instead
of an ordinary ampere-meter.

The electrolytic process is used for the preparation of
oxygen and hydrogen commercially. 2 The vessels holding the
electrolytes are of iron, as also the electrodes; 15 per cent,
soda solution is employed, and as the water is electrolyzed
away it must be replaced from time to time, distilled water
being used to prevent accumulation of chlorides. The gases
are collected separately in domes, under a pressure of about
60 mm. of water greater pressure causes a risk of mixing.
In order to reduce the resistance of the cell, it is packed in
a wooden box with sand, so that the heat developed by the
current keeps the temperature up to about 70 C. The voltage
required is then only about 2*8 volts for each cell. The cells
are constructed to take 600 amperes, and yield 220 litres of
hydrogen and no of oxygen per hour, the purity of the gases
being about 97 per cent.

2. Silver Voltameter. This is undoubtedly the most
accurate of all. The weight of silver deposited from a solution
by a measured current in a measured time has been determined
several times, the most important determinations being those
of F. and W. Kohlrausch 3 and Lord Rayleigh. 4 The former
found o'ooiu83 gm. per coulomb, the latter 0*0011180. The
greatest difficulty in such experiments is the measurement of
the current in electromagnetic measure, i.e. in accordance with
the definition of the ampere. Many subsequent experimenters

1 Ostwald, Zeitschr. fhys. Chem., 35. 36 (1900).

2 Zeitschr.f. Elektroch., 7. 857 (1901).

3 Wied., 27. i. (1886).

4 Phil. Trans., 175. 458 (84).



MECHANISM OF CONDUCTION IN ELECTROLYTES 9



have studied the voltameter in itself, but their work is neces-
sarily dependent on the electrical measurements referred to.
Lord Rayleigh's form of voltameter consisted of a platinum
bowl to serve as cathode, a wire or rod of pure silver for anode,
suspended in the middle of the bowl, and a strong solution of
silver nitrate or chlorate as electrolyte. The weight deposited
on the cathode is determined : the loss of weight of the anode
cannot be depended on, as partial oxidation takes place. This
arrangement of apparatus is not quite free from irregularity in
its action ; it has been
subjected to careful
chemical criticism by
Richards, 1 who finds
that the irregularities
are due to a subsidiary
reaction at the anode,
and can be eliminated
by enclosing the
anode in a porous
pot, to prevent diffu-
sion between it and
the cathode. The ap-
paratus, in his hands,
took the form shown



in Fig. 5 (actual size).
E is a platinum cru-
cible, with lip ; it con-
tains 10 per cent.
AgNO 3 solution,
freshly prepared. C
is the anode, of pure
silver rod, suspended
by a silver wire from
a glass rod, A, which p IGt ^

served to ensure good
electrical insulation. Between anode and cathode is placed the

1 Zeitschr.phys. Chcm. ,32. 321 (1900) and 41 302 (1902), or Free. Amer.
Acad., 35. 123 and 37




10



ELECTRO- CHEMISTR V



cylinder D of porous earthenware (Pukal of Berlin). This,
which is only i mm. thick, is thoroughly cleansed with nitric
acid and water beforehand, and the level of liquid inside it
being a trifle lower than outside, if any diffusion takes place it
is towards the anode. The strength of current used may be
about o'oi ampere per square centimetre of cathode surface.
The silver is deposited in a crystalline form, and needs to be
very thoroughly washed with water, to remove the mother
liquor from the crystals ; it is finally washed with alcohol and
dried at 160 C. After use the silver should be dissolved off
with nitric acid and the bowl cleaned for further use. The bowl
should be kept free from scratches, to ensure a good deposit.

Richards finds that Rayleigh's deposits were too heavy, the
correct value being o'ooni75, and considers that the improved
instrument can be relied upon to one part in ten thousand
or more.

3. Copper Voltameter. This is a convenient instrument,
very simple in manipulation, and satisfactory when the highest
degree of accuracy is not required. In its
usual form it consists of a thin copper sheet
for cathode, suspended between a pair of
thicker sheets of copper for anode, the
solution being any copper salt, commonly
A the sulphate. A convenient construction
is shown in Fig. 6. A is a square glass
jar, fitted with an ebonite lid. The anode
plates B, B are bent out of one sheet of
copper, and are fastened to the terminal D.
The cathode C has a lug passing through
a slot in the lid, and is provided with a
detachable binding screw E. The electrolyte is 10 per cent.
CuSO 4 . The anode oxidises on use, and consequently cannot
be employed for measurement. The cathode, on the other
hand, receives, under proper conditions, an adherent de-
posit of metallic copper. It is removed from the solution,
washed, dried with filter paper, and weighed. The weight
of copper obtained is always a little too low : x if the current
r l Richards, Zeitschr. phys. Chem. t 32. 328.




FIG. 6.



MECHANISM OF CONDUCTION IN ELECTROL YTES 1 1


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