Principles of Electrochemistry , Second Edition doc

Principles of Electrochemistry
Second Edition
Jin Koryta
Institute of Physiology,
Czechoslovak Academy of
Sciences,
Prague
•Win Dvorak
Department of Physical Chemistry, Faculty of Science,
Charles University, Prague
Ladislav Kavan
/. Heyrovsky Institute of Physical Chemistry and Electrochemistry,
Czechoslovak Academy of
Sciences,
Prague
JOHN WILEY & SONS
Chichester • New York • Brisbane • Toronto • Singapore
Copyright © 1987, 1993 by John Wiley & Sons Ltd.
Baffins Lane, Chichester,
West Sussex PO19 1UD, England
All rights reserved.
No part of this book may be reproduced by any means,
or transmitted, or translated into a machine language
without the written permission of the publisher.
Other Wiley Editorial Offices
John Wiley & Sons, Inc., 605 Third Avenue,
New York, NY 10158-0012, USA
Jacaranda Wiley Ltd, G.P.O. Box 859, Brisbane,
Queensland 4001, Australia
John Wiley & Sons (Canada) Ltd, Worcester Road,
Rexdale, Ontario M9W 1L1, Canada

John Wiley & Sons (SEA) Pte Ltd, 37 Jalan Pemimpin #05-04,
Block B, Union Industrial Building, Singapore 2057
Library of Congress Cataloging-in-Publication Data
Koryta, Jifi.
Principles of electrochemistry.—2nd ed. / Jin Koryta, Jin
Dvorak, Ladislav Kavan.
p.
cm.
Includes bibliographical references and index.
ISBN 0 471 93713 4 : ISBN 0 471 93838 6 (pbk)
1.
Electrochemistry. I. Dvorak, Jin, II. Kavan, Ladislav.
III.
Title.
QD553.K69 1993
541.37—dc20 92-24345
CIP
British Library Cataloguing in Publication Data
A catalogue record for this book is available
from the British Library
ISBN 0 471 93713 4 (cloth)
ISBN 0 471 93838 6 (paper)
Typeset in Times 10/12 pt by The Universities Press (Belfast) Ltd.
Printed and bound in Great Britain by Biddies Ltd, Guildford, Surrey
Contents
Preface to the First Edition xi
Preface to the Second Edition xv
Chapter 1 Equilibrium Properties of Electrolytes 1
1.1 Electrolytes: Elementary Concepts 1
1.1.1 Terminology 1

1.1.2 Electroneutrality and mean quantities 3
1.1.3 Non-ideal behaviour of electrolyte solutions 4
1.1.4 The Arrhenius theory of electrolytes 9
1.2 Structure of Solutions 13
1.2.1 Classification of solvents 13
1.2.2 Liquid structure 14
1.2.3 Ionsolvation 15
1.2.4 Ion association 23
1.3 Interionic Interactions 28
1.3.1 The Debye-Huckel limiting law 29
1.3.2 More rigorous Debye-Hiickel treatment of the activity
coefficient 34
1.3.3 The osmotic coefficient 38
1.3.4 Advanced theory of activity coefficients of electrolytes 38
1.3.5 Mixtures of strong electrolytes 41
1.3.6 Methods of measuring activity coefficients 44
1.4 Acids and Bases 45
1.4.1 Definitions 45
1.4.2 Solvents and self-ionization 47
1.4.3 Solutions of acids and bases 50
1.4.4 Generalization of the concept of acids and bases 59
1.4.5 Correlation of the properties of electrolytes in various solvents 61
1.4.6 The acidity scale 63
1.4.7 Acid-base indicators 65
1.5 Special Cases of Electrolytic Systems 69
1.5.1 Sparingly soluble electrolytes 69
v
VI
1.5.2 Ampholytes 70
1.5.3 Polyelectrolytes 73

Chapter 2 Transport Processes in Electrolyte Systems 79
2.1 Irreversible Processes 79
2.2 Common Properties of the Fluxes of Thermodynamic Quantities 81
2.3 Production of Entropy, the Driving Forces of Transport
Phenomena 84
2.4 Conduction of Electricity in Electrolytes 87
2.4.1 Classification of conductors 87
2.4.2 Conductivity of electrolytes 90
2.4.3 Interionic forces and conductivity 93
2.4.4 The Wien and Debye-Falkenhagen effects 98
2.4.5 Conductometry 100
2.4.6 Transport numbers 101
2.5 Diffusion and Migration in Electrolyte Solutions 104
2.5.1 The time dependence of diffusion 105
2.5.2 Simultaneous diffusion and migration 110
2.5.3 The diffusion potential and the liquid junction potential . . . Ill
2.5.4 The diffusion coefficient in electrolyte solutions 115
2.5.5 Methods of measurement of diffusion coefficients 118
2.6 The Mechanism of Ion Transport in Solutions, Solids, Melts, and
Polymers 120
2.6.1 Transport in solution 121
2.6.2 Transport in solids 124
2.6.3 Transport in melts 127
2.6.4 Ion transport in polymers 128
2.7 Transport in a flowing liquid 134
2.7.1 Basic concepts 134
2.7.2 The theory of convective diffusion 136
2.7.3 The mass transfer approach to convective diffusion 141
Chapter 3 Equilibria of Charge Transfer in Heterogeneous
Electrochemical Systems 144

3.1 Structure and Electrical Properties of Interfacial Regions 144
3.1.1 Classification of electrical potentials at interfaces 145
3.1.2 The Galvani potential difference 148
3.1.3 The Volta potential difference 153
3.1.4 The EMF of galvanic cells 157
3.1.5 The electrode potential 163
3.2 Reversible Electrodes 169
3.2.1 Electrodes of the first kind 170
3.2.2 Electrodes of the second kind 175
Vll
3.2.3 Oxidation-reduction electrodes 177
3.2.4 The additivity of electrode potentials, disproportionation . . . 180
3.2.5 Organic redox electrodes 182
3.2.6 Electrode potentials in non-aqueous media 184
3.2.7 Potentials at the interface of two immiscible electrolyte
solutions 188
3.3 Potentiometry 191
3.3.1 The principle of measurement of the EMF 191
3.3.2 Measurement of pH 192
3.3.3 Measurement of activity coefficients 195
3.3.4 Measurement of dissociation constants 195
Chapter 4 The Electrical Double Layer 198
4.1 General Properties 198
4.2 Electrocapillarity 203
4.3 Structure of the Electrical Double Layer 213
4.3.1 Diffuse electrical layer 214
4.3.2 Compact electrical layer 217
4.3.3 Adsorption of electroneutral molecules 224
4.4 Methods of the Electrical Double-layer Study 231
4.5 The Electrical Double Layer at the Electrolyte-Non-metallic

