8 Electrolyte Solutions By H. P. BENNETT0 Department of Chemistry Queen Elizabeth College Campden Hill Road. London W8 7AH 1 Introduction At the present time increasing numbers of books and journals make it a daunting task to broaden one’s chemical knowledge even marginally beyond specialized personal interests and this introduction is therefore clouded by a recent protest’ against the proliferation of journals which gains the sympathy of the writer but is unlikely to influence publishers. There are encouraging signs however that the output of material (which like fuel consumption cannot increase indefinitely) is accompanied by some fortunate rationalization between closely related topics in different corners of Physical Chemistry. This chapter attempts to draw atten- tion to these desirable cross-links and hopefully maintains the critical approach adopted by the authors of previous report^.^.^ No attempt is made to provide a complete coverage of the literature a task which has been very adequately performed in the recent Specialist Periodical but books of special interest which have since appeared are briefly mentioned.The second volume of the timely series6-* on ‘Water’ deals at length with water in crystalline hydrates and maintains the high standards of Volume 1. A short chapter by Franks on solutions of simple non-electrolytes illustrates the limita- tions in our understanding of even these the simplest of aqueous solutions. Volume 3 is of special interest since it covers the properties of electrolyte solutions.A variety of interesting papers presented at a Symposium held in honour of Frank appears in a double issue of the Journal ojSolution Chemistry,together with reveal- ing discussion^.^ The well-known series ‘Modern Aspects of Electrochemistry’ Chem. in Britain. 1974 10 32. A. D. Pethybridge and J. E. Prue Ann. Reports (A) 1968 65 129. D. R. Rosseinsky Ann. Reports (A) 1971 68 81. A. K. Covington and T. H. Lilley in ‘Electrochemistry’ ed. G. J. Hills (Specialist Periodical Reports) The Chemical Society London 1972 Vol. 2. T. H. Lilley in ‘Electrochemistry’ ed. G. J. Hills (Specialist Periodical Reports) The Chemical Society London 1973 Vol. 3. ‘Water A Comprehensive Treatise’ ed. F. Franks Plenum Press New York Vol. 1 ‘The Physics and Physical Chemistry of Water’ 1972.Ref. 6 Vol. 2 ‘Water in Crystalline Hydrates; Aqueous Solutions of Simple Nonelec- trolytes’ 1973. ’ Ref. 6 Vol. 3 ‘Aqueous Solutions of Simple Electrolytes’ 1974. J. Solution Chem. 1973 2 95-356. 223 224 H. P.Bennett0 continues to emphasize the properties of the electrolyte-electrode interface as the focal point of electrochemistry. The latest issue” gives space to an interest- ing survey by Mandel on a new interdisciplinary subject bioelectrochemistry. The scope this offers and a measure of its progress may be judged from the collected papers of the first International Symposium.’ la Proceedings of a second meeting held in October 1973 are expected to be available in 1974.lIb The literature reflects the growth of interest in non-aqueous and mixed solvent systems; this is most noticeable from the increased number of references cited in the ‘Electrolyte Solutions Bulletin’,’2 which continues to provide a valuable survey.Non-aqueous systems are discussed in the accompanying report l3 by Cox and will not be dealt with specifically though some overlap is inevitable. However a recent specialist text ‘The Physical Chemistry of Organic Solvent Systems’,I4 deserves our interest because of its coverage of many theoretical aspects of electrolyte solutions. Well-written extended accounts are presented of thermodynamic measurements acid-base properties conductance and spectro- scopy. Shorter discussions on solvent effects in reaction kinetics and organo- electrode processes are likely to be soon outdated in view of the pace of recent developments.The first volume of a monumental reference series on ‘Non-aqueous Electrolytes’ by Janz and Tomkins’ lists conductance data and contains a valuable section on purification methods. Volume 2 in preparation will contain the summarized results of e.m.f. studies. Those who are more practically orientated will also be interested in the Proceedings of a Symposium on the subject of ‘Ion Selective Electrodes’ which have appeared in an inexpensive book form.16 The contributions mainly from Eastern Europe are in English with editing by Pungor. A revised edition of Bates’ standard work’ ’on pH expands those chapters dealing with the establish- ment of pH scales in non-aqueous and mixed solvents and with acid-base phenomena in these media.The famous Weissberger series has added two volumes on ‘Electrochemical Methods’;’’ in part IIAreadable up-to-date chap- ters are devoted to potentiometric methods (redox and pH methods and ion- selective electrodes) conductance transport numbers polarography and related lo ‘Modern Aspects of Electrochemistry’ No. 8 ed. J. O’M. Bockris and B. E. Conway Butterworths London 1973; cf. D. M. Draiic. in ‘MTP International Review of Science Physical Chemistry,’ Butterworths London 1973 Series One Volume 6. I ’ (a) ‘Biological Aspects of Electrochemistry’ (Proc. of 1st C.I.T.C.E. International Symposium Rome 1971) ed. G. Milazzo P. E. Jones and L. Rampazzo Birkhauser Verlag Basle 197 1 ; (b)Bioelectrochemistry and Bioenergetics 1974 1.I * ‘Electrolyte Solutions Bulletin’ ed. A. K. Covington University of Newcastle Library. l3 B. G. Cox Ann. Reports (A) 1974 p. 249. ‘Physical Chemistry of Organic Solvent Systems’ ed. A. K. Covington and T. Dickin- son Plenum Press London 1973. Is ‘Nonaqueous Electrolytes Handbook’ G. J. Janz and R. P. T. Tomkins Academic Press New York 1972. l6 ‘Ion Selective Electrodes’ ed. E. Pungor Akademiai Kiado Budapest 1973. I ’ R. G. Bates ‘Determination of pH ; Theory and Practice’ Wiley-Interscience New York 1973 2nd edn. ‘Techniques of Chemistry’ Vol. 1 ‘Physical Methods of Chemistry’ Part IIA ‘Electro- chemical Methods’ ed. A. Weissberger and B. W. Rossiter Wiley-Interscience New York 1971. Electrolyte Solutions 225 electroanalytical techniques.In a similar vein the first volume of a series’’ entitled ‘Techniques of Electrochemistry’ describes the measurement of reversible electrode potentials overpotentials double-layer and adsorption phenomena surface area and porosity and electrode processes. These volumes do much to remedy the lack of authoritative summaries on the techniques of electrochemistry. Finally since the electrochemistry of future generations depends to some extent on the education given in this one some notes on a few of the many recent texts may be of interest. Whereas the importance of mathematics as an integral part of chemistry has been recognized,” the gap between the mathematical grasp of the average student and that which writers would like them to have is much in evidence.Such is the case in the finely produced but difficult new edition of Moore’s ‘Physical Chemistry’,’ where the treatment of electrochemistry is commendable but the omission of the concise summary of ‘ionic equilibria’ from the previous edition is regretted. Bockris continues to add to his now formidable output. With Fredlein he has compiled a stimulating monograph ‘A Workbook of Electrochemistry’,’’ which leans towards the more recent develop- ments of the subject. It will provide insight and amusement to research workers and a challenge to the more sophisticated undergraduate. A more conventional work ‘Electrochemical Science’,’ reproduces much of the material of ‘Modern Electr~chernistry’’~ in a shorter but still readable form.It has the authors’ characteristic emphasis on the chemistry of electrode processes and contains more than a suggestion of propaganda. A short tidy text25 in the Oxford Series contains a good summary of the chemistry of molten salts but surprisingly gives only passing mention to the solvation of ions. 2 Structural Aspects The structural properties of water6 and simple sol~tions~*’~ continue to receive attention. While new attempts to describe the pure liquid favour the cell” and lattice’* models and the importance of quantum effects in hydrogen bonds is ~tressed,~’ a good description of the heat capacity is still lacking. Walrafen continues his experimental approach to the problem with a study of the weak l9 ‘Techniques of Electrochemistry’ ed.E. Yeager and A. J. Salkind Wiley New York 1972 Vol. 1. ’O C. A. Coulson Chem. in Britain 1974 10 16. 2’ W. J. Moore ‘Physical Chemistry’ Longmans London 1973 5th edn. (U.K.). 22 J. O’M. Bockris and R. A. Fredlein ‘A Workbook of Electrochemistry’ Plenum Press New York 1973. 23 J. O’M. Bockris and D. M. DrBziC ‘Electrochemical Science’ Taylor and Francis London 1972. 24 J. O’M. Bockris and A. K. N. Reddy ‘Modern Electrochemistry’ Plenum Press New York 1970 Vols. 1 and 2. 25 J. Robbins ‘Ions in Solution (2); An Introduction to Electrochemistry’ Oxford University Press Oxford 1972. * ‘Water and Aqueous Solutions Structure Thermodynamics and Transport Proper- ties’ ed. R. A. Horne Wiley-Interscience New York 1972.l7 0.Weres and S. A. Rice J. Amer. Chem. SOC.,1972 94 8983. D. A. Lavis J. Phys. Chem. 1973 6 1530; D. E. O’Reilly Phys. Rev. (A) 1973 2; 1659. 