7 ELECTROLYTE SOLUTIONS By A. D. Pethybridge and J. E. Prue (Department of Chemistry, The University, Whiteknights, Reading, RG6 2A D) Raman and Infrared Spectroscopy.-The availability of commercial instru- ments and of laser sources of excitation has resulted in increased activity. In our understanding of electrolyte solutions, real progress beyond the assunip- tions of the continuum model for the solvent demands a satisfactory molecular picture of the solvent, and in particular of water, which we do not have at present. One of the best prospects of experimental progress is from spectro- scopic measurements, and an interesting paper by Walrafenl which reports Raman studies of the structure of water will be found in the recently pub- lished proceedings of a symposium on hydrogen-bonded solvent systems.Neither the assignment of frequencies nor the interpretation of intensity variations is easy and such work has not yet led to generally accepted conclu- sions, but there can be no doubt that the spectroscopic study of water itself and of HDO in water2 over wide temperature and pressure ranges will be the subject of much experimental effort in the near future. Rather more clear-cut conclusions have already emerged about ion-ion interactions in particular cases. An interesting paper by Irish and Davis3 reports a detailed study of the vibrational spectrum of the nitrate ion in aqueous alkali-metal nitrate solutions. Raman results are complemented by i.r. spectra. Above a concentration of 1 . 5 ~ , the positions, molar intensities, and especially the halfwidths of bands show pronounced dependence on both the concentration and the identity of the cation.The halfwidth changes are ascribed to the interaction of solvated pairs of ions. The appearance of a new nitrate band at 740 cm.-l in lithium and sodium nitrate solutions more concentrated than 7~ is ascribed to the effect of direct cation-anion contact. It is also of interest that the separation of two of the nitrate frequencies for lithium nitrate shows a cube-root dependence on concentration in a plot which includes a value for the molten salt. Other spectroscopic studies across the entire concentration scale up to and including the molten salt would be worthwhile. The same autliors4 report vibrational assignments for the species HgNO3’ and Hg(N03)2 from studies on aqueous mercury(rr) nitrate solutions.They conclude that the nitrate ion is monodentate in HgN03f. A paper5 characteristic of much recent spectroscopic work on nitrate solutions deals with aqueous cadmium nitrate and contains plentiful ref- erences to similar work. A detailed band assignment is made for the free G. E. Walrafen in, ‘Hydrogen-bonded solvent systems,’ eds. A. K. Covington and G. E. Walrafen, J. Chem. Phys., 1968, 48, 244. D. E. Irish and A. R. Davis, Canad. J. Chem., 1968, 46, 943. A. R. Davis and D. E. Irish, Inarg. Chem., 1968, 7 , 1699. 5 A. R. Davis and R. A. Plane, Inarg. Chetti., 1968, 7, 2565. P. Jones, Taylor and Francis, Ltd., London, 1968, p. 9. 129130 A . D . Pcthybridgc and J . E. Prue nitrate ion and for the inner-sphere species, CdN03+, for which a stability quotient is calculated from intensity measurements. A nitrate band at 740 cm.-l is again ascribed to the inner-sphere cation-anion complex.A study6 of bismuth nitrate solutions provides evidence for bidentate co-ordination by some nitrate ions, and a band at 235 cm.-l assigned to the symmetric metal- oxygen stretch is cited as evidence for covalency. It seems that up to four nitrate ions can attach themselves to a bismuth ion. The spectrum of the nitrate ion in acetonitrile solutions of zinc, cadmium, and mercury(I1) nitrates is strongly perturbed by cations, but only in the case of mercury(r1) is a metal-oxygen frequency dete~ted.~ Useful sources of reference to studies of particular complexes in solution are two recent reviews by Hester.8 Although the vibration of an ionic bond is not expected to produce a Raman line, it will have a large change of dipole moment associated with the vibration and should produce an intense line in the i.r.spectrum. It is of particular interest therefore that French and Woodg report the observation of far i.r. vibrational spectra of some ion pairs in non-aqueous solvents. A band at 175 cm.