Phase Interface 235
4.5.1 Semiconductor-electrolyte interfaces 235
4.5.2 Interfaces between two electrolytes 240
4.5.3 Electrokinetic phenomena 242
Chapter 5 Processes in Heterogeneous Electrochemical Systems . . 245
5.1 Basic Concepts and Definitions 245
5.2 Elementary outline for simple electrode reactions 253
5.2.1 Formal approach 253
5.2.2 The phenomenological theory of the electrode reaction 254
5.3 The Theory of Electron Transfer 266
5.3.1 The elementary step in electron transfer 266
5.3.2 The effect of the electrical double-layer structure on the rate of
the electrode reaction 274
5.4 Transport in Electrode Processes 279
5.4.1 Material flux and the rate of electrode processes 279
5.4.2 Analysis of polarization curves (voltammograms) 284
5.4.3 Potential-sweep voltammetry 288
5.4.4 The concentration overpotential 289
5.5 Methods and Materials 290
5.5.1 The ohmic electrical potential difference 291
5.5.2 Transition and steady-state methods 293
Vlll
5.5.3 Periodic methods 301
5.5.4 Coulometry 303
5.5.5 Electrode materials and surface treatment 305
5.5.6 Non-electrochemical methods 328
5.6 Chemical Reactions in Electrode Processes 344
5.6.1 Classification 345
5.6.2 Equilibrium of chemical reactions 346
5.6.3 Chemical volume reactions 347

5.6.4 Surface reactions 350
5.7 Adsorption and Electrode Processes 352
5.7.1 Electrocatalysis 352
5.7.2 Inhibition of electrode processes 361
5.8 Deposition and Oxidation of Metals 368
5.8.1 Deposition of a metal on a foreign substrate 369
5.8.2 Electrocrystallization on an identical metal substrate 372
5.8.3 Anodic oxidation of metals 377
5.8.4 Mixed potentials and corrosion phenomena 381
5.9 Organic Electrochemistry 384
5.10 Photoelectrochemistry 390
5.10.1 Classification of photoelectrochemical phenomena 390
5.10.2 Electrochemical photoemission 392
5.10.3 Homogeneous photoredox reactions and photogalvanic effects 393
5.10.4 Semiconductor photoelectrochemistry and photovoltaic effects 397
5.10.5 Sensitization of semiconductor electrodes 403
5.10.6 Photoelectrochemical solar energy conversion 406
Chapter 6 Membrane Electrochemistry and Bioelectrochemistry . . 410
6.1 Basic Concepts and Definitions 410
6.1.1 Classification of membranes 411
6.1.2 Membrane potentials 411
6.2 Ion-exchanger Membranes 415
6.2.1 Classification of porous membranes 415
6.2.2 The potential of ion-exchanger membranes 417
6.2.3 Transport through a fine-pore membrane 419
6.3 Ion-selective Electrodes 425
6.3.1 Liquid-membrane ion-selective electrodes 425
6.3.2 Ion-selective electrodes with fixed ion-exchanger sites 428
6.3.3 Calibration of ion-selective electrodes 431
6.3.4 Biosensors and other composite systems 431

6.4 Biological Membranes 433
6.4.1 Composition of biological membranes 434
6.4.2 The structure of biological membranes 438
6.4.3 Experimental models of biological membranes 439
6.4.4 Membrane transport 442
6.5 Examples of Biological Membrane Processes 454
IX
6.5.1 Processes in the cells of excitable tissues 454
6.5.2 Membrane principles of bioenergetics 464
Appendix A Recalculation Formulae for Concentrations and
Activity Coefficients 473
Appendix В List of Symbols 474
Index
477
Preface
to the
First
Edition
Although electrochemistry has become increasingly important in society
and
in science the proportion of physical chemistry textbooks devoted to
electrochemistry has declined both in extent and in quality (with notable
exceptions, e.g. W. J. Moore's Physical Chemistry).
As recent books dealing with electrochemistry have mainly been ad-
dressed to the specialist it has seemed appropriate to prepare a textbook of
electrochemistry which assumes a knowledge of basic physical chemistry at
the
undergraduate level. Thus, the present text
will
benefit the more

advanced undergraduate and postgraduate students and research workers
specializing in physical chemistry, biology, materials science and their
applications.
An attempt has been made to include as much material as
possible so that the book becomes a starting point for the study of
monographs
and original papers.
Monographs
and
reviews
(mainly published after 1970) pertaining to
individual sections of the book are quoted at the end of each section. Many
reviews
have appeared in monographic series, namely:
Advances in
Electrochemistry
and
Electrochemical
Engineering
(Eds P.
Delahay,
H. Gerischer and C. W. Tobias), Wiley-Interscience, New
York,
published since 1961, abbreviation in References AE.
Electroanalytical
Chemistry
(Ed. A. J. Bard), M. Dekker, New
York,
published since 1966.
Modern

Aspects
of
Electrochemistry
(Eds J. O'M. Bockris, В. Е. Conway
and
coworkers), Butterworths, London, later Plenum Press, New
York,
published since 1954, abbreviation MAE.
Electrochemical
compendia include:
The
Encyclopedia
of
Electrochemistry
(Ed. C. A. Hempel), Reinhold, New
York,
1961.
Comprehensive
Treatise of
Electrochemistry
(Eds J. O'M. Bockris, В. Е.
Conway, E.
Yeager
and coworkers), 10 volumes, Plenum Press, 1980-
1985, abbreviation CTE.
Electrochemistry
of Elements (Ed. A. J. Bard), M. Dekker, New
York,
a
multivolume series published since 1973.