226 H. P. Bennett0 Raman bands in water.29 The controversial non-electrolyte urea has been termed a ‘structure breaker’ on the evidence3’ of its effect on the activation parameters for aqueous fluidity but a study by Lucas31 of hydrophobic hydra- tion suggests that the variations of solute partial molar properties arise from the properties of the pure liquid rather than from solute structural effects. Clearly some separation into specific hydrogen-bonding effects and hydrophobic effects would be desirable. Separation of different hydrophobic effects is evident from a of the heat capacities of bolaform electrolytes in H20 and D,O; the AC; values are related to the number of carbon atoms between nitrogen centres.The formation of weak hydrogen bonds between neon and water33 may be of more than novel interest in view of the experimental scope of molecular beam electric resonance spectro~copy.~~ Earlier reports35 of structure-induced effects of dissolved gases on the pH of water have now been attributed to the presence of CO in the solutions,36 and the apparent failure of Henry’s law in solutions of mixed gases,37 has been q~estioned.~~ Praises to the scientific method were sung at the funeral of ‘anomalous water’ (p~lywater)~~ which has been removed to the area of silicate chemistry by its dis~overer,~’ but the spectre of thermal anomalies lives on ;a reputable experimental school has detected a sizeable ‘kink’ in the temperature dependence of the energy-volume coefficient for aqueous solutions.41 An interesting stage of development has been reached when fine probes (e.g.spectro~copy,’~*~~.~~ neutron ~cattering~~) ellip~ometry,~~ are revealing details of the molecular structure and dynamics in solutions yet it remains a problem to fit the information into a coherent theory compatible with thermodynamic res~lts~~,~’ and consistent with statistical mechanical appro ache^.^^.^^ Attempts 29 G. Walrafen and L. A. Blatz J. Chem. Phys. 1973 59 2646; also ref. 9. 30 J. L. Macdonald J. Serphillips and J. J. Guerrera J. Phys. Chem. 1973 77 370. 3’ M. Lucas J. Phys. Chem. 1973,77 2479.32 J. A. Burns and R. E. Verrall J. Solution Chem. 1973 2 489; see also F. Franks D. S. Reid and A. Suggett in ref. 9. 33 M. Losonczy J. W. Moskowitz and F. H. Stillinger J. Chem. Phys. 1973 59 3264. 34 T. R. Dyke B. S. Howard and W. Klemperer J. Chem. Phys. 1972 56 2442. 35 E. M. Holleran J. T. Hennessy and F. R. LaPietra J. Phys. Chem. 1967 71 3081. 36 G. H. Fricke R. L. Carpenter and R. Battino J. Phys. Chem. 1973,77,826. 37 D. M. Maharajh and J. Walkeley J.C.S. Faraday Z,1973 69 842. 38 A. L. Myers and J. A. Quinn Nature 1972 239 32. 39 L. Allen New Scientist 1973 59 376; cf. J. Finney ibid. p. 382. 40 B. V. Djerjaguin and N. V. Churaev Nature 1973 244 430; cf. ibid. 1973 245 343. 41 I. Lee and J. B. Hyne Cunad. J. Chem. 1973,51 1885. 42 Ref.14 Chap. 4. 43 M. J. Blandamer ‘Introduction to Chemical Ultrasonics’ Academic Press London 1973. 44 W. K. Paik in ‘MTP International Review of Science Physical Chemistry’ Butter- worths London 1973 Series One Volume 6. 45 P. S. Leung and G. J. Safford J. Solution Chem. 1973 2 525. 46 H. S. Harned and B. B. Owen ‘Physical Chemistry of Electrolytic Solutions’ Reinhold New York 1958. 47 R. A. Robinson and R. H. Stokes ‘Electrolyte Solutions’ Butterworths London 2nd edn. 1959. 48 H. L. Friedman in ‘Modern Aspects of Electrochemistry’ no. 6 ed. J. O’M. Bockris and B. E. Conway Butterworths London 1971 ; H. L. Friedman Chem. in Britain 1973 9 300. 49 ‘Ionic Interactions’ ed. S. Petrucci Academic Press New York 1971 Vol. 1. Electrolyte Solutions 227 to accommodate both the solvational and interionic aspects of such a theory inevitably lead to the question ‘how structured are electrolyte solutions?’ which not only invites the dangers of looking at one sort of structural index in isolation but involves difficulties of definition.Perhaps the best descriptions are those thermodynamic parameters (the more the better) which render unnecessary the terms ‘structured’ ‘degrees of structure’ and ‘structuredness’. Even ‘struc- ture’ can lead to ambiguity. An explicit meaning,” ‘the mutual relation of the constituent parts of a whole as determining its peculiar nature or character’ might be used together with a hypothetical scale for simple substances fixed by the perfectly ordered crystal at one extreme and the completely random gas at the other.Unfortunately these states do not ordinarily exist; the complex electronic structures of solvent molecules give rise to the intermolecular forces which in turn determine the familiar bulk physical properties of a medium.” Meaningful correlation of solvent structural effects may therefore require reference to some system of corresponding states and moves in this direction are already to be found in the field of reaction kinetic^,'^-'^ where AH* -AS* relations are linked with solvent properties. The influence of solvent structure often appears to be minimized at high temperatures where fluid properties tend to converge.54 Reports of AH -AS correlations in the thermodynamic properties of electrolytes are also ~ommon,~*~~-~’ and may be further clarified now that investigations other than those in water at 298 K and 1 atm are on the increase.Some of the recent work at high temperatures and pressures has been inter- preted with a surprising simplicity. For example Norths8 has presented a treatment for equilibrium constants in aqueous solution in which the hydrated solutes are considered to be incompressible and the pressure dependence of AVO is presumed to be proportional to the change in number of solvated mole- cules released in the reaction. A simple relation accounts for the ionization constants up to 12000atm and improves on earlier equations which show deviations above 2Watm. The derivation of solvation numbers from com- pressibilities and ionic vibration potentials however has led to a controversys9 which shows that these coefficients continue to be usefully picturesque6’ but difficult to define unambiguously.Shorter Oxford English Dictionary. ” G. C. Maitland and E. B. Smith Chem. SOC.Rev. 1973 2 181. ” C. E. Waring and P. Becher J. Chem. Phys. 1947 15 488. 53 H. L. Frisch T. A. Bak and E. R. Webster J. Phys. Chem. 1962 66 2101. ’4 H. P. Bennett0 and E. F. Caldin in ref. 9; see also C. M. Criss ref. 14 chap. 2 ’’ E. M. Arnett J. Phys. Chem. 1972,76 2474. s6 J. H. Norman P. Winchell and R. J. Thorn Inorg. Chem. 1971 10 2365. 57 R. Lumry and S. Rajender Biopolymers 1970 9 1125; D. J. G. Ives and P. Marsden J. Chem. SOC.,1965 649. 58 N. A. North J. Phys. Chem. 1973 79 931; CJ L.B. Yeatts and W. L. Marshall J. Phys. Chem. 1972 76 and refs. therein. 59 J. E. Desnoyers J. Phys. Chem. 1973,77 567. 6o J. O’M. Bockris and P. P. S.Saluja J. Phys. Chem. 1972 76 2140. 228 H. P.Bennett0 3 Electrolyte Solution Theory The theory of Debye and Hucke16’ has reached and passed its fiftieth year with little comment. As a vehicle for the extrapolation and correlation of data it has quietly become the cornerstone of our understanding of electrolyte solutions but the present position is here examined in view of the active challenge of modern alternatives. Debye-Huckel Theory.-We can profitably look back on the developments over the past half-century noting’some aspects which may be unfamiliar to many who are usually concerned only with the ‘route to infinite dilution’.Like jazz and short skirts many ideas of the early twenties are in good trim but it appears that some problems remain unresolved. The concept of non-ideality resulting from long-range forces between ions in solution had been considered by many people before 1923 but did not readily gain acceptance in the face of heavy opposition led by Arrhenius. Milner’s (1912) account62 of the electrostatic virial though later found to be fundamentally correct,61 was not popular on account of the complex numerical methods used. A period of confusion and controversy then followed the appearance in 1918 of Ghosh’s ill-fated lattice theory which described the concentration dependence of the osmotic coefficients and conductance behaviour in terms of a simple cube-root law.63 The theory was inadequately formulated and contained errors of fact and logic ;by 1923 it had been discounted and only its postulate of explain- ing electrolyte non-ideality in terms of coulombic effects is retained in Debye’s theory.In the years 1918 -1923 which S~atchard~~ described as a ‘swear word’ period an effective execution of the lattice theory was performed principally by Partington Kraus Kendall and (inevitably) Arrhenius6’ Bjerrum at first made use of the cube-root law,66 but little mention of it was made in the literature until Frank re-examined the empirical basis of the cube-root law and put forward his novel views on the ‘quasi-lattice loud'.^^*^* The way had been cleared for Debye’s theory by the keen interest in some important but empirical work during the years preceding.Lewis and Randall69 had established ionic strength as an ionic concentration scale and Bronsted’s principle of specific interactions7’ underlined the importance of the effects on a given species owing to ions of the opposite sign. (The limitations of the principle “ P. Debye and E. Huckel Phys. Z. 1923,24 185; ‘Collected Papers of P. J. W. Debye’ ed. R. M. Fuoss Interscience New York 1954. ’’ R. S. Milner Phil. Mag. 1912 23 551 ; Trans. Faraday SOC. 1919 15 148. 63 J. C. Ghosh J. Chem. SOC.,1918 113 449 707. 64 G. Scatchard Chem. Rev. 1933 13 1. 65 H. M. Dawson Ann. Reports 1922 19 15. 66 N. Bjerrum Z. Elektrochem 1918 24 321 ;Z. anorg. Chem. 1920 109 275.’’ H. S. Frank and P. T. Thompson J. Chem. Phys. 1959,31 1086; see also R. A. Robin-son and R. H. Stokes in ref. 47. 68 ‘Structure of Electrolytic Solutions’ ed. W. J. Hamer Wiley New York 1959. 69 G. N. Lewis and M. Randall ‘Thermodynamics and the Free Energy of Chemical Substances’ McGraw-Hill. New York. 1923. ’’ J. N. Bronsted and V. K. La Mer J. Amer. Chem. SOC.,1924,46 1098 and refs. therein. Electrolyte Solutions have more recently been re~ealed.