-l is found for sodium tetraphenylborate in pyridine, 1,4-dioxan, piperidine, and tetrahydrofuran. The wavenumber is independent of the solvent but does depend on the cation. These facts, and the value of the isotope shift found for ammonium tetraphenylborate on deuteriation of the ammonium ion suggest that the ion pairs are of the ‘contact’ rather than the ‘solvent- separated‘ variety.(The opposite conclusion for sodium tetraphenylborate in tetrahydrofuran has been reached from conductivity measurements by polymer chemists.1° However, it is questionable whether the conductivity measurements were of adequate precision or sufficiently rigorously analysed to lead to reliable conclusions.) French and Wood stress that the detailed analysis of ion-pair vibrational spectra will obviously require a more sophisti- cated ion-pair potential function than the hard-sphere model. Precise Raman intensity measurements continue to provide information on the degree of ionisation of strong electrolytes in concentrated solutions. Clarke and Woodwardl1 have measured degrees of ionisation of methyl- mercury( 11) methanesulphonate (1-5~) and sulphate (0.2-0.7~) by measure- ment of the integrated intensities of bands characteristic of the anions. In addition to problems of band overlap, there is no doubt that some earlier workers (but not Woodward) were over-optimistic concerning the independ- ence of molar integrated intensities of effects other than chemical bond formation. In the present paper, and in earlier ones dealing with the ionization of methanesulphonic acidl2a and of methylmercury(1r) nitrate,12b the anion 6 R. P.Oertel and R. A. Plane, Znorg. Chem., 1968,7, 1192. 7 C. C. Addison, D. W. Amos, and D. Sutton, J . Chern. SOC. ( A ) , 1968,2285. 8 R. E. Hester, Co-ordination Chem. Rev., 1967,2,319; Analyt. Chetn., 1968,40,32OR. M. J. French and J. L. Wood, J . Clrem. Phys., 1968, 49, 2358.10 D. Nicholls, C. Sutphen, and M. Szwarc, J . Phys. Chetn., 1968,72, 1021 ; J. Comyn, l1 J. H. R. Clarke and L. A. Woodward, Trans. Faraduy SOC., 1968,64, 1041. l2 (a) J. H. R. Clarke and L. A. Woodward, Trans. Faraday SOC., 1966, 62, 2226; F. S. Dainton, and K. J . Ivin, Electrochim. Acta, 1968, 13, 1851. (b) ibid., 3022.Electrolyte Solutions 131 concentration is calculated from the observed intensity and a molar integrated intensity equal to that of an ammonium salt solution (assumed to be com- pletely ionised) of equal refractive index. The justification for this is discussed, but it is recognised that with, for instance, different metal nitrate solutions (supposedly completely ionized) the molar intensities of solutions of the same refractive index can in some cases differ by as much as 10%. Clarke and Woodward use the word ‘dissociation’ where the present writers prefer ‘ionisation’ because in this method anions present in ion pairs (which, as well as higher aggregates, will undoubtedly occur in such concentrated solutions) are counted as ions.This raises a further general point in connection with questionable attempts to extrapolate ionisation quotients at high concentra- tions to obtain thermodynamic equilibrium constants. Consider a commonly invoked scheme of ionisation followed by dissociation such as K1 Ii 2 A-B +- A+B- $ A+ + B- From a degree of ionization given by the quantity which is conventionally calculated is We find on expansion of the right-hand side of equation (3) and substitution of the equilibrium constants K1 and.Kz, that even if changes of activity coefficients with concentration are ignored, Q = f(Kl,Kz,c); attempts to extrapolate such a function to c = 0 by assuming its concentration dependence to be solely determined by changes in activity coefficients are therefore wrong, and extrapolation on an empirical basis only is unreliable. According to Clarke and Woodward the degree of ionisation of methane- sulphonic acid is about 0.5 in an 1 IM solution. An estimate based on acidity function meas~remeiitsl~ gives about the same value for the degree of ionisa- tion at 3 ~ ! It has been claimed14 that this gross discrepancy can be avoided by changes in the assumptions made about the hydration of the proton in analysing the acidity function data.The polynuclear species reported as hydrolysis products of metallic cations in solution are sometimes surprising. The conclusion that the major species produced from bismuth(n1) is Bis(OH)lP, first reported