xi
Xll
Physical
Chemistry.
An
Advanced
Treatise
(Eds H. Eyring, D. Henderson
and
W. Jost), Vol. IXA,B, Electrochemistry, Academic Press, New
York,
1970, abbreviation
PChAT.
Hibbert,
D. B. and A. M. James,
Dictionary
of
Electrochemistry,
Macmillan, London, 1984.
There
are several more recent textbooks, namely:
Bockris, J. O'M. and A. K. N. Reddy,
Modern
Electrochemistry,
Plenum
Press, New
York,
1970.
Hertz,
H. G.,

Electrochemistry—A
Reformulation
of
Basic
Principles,
Springer-Verlag, Berlin, 1980.
Besson, J.,
Precis
de Thermodynamique et
Cinetique
Electrochimique,
Ellipses, Paris, 1984, and an introductory text.
Koryta, J., Ions
y
Electrodes
y
and Membranes, 2nd Ed., John
Wiley
& Sons,
Chichester, 1991.
Rieger, P. H.,
Electrochemistry,
Prentice-Hall, Englewood Cliffs, N.J.,
1987.
The
more important data compilations are:
Conway, В. Е.,
Electrochemical
Data, Elsevier, Amsterdam, 1952.
CRC Handbook of

Chemistry
and
Physics
(Ed. R. C. Weast), CRC Press,
Boca Raton, 1985.
CRC Handbook
Series
in
Inorganic
Electrochemistry
(Eds L. Meites, P.
Zuman,
E. B. Rupp and A. Narayanan), CRC Press, Boca Raton, a
multivolume series published since 1980.
CRC Handbook
Series
in
Organic
Electrochemistry
(Eds L. Meites and P.
Zuman),
CRC Press, Boca Raton, a multivolume series published since
1977.
Horvath,
A. L., Handbook of
Aqueous
Electrolyte
Solutions,
Physical
Properties,

Estimation
and
Correlation
Methods, Ellis Horwood, Chiches-
ter,
1985.
Oxidation-Reduction
Potentials
in
Aqueous
Solutions
(Eds A. J. Bard, J.
Jordan
and R. Parsons), Blackwell, Oxford, 1986.
Parsons, R., Handbook of
Electrochemical
Data, Butterworths, London,
1959.
Perrin,
D. D.,
Dissociation
Constants
of
Inorganic
Acids
and
Bases
in
Aqueous
Solutions,

Butterworths, London, 1969.
Standard
Potentials
in
Aqueous
Solutions
(Eds A. J. Bard, R. Parsons and
J.
Jordan), M. Dekker, New
York,
1985.
The
present authors, together with the late (Miss) Dr V. Bohackova,
published their
Electrochemistry,
Methuen, London, in 1970. In spite of the
favourable attitude of the readers, reviewers and publishers to that book
(German,
Russian, Polish, and Czech editions have appeared since then) we
now consider it out of date and therefore present a text which has been
largely
rewritten. In particular we have stressed modern electrochemical
хш
materials (electrolytes, electrodes, non-aqueous electrochemistry in gene-
ral),
up-to-date charge transfer theory and biological aspects of electro-
chemistry. On the other hand, the presentation of electrochemical methods
is quite short as the reader has access to excellent monographs on the
subject (see page 301).
The

Czech manuscript has been kindly translated by Dr M. Hyman-
Stulikova. We are much indebted to the late Dr A
Ryvolova,
Mrs M.
Kozlova and Mrs D. Tumova for their expert help in preparing the
manuscript. Professor E. Budevski, Dr J. Ludvik, Dr L. Novotny and Dr J.
Weber
have supplied excellent photographs and drawings.
Dr
K. Janacek, Dr L. Kavan, Dr K. Micka, Dr P. Novak, Dr Z. Samec
and
Dr J.
Weber
read individual chapters of the manuscript and made
valuable comments and
suggestions
for improving the book. Dr L. Kavan is
the
author of the section on non-electrochemical methods (pages 319 to
329).
We are also grateful to Professor V. Pokorny, Vice-president of the
Czechoslovak Academy of Sciences and chairman of the Editorial Council
of the Academy, for his support.
Lastly we would
like
to mention with devotion our teachers, the late
Professor J. Heyrovsky and the late Professor R. Brdicka, for the
inspiration we received from them for our research and teaching of
electrochemistry, and our colleague and friend, the late Dr V. Bohackova,
for all her assistance in the past.

Prague, March 1986
Jifi
Koryta
Jin
Dvorak
Preface to the Second Edition
The new edition of Principles of Electrochemistry has been considerably
extended by a number of new sections, particularly dealing with 'electro-
chemical material science' (ion and electron conducting polymers, chemically
modified electrodes), photoelectrochemistry, stochastic processes, new asp-
ects of ion transfer across biological membranes, biosensors, etc. In view of
this extension of the book we asked Dr Ladislav Kavan (the author of the
section on non-electrochemical methods in the first edition) to contribute as
a co-author discussing many of these topics. On the other hand it has been
necessary to become less concerned with some of the 'classical' topics the
details of which are of limited importance for the reader.
Dr Karel Micka of the J. Heyrovsky Institute of Physical Chemistry and
Electrochemistry has revised very thoroughly the language of the original
text as well as of the new manuscript. He has also made many extremely
useful suggestions for amending factual errors and improving the accuracy
of many statements throughout the whole text. We are further much
indebted to
Prof.
Michael Gratzel and Dr Nicolas Vlachopoulos, Federal
Polytechnics, Lausanne, for valuable suggestions to the manuscript.
During the preparation of the second edition Professor Jiff Dvorak died
after a serious illness on 27 February 1992. We shall always remember his
scientific effort and his human qualities.
Prague, May 1992 Jifi Koryta
xv