~’) Debye’s more rigorous approach achieved its full impact following the appearance of Noyes’ critical English language treatment,72 and in the next ten or so years the theory was applied to many dif- ferent properties of solutions. These developments may be traced in the Annual Reports for this period.65,73-75 The testing of a limiting law requires accurate data extending to very low concentrations but the challenge to experimenters was accepted and amongst the most searching of critical investigations were those of La Mer and ~o-workers,~~,~~ whose solubility determinations were extended to moll-solutions.The results confirmed that in general the limiting law was satisfactorily approached for 1 1 electrolytes in aqueous and non-aqueous solvents and at elevated temperatures but many more stringent tests did not stop the seal of approval being given at a meeting to mark the ‘coming of age’ of the theory.77 At this time the mathematical inconsistency of the Poisson-Boltzmann equation used by Debye was clearly demonstrated by On~ager,~~ and deserves some amplifi~ation.~~,~~*~~~~’-~~ The Poisson equation (1)* is derived from Coulomb’s law and requires that electrostatic fields should be superimposable to give a charge density p(r).4 is (1) * Confusion over units and concentration scales has sometimes led to inconsistencies in Debye-Huckel calculations (e.g. for limiting slopes). SI units are preferred and the following type of formulation is recommended. A is the distance of separation of two point charges which gives a coulombic interaction energy IEl = 2kT joules (i.e. the Bjerrum distance) and A and B are the familiar non-SI constants of the theory where E~ is the permittivity of a vacuum and E the relative permittivity .(or dielectric constant) of the solvent. 71 R. H. Wood and R.W. Smith J. Phys. Chem. 1965,69,2974. 12 A. A. Noyes J. Amer. Chem. SOC. 1924,46 1080 1098. 13 J. E. Coates Ann. Reports 1925,22 27; J. E. Coates and J. A. V.Butler Ann. Reports 1926 23 21 ;H. Hunter Ann. Reports 1927 24 22. 74 J. H. Wolfenden Ann. Reports 1932 29 21. 7s R. P. Bell Ann. Reports 1933 30 21. 76 V. K. La Mer C. V. King and C. F. Mason J. Amer. Chem. SOC. 1927 49 410; J. W. Williams Chem. Rev. 1931 8 303. 71 Chem. Rev. 1933 13 1. 78 L. Onsager Chem. Rev. 1933 13 73; CJ R. H. Fowler Proc. Cumb. Phil. SOC.,1925 22 861. 79 F. Vaslow ref. 26 Chapter 12. 80 B. E. Conway in ‘Physical Chemistry An Advanced Treatise’ ed. H. Eyring Academic Press New York 1970 Vol. 9B. 81 G. Braunstein in ref. 49. 230 H.P. Bennett0 the average potential at any point. Strictly speaking this equation is only valid for a system of charges at rest. The charge density (p = &eni) is found from the Boltzmann equation in the form n = n exp [ -W(r)/kT] (2) where W(r)is the potential of mean force and no is the average number of ions at any point in the bulk of solution. Equations (1) and (2) are combined to form the Poisson-Boltzmann (PB) equation The relation between charge and potential in equation (2)is non-linear and W(r) cannot be identified with the average electrostatic potential 4 of equation (1); fluctuations in W(r)give exponential movements of ions rather than linear ones as required by equation (l).79The combination of equations (1) and (2) also leads to the nonsensical result that the electrostatic effects of two ions k and 1 do not have the symmetrical reciprocal relationship required for thermodynamic consistency (4) (2) = (2) Most authorities agree that for a sufficiently dilute solution the PB equation may be linearized thus allowing 4 to be used in the calculation of average charge distribution.Even in dilute solutions however there is a finite probability that ions will approach one another to within a distance where Ze4 > kT and it is therefore only at zero concentration that the equality of Zec$ with W is valid and the inconsistency disappears [equation (5)]. The linearization should be regarded as a necessary requirement of the primitive Debye-Hiickel model. W lim [exp( -W/kT)]= 1 N 1 -(5) m-0 kT The inclusion of the ion-size parameter ‘a’ and higher terms of the expansion lead in the simplest case of a 1 1 electrolyte to equation (6),for the activity coefficient in which X and Y terms are functions of IC and a and the cubic and lny = -A,Born*(l + aBOrnf)-’+ -2 -2Y3) + -2 (2 )’(? (2 )5 higher terms are customarily neglected unless E is small.** Experimental results are better fitted by judicious adjustment of a a catch-all correction for close- range and ‘hard core’ effects by including the higher terms and by use of an additional linear parameter in m.79 These methods are to be preferred to the use 82 T.H. Gronwall V. K. La Mer and K. Sandved Phys. Z. 1929,29 358. Electrolyte Sohtions 231 of polynomial fits which obscure the theoretical basis of the extrapolation and sometimes conceal experimental inaccuracies but not too much significance can be attached tothe value of a.The certainty of values of a derived from experi- mental ‘best fits’ depends greatly on the accuracy of the res~lts.~~~*~ None of these practically expedient procedures solves the fundamental problem however nor does the assumption of Bjerrum ion-pairing which avoids the inconsistency by arbitrarily defining the onset of association in terms of A (even when r > A, Ze+/k T need not be small). The inconsistency of association constants obtained from different theories and from experiment has led recent investigators85986 to refine the ion-pairing concept in relation to the Debye-Huckel equation.One treatment shows that a degree of dissociation at infinite dilution can be expressed as where b is the Bjerrum parameter defined by The only arbitrary parameter is a so that for purely electrostatic attraction no other assumptions are required by the model. Nevertheless all extensions to the Debye-Huckel equations must be regarded as semi-empirical and since Onsager and many others have failed to find a satisfactory solution there would seem to be little hope for the primitive model although it continues to attract attention.87i88 It would be surprising if experiment did not reveal evidence of the theoretical limitations mentioned above but the only serious early misgivings were those arising from Lange’s determinations of heats of solution (AHsol)and dilu- ti~n.~**’~*~’ The limiting law is approached but not convincingly and large deviations from the limiting slope plus the specificity of effects for different ions could not be adequately accounted for.The effect was attributed to a net decrease in long-range ion-solvent interaction possibly the first time that the two types of interaction had been linked. A thorough examination of tests of the theory reveals that many critics have been generous especially though not exclusively for cases involving non-symmetrical and higher valency electrolytes and solvents of low er for which the consequences of the inconsistency of the PB equation are more serious.80 To state that the theory is obeyed ‘less well’ for these cases is an understatement only the sign of the effects can be predicted with any 83 T.Mussini Chimica e Zndustria 1973,55 637. 84 H. P. Bennett0 and J. J. Spitzer J.C.S. Furaday Z 1973 69 1491. H. Falkenhagen and W. Ebeling in ref. 49. 86 H. Yokoyama and H. Yamatera Chem. Letters 1973 337. C. W. Owthwaite Mol. Phys. 1972 21 and refs. therein. A. S. Blokhin and G. A. Martynov Electrochimiya 1973 4 494. E. Lange and A. L. Robinson Chem. Rev. 1931,9 89. 232 H. P. Bennett0 ~onfidence.~~ Even when conditions are favourable the slope of an extrapolation may not always approach the theoretical limiting value the line may be linear but the slope in error or the discrepancy can be greater for larger ions when the approximation should be most appropriate.That the ion-size or other parameters may provide a better extrapolation does not affect the argument that the law is less satisfactory than one might expect for dilute solutions where KU << 1 even allowing for experimental error. It has recently been ~tressed~*~*~~ that the excess functions for electrolytes are subject to the 'compensation law'57990 through which enthalpic and entropic contributions to a free energy function tend to cancel. If this is also true of the coulombic contributions AH and AS functions should provide a better test of interionic theories. Thus the temperature coefficients of activity (partial molal heat contents) are more sensitive than the y values themselves. Clear evidence of odd behaviour is described by Harned and and we may look for examples in recent calorimetric work in water and in mixed and non-aqueous solvents.Many instances of satisfactory agreement with theory may be fo~nd,~'-'~ have measured but there are notable exceptions. Chang and Cri~s~~ AH,, for NaClO in NN'-dimethylformamide in the range 10-75 "C. At lower temperatures the extrapolations are satisfactory but in the higher range the observed limiting slope reaches nearly four times the theoretical value. Similar discrepancies are noted for solution of bivalent salts in solvents of high dielectric constant,95 reminiscent of earlier results in liquid ammonia.96 (In this solvent it is difficult to rationalize y+ results from e.m.f. studies97 with ion-pairing invoked in the interpretation of conductance beha~iour.~~ The slope of the AH,, us.rn) plot rapidly increases in dilute solutions and it must change direc- tion dramatically in order to approach limiting law behaviour ;99 further accurate examination perhaps employing flow microcalorimetry,' O0 would be desirable.) Campbell and Bhatnagar"' have measured AH,, for NaClO and dioxan- H,O mixtures and find that the experimental concentration dependence crosses the positive theoretical slope as the dioxan concentration is increased. Near the 50% composition it changes sign and in 70% dioxan it is markedly negative. 