Electrochemistry Volume 5

A Review of the Literature Published up to March 1974

By H. R. Thirsk

The Royal Society of Chemistry

Copyright © 1975 The Chemical Society
All rights reserved.
ISBN: 978-0-85186-047-3

Contents

Chapter 1 Electrolyte Solutions By T. H. Lilley, 1,
Chapter 2 Electron-transfer Reactions By P. P. Schmidt, 21,
Chapter 3 Membrane Phenomena By N. Lakshminarayanaiah, 132,
Erratum, 301,
Author Index, 302,

CHAPTER 1

Electrolyte Solutions

BY T. H. LILLEY

1 Introduction

The most studied solvent system for ionic species continues to be liquid water, although there is an increasing number of papers published in which the solvents used are partly aqueous, non-aqueous, and particularly aprotic. Since the last Report in this series was published, several books and reviews have appeared. The most general reviews are those given in the recent Annual Report* but others which are relevant include a discussion of hydrophobic hydration and interaction and a wide-ranging article on the subject of acidity and experimental methods for the determination of equilibrium constants. The review by Sarma and Ahluwalia is particularly pertinent since many of the examples given are drawn from investigations on aqueous systems containing tetra-alkylammonium ions. The seventh and eighth volumes of the series by Conway and Bockris have been published, and although, as usual, most attention is directed towards interfacial problems, solution electro-chemists can profit by a reading of at least parts of these. A further two volumes in the series edited by Franks have also been published. Volume 2 deals with the properties of water and crystalline hydrates and aqueous solutions of non-electrolytes, and Volume 3 deals with various aspects of the properties of aqueous ionic solutions. As in the previous volume, the range of investigations and techniques considered by the contributors is very wide, and one would imagine that most electrochemists find Volume 3 particularly valuable.

The papers have appeared which resulted from a Symposium held in honour of H. S. Frank, and the same articles have been collected and published as a book. The Journal of Solution Chemistry has also published a series of papers as a memorial to J. E. Prue.

A new and extended edition has been published of Bates’ book on pH, and in a related area some reviews on the application of ion-selective electrodes have appeared.

There still does not appear to be an entirely suitable book available for under-graduate teaching in the field of electrolyte solutions but an abbreviated form of an earlier text and a short book by Robbins both, in their own ways, go some way to fill the gap.

Two extensive and expensive books have appeared’ which reflect the growing interest in non-aqueous solvents. The more digestible of the two is edited by Covington and Dickinson, and thorough and comprehensive chapters are included on both equilibrium and non-equilibrium investigations on ionic solutions. The well-presented tables seem certain to ensure that this text will become the counterpart for non-aqueous solutions of the important monograph by Robinson and Stokes. In the other, Janz has continued his compilations of physico-chemical data with the first volume of a series entitled the on-aqueous Electrolytes Handbook’.

A very fine book with the title ‘Ions and Ion Pairs in Organic Reactions’, edited by Szwarc, has been published. This is the first of two volumes, the second of which deals with the influence of ion pairs on reaction kinetics. The first volume is of particular interest not only for the authoritative and readable nature of the various chapters (the chapter by Kebarle on ion solvation in the gas phase is particularly good) but also in illustrating the similarity of the problems facing the contributors and those interested in more classical solution-electrochemical problems.

2 Liquid Water

Experimental data, usually of very high precision, continue to be published on liquid water and its isotopic variations. Measurements have been reported on the volumetric properties of ordinary water in the temperature range 278 — 353 K and an extensive study has been presented of its specific volumes at high temperatures and pressures. The already fairly extensive literature on the properties of super-cooled water has been supplemented by an investigation of some of its properties (heat capacity, expansibility, and 1H chemical shift) from the normal freezing temperature to 235 K. Other measurements include determinations of the thermal conductivity as a function of temperature and pressure and of the viscosity near the temperature of maximum density at atmospheric pressure. Some spectroscopic studies have been presented, including two n.m.r. investigations, one dealing with spin–lattice relaxation times and the other with the temperature and pressure dependences of proton chemical shifts. This latter work is of considerable importance in investigations on the perturbation of solvent chemical shifts by the addition of solutes. Kudish, Wolf, and Steckel have continued their investigations into the properties of isotopic forms of water and have presented some experimental data on the density and viscosity of H217O at different temperatures.