Chapter 1
Equilibrium Properties of
Electrolytes
Substances are frequently spoken of as being electro-negative, or electro-positive,
according as they go under the supposed influence of direct attraction to the positive
or negative pole. But these terms are much too significant for the use for which I
should have to put them; for though the meanings are perhaps right, they are only
hypothetical, and may be wrong; and then, through a very imperceptible, but still
very dangerous, because continual, influence, they do great injury to science, by
contracting and limiting the habitual views of those engaged in pursuing it. I propose
to distinguish such bodies by calling those anions which go to the anode of the
decomposing body; and those passing to the cathode,
cations•;
and when I have the
occasion to speak of these together, I shall call them ions. Thus, the chloride of lead
is an electrolyte, and when electrolysed evolves two ions, chlorine and lead, the
former being an anion, and the latter a cation.
M. Faraday, 1834
1.1 Electrolytes: Elementary Concepts
1.1.1 Terminology
A substance present in solution or in a melt which is at least partly in the
form of charged species—ions—is called an electrolyte. The decomposition
of electroneutral molecules to form electrically charged ions is termed
electrolytic
dissociation. Ions with a positive charge are called cations; those
with a negative charge are termed anions. Ions move in an electric field as a
result of their charge—cations towards the cathode, anions to the anode.
The cathode is considered to be that electrode through which negative
charge, i.e. electrons, enters a heterogeneous electrochemical system
(electrolytic cell, galvanic cell). Electrons leave the system through the

anode. Thus, in the presence of current flow, reduction always occurs at the
cathode and oxidation at the anode. In the strictest sense, in the absence of
current passage the concepts of anode and cathode lose their meaning. All
these terms were introduced in the thirties of the last century by M.
Faraday.
R. Clausius (1857) demonstrated the presence of ions in solutions and
verified the validity of Ohm's law down to very low voltages (by electrolysis
1
of a solution with direct current and unpolarizable electrodes). Up until that
time,
it was generally accepted that ions are formed only under the
influence of an electric field leading to current flow through the solution.
The electrical conductivity of electrolyte solutions was measured at the
very beginning of electrochemistry. The resistance of a conductor R is the
proportionality constant between the applied voltage U and the current /
passing through the conductor. It is thus the constant in the equation
U = RI, known as Ohm's law. The reciprocal of the resistance is termed the
conductance. The resistance and conductance depend on the material from
which the conductor is made and also on the length L and cross-section S of
the conductor. If the resistance is recalculated to unit length and unit
cross-section of the conductor, the quantity p = RS/L is obtained, termed
the resistivity. For conductors consisting of a solid substance (metals, solid
electrolytes) or single component liquids, this quantity is a characteristic of
the particular substance. In solutions, however, the resistivity and the
conductivity K = l/p are also dependent on the electrolyte concentration c.
In fact, even the quantity obtained by recalculation of the conductivity to
unit concentration, A = K/C, termed the molar conductivity, is not inde-
pendent of the electrolyte concentration and is thus not a material constant,
characterizing the given electrolyte. Only the limiting value at very low
concentrations, called the limiting molar conductivity A

0
, is such a quantity.
A study of the concentration dependence of the molar conductivity,
carried out by a number of authors, primarily F. W. G. Kohlrausch and W.
Ostwald, revealed that these dependences are of two types (see Fig. 2.5)
and thus, apparently, there are two types of electrolytes. Those that are
fully dissociated so that their molecules are not present in the solution are
called strong
electrolytes,
while those that dissociate incompletely are weak
electrolytes. Ions as well as molecules are present in solution of a weak
electrolyte at finite dilution. However, this distinction is not very accurate
as,
at higher concentration, the strong electrolytes associate forming
ion pairs (see Section
1.2.4).
Thus,
in weak electrolytes, molecules can exist in a similar way as in
non-electrolytes—a molecule is considered to be an electrically neutral
species consisting of atoms bonded together so strongly that this species can
be studied as an independent entity. In contrast to the molecules of
non-electrolytes, the molecules of weak electrolytes contain at least one
bond with a partly ionic character. Strong electrolytes do not form
molecules in this sense. Here the bond between the cation and the anion is
primarily ionic in character and the corresponding chemical formula
represents only a formal molecule; nonetheless, this formula correctly
describes the composition of the ionic crystal of the given strong electrolyte.
The first theory of solutions of weak electrolytes was formulated in 1887
by S. Arrhenius (see Section
1.1.4).

If the molar conductivity is introduced
into the equations following from Arrhenius' concepts of weak electrolytes,
Eq. (2.4.17) is obtained, known as the Ostwald dilution law; this equation
provides a good description of one of these types of concentration
dependence of the molar conductivity. The second type was described by
Kohlrausch using the empirical equation (2.4.15), which was later theoreti-
cally interpreted by P. Debye and E. Hiickel on the basis of concepts of the
activity coefficients of ions in solutions of completely dissociated el-
ectrolytes, and considerably improved by L. Onsager. An electrolyte can be
classified as strong or weak according to whether its behaviour can be
described by the Ostwald or Kohlrausch equation. Similarly, the 'strength'
of an electrolyte can be estimated on the basis of the van't Hoff coefficient
(see Section
1.1.4).
1.1.2
Electroneutrality
and mean quantities
Prior to dissolution, the ion-forming molecules have an overall electric
charge of zero. Thus, a homogeneous liquid system also has zero charge
even though it contains charged species. In solution, the number of positive
elementary charges on the cations equals the number of negative charges of
the anions. If a system contains s different ions with molality m,
(concentrations c, or mole fractions x
t
can also be employed), each bearing
2/
elementary charges, then the equation
0 (1.1.1)
1=1
called the electroneutrality condition, is valid on a macroscopic scale for

every homogeneous part of the system but not for the boundary between
two phases (see Chapter 4).
From the physical point of view there cannot exist, under equilibrium
conditions, a measurable excess of charge in the bulk of an electrolyte
solution. By electrostatic repulsion this charge would be dragged to the
phase boundary where it would be the source of a strong electric field in the
vicinity of the phase. This point will be discussed in Section 3.1.3.
In Eq. (1.1.1), as elsewhere below, z, is a dimensionless number (the
charge of species i related to the charge of a proton, i.e. the charge number
of the ion) with sign z
t
> 0 for cations and z, < 0 for anions.
The electroneutrality condition decreases the number of independent
variables in the system by one; these variables correspond to components
whose concentration can be varied independently. In general, however,
a number of further conditions must be maintained (e.g. stoichiometry
and the dissociation equilibrium condition). In addition, because of the
electroneutrality condition, the contributions of the anion and cation to a
number of solution properties of the electrolyte cannot be separated (e.g.
electrical conductivity, diffusion coefficient and decrease in vapour pressure)
without assumptions about individual particles. Consequently, mean values
have been defined for a number of cases.
For example, the molality can be expressed for an electrolyte as a whole,
m
x
\
the amount of substance ('number of moles') is expressed in moles of
formula units
as if the
electrolyte were