90 D. J. G. Ives and P. Marsden J. Chem. SOC.,1965 649. 91 W. L. Marshall and R. Slusher J. Chem. Thermodynamics 1973 5 189. 92 D. D. Ensor and H. L. Anderson J. Chem. and Eng.Data 1973 18 205. 93 C. F. Boudreau and C. A. Wulff J. Chem. Thermodynamics 1970 2 125. 94 S. Chang and C. M. Criss J. Solution Chem. 1973 2 457; see also A. S. Levine and S. Lindenbaum J. Solution Chem. 1973 2 445; C. de Visser and G. Somsen J.C.S. Faraday I 1973 69 1440. 95 A. Finch P. J. Gardner and C. J. Steadman J. Phys. Chem. 1971,75 2325. 96 S. R. Gunn and L. C. Green J. Phys. Chem. 1960 64 1066. 97 J. Sedlet and T. De Vries J. Amer. Chem. SOC.,1951 73 5808; and ref. 41. 98 V. F. Hnizda and C. A. Kraus J. Amer. Chem. SOC.,1949.71 1565. 99 Such a change seems unlikely in view of a comparable picture for the solubilities of salts at very low ionic strengths; see V. J. Anhorn and H. Hunt J. Phys. Chem. 1941 45 35 1. loo J.-L. Fortier P.-A.Leduc P. Picker and J. E. Desnoyers J. Solution Chem. 1973 2 467. Io1 A. N. Campbell and 0.N. Bhatnagar Canad. J. Chem. 1971.49 217. Electrolyte Solutions 23 3 The AH,, us. mf plot shows a minimum at mf = 0.6 and the proposition is made that dioxanation of ions decreases in favour of hydration as the concentration is increased. This unusual effect calls for investigation at lower concentrations and suggests that the interdependence of interionic effects and structure in a mixed solvent is greater than has been previously supposed. It also shows that much care must be exercised in using extrapolation procedures. The alkylammonium halides' O2 are a class of electrolytes which appear to exhibit 'non-electrical attractive forces' in ~olution.~'~' Recent AH,, results illustrate the variety of O3 concentration dependences in H20'049'05 and in N-methylacetamide (NMA),'" while the extrapolation of apparent molal values (4")is found to be similar in H20,106.107 NMA and f~rmamide.''~ The evidence does not bear out earlier well-supported interpretations invoking water-structure,"' but again might appear to connect the coulombic and structural contributions and point to an interpretation in terms of a 'statistical lattice' model.'09 Wood and Belkin' lo find low values for excess enthalpies and entropies of tetraethanolammonium bromide in water in the range 0.5-3m by comparison with tetrapropylammonium bromide.The substitution of hydroxy-groups for terminal methyl groups results in a drastic change of properties and is attributed to the destruction of hydrophobic hydration ;the solvation interactions thus appear to be predominant in these concentrated solutions.It is clear from past and recent evidence that deviations from the Debye- Hiickel law cannot unambiguously be attributed to solvation or ion-association effects. Debye6' always emphasized the limiting character of his law but he believed' ' the shortcomings of his simple coulombic description were due to non-coulombic effects. But though these effects may well be important there seems to be enough theoretical and experimental evidence to suggest that the coulombic picture provided for moderately dilute solutions is an incomplete one and it may be argued that in consequence many assignments of ion-pairing and structural effects of ions are questionable.A pessimistic view is that the descrip- tion of the effect of ions in the solution on a particular ion is only correct when there are no ions present or that the theory starts correctly in the limit of infinite dilution and gets steadily worse. Frank's assessment that the linearized PB equation cannot realistically describe the distribution of 1 1 electrolytes in solutions more concentrated than 0.001m,applies the 'limiting axiom' to the 'real' solution and poses the question 'can the model describe any real solution?' Io2 T. S. Sarma and J. C. Ahluwalia Chem. SOC.Rev. 1973 2 203; W.-Y. Wen ref. 26 chap. 15. '03 G. Kelbg Z. phys. Chem. (Leipzig) 1960 214 8 26 141 153. J. Falconi Ph.D.thesis University of Delaware 1972; see W. Y. Wen J. Solution Chem. 1973 2 253. Io5A. S. Levine and R. H. Wood J. Phys. Chem. 1973,77 2390. lo6 F. Franks and H. T. Smith Trans. Faraday SOC.,1967 63 2586. lo' R. W. Kreis and R. H. Wood J. Phys. Chem. 1971 75 2319. Ref. 7 p. 40. log Ref. 46 p. 367. 'lo R. H. Wood and F. Belkin J. Chem. and Eng. Data 1973 18 184. ' P. Debye in 'Electrolyte Solutions' ed. B. Pesci Pergamon Oxford 1972. 234 H. P. Bennett0 This opinion is made more palatable by the existence of alternative approaches (see ref. 112 and sections below) and does not imply that the primitive model has nothing further to offer. Several lines of investigation show that a consistent merging of equations (1) and (2) must produce an ill-defined oscillating solu- for 4 at some high concentration when KU -1-2 which might ti~n'~*"~~''~ describe the onset of quasi-lattice behavio~r~~,~' or discontinuities in solution proper tie^.^^ Another possibility is that in a real solution the atmosphere- potential near an ion is dominated by the nearest ions may be of positive or negative sign and has non-spherical symmetry.This would require a general- ized Poisson law of the form (9),which could provide more meaningful solutions v2@ = fK2$ (9) than the PB equation. In replacing equation (9)by equation (3),two tacit assump- tions are made which are glossed over in most discussions. The assumption of spherical symmetry allows the field around an ion to be the same in all directions so that it is a function of the distance and not the direction;'15 this rules out discreteness of charge6' in the ionic atmosphere.The assumption of one partic- ular sign denies the possibility of lattice formation. Neither assumption seems to be obvious or logical and in making the simplification it appears that a work- able solution has been trapped in the PB equation which in its linearized form imposes an idealized model on the three-dimensional structure. To conclude the problem which remains is not the one which Debye and Huckel tackled magnificently to produce an attractively simple limiting law and an eminently applicable picture of the ionic atmosphere ;rather it is to find an alternative for the concentration range of practical importance.'' Statistical Mechanical Calculations.-By comparing the calculated thermodyna- mic properties of model solutions with the thermodynamic excess functions of real aqueous solutions it is possible to reach detailed conclusions about the contributions of solvation to interionic effects and to other solute-solute forces.',' '791 '* No attempt is made here to discuss the many recent results in this field but a particularly interesting summary by Rasaiah' l9 is recommended. In simple terms the method sets out to calculate the potential of average force W(r),represented by the sum of pair potentials for all configurations.'20 For ions k I these pair potentials are represented by an equation of the type (lo) I" D. G. Hall J.C.S. Faraday 11 1973 69 975. F.H. Stillinger and R. Lovett J. Chem. Phys. 1968 48 3858. J. C. Rasaiah D. N. Card and J. P. Valleau J. Chem. Phys. 1972 56 248; J. C. Rasaiah ibid. p. 3071. I ' Ref. 46 p. 47. l6 W. D. Bancroft J. Amer. Chem. SOC.,1926 48 94. I H. L. Friedman 'Ionic Solution Theory' Wiley-Interscience New York 1962; H. L. Friedman C. V. Krishnan and C. Jolicoeur Ann. New York Acad. Sci. 1973 204,79. I l8 R. 0. Watts in 'Statistical Mechanics' ed. K. Singer (Specialist Periodical Reports) The Chemical Society London 1973 Vol. 1 p. 56. 11' J. C. Rasaiah in ref. 9. J. E. Mayer J. Chem. Phys. 1950 18 1426. Electrolyte Solutions 235 in which the terms on the right are the respective contributions from long-range (coulombic) and short-range interactions.In the derived binary distribution function the first term is expressed as an expansion in (ekel/4mO~,r) which in its first approximation yields the Debye-Huckel limiting law directly. Without provision for the short-range repulsive forces however the higher approximation of the expansion is divergent so that the method faces a situation paralleled by the use of a in the Debye-Huckel theory and can never be entirely rigorous.’ 2’ 9122 The sensible solution of the equations requires evaluation of the second ‘hard- core’ term of equation (lo) which caters for the effects of solvation solvent 4kdr) = okl(r) + (10) structure ionic polarizability quantum-mechanical repulsions etc. and it is in the calculation of these contributions from reasonable physical models that many recent advances have been made.The concepts of structural effects of ions on the medium are incorporated by considering the properties of the solvent co-spheres’ 23*124 which surround each ion. When overlap of co-spheres occurs the sum of the co-sphere volumes is reduced; the return of a portion of solvent to its ‘normal state’ is considered to give a free energy change so that the change in the chemical state of the solvent contributes to the potential of force between the solute species. This contribution called the Gurney potential,’ l7 is correspondingly assigned to the term u;.