from e.m.f. measure- ments, is well substantiated by ultracentrifuge and X-ray measurements. The vibrational spectrum of this complex both in solution and in the solid state has now been thoroughly studied.15a The work confirms that the bismuth l3 K. N. Bascombe and R. P. Bell, J. Chem. SOC., 1959, 1096. l4 J. G. Dawber, Chem. Comm., 1968, 5 8 . l5 (a) V. A. Maroni and T. G. Spiro, Inorg. Chern., 1968,7, 183; (6) ibid., 188.132 A. D. Pethybridge and J . E. Priie atoms lie at the corners of a regular octahedron with the hydroxy-groups along the edges.A normal co-ordinate analysis has been done; an anomalously high intensity for a low-frequency Raman band is cited as evidence for bis- muth-bismuth bonding. A similarly thorough analysis has been madel50 of the complex Pb4(0H)44+, which is a distorted cube with the lead and oxygen atoms arranged tetrahedrally. There is again evidence for metal-metal bond- ing. Nuclear Magnetic Resonance.-This has been an area of intense activity during the past year, although much of the work has increased under- standing of n.m.r. phenomena rather than substantially enhancing know- ledge of electrolyte solutions. For some cations with a sufficiently slow exchange rate of water molecules between the first co-ordination sphere and the bulk solvent, separate 1H signals can be observed for water molecules in the two situations and solva- tion numbers calculated from the areas of peaks for solvated ions.Separation of signals is achieved by temperature lowering and/or dilution of aqueous solutions with organic solvents. The ion Mg(H20)s2+ can be 'seen' in con- centrated aqueous solutions of the nitrate or perchlorate at temperatures below -70°c,16 and in solutions in aqueous acetone16, l7 over a much wider range of temperature and concentration. In methanolic acetone the ion Mg(MeOH)62f is formed.16 Complete analysis of line shapes should eventually give rate constants for the solvent exchange. As well as Mg(H20)s2+ the existence of AI(HZO)~~+,~~ Be(H~0)4~+,l~ Ga(HzO)s3-t,18 Co(H20)s2+,19 and N i ( H z o ) ~ ~ + , ~ ~ has been confirmed in similar manner.In mixed aqueous solvents, whilst dimethyl sulphoxide and NN-dimethylformamide compete with water for the inner-sphere of aluminium ions, acetone, tetramethylurea, dioxan, and tetrahydrofuran do not.21 In solutions of aluminium perchlorate in water-methyl cyanide mixtures, a separate signal has been found22 for each of the six species [AI(H20)6-n(MeCN)n]3+ with n = 1-6. When the 1H signal of solvent-OH in the co-ordination sphere of a cation can be separately seen, e.g. as with magnesium perchlorate in methanol, the residual shift of the main solvent signal from that of the pure solvent is due to the anion, and this makes possiblez3 the unambiguous calculation of a molal anion-shift without the usual arbitrary division of shifts between anions and cations. l6 N.A. Matwiyofl'and H. Taube, J . Amer. Chern. Suc., 1968,90, 2796. l7 R. G. Wawro and T. J. Swift, J. Amer. Chem. SOC., 1968, 90, 2792; A. Fratiello, A. Fratiello, R . E. Lee, V. M. Nishida, and R. E. Schuster, J . Chem. Phys., 1968, R. E. Lee, V. M. Nishida, and R. E. Schuster, Chem. Comm., 1968, 173. 48, 3705. l9 N. A. Matwiyoff and P. R. Darley, J . Phys. Chem., 1968,72, 2659. 2o T. J. Swift and G. P. Weinberger, J . Amer. Chem. SOC., 1968, 90, 2023. 21 A. Fratiello, R. E. Lee, V. M. Nishida, and R. E. Schuster, J . Chem. Phys., 1967, 47, 495 1. 32 L. D. Supran and N. Sheppard, Chern. Cumm., 1967, 852. 23 R. N. Butler, E. A. Philpott, and M. C. R. Symons, Clrem. Cutnm., 1968, 371.Electrolyte Solutions 133 Earlier work has been continued in which the addition of a suitable para- magnetic cation (e.g.Co2+) to shift the 1 7 0 signal of non-co-ordinated water molecules enables the signal of water co-ordinated to the diamagnetic cations Be2+, A13+, or Ga3+ to be seen separately.24 The technique has also been used25 to study the hydration of organometallic cations. The complexes of cobalt(r1) formed in concentrated aqueous hydrochloric acid solutions have been studied26 by observations of 1 7 0 and 35Cl line shifts. The relative solvating abilities of solvent molecules in pure solvents and in solvent mixtures is also often studiedz7* 28 by observations of chemical shifts. Sometimes the conclusions are surprising, e.g. that sodium ions interact more