not
dissociated.
For a
strong
electrolyte whose formula unit contains
v+
cations
and v_
anions,
i.e. a
total
of v =
v+
+ v_
ions,
the
molalities
of
the ions
are
related
to the
total
molality
by a
simple relationship,
ra+ =
v
+
m

l
and
m_
=
v_m
Y
.
The
mean
molality
is
then
m
±
=
(ml+m
v
-)
l/v
=
m,«
+
vr-)
1/v
(1.1.2)
The mean molality values
m
±
(moles
per

kilogram), mole fractions
x
±
(dimensionless number) and concentrations
c
±
(moles
per
cubic decimetre)
are related
by
equations similar
to
those
for
non-electrolytes (see Appendix
A).
1.1.3 Non-ideal behaviour
of
electrolyte
solutions
The chemical potential
is
encountered
in
electrochemistry
in
connection
with
the

components
of
both solutions and gases. The chemical potential \i
{
of component
/ is
defined
as the
partial molar Gibbs energy
of
the system,
i.e. the partial derivative
of
the Gibbs energy
G
with respect
to
the amount
of substance
n
t
of
component
i at
constant pressure, temperature
and
amounts
of all the
other components except
the ith.

Consider that
the
system does
not
exchange matter with
its
environment
but
only energy
in
the form
of
heat
and
volume work. From this definition
it
follows
for a
reversible isothermal change
of the
pressure
of one
mole
of an
ideal
gas
from the reference value
p
rcf
to the

actual value
/?
act
that
A*act-^ef=/^ln— (1.1.3)
Prcf
which
is
usually written
in the
form
\i
=
/i°
+ RT
Inp (1.1.4)
where
p is the
dimensionless pressure ratio
p
act
/p
re
f'
The reference state
is
taken
as
the state
at

the given temperature and
at a
pressure
of
10
5
Pa.
The
dimensionless pressure
p is
therefore expressed
as
multiples
of
this
reference pressure. Term jU° has the significance
of
the chemical potential
of
the
gas at a
pressure equal
to the
standard pressure,
p = 1, and is
termed
the standard chemical potential. This significance
of
quantities fj,°
and p

should
be
recalled,
e.g.
when substituting pressure values into
the
Nernst
equation
for gas
electrodes
(see
Section
3.2); if the
value
of the
actual
pressure
in
some arbitrary units were substituted (e.g.
in
pounds
per
square
inch),
this would affect the value
of
the standard electrode potential.
The chemical potential //,
of
the components

of an
ideal mixture
of
liquids
(the components
of an
ideal mixture
of
liquids obey the Raoult law over the
whole range
of
mole fractions and
are
completely miscible)
is
^1
=
pT +
RT
In
Xi
(1.1.5)
The standard term y,* is the chemical potential of the pure component i (i.e.
when x
t
= 1) at the temperature of the system and the corresponding
saturated vapour pressure. According to the Raoult law, in an ideal mixture
the partial pressure of each component above the liquid is proportional to
its mole fraction in the liquid,
Pi=P°Xi (1.1.6)

where the proportionality constant p° is the vapour pressure above the pure
substance.
In a general case of a mixture, no component takes preference and the
standard state is that of the pure component. In solutions, however, one
component, termed the solvent, is treated differently from the others, called
solutes. Dilute solutions occupy a special position, as the solvent is present
in a large excess. The quantities pertaining to the solvent are denoted by the
subscript 0 and those of the solute by the subscript 1. For x
l
->0 and x
o
-*l,
Po
=
Po
an
d Pi
—
kiXi. Equation (1.1.5) is again valid for the chemical
potentials of both components. The standard chemical potential of the
solvent is defined in the same way as the standard chemical potential of the
component of an ideal mixture, the standard state being that of the pure
solvent. The standard chemical potential of the dissolved component juf is
the chemical potential of that pure component in the physically unattainable
state corresponding to linear extrapolation of the behaviour of this
component according to Henry's law up to point x
x
= 1 at the temperature
of the mixture T and at pressure p = k
lt

which is the proportionality
constant of Henry's law.
For a solution of a non-volatile substance (e.g. a solid) in a liquid the
vapour pressure of the solute can be neglected. The reference state for such
a substance is usually its very dilute solution—in the limiting case an
infinitely dilute solution—which has identical properties with an ideal
solution and is thus useful, especially for introducing activity coefficients
(see Sections 1.1.4 and 1.3). The standard chemical potential of such a
solute is defined as
A*i = Km (pi-RT Inx
t
) (1.1.7)
JC(j-»l
where y
l
is the chemical potential of the solute, x
x
its mole fraction and x
{)
the mole fraction of the solvent.
In the subsequent text, wherever possible, the quantities jU° and pf will
not be distinguished by separate symbols: only the symbol $ will be
employed.
In real mixtures and solutions, the chemical potential ceases to be a linear
function of the logarithm of the partial pressure or mole fraction.
Consequently, a different approach is usually adopted. The simple form of
the equations derived for ideal systems is retained for real systems, but a
different quantity a, called the activity (or fugacity for real gases), is
introduced. Imagine that the dissolved species are less 'active' than would
correspond to their concentration, as if some sort of loss' of the given

interaction were involved. The activity is related to the chemical potential
by the relationship
[i^tf +
RTlna,
(1.1.8)
As in electrochemical investigations low pressures are usually employed, the
analogy of activity for the gaseous state, the fugacity, will not be introduced
in the present book.
Electrolyte solutions differ from solutions of uncharged species in their
greater tendency to behave non-ideally. This is a result of differences in the
forces producing the deviation from ideality, i.e. the forces of interaction
between particles of the dissolved substances. In non-electrolytes, these are
short-range forces (non-bonding interaction forces); in electrolytes, these
are
electrostatic
forces whose relatively greater range is given by Coulomb's
law. Consider the process of concentrating both electrolyte and non-
electrolyte solutions. If the process starts with infinitely dilute solutions,
then their initial behaviour will be ideal; with increasing concentration
coulombic interactions and at still higher concentrations, van der Waals
non-bonding interactions and dipole-dipole interactions will become impor-
tant. Thus, non-ideal behaviour must be considered for electrolyte solutions
at much lower concentrations than for non-electrolyte solutions. 'Respecting
non-ideal behaviour' means replacing the mole fractions, molalities and
molar concentrations by the corresponding activities in all the thermo-
dynamic relationships. For example, in an aqueous solution with a molar
concentration of 10~
3
mol • dm~
3