The problem of obtaining a quantitative model for water remains, and some groups of workers have turned their attention to the most elementary interaction, viz. the water dimer. Investigations of this nature, in which the intermolecular potential is mapped, are of undoubted importance and are of particular relevance to molecular dynamic and in attempts to describe the properties of liquid water using statistical-mechanical approaches. The vibrational spectrum of water continues to attract both experimental and theoretical attention. Walrafen has continued’ his extensive Raman spectroscopic investigations and has examined the pressure dependence of the water spectrum, using his isotopic substitution technique. Work has also been presented describing an investigation into the behaviour of ice VI. The Raman spectrum of water has also been reinvestigated in the temperature range 263–363 K. Theoretical approaches to the problem of vibrations and structure of liquid water have been presented. Kell has examined the distribution function of water in an attempt to obtain a satisfactory model for the liquid. Other more general discussions have also been presented of attempts to quantify the water structure problem and its perturbation by solutes, and the paper by Franck on fluids at high temperatures and pressures has considerable relevance to this problem.

Relevant references on the properties of non-aqueous solvents have been given earlier, and others will be given in the section on non-aqueous-aqueous mixtures.

3 Thermodynamics of Solutions containing a Single Electrolyte

Theoretical Aspects. — There continues to be a considerable amount of work published each year on the thermodynamic properties of solutions, particularly when water is the solvent. Before surveying the recent experimental publications, mention will be made of the more recent theoretical approaches to ionic solutions.

In the last Report on Electrolytes reference was given to the important Monte-Carlo computations by Vorontsov-Vel’yaminov and El’yashevich and Card and Valleau. This latter work has recently been refined for a 1:1 electrolyte in a structureless solvent of dielectric constant 78.5 at 298 K. There have also been a number of attempts to improve the analytical approach to the Debye-Hückel theory using mean electrostatic potentials and by numerical solutions. Stokes has also pointed out the problem of the non-electrostatic term when a comparison between experimental and theoretical work is made.

There have also been some attempts to incorporate solvent effects in very refined theoretical approaches. More ‘chemical’ approaches have also been forthcoming. The work of Gurney has been seminal in the interpretation of the properties of solutions over the past twenty years and it is of considerable interest that attempts have been made to put the approach suggested by him onto a quantitative basis. Friedman has been particularly active in this respect (see also the discussions by Wen). As in all physico-chemical investigations of solutions, at finite concentrations, the principal role is played by the solute-solute intermolecular potential, Friedman has invoked the Gurney ideas and has represented the distance variation of this potential [u ij (r)] for the interaction of two spherical ionic species by

u ij(r) = (eiej) /εr + CORij + CAVij + GURij

The first term is the conventional Coulombic one, the second term is taken to represent the short-range, closed shell, contribution, and the third term represents the fact that the dielectric constant of the ions differs from that of the solvent in which they are immersed. The novel feature is the inclusion of the final term, which represents the contribution to the interionic potential from the necessary exclusion of solvent adjacent to ions as they form a contact ‘ion-pair’. This has been represented diagramatically by the ‘reaction’:

[ILLUSTRATION OMITTED]

There are many problems, both theoretical and practical, in treating a model of this nature since so many coefficients are unknown, even for simple monatomic ionic species. However, several sets of coefficients have been used in the expression for the intermolecular potential, and, by using previously tested statistical-mechanical approximations to make the transformation from the expression for the inter-molecular potential to the measured thermodynamic properties, some general features appear to be evident regarding the change in the solvent on transferring it from solute co-spheres to the bulk solvent. The problem of interrelating statistical-mechanical approaches to experimental properties has also been dealt with in considerable detail. Friedman and his co-workers have also considered the application of their approach to electrolyte mixtures, the interaction of non-electrolytes, and the interaction between electrolytes and non-electrolytes.

In a continuing series of papers Pitzer and his collaborators have developed a semi-empirical method, which will probably be much used, for representing the thermodynamic properties of both single and mixed electrolyte solutions. The basic expression with which they begin is a polynomial expression for the excess Gibbs function (Gex) in a system containing nw moles of a given solvent and ni moles of species i:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where f(I) and λij(I) are functions which are dependent upon the ionic strength and μijk is also notionally dependent on ionic strength, although this dependence is suppressed. It is apparent that the above equation is formally similar to those which have been used earlier if f(I) represents some form of the Debye-Hückel (electrostatic) contribution and λij (I) and μijk represent more-specific, short-range, ion–ion interaction terms. Different functional dependences of the f(I) term have been examined, including an expression allowing for the contribution to non-ideality from the finite size of the ionic species and also the expression suggested by Glueckauf. All of these terms contain one unknown parameter, which should have some relation to the sizes of the various ionic species. The terms representing more-specific interactions λij(I), μijk were transposed, so that they have the same form as those used in the virial expansion of non-ideal gases and non-aqueous solutions. For a particular electrolyte the expressions used bring in more adjustable parameters. In the initial paper the above formulation was tested using the experimental osmotic coefficients of a range of 1:1, 2:1, and 1:2 electrolytes over a somewhat limited molality range, so that the term representing triplet interactions between species could be suppressed. It was found that the best fit to the experimental data resulted from the following representations of the functional dependences of f and the second virial coefficient (B):

f = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

B = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

with b and α taking, respectively, the values 1.2 and 2.0. The terms β(o) and β(1) were dependent on the solute. The procedure was also extended to 6 molal solutions and the triplet interaction term empirically evaluated. The fit to the experimental data is certainly within the probable experimental error up to molalities of 6, using three adjustable parameters (β(o),β(1), and the triplet term) and the suggested procedure, does appear to be a useful way of representing experimental data. The problem which is not resolved is the meaning, if any, of the adjustable parameters. In later papers the interrelationships between parameters and their possible link with structure and the extension of the procedure to mixtures of electrolytes and solutions containing electrolytes which tend to associate have been considered.