(r). An interesting comparison is made with the model for hydrophobic interactions used by Yaacobi and Ben-Naim12’ in discussing the excess functions of methane and ethane in water-ethanol mixtures.In co-sphere treatments the operation of the ‘compensation la^'''^'^ for changes in solvent structure within the co- spheres leads to some uncertainties and the definition of co-sphere volume seems to be rather arbitrary. A further refinement of the model takes into account the ‘granularity’ of the solvent,’ l9 which superimposes a small oscillation upon the potential function and may have a considerable effect on the short-range forces. Models of solutions have been studied’17 up to a concentration of 1 mol 1-’ for alkali halides alkaline earth halides tetra-alkylammonium halides non- electrolytes and various mixtures. When the solvation parameters are adjusted to fit the experimental data good agreement is claimed for osmotic and activity coefficients heats of dilution and apparent molal volumes.The picture which emerges is to some degree exigent of the intuitive model used for the calculations and in view of the corrections for the various interactions it is difficult to judge whether the description of the solution is realistic or merely functional. For the purposes of application the theory would seem to offer a significant improvement The necessity to assign finite radii to the ions in all statistical approaches was first realised by H. Kramers. See R. P. Bell ref. 75. 12’ R. H. Stokes J. Chem. Phys. 1972 56 3382. H. S. Frank Z. phys. Chem. (Leiprig) 1965 228 364. 124 R. W. Gurney ‘Ionic Processes in Solution’ Dover New York 1953 p. 251. 12’ M.Yaacobi and A. Ben-Naim J. Solution Chem. 1973,2,425; see also H. L. Friedman and C. V. Krishnan in ref. 9. H. P. Bennett0 on the extended Debye-Huckel theory if simple methods for representing the various parameters can be devised. Care will be needed in using the theory since most experimental work is done at constant pressure whereas the theoretical equations apply to a state of osmotic equilibrium; i.e. V is the independent variable.8' Friedman has discussed the conversion of conventional thermo- dynamic relations from the Lewis-Randall convention to the forms required for use in the McMillan-Mayer system.'26 The study leads to the conclusion that for nearly ideal mixtures liquid structure effects associated with the packing of molecules contribute a negative term to the potential of force between solute particles in the solvent.Further results of statistical calculations will be awaited with interest especially when they are complemented by the results of computer simulation 'experi- merits' 118,119.12 7 As in the Debye-Huckel theory the statistical picture for electrolytes having ions of unequal radii presents some difficulties and it would be useful (but expensive) to have comparisons from the Monte Carlo method for ions which do not have the rather conventional value of 4.25 Both types of study have yet to attempt the description of solutions in solvents other than water surely a major requirement for any solution theory and until they are tested in this way the results and some of the underlying concepts should perhaps be viewed with reservation.Even for the interactions in a system of noble gas molecules the pairwise additivity assumption is an approximation,' 28 and total confidence in this postulate for solutions cannot be upheld in view of the admitted possibility of simultaneous overlap of more than two co-spheres.' 17i129 An other source of errors may exist in the energetic co-operativity of hydrogen-bonding in water,6 which imposes its own orientational restrictions. Unfortunately the effects of orientation-dependent forces have not been evaluated although it is known that the number and kind of terms which appear in the series for the interaction energy of the pair correlation function are related to the symmetry of the molecules.' 30 (An interesting new application of n.m.r.spectroscopy may throw light on such problems; it has been shown that interionic forces can be studied through the enhancement of spin relaxation times for 'Li' produced by excess of Mn2+ or Ni2+ in the A separate question relates to the radial symmetry assumed for the coulombic potential ;as in the treatment of the Poisson equation (9) it has always been expedient to rule out any dependence of the potential on the direction of the radius vector. Whether this is justified or not may have to be decided by more rigorous tests of the statistical methods against experimental data. A complex approach to the thermodynamics of aqueous electrolytes has recently been formulated by Pit~er.'~~ A system of equations is developed on the basis of an analysis of the Debye-Huckel model together with the results of lZ6 H.L. Friedman J. Solution Chem. 1972 1 387 413 419. 12' D. N. Card and J. P. Valleau J. Chem. Phys. 1970 52 6232. lz8 J. S. Rowlinson Discuss. Faraday SOC.,1965 No. 40 p. 19. lz9 F. Vaslow J. Phys. Chem. 1967 71,4385. I3O W. A. Steele J. Chem. Phys. 1963 39 3197. 13* L. P. Hwang C. V. Krishnan and H. L. Friedman Chem. Phys. Lerrers 1973,20,391. K. S. Pitzer J. Phys. Chem. 1973 77 268; K. S. Pitzer and G. Mayorga ibid. p. 2300. Electrolyte Solutions 237 calculations for 'hard core' effects and an ionic strength dependence is proposed for the effect of short-range forces in binary interactions. The equations yield values of activity and osmotic coefficients for single and mixed electrolytes which are in fair agreement with experiment up to concentrations of several molal a distinct improvement on the earlier formulations of S~atchard~~ and of Guggen- heim.'33 A similar objective is achieved by Robinson and Bates,'34 who use a simpler hydration convention which permits calculation of single ion activities for unassociated electrolytes.Specific differences in values of yi are accounted for in terms of solvent activity and a fixed hydration number characteristic of each ionic species which is assumed to be zero for C1-. Both of these treatments provide a valuable means of estimating ionic activities at high concentrations. Solutions as Lattices-The idea that ions in a solution will naturally tend to assume a lattice-like arrangement springs from intuitive feeling.This concept has been adamantly resisted since the time of Gh~sh~~ by most electrochemists but is acceptable to students of fused salts and concentrated solutions.49 While it is easy to appreciate that quasi-crystalline behaviour can exist in a concentrated solution,' 35 most authorities doubt the integrity of such structures in more dilute solutions on the grounds that any simple 'lattice expansion' would be eradicated by thermal motions. It is often suggested however that a change of structure occurs at some critical concentration where the oscillating nature of electrical potentials which is characteristic of the lattice vanishes and the solution there- after takes on the cloak of the Debye-Huckel lattice Both the experimental evidence79 for such discontinuities and the theoretical predictions of where they occur are uncertain but the concentration is considered to be beyond the range (ca.0.0014.5 moll-') in which many properties of solutions exhibit a dependence on the cube-root of concentration. The cube-root relation is an accurate natural law which has been well described by Frank68*69 and other~,'~*'~~*' 37 and is often rediscovered by experimentalists after a period of torture at the hands of the ion-size parameter of the Debye-Huckel the~ry.~~,'~~ Thus the activity coefficients are well represented by an equation of the form logy = -Ac' + BC (11) where A is now a Madelung-like constant for the crystal and B is a constant of unknown significance.In a recent report Bahe' 39 correlates the partial molal heat contents of nine electrolytes in water against a cube-root function (Figures 1 and 2). This picture may be compared with the one presented by Harned and and else~here.~~,~~.~~ Some theoretical justification for the constant B of equation (11) is given'39 in terms of repulsive energy (ccl/r3) generated from E. A. Guggenheim and J. C. Turgeon Trans. Furuduy SOC.,1955 51 747. '34 R. A. Robinson and R. G. Bates Analyr. Chem. 1973.45 1666. See also ref. 9. 135 H. Bertagnolli J.-V. Weidner and H. W. Zimmermann Ber. Bunsengesellschafr phys. Chem.. 1974,78 1. 136 E. Glueckauf in ref. 68. 13' J. E. Desnoyers and B. E. Conway J.Phys. Chem. 1964,68,2305. 13' A. Vesala Suomen Keni.. 1973. 46,43. '" L. W. Bahe J. Phys. Chem. 1972 76 1062 1608. H. P. Bennett0 Figure 1 The variation of apparent relative partial molar heat contents (negative heats of dilution) of NaCl with the cube root of the molar concentration at 25 "C at low con- centrations. Experimental slope 217.0; predicted slope 21 7.5 (Reproduced by permission from J. Phys. Chem. 1972,76 1609) the interaction of the dielectric gradient near ions with the classical coulombic field first predicted by Friedman.' ' Though B still remains an adjustable parameter the existence of quasi-lattice behaviour in solutions of moderate concentration seems to be the most acceptable interpretation of the results and receives support from a consideration of the working range of the law.Its extension into the more dilute range is generally more pronounced for electrolytes of higher valency which usually have higher lattice energies. Where the limiting law is closely approached the cube-root law is less in evidence and vice versa. This is well illustrated by the precise activity coefficients of HCl. In H,O the limiting law is fair but the cube-root relationship is e~act;"~.'