, sodium chloride has an activity of
0.967 x 10~
3
. Non-electrolyte solutions retain their ideal properties up to
concentrations that may be as much as two orders of magnitude higher, as
illustrated in Fig. 1.1.
Thus,
the deviation in the behaviour of electrolyte solutions from the
ideal depends on the composition of the solution, and the activity of the
components is a function of their mole fractions. For practical reasons, the
form of this function has been defined in the simplest way possible:
a
x
= y
x
x (1.1.9)
where the quantity y
x
is termed the activity coefficient (the significance of
the subscript x will be considered later). However, the complications
connected with solution non-ideality have not been removed but only
transferred to the activity coefficient, which is also a function of the
concentration. The form of this function can be found either theoretically
(the theory has been quite successful for electrolyte solutions, see Section
1.3) or empirically. Practical calculations can be based on one of the
theoretical or semiempirical equations for the activity coefficient (for the
simple ions, the activity coefficient values are tabulated); the activity
coefficient is then multiplied by the concentration and the activity thus
-2
-1 0

Log
of
molality
Fig. 1.1 The activity coefficient y of a non-
electrolyte and mean activity coefficients y
±
of
electrolytes as functions of molality
obtained is substituted into a simple 'ideal' equation (e.g. the law of mass
action for chemical equilibrium).
Activity a
x
is termed the rational activity and coefficient y
x
is the rational
activity coefficient. This activity is not directly given by the ratio of the
fugacities, as it is for gases, but appears nonetheless to be the best means
from a thermodynamic point of view for description of the behaviour of real
solutions. The rational activity corresponds to the mole fraction for ideal
solutions (hence the subscript x). Both a
x
and y
x
are dimensionless
numbers.
In practical electrochemistry, however, the molality m or molar con-
centration c is used more often than the mole fraction. Thus, the molal
activity a
my
molal activity coefficient y

m)
molar activity a
c
and molar activity
coefficient y
c
are introduced. The adjective 'molal' is sometimes replaced by
'practical'.
The following equations provide definitions for these quantities:
Yi,m o>
lim Yi.m =
0
lim Yi,
c
=
0
(1.1.10)
The standard states are selected asm? = l mol • kg"
1
and c? = 1 mol • dm
3
.
In this convention, the ratio ra//m° is numerically identical with the actual
molality (expressed in units of moles per kilogram). This is, however, the
dimensionless relative molality,
in the
same
way
that pressure
p in Eq.

(1.1.4)
is the
dimensionless relative pressure.
The
ratio cjc®
is
analogous.
The symbols ra—»0
and
c—>0
in the
last
two
equations indicate that
the
molalities
or
concentrations
of all the
components except
the
solvent
are
small.
Because
of the
electroneutrality condition,
the
individual
ion

activities
and activity coefficients cannot
be
measured without additional extrather-
modynamic assumptions (Section
1.3).
Thus, mean quantities
are
defined
for
dissolved electrolytes,
for all
concentration scales.
E.g., for a
solution
of a
single strong binary electrolyte
as
a±
=
(£ix
+
fl )
1/v
,
Y
± =
(r:
+
r-)

1/v
(1.1.11)
The numerical values
of the
activity coefficients
y
x
, y
m
and y
c
(and
also
of
the activities
a
x
, a
m
and a
c
) are
different
(for the
recalculation formulae
see
Appendix
A).
Obviously,
for the

limiting case
(for a
very dilute solution)
y
±
,*
= y
±
,m =
y±.c«i (1.1.12)
The activity coefficient
of the
solvent remains close
to
unity
up to
quite
high electrolyte concentrations;
e.g. the
activity coefficient
for
water
in an
aqueous solution
of 2
M
KC1
at
25°C equals
y

0>x
= 1.004,
while
the
value
for
potassium chloride
in
this solution
is
y±
>x
=
0.614, indicating
a
quite large
deviation from
the
ideal behaviour. Thus,
the
activity coefficient
of the
solvent
is not a
suitable characteristic
of the
real behaviour
of
solutions
of

electrolytes.
If the
deviation from ideal behaviour
is to be
expressed
in
terms
of
quantities connected with
the
solvent, then
the
osmotic
coefficient
is
employed.
The
osmotic pressure
of the
system
is
denoted
as
JZ
and the
hypothetical osmotic pressure
of a
solution with
the
same composition that

would behave ideally
as
JT*.
The
equations
for the
osmotic pressures
JZ
and
JZ*
are
obtained from
the
equilibrium condition
of the
pure solvent
and of
the solution. Under equilibrium conditions
the
chemical potential
of the
pure solvent, which
is
equal
to the
standard chemical potential
at the
pressure
/?, is
equal

to the
chemical potential
of the
solvent
in the
solution
under
the
osmotic pressure
JZ,
li%(T,
p) = ii
o
(T, p +
JZ)
= iil(T
y
p + jz) + RT\n a
0
(1.1.13)
where
a
0
is the
activity
of the
solvent
(the
activity
of the

pure solvent
is
unity).
As
approximately
p
+ Jt)-
l*°o(T,
p) =
V
O
JZ
(1.1.14)
we obtain
for the
osmotic pressure
JZ=
\na
0
(1.1.15)
where
v
0
is the
molar volume
of the
solvent.
For a
dilute solution
In

a
0
= In x
0
= In (1 - E *,-) ~ - E
x
t
••
—
M
o
E m
h
giving
for the
ideal osmotic
pressure (M
o
is the relative molecular mass of the solvent)
**=^2>
(1.1.16)
and in terms of molar concentration c of a single electrolyte dissociating into
v ions
JT*
=
VRTC
(1.1.17)
The ratio
JI/JI*
(which is experimentally measurable) is termed the molal