The Robinson–Stokes hydration treatment has been extended by Högfeldt and applied, in a preliminary communication, to the activity coefficients of aqueous KCl solutions. Other empirical representations of activity behaviour have also been presented.

Activity and Osmotic Coefficients. — There have been several reports on thermodynamic properties of aqueous systems at 298 K. An experimental paper on the determination of vapour pressures has been published. The isopiestic method has been applied to NH4Br, methanesulphonic acid, Na dithionate, and Na2SO3 solutions by Covington and his co-workers, and data to high concentrations have also been obtained on iodic acid solutions. The same experimental technique has been used to NaBr, NaI, KF, CaCl2 solutions between 273 and 363 K. Platford has described an investigation on NaCl, KCl, CaCl2, Na2SO4, and MgSO4 at 273 K. Studies have also been reported on some salt solutions at 353 K. Vapour–liquid equilibria of aqueous NaCl solutions from 1 to 6 mol kg-1 and from 298 to 373 K, and of aqueous LiCl solutions from 1 to 18.5 mol kg-1 over the same temperature range, have been investigated. The vapour pressures of saturated BeSO4 solutions have been reported. Two extremely precise and elegant investigations on the vapour pressures of aqueous NaCl and aqueous KCl over a range of temperatures have been published. The first is the more comprehensive, and describes the determination of the vapour pressures of NaCl solutions from 4 mol kg-1 to the solubility limits in the temperature range 348–573 K; it complements the earlier work at lower molalities.

The freezing-temperature technique has been used to investigate the interaction of Na, K, Mg, and Ca ions with various anions in aqueous solutions. The same method has been used to determine the osmotic coefficients of aqueous CsCl and a series of tetra-alkylammonium bromide solutions. The activity coefficients and osmotic coefficients of aqueous Th(NO3)2 at different temperatures have been presented as part of a comprehensive study of those solutions. The activity coefficients of some Tb halides in water have been reported. An investigation, using Rb amalgam electrodes, of the activity coefficients of RbCl in aqueous solution has been published,’ and confirmation of the correctness of the activity coefficients of CaCl2 in water at 298 K has ensued from a study using electrodes that are responsive to calcium ion.

Enthalpies and Heat Capacities. — Investigations of enthalpy of dilution, from which relative partial molar enthalpies may be obtained, of the salts Na2SO4 Li2SO4 Ca(ClO4)2, Mn(ClO4)2, CO(ClO4)2, Ni(ClO4)2, La(ClO4)3, Ba(ClO4)2, tetra-ethanolammonium bromide, HBr, HI, and some alkali-metal halides in water at 298 K have been reported. Data have been published on some tetra-alkylammonium bromides in H2O and D2O. The enthalpies of dilution of aqueous NaCl solutions have been determined over the temperature range 313–353 K and from approximately 0.1 to 6 mol kg-1, and a study of aqueous Bu4N butyrate as a function of temperature has been made. Des-noyers and co-workers have described’ a calorimeter suitable for determinations of enthalpy of dilution.

A rather interesting investigation of the enthalpy of dilution at 308 K of several salts in N-methylacetamide has been supplemented by an investigation of the heat of dilution of Bu4NBr in mixtures of this solvent with water. A very marked dependence of the excess enthalpy on the solvent composition indicates that relatively small amounts of N-methylacetamide induce a disruption of the hydrophobic interaction between the ionic species. In a similar vein, de Visser and Somsen have reported experimental data on the enthalpy of solution of Bu4NBr in a series of mixtures of solvents with water and in mixtures of non-aqueous solvents. The degree of dependence of the enthalpy on the mole fraction of solution depends markedly on the solvent mixture used, and no generalized effect is observed for systems in which water is one of the components. Results have also been given of the enthalpy of solution of some salts in NN-dimethylformamide (DMF) and in this solvent when a small amount of water had been added. The enthalpies of solution of a series of salts in dioxan–water mixtures over somewhat limited solvent compositions have been presented.

(Continues…)Excerpted from Electrochemistry Volume 5 by H. R. Thirsk. Copyright © 1975 The Chemical Society. Excerpted by permission of The Royal Society of Chemistry.
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