with the amine than with water in an ethylenediamine-water mixture.2g In such cases one doubts whether the chemical shift observations are very directly related to the strengths of chemical interactions.A useful review3O of the study of ion-solvent and ion-ion interactions by magnetic resonance tech- niques has appeared recently, as well as a chapter on n.m.r. studies of electro- lyte solutions.31 In the quantitative study of the ionisation of strong acids, new lH studies from 0-65"c of concentrated perchloric acid solutions in water and deuteri- ated water are reported,32a and there is further discussion of this and the corresponding nitric acid system in a subsequent paper.32b In some respects the problems are similar to those in Raman studies. It is clear that the lH shift of H30' is more dependent on its state of solvation and on the specific effects of anions than was initially thought.Measurements of degrees of ionisation of methanesulphonic acid by observation of the IH resonance of ionisable protons and of methyl protons agree well33 with the Raman results of Clarke and Woodwardlzlf at concentrations > 1 0 ~ . (Covington and Lilley33 calculate the chemical-shift contribution from hydroxonium ions from mea- surements on dilute solutions of the acid itself in order to allow for the specific effect of the anions). In solutions more dilute than 7 . 5 ~ , where the degree of ionisation is above 0.8, there are discrepancies between the Raman and n.m.r. work. There is therefore a large discrepancy between the acidity constant values of 73 and 16 mole l.-l calculated by the two pairs of investi- gators.The questionable nature of the necessary extrapolation was com- mented upon earlier. Electron Spin Resonance.-For the rather specialised class of anions which 24 D. Fiat and R. E. Connick, J . Amer. Cl7em. Soc., 1968, 90, 608. 35 G. E. Glass, W. B. Schabacher, and R. S . Tobias, Zmrg. Chem., 1968, 7, 2741. 26 A. H. Zeltmann, N. A. Matwiyoff, and L. 0. Morgan, J . Phys. Chem., 1968,72, 121. 27 J. C . Fanning and R. S. Drago, J . Amer. Chem. SOC., 1968, 90, 3987. 28 A. Fratiello, R. E. Lee, D. P. Miller, and V. M. Nishida, Mol. Phys., 1967, 13, 349. 29 E. G. Bloor a i d R. G. Kidd, Canad. J. Chem., 1968,46,3425. 30 J. Burgess and M. C . R. Symons, Quart. Rev., 1968, 22,276. 31 C. Durell, in 'Progress in Nuclear Resonance Spectroscopy,' eds.J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Pergamon Press, Oxford, 1968, vol. 4. 32 (a) R. W. Duerst, J. Chem. Phys., 1968,48,2275; (b) 0. Redlich, R. W. Duerst, and A. Merbach, ibid., 1968, 49, 2986. 33 A. K. Covington and T. H. Lilley, Tmrs. Foradoy Suc., 1967, 63, 1749.134 A . D . Pethybridge andJ. E. Prue are paramagnetic, e.g. semi-quinones, aromatic nitro-anions, and hydrocarbon radical anions, this method is potentially capable of providing detailed structural and kinetic information about ion pairs in organic solvents, and in particular about the distribution between ‘contact’ and ‘solvent-separated‘ varieties. Three review-type articles30, 34 have recently appeared. Ultraviolet and Visible Spectrophotometry.-Two papers35 report an excel- lent study over a temperature range of the equilibria: $Cr2072- + 3H20 + HCr04- + Cr042- + H+ Rather surprisingly, the outer-sphere association constant of the hydroxy-ion with the tris(ethylenediamine)cobalt(IzI) ion in dioxan-water and in dioxan- deuterium oxide mixtures is four times greater than with the tris(ethy1ene- diamine)chromium(rrr) c0mplex.~6 The ion-pair between tris(ethy1enediamine)- ruthenium(ru) and the iodide ion has a well-defined electron transfer band in the visible at a lower energy than the first cl-d tran~ition.3~ Conventional studies38 of the effect of added thiosulphate and selenite ions on the spectrum of tris(ethylenediamine)cobalt(m) refute the astonishing conclusion39 from optical rotation and circular dichroism measurements that, in 2~-sodium perchlorate, complexes such as [Co en33+ SZO,~-]+ with a stability quotient of 150 1.mole-l are formed as well as further complexes up to [Co en,3+(S2032-)4]5-. Spectroscopic studies40 of the association of copper(1r) with sulphate and of bis(ethylenediamine)copper(II) with thiosulphate ions add little to what is already known.41 Plots against the ionic strength Z of log(K’/yi) where K’ is the association quotient and