osmotic coefficient
The rational osmotic coefficient
is
defined
by the
equation
In
a
0
=<t>
x
\nx
Q
(1.1.19)
For a solution of a single electrolyte, the relationship between the mean
activity coefficient and the osmotic coefficient is given by the equation
In
rm
= -(l-ct>
m
)-\ (l-4>
m
,)dlnm' (1.1.20)
following from the definitions and from the Gibbs-Duhem equation.
In view of the electrostatic nature of forces that primarily lead to
deviation of the behaviour of electrolyte solutions from the ideal, the
activity coefficient of electrolytes must depend on the electric charge of all
the ions present. G. N. Lewis, M. Randall and J. N. Br0nsted found
experimentally that this dependence for dilute solutions is described quite
adequately by the relationship

log
y
±
=Az
+
z_Vi
(1.1.21)
in which the constant A for 25° and water has a value close to 0.5
dm
3/2
• mol~
1/2
. Quantity /, called the ionic strength, describes the electro-
static effect of individual ionic species by the equation
/
= JXc,zf (1.1.22)
i
(In fact, the symbol I
c
should be used, as the molality ionic strength l
m
can
be defined analogously; in dilute aqueous solutions, however, values of c
and m, and thus also I
c
and /
m
, become identical.) Equation (1.1.21) was
later derived theoretically and is called the Debye-Hiickel limiting law. It
will be discussed in greater detail in Section 1.3.1.

1.1.4 The A
rrhenius
theory of
electrolytes
At the end of the last century S. Arrhenius formulated the first
quantitative theory describing the behaviour of weak electrolytes. The
10
existence of ions in solution had already been demonstrated at that time,
but very little was known of the structure of solutions and the solvent was
regarded as an inert medium. Similarly, the concepts of the activity and
activity coefficient were not employed. Electrochemistry was limited to
aqueous solutions. However, the basis of classical thermodynamics was
already formulated (by J. W. Gibbs, W. Thomson and H. v. Helmholtz)
and electrolyte solutions had also been investigated thermodynamically
especially by means of cryoscopic, osmometric and vapour pressure
measurements.
Van't Hoff introduced the correction factor i for electrolyte solutions; the
measured quantity (e.g. the osmotic pressure, Jt) must be divided by this
factor to obtain agreement with the theory of dilute solutions of non-
electrolytes (jz/i = RTc). For the dilute solutions of some electrolytes (now
called strong), this factor approaches small integers. Thus, for a dilute
sodium chloride solution with concentration c, an osmotic pressure of 2RTc
was always measured, which could readily be explained by the fact that the
solution, in fact, actually contains twice the number of species correspond-
ing to concentration c calculated in the usual manner from the weighed
amount of substance dissolved in the solution. Small deviations from
integral numbers were attributed to experimental errors (they are now
attributed to the effect of the activity coefficient).
For other electrolytes, now termed weak, factor / has non-integral values
depending on the overall electrolyte concentration. This fact was explained

by Arrhenius in terms of a reversible dissociation reaction, whose equi-
librium state is described by the law of mass action.
A weak electrolyte B
v+
A
v
_ dissociates in solution to yield v ions
consisting of v+ cations B
z+
and v_ anions A
z
~,
B
v+
A
v
_<=*
v
+
B
z+
+ v_A
z
~ (1.1.23)
Thus the magnitude of the constant called the thermodynamic or real
dissociation constant,
°^ (1.1.24)
is a measure of the 'strength of the electrolyte'. The smaller its value, the
weaker the electrolyte. The activity can be replaced by the concentrations
according to Eq. (1.1.10), yielding

rp>z+iv+r
AZ-IV
v+ v_ v+ v_
K
—F^—A—T
= K
(1.1.25)
B
v+
A
v
_ y
BZ
y
BA
where
K'=-
[B
v
A
v
_]
11
is called
the
apparent dissociation constant. Constant
K
depends
on the
temperature;

the
dependence
on the
pressure
is
usually neglected
as
equilibria
in the
condensed phase
are
involved. Constant
K'
also depends
on the ionic strength and increases with increasing ionic strength,
as
follows
from substitution
of
the limiting relationship (1.1.21) into Eq. (1.1.25). For
simplicity, consider monovalent ions, that
is
v+
=
v_
=
1,
so
that_log y
B

=
log y
A
=
~AV7and log
y
BA
=
0. Obviously, then,
y
B
=
y
A
=
10°
sV/
, y
BA
= 1
and substitution and rearrangement yield
/T
=
/aO
v7
(1.1.27)
It should
be
noted that the activity appearing
in

the dissociation constant
K
is the
dimensionless relative activity,
and
constant
K'
contains
the
dimensionless relative concentration
or
molality terms. Constants
K
and
K'
are thus also dimensionless. However, their numerical values correspond
to
the units selected
for
the standard state, i.e. moles per cubic decimetre
or
moles per kilogram.
Because
the
dissociation constants
for
various electrolytes differ
by
several order
of

magnitude, the following definition
pK=-\ogK\
pK'
=-log
K'
(1.1.28)
is introduced
to
characterize
the
electrolyte strength
in
terms
of a
logarithmic quantity. Operator/? appears frequently
in
electrochemistry and
is equal
to
the log operator times —1 (i.e.
px
= —logjc).
The degree
of
dissociation
a is
the equilibrium degree
of
conversion,
i.e.

the fraction
of
the number
of
molecules originally present that dissociated
at
the given concentration. The degree
of
dissociation depends directly
on
the
given dissociation constant. Obviously
a
= [B
2+
]/v+c
=
[A
2
~]/v_c,
[B
v+
A
v
_]
=
c(l
—
a)
and the dissociation constant

is
then given
as
~-
1
—
a
(1.1.29)
The most common electrolytes are uni-univalent (v
=
2, v+
=
v_
=
1),
for
which
The relationship
for a
follows:
In moderately diluted solutions,
i.e. for
concentrations fulfilling
the
condition,
c» K
f
,
a^(K'/c)
l/2