~~ in methanol the cube-root law similarly extends to below 0.002rn.84In general there is an overlap of the concentration ranges in which the two laws apply and though this makes the analysis of results difficult it may give a clue to the manner of formation of the Ghosh lattice. When ions are progressively added to a Debye-Huckel cloud each is presumed to be fully used in the formation of ionic atmospheres.For large values of KU the electrical free energy is given by Gclcc= ( -z~e2/4n&,&,a) (12) comparable with the coulombic stabilization for a cubic crystal having a as the smallest anionation distance; only the 'Madelung constant' is missing. 140 I4O R. A. Robinson and R. H. Stokes ref. 47 1st edn. 1955 p. 238. Electrolyte Solutions KCL NaCl KB r t t-\"\ t t \O I I I 1 0.2 04 0.6 0.8 1.0 1.2 1.4 1.6 t/mol 1-1 Figure 2 Correlation of I,(= R -Fl;) with concentration for 1 1 electrolytes at 25 "C. Each division on the ordinate represents 100 cal mol-'. Data for each salt are displaced 100cal mol-' from euch neighbour and the right angle adjacent to each salt represents the origin (0,O) for that salt (Reproduced by permission .from J.Phys. Chew. 1972 76 1609) However the electrical stabilization predicted by the limiting law is too great. The real behaviour is closer to that expected for build-up of a lattice in which successive additions of ions contribute less and less to the energy of the dis- tr1buti0n.l~~The two representations can be both compatible and comple- mentary since a lattice-cloud presumably degenerates on dilution and takes on spherical character at infinite dilution where it is indistinguishable from the Debye ionic atmosphere. The assumption of a radially symmetric distribution of ions is probably correct in this limit but there is no guarantee that it remains so in solutions of practical interest where the symmetry might become or be of a type dictated by the solvent or be typical of the solid crystal.At what point such a change might be expected to begin is debatable and it could be 14' J. Sherman Chern. Reo. 1932 11 93. 14' L. Onsager J. Phys. Chem. 1939,43,189. The minimum energy for a set of point dipoles is attained in a hexagonal close-packed crystal. 240 H. P.Bennett0 argued that for a 1 1 electrolyte it occurs when more than two ions are present in the solution. The solvent is imagined to play a role in the formation of a lattice-like dis- tribution. It is easy to envisage a difference between the solvent lying between ions of like sign and that lying between ions of unlike sign and the popular co- spherelZ4 concept might therefore appear in a coulombic guise.Dielectric gradient effects near the ions are also clearly im~0rtant.l~~ It should be noted that recent Monte Carlo calculations for a primitive model 1 1 electrolyte (r = r = 4.25A)fail to predict any distinct oscillatory character in the dis- tribution function for a solution at high concentration.’ 27 [Unsymmetrical and high-valence electrolytes do appear to give oscillations in g(r),but probably not in ‘dilute solutions’.] The computer simulation does not however take into account the molecular structure of the solvent though this factor can be built into statistical models. The main weakness of the quasi-lattice concept is the lack of a firm theoretical basis.Further tests of Bahe’s theory’ 39 are awaited with interest but the major problem is the integration of the two observed laws. Unlike the Debye-Huckel theory which is firmly anchored by the limiting-law the lattice theory seems to provide no common point of reference for all electrolytes. The choice of the reference state is however rather one of convenience and some other state such as that of ‘persisting structure’ may eventually prove to be more acceptable than infinite dilution.’39 It appears that a basic postulate of structure is necessary in setting out to describe any distribution function ; in Debye’s formulation it is implicit in the statement that ‘in a volume of solution near a central ion there are more ions of unlike sign than of like sign’,6’ and an alternative postulate may be hidden in some other empirical relationship such as the cube-root law.The scope for testing the idea is at present surprisingly limited because so much work has been concentrated on dilute solutions in order to derive precise standard state solvation coefficients. Sensitive tests in many solvents will be necessary to distinguish between a Debye lattice and any other since the free energy difference is expected to be ~ma11.l~~ However the enthalpies of the two types of distribution will differ and a fuller account of these parameters should clarify the nature of structure in solutions of intermediate concentrations. 4 Thermodynamics of Ionic Solvation The elucidation of primary interactions between ions and solvate molecules in the gas phase continues.Leaders in this field are Kebarle and co-workers who have extended their mass spectrometric studies of hydrated protons,’44 and have placed the strength of the interactions of some solvent molecules with C1- in the order H,O > MeOH > MeCN just that expected from the study of ‘solvent activity coefficient^'.'^ Solvation of 0,-by these ligands is also 143 R. W. Gurney ‘Ions in Solution’ Dover New York 1962. 144 R. Yamdagni J. Payzant and P. Kebarle J. Amer. Chem. SOC.,1972,94,7627;Cunud. J. Chem. 1973 51 2507. Electrolyte Solutions 241 observed and a later study throws light on the interactions of protons in mixed hydrate-ammoniate complexes. 14’ Su and Bowers’46 have investigated the effect of molecular size in ion-polar-molecule collision reactions of C,H,+ with NH, MeNH, Et,NH and Me3N and correlate the rate constants for proton- transfer with the polarizability of the substrate.An interesting theoretical of cation hydration compares the results of semi-empirical and ab initio calculations with experimental results from mass spectrometry and there is hope therefore that the results of gas-phase and theoretical studies will eventually be usefully compared with estimates of primary solvation parameters obtained from solution work. An assessment of the relative influence of the primary interactions and that of solvent structure would provide insight into many present problems particularly in mixed aqueous systems.These continue to be popular for obvious practical reasons but are prone to uncertainties in the interpretation of results. One important aspect concerns the bonding effects in mixed solvate complexes and is of concern to those interested in ligand-sub- stitution proces~es.’~~ Another is that perennial headache specific solvation which is yielding to examination by n.m.r. methods. 149 Much information in mixed solvents has been accumulated from e.m.f. studies,’” in the form of the free energies of transfer of electrolytes from water (AGP). For many years Feakins and co-workers have been resolutely active in this field,”’ and have latterly received much support notably from De Ligny,’” Kundu,’ 53 Roy,’ and their co-workers. The methanol-water system is partic- ularly well chartedlS4 with reliable (and some not so reliable) data and has been a centre of attention for those attempting to evaluate single-ion solvation coeffi- cients in different solvent^.'^^'^^ A recent report discusses cross-checks on the differences AGP(C1- -Br-) AGP(C1- -I-) by independent studies both of the more conventional HX cell and of double cells which incorporate amalgam electrodes.The agreements found are gratifying and important in an area where the certainty in interpretation of subtle solvent effects may hinge on the relia- bility of data. Inflections in the plots of AGp oersus solvent composition have been tenuously attributed to the ‘non-electrolyte effects’ which may be elaborated as follows. In order to become solvated a solute must find or create some room in the solvent structure and for the simplest case the cavity-forming process may be 14’ J.D. Payzant A. J. Cunningham and P. Kebarle Canad. J. Chem. 1973,51 3242. 146 T. Su and M. T. Bowers J. Amer. Chem. SOC.,1973,95 7609 761 I. 14’ P. A. Kollman and I. D. Kuntz J. Amer. Chem. SOC.,1972 94 9236. I 48 D. N. Hague in ‘Inorganic Reaction Mechanisms’ ed. J. Burgess (Specialist Periodical Report) The Chemical Society London 1973 Vol. 2. 149 A. K. Covington K. E. Newman and T. H. Lilley J.C.S. Faraday I 1973 69 973; A. Clausen A. A. El-Harakany and H. S. Schneider Ber. Bunsengesellschaft phys. Chem. 1973,77,994. 150 M. Salomon in ref. 14. ” D. Feakins and P. J. Voice J.C.S. Faraday I 1972 68 1390.I 52 D. Bax C. L. De Ligny and M. Alfenaar Rec. Trav. chim. 1972,81,452. 5’ K. K. Kundu and K. Mazumdar J.C.S. Faraday I 1973,69,730,806 and refs. therein. ’” C. F. Wells J.C.S. Faraday I 1973,69 984. Is’ 0.Popovych Crit. Rev. Analyt. Chem. 1970 1,73. H. P. Bennett0 quantified in terms of the shape and size of the molecules and the intermolecular forces; this concept is used in the scaled-particle theory description of simple solutions.’ 56 For a dissolved ion an analogous effect is presumed to contribute to the free energy in addition to electrolytic effects which are of both short and long range. [A contribution from cavity-formation is included in the term &(r) of the statistical mechanical description mentioned above.] All attempts to unravel the two types of contribution would appear to have an arbitrary basis since the structural influences of an ion and a non-electrolyte are intrinsically differentlS1 but in principle it is possible to effect a separation on empirical grounds e.g.a value of 4G:(ion) may be corrected for the ‘non-electrolyte effect’ by subtraction of the Aq for a noble gas molecule of the same size as the ion.’52 It turns out however that a more suitable subtraction is one which uses the noble gas molecule ofthe same electronic structure as the ion rather than one of the same size.’ ’ This is reasonable if one considers firstly that the effective radius will be slightly larger than the crystallographic one (a hydrated radius of the Stokes type is not appropriate in view of the great lability of the primary solvation shells) and secondly that an important contribution to the close- range interaction will come from dispersion interactions.The new procedure gives an improved linearity to the plots of AGP(MC1) versus reciprocal cation radius and it appears that the contributions to the solvation of alkali-metal cations are simply (i) primary interactions of the ‘acid-base’ type (ar; ‘),Is7 (ii) secondary Born-type interactions and (iii) dispersion interactions normally included in (i). According to this model the inflections in the plots of AG,’ versus solvent composition for both cations and noble gases arise mainly from the changes in the dispersion interactions (i.e.‘polarizability’) afforded by the solvent which also largely determine the structpral peculiqrities of the medium itself.These ideas are also pertinent for Group I1 cations,”* where the AG values are similarly interpreted with the aid of Pearson’s ‘hard’ and ‘soft’ concept. As a result of the aforementioned correction the single ion values obtained from the univalent cation plots are certainly more reliable than those from any anion plot since in this case the halide-solvent interactions are probably more complex and the extrapolation to r;’ = 0 is a much longer one anyway. However the separation of AGP into single-ion values by any procedure is still hazardous and will remain so until some aspects of ionic solvation are better clarified; but while single-ion quantities are not essential to this better understanding they are undoubtedly of great practical value e.g.in setting up pH scales for mixed solvents.17 Some progress towards understanding the ‘non-electrolyte effect’ in other mixed solvents has been made in a recent study of the thermodynamics of transfer af some non-electrolytes from water to DMSO-water methanol-water and dioxan-water mixtures.’ 59 The transfer of ions to non-aqueous solvents is dealt ”’ E. Wilhelm and R. Battino Chem. Rev. 1973 73 1. D. Feakins and P. Watson J. Chem. SOC.,1963 4734. Is’ D. Feakins A. S. Willmott and A. R. Willmott J.C.S. Furuduy I 1973 69 122. Is9 B.G. Cox,J.C.S.PerkinIZ 1973 607. Electrolyte Solutions with elsewhere,13 but we Mention an experimental approach made to the problem of liquid-junction potentials between different solvents ;'6o some empirical rules may enable the single-ion transfer coefficients to be simply estimated with sufficient accuracy for useful application in physical organic chemistry.Elsewhere Frank16' has returned to the same problem and discusses the computer slmula- tion of the behaviour for 8concentration cell with transference. There would seem to exist a possibility for determining single-ion activities from the rapid time-rise of the cell potential. The marked differences in solvation of cations and anions are generally considered to reside in the primary interactions.' 51 Secondary solvatidn is a complicating factor however and the relative importance of the two types of interaction is not unequivocally established.The problem may be partly resolved through investigations of 'iso-dielectric' sy~terns.~~,'~~ The chemical nature of solvation is revealed in Aq values for solvent mixtufes having a uniform permittivity since the Born-type interactions are invariant and there is thus considerable scope for the application of this method in a variety of mixtures over a wide range of E,. For instance in methanol-propene glycol mixtures methanol is the more 'basic' molecule with respect to ion solvation,'62 and changes of anionic solvation apparently dominate AG in protic-hydroxylic mi~tures.'~ Further work promises to clarify the ways in which the 'acid-base' interactions are modified by co-operative 15' solvent-~tructural,~~~~ 63 and specific solva- tion14' effects.An attempt to link such effects with kinetic parameters in a general way has been recently described. 164 The methods of separation of thermodynamic solvation parameters into single- ion quantities have been widely re~iewed,'~.'~~.'~~~'~~ but some uncertainty still exists concerning 'real' free energie~."~*'~~*'~~ The method based on the direct measurement of Volta-potential differences,' le9 clearly described by Case,'67 avoids the uncertainties of extrapolations of data against some function of the crystal radii,'" or of a similar extra-thermodynamic assumption,' 71 but it requires the estimation of surface potentials. Ibo B. G. Cox A. J. Parker and W. E. Waghorne J. Amer. Chem. SOC.,1973 95 1010. 16' R. N. Goldberg and H.S. Frank J. Phys. Chem. 1972,76 1758. 162 K. K. Kundu A. L. De and M. N. Das J.C.S. Dalton 1972 386 and preceding papers. K. G. Breitschwerdt and H. Wolz Ber. BunsengeseNschaftphys. Chem. 1973,77 1OOO. H. Strehlow W. Knoche and H. Schneider Ber. Bunsengesellschaft phys. Chem. 1973 77 760. Ib5 C. M. Criss in ref. 14. J. I. Padova in 'Modern Aspects of Electrochemistry' no. 7 ed. J. O'M.Bockris and B. E. Conway Butterworths London 1972. 16' B. Case in 'Reactions of Molecules at Electrodes' ed. N. S. Hush Wiley-Interscience London 197 1. '68 J. E. B. Randles Trans. Faraday SOC.,1956. 52 1573. Ib9 B. Case and R. Parsons Trans. Faraday Soc. 1967 63 1221; V. A. Rabinovitch T. E. Alekseeva and L. A. Voronina Elektrokhimiya 1973 9 1434. P.L. Mateo G. G. Hurtado and J. B. Vidalaba Anafes de Quim. 1973 69 717. I" R. Alexander A. J. Parker J. H. Sharp and W. E. Waghorne J. Amer. Chem. SOC. 1972 95 1148. H. P.Bennett0 The surface potential167 is an important property which has relevance to many problems e.g. electrode kinetics,17* but it is only indirectly related to the ther- modynamics of ion solvation. The passage of ions through interfaces in the transfer of complete electrolytes from one solvent to another is a process re- quiring zero work,lS5 and the standard free energy of transfer AG thus adequately describes the differences in solvation energies ; no qualifying term 'hypothetical' is needed That the measured quantities are independent of surface properties is clear from the agreements between transfer data obtained with electrodes having different surface characteristics; e.g.one may use either a calomel or a silver-silver chloride electrode in conjunction with a hydrogen electrode to obtain the same value of AG. The single-ion values obtained by extrapolation are no less real than any others since the implication is made that only the differences in solvation for an ion in two bulk solvents is being considered for which surface processes are of no importance. Though it is sometimes said to be necessary to know 'real' free energies of transfer in order to understand ionic solvation the literature shows otherwise. It might be a logical step (and one that would cause least confusion to outsiders) to omit the term 'real' and to tabulate only free energies of transfer.'Real' values would then require correction by a surface-potential term but the fact that the uncertainties in estimating this term are about as great as those of the extra-thermodynamic assumptions argues for this compromise. Fortunately the results from two types of experiment are in sufficient agreement that the same conclusions about ion solvation are reached. '50*167*169 The direct method of measurement may be refined e.g. by further examination of the concentration dependences of the compensation potentials and surface potentials; the extra- polations on the other hand can be improved along the lines indicated earlier. When the quantitative results from both sources agree it may be claimed that the correct absolute single-ion transfer values have been obtained.An approach which might be followed in the future is the determination of the entropies of transfer from temperature coefficients of the Volta potentials ;an advantage would be that higher temperatures would minimize the surface structural effects and hence the solvent surface potentials. Two important papers on entropies of solution have a~peared.'~~.'~~ One deals with ions in water and gives support to the well-known structural concept of Frank and Wen;'73 the other discusses entropies of transfer from water to non-aqueous solvents. '74 5 Transport and Related Properties The long debate over the relative merits of different forms of the Fuoss-Onsager conductance equation and its modern equivalents appears to be largely resolved ; M.Salomon J. Electrochem. SOC. 1971 118 1609. B. G. Cox and A. J. Parker J. Amer. Chem. SOC. 1973.95 6879. M. H. Abrahams J.C.S. Faraday t 1973,69 1375. Electrolyte Solutions 245 an excellent summary is given by Fernandez-Prini.' 75 The conductivities of 1 1electrolytes can be fairly well correlated but the less popular unsymmetrical and multivalent electrolytes do not so conform and even a sophisticated treat- ment' 76 requires an additional parameter in concentration to fit experimental results. The reasons may perhaps be sought in the same fundamental weaknesses as are present in the Debye-Huckel theory for other than very dilute solu- tion~,~~,~~ and the credibility of the equations proposed also greatly depends on one's faith in the various correction terms which seem to be a function of time and fashion.The impressive agreement of different equations for dilute solutions may convince the investigator that ion-association has some real significance but small values of the' derived constants should be treated circumspectly. In more concentrated solutions where the equations do not agree,' 75 spectro-scopic measurements may provide some useful comparisons and recent n.m.r. work,' 77 anda Raman study,' 78 giveindependent evidenceofcontact and solvent- separated ion-pairs agreeing in one case' 78 with ultrasonic relaxation measure- ments. Any doubts about conductance theory could be partially ascribed to mere prejudice if it were not for the additional evidence from transference number measurements.' 79 The Fuoss-Onsager equation for the concentration depen- dence takes the form for a 1 1 electrolyte where /3 is the electrophoretic parameter.Even in water the results are less than adequately described by this relation,'80 but in other solvents it fails almost ~ompletely.'~~.'~~ Wildly unrealistic values of a are required and there are sharp minima in the plots of t+(c) against c for the limiting transport number (calculated from results at a concentration c using different values of a in the several equations). In Spiro's words,'79 'one is indeed forced to wonder whether the conductance sum cancels out some aspect of theory that is revealed only by testing the conductance ratio'.The little work that has been done on electrolytes of other valence types in water often shows a similar failure of the limiting Onsager 1aw,46*181 and is all too readily dismissed as experimental error. It seems not unreasonable to suppose that the start of divergence of the various conductance equations marks the onset of behaviour which might be R. Fernandez-Prini ref. 14 chap. 5; see also G. J. Hills in 'Electrochemistry' ed. G. J. Hills (Specialist Periodical Reports) The Chemical Society London 1970 Vol. I p. 73 and M. Wootten in ref. 5 p. 20. 176 T. J. Murphy and E. G. D. Cohen J. Chem. Phys. 1970,53,2173. 17' M. S. Greenberg R. L. Bodner and A. 1. Popov J. Phys. Chem. 1973,77,2449. ' 78 A. R. Davis and B. G. Oliver J. Phys. Chem.1973 77 13 15. 179 M. Spiro ref. 14 chap. 5. D. P. Sidebottom and M. Spiro J.C.S.Furuday I 1973.69. 1287. For other recent work see G. A. Vidulich C. P. Cunningham and R. L. Kay J. Solution Chem. 1973 2 23 (methanol); A. R. Tourky S. Z. Mikhail and A. A. Abdel-Hamid Z. phys. Chem. (Leipzig) 1973 252 289 (t-butyl alcohol-H,O). E.g. see J. L. Dye M. P. Faber and D. J. Karl J. Amer. Chem. Soc. 1960 82 314. H. P. Bennett0 better described by another theory (which need not rule out ion-pairing but would put it into a different context). Some efforts in the direction of a lattice theory'82 are certainly more successful than the usual approach for moderately dilute solutions ;in HCN the conductance of KCl obeys a cube-root law while in N-methylacetamide several salts obey a square-root law far beyond the Debye-Hiickel-Onsager range but the slope is wrong.82 While further accurate data are necessary it is tentatively suggested that the minima in the plots of t+(c) 0s. c found by Sidebottom and Spiro coincide with the takeover of quasi-lattice properties. Recently reported cases of ion-aggregation5 might be interpreted in a similar way. Interest has grown in the transport by ions of non-electrolytes in mixed solvents which has important implications to-specific s~lvation,'~~ kinetic^,'^' and transport processes in biological systems.' ' solvent-exchange The Washburn number'" of water W, in a binary aqueous mixture is the number of moles of water transported per faraday towards the cathode in an electrolysis relative to the co-solvent.It should not be confused with 'solvation number'; the relation of W to the transport numbers t+ ,t-,and the number of moles of water n and h-transported (relative to methanol) by the cation and anion respectively is given by W = n+t+-n-t-(14) A precise e.m.f. method' 83 employing cells with and without a liquid junction gives W at infinite dilution of electrolyte as an average for an interval in the solvent composition range. In methanol-water mixtures,'84 little specificity in W is found among different cations for alkali-metal chlorides but solvent structure has a profound effect on the relative solvation of halide ions by the two solvent components (i.e.n-) and two regions of structural peculiarity are identi- fied.Parallels may be drawn between the solvent effects on Washburn numbers and the self-diffusion of water in methanol-water mixtures.' 85 The solvent-sorting effect of ions which is also present in glycol-water mixtures,'86 does not appear to stem from variations in transport number with solvent composition and is confirmed by the results from a vapour pressure meth~d.'~' In saturated KCl however the lower W and W,values show that the differences in composi- tion between the primary solvation shells of the ions and the bulk solvent are much smaller than at low salt concentrations presumably because the structural influence of the solvent medium has been eliminated. Further developments in the theory and interpretation of transport properties appear to lie in the direction of transition-state theory.17' The application to la2 G.Kortiim and H. Quabek Ber. Bunsengesellschaft phys. Chem. 1968 72 53; cf. J. F. Casteel and E. S. Amis J. Phys. Chem. 1973 77 688. IE3 D. Feakins and J. P. Lorimer Chem. Comm. 1971,646. D. Feakins K. H. Khoo J. P.Lorimer and P. J. Voice J.C.S. Chem. Comm. 1972 1336. T. Erdey-Gruz G. Inzelt and C. P. Fodorne Magyar Kkm. Fu/y&rar 1973 79 20; 173. IE6K. H. Kho0,J.C.S. Faraday I 1973 69 1311. C. L. De Ligny and A. G. Remijnse J. Electroanalyt. Chem. 1973,45 488. Electrolyte Solutions 247 conductivity pioneered by Hillsla8 promises to integrate solvation with solvent effects and is supported by a recent study of five electrolytes near the phase transition in N-methylacetamide.' 89 The values of E for conductance are very close to E for viscous flow in the pure liquid indicating that cavity formation is a process common to both transition states.The transition-state treatment for the viscous effects of electrolytes (Jones-Dole B coefficient^'^') established by Nightingale,'" has been given a somewhat different form by Feakins and co-worker~.'~' For small ionic solutes a simple relationship results from the consideration of the solution in the limit of infinite dilution. In equation (15) B = (Vq -V;)/lO00 + V;[(Ap;* -A/A; *)/lOMlRT] (15) Vy and Vi are the partial molar volumes of the solvent and solute respectively; ApY* is the activation free energy for viscous flow of the solvent and Apl* the 'ionic activation free energy' at infinite dilution.The structural effects of ions are thus meaningfully separated into quantities formally relating to the sizes of the ions the fluid properties of the solvent and the ion-solvent interactions and the possibilities for combining the results of thermodynamic and transport properties are obvious. However the precise measurement of B coefficients is no easy matter and the comparability of results is still affected by the lack of con- formity in the assignment of a value to the Debye-Hiickel parameter A of the Jones-Dole equation (16) qr= 1 +A&+BC (16) in which q is the viscosity relative to that of the pure solvent; probably the experimentally determined value of A should be used. A case may be made for thinking that if the theoretical limitations inherent in the A coefficient are not recognized in the separation of A and B some lattice-coulombic effects6' may be partly reflected in the derived B values.The consequences of this may not be too serious however if both the B coefficients and the lattice phenomenon have a common origin in solvation and its attendant modifications of solvent organiza- tion around the ions.'39 Unfortunately it is not yet possible to be sure of the dielectric properties in this region though some recent studies may be noted.' 92-' 95 The future for a structural theory of solutions appears to lie in the coalition of ideas from transport kinetic and thermodynamic studies and will need to place emphasis on parameters such as those appearing in equation (15) in the hope that the mystery will be taken away from B coefficients the electrophoretic effect etc.Some established correlations suggest further possibilities e.g. that "* S. B. Brurnmer and G. J. Hills Trans. Furaday SOC.,1961 57 1816 1823. P. P. Rastogi Z. phys. Chem. (Frankfurt) 1973 85 1. E. R. Nightingale and R. F. Benck J. Phys. Chem. 1959 63 1777. 19' D. Feakins D. J. Freemantle. and K. G. Lawrence J.C.S. Furuduy I 1974 70,795. 19' G. Schwarzenbach L. Fabbrizzi P. Paelotti and M. C. Zobrist Helo. Chim. Acru 1973 56 670. 193 J. T. Edward J. Chem. Phys. 1972 57 5251. 194 R. Fernandez-Prini J. Phys. Chem. 1973,77 1314. 19' S. K. Jalotta and R. Patterson J.C.S. Furaduy I 1973 69 1510. H. P.Bennett0 the B coefficients relate to AV" for ionic cond~ctance.'~~ What then is the behaviour of B when the pressure is varied in view of the single value of AV* found'96 when the solution is compressed to the specific volume of the solvent? The solubilities of gases in a pure solvent approach a common value at the solvent boiling (as does the solvent vi~cosity);~~ this suggests that 'non-electrolyte effects' will also converge and inspection of the limited data on B coefficients shows a similar trend. Since the Onsager treatment of transport numbers,' 79 diffusion etc. is unreliable for describing concentra- tion dependences in solutions of moderate concentration a lattice theory might be more compatible with the results together with descriptions of the solvent- exchange proces~,~~*'~~ namics.'99 non-Brownian motions,'98 and solution micrody-196 S.B. Brummer and A. B. Gancy ref. 26 chap. 19. 19' 0.Ya. Samoilov ref. 26 chap. 14. 198 H. L. Friedman ref. 26 chap. 18. 199 I. R. Lantzke D. E. Irish and T. E. Gough ref. 14 chap. 4; H. G. Hertz ref. 8 chap. 7.