«l
(1.1.32)
12
Id
7
16
5
Concentration
10
1
Fig. 1.2 Dependence of the dissociation degree a of a week
electrolyte on molar concentration c for different values of the
apparent dissociation constant K' (indicated at each curve)
In the limiting case (readily obtained by differentiation of the numerator
and denominator with respect to c) it holds that ar-»l for c—»0, i.e. each
weak electrolyte at sufficient dilution is completely dissociated and, on the
other hand, for sufficiently large c, cv—>0, i.e. the highly concentrated
electrolyte is dissociated only slightly. The dependence of a on c is given in
Fig. 1.2.
For strong electrolytes, the activity of molecules cannot be considered, as
no molecules are present, and thus the concept of the dissociation constant
loses its meaning. However, the experimentally determined values of the
dissociation constant are finite and the values of the degree of dissociation
differ from unity. This is not the result of incomplete dissociation, but is
rather connected with non-ideal behaviour (Section 1.3) and with ion
association occurring in these solutions (see Section
1.2.4).
Arrhenius also formulated the first rational definition of acids and bases:
An acid (HA) is a substance from which hydrogen ions are dissociated in
solution:

A base (BOH) is a substance splitting off hydroxide ions in solution:
This approach explained many of the properties of acids and bases and
many processes in which acids and bases appear, but not all (e.g. processes
13
in non-aqueous media, some catalytic processes, etc.). It has a drawback
coming from the attempt to define acids and bases independently. However,
as will be seen later, the acidity or basicity of substances appears only on
interaction with the medium with which they are in contact.
References
Dunsch, L., Geschichte der Elektrochemie, Deutscher Verlag fur
Grundstoffindustrie, Leipzig, 1985.
Ostwald, W., Die Entwicklung der Elektrochemie in gemeinverstdndlicher
Darstellung, Barth, Leipzig, 1910.
1.2 Structure of Solutions
1.2.1 Classification of solvents
The classical period of electrochemistry dealt with aqueous solutions.
Gradually, however, other, 'non-aqueous' solvents became important in
both chemistry and electrochemistry. For example, some important sub-
stances (e.g. the Grignard reagents and other homogeneous catalysts)
decompose in water. A number of important biochemical substances
(proteins, enzymes, chlorophyll, vitamin B
12
) are insoluble in water but are
soluble, for example, in anhydrous liquid hydrogen fluoride, from which
they can be reisolated without loss of biochemical activity. The whole
aluminium industry is based on electrolysis of a solution of aluminium oxide
in fused cryolite. Many more examples could be given of chemical processes
employing solvents other than water. Basically any substance can be used as
a solvent at temperatures between its melting and boiling points (provided it
is stable in this temperature range). Three types of solvent can be

distinguished.
Molecular solvents consist of molecules. The cohesive forces between
neighbouring molecules in the liquid phase depend on hydrogen bonds or
other 'bridges' (oxygen, halogen), on dipole-dipole interactions or on van
der Waals interactions. These solvents act as dielectrics and do not
appreciably conduct electric current. Autoionization occurs to a slight
degree in some of them, leading to low electric conductivity (for example
2H
2
O^H
3
O
+
+ OH~; in the melt, 2HgBr
2
<=»HgBr
+
+ HgBr
3
~; in the
liquefied state, 2NO
2
^±NO
+
+ NO
3
").
Ionic solvents consisting of ions are mostly fused salts. However, not all
salts yield ions on melting. For example, fused HgBr
2

,
POC1
3
,
BrF
3
and
others form molecular liquids. On mixing, however, the molecular solvents
H
2
O and H
2
SO
4
can form ionic solvents that contain only the H
3
O
+
and
HSO
4
~
i°
ns
-
Ionic solvents have high ionic electric conductivity. Most exist
at high temperatures (e.g., at normal pressure, NaCl between 800 and
1465°C) but some salts have low melting points (e.g. ethylpyridinium
bromide at -114°C, tetramethylammonium thiocyanate at -50.5°C) and, in
14

addition, there is a number of low-melting-point eutectics (for example
AICI3 + KC1 + NaCl in a ratio of 60:14:26 mol % melts at 94°C). The ions
present in these solvents can be either monoatomic (for example Na
+
and
Cl~
in fused NaCl) or polyatomic (for example cryolite—Na
3
AlF6—contains
Na
+
, A1F
6
3
", AIF4- and F" ions).
1.2.2 Liquid
structure
Molecular liquids are not at all amorphous, as would first appear.
Methods of structural analysis (X-ray diffraction, NMR, IR and Raman
spectroscopy) have demonstrated that the liquid retains the structure of the
original crystal to a certain degree. Water is the most ordered solvent (and
has been investigated most extensively). Under normal conditions, 70 per
cent of the water molecules exist in 'ice floes', clusters of about 50 molecules
with a structure similar to that of ice and a mean lifetime of 10~
n
s.
Hydrogen bonds lead to intermolecular spatial association. Hydrogen bonds
are also formed in other solvents, but result in the formation of chains (e.g.
in alcohols) or rings (e.g. rings containing six molecules are formed in liquid
HF).

Thus, the degree of organization is lower in these solvents than in
water, although the strength of hydrogen bonds increases in the order: HC1,
H
2
SO
4
(practically monomers) < NH
3
< H
2
O < HF. Mixing of a highly
organized solvent with a less organized one leads to structure modification.
If, for example, ethanol is added to water, ethanol molecules first enter the
water structure and strengthen it; at higher concentrations this order is
reversed.
It is not the purpose of chemistry, but rather of statistical thermo-
dynamics, to formulate a theory of the structure of water. Such a theory
should be able to calculate the properties of water, especially with regard to
their dependence on temperature. So far, no theory has been formulated
whose equations do not contain adjustable parameters (up to eight in some
theories). These include continuum and mixture theories. The continuum
theory is based on the concept of a continuous change of the parameters of
the water molecule with temperature. Recently, however, theories based on
a model of a mixture have become more popular. It is assumed that liquid
water is a mixture of structurally different species with various densities.
With increasing temperature, there is a decrease in the number of
low-density species, compensated by the usual thermal expansion of liquids,
leading to the formation of the well-known maximum on the temperature
dependence of the density of water (0.999973 g • cm"
3

at 3.98°C).
There are various theories on the structure of these species and their size.
Some authors have assumed the presence of monomers and oligomers up to
pentamers, with the open structure of ice I, while others deny the presence
of monomers. Other authors assume the presence of the structure of ice I
with loosely arranged six-membered rings and of structures similar to that of
ice III with tightly packed rings. Most often, it is assumed that the structure