the mean free-ion activity coefficient yk is given by (4) are found approximately to converge to a common intercept with any reason- able assumption about p. This is simply a consequence of the fact that -log yh = 4AZ*/(1 + pZ6) AI+/(l + ( p + Ap)I’) A I i / ( l + pZ*) - AApI ( 5 ) provided that A p is small. What is crucial is the calculation of K’ values and these are less certain than the authors imply.They are obtained from experi- ments at constant ionic strength. It is assumed that the association quotient does not vary with ionic composition at a fixed ionic strength, which is probably ~njustified.4~ No comment is made on the large variation with ionic strength of the values obtained for the difference between the molar absorp- tivities of free and associated copper ions. More importance attaches to the 34 (a) N. Hirota, J.Phys. Chem., 1967,71, 127; (b) M. C. R. Symons, ibid., 172. 35 (a) H. G. Linge and A. L. Jones, Austral. J. Chem., 1968,21, 1445; (b) ibid., 2189. 36 S. C. Chan, J . Chem. Suc. ( A ) , 1967, 2103. 37 Sr. H. Elsbernd and J. K. Beattie, Znurg. Chem., 1968, 7, 2468. 38 J.Olsen and J. Bjerrum, Acta Chem. Scand., 1967, 21, 1112. 39 R. Larrson, S. F. Mason, and B. J. Norman, J . Chern. SOC. ( A ) , 1966, 301. *O P. Hemmes and S. Petrucci, J . Phys. Chem., 1968, 72, 3986. 41 R. A. Matheson, J . Phys. Chem., 1967, 71, 1302.Electrolyte Solutions 135 ultrasonic absorption results in the same paper.40 The observation of a common absorption maximum for both complexes shows that inner-sphere complex formation occurs by the exchange of the anions with weakly attached water molecules in the axial positions of both CU(H20)s2+ and Cu en,(H~0)2~+. In the spectrophotometric experiments, the inner-sphere complexes probably act as optical 'markers' for ions in the associated class, not all of which are necessarily optically different from free ions.A continuation42 of earlier work on the absorption spectra of cobalt(r1) and nickel(r1) halide solutions up to high temperatures and pressures, leads to the conclusion that in concentrated alkali-metal halide solutions the deep blue colour of both cobalt and nickel solutions above 200-250"c is due to the presence of tetrahedral complexes such as CoC13(H20)-, NiC12(H20)2, or NiC13(H20)-. An interesting paper43 claims that precise differential refractonietry on solutions of the strong trifluoroacetic acid can be used to obtain values for both the acidity constant Ku and the apparent molar volume change AVO on dissociation. The method of analysing the data in which A Vo is an adjustable parameter as well as Ku is such that it is probably a conventional dissociation constant that is measured.The concentration of associated species is [see equation (l)], [A-B] + [A+B-1, and Ku = K1K2/(1 + KI). Conductivity.-A good general review44 of the techniques and results of precise measurements with special reference to non-aqueous solvents has been published. The non-specialist may be surprised to learn that to describe the concentration dependence of molar conductance there is still no agreement about the exact equation which incorporates an ion-size parameter and corresponds to the Debye-Huckel equation. This is particularly irritating as the number of results with an accuracy of about 0.01 % in the molar conduct- ance increases. However, it now seems to be generally agreed45 that retention of terms of order c3j2 is necessary.Although there is some evidence46 that the numerical difference between the predictions of the latest version of the Fuoss-Onsager equation 45c and that of has diminished, a paper by Pitts, Tabor, and which compares the two treatments, emphasises that some physical assumptions implicit in the Fuoss-Onsager treatment as well as mathematical details are open to criticism. A recent paper by Hsia and F u o s ~ ~ ~ which analyses results for aqueous solutions of caesium bromide and iodide begins with the surprising sentence 'Association of 1 :1 electrolytes has not 42 H.-D. Liidemann and E. U. Franck, Ber. Bunsengesellschaft Phys. Chem., 1968, 43 E. Grunwald and J. F. Haley, jun., J. Phys. C/iem., 1968,72, 1944. 44 J. Barthel, Angew. Chem., 1968, 80, 253.45 (a) R. Fernhndez-Prini and J. E. Prue, 2. phys. Chem. (Leipzig), 1965, 228, 373; (6) J.-C. Justice, J. Chim.phys., 1968, 65,353; (c) R. M. Fuoss and Kai-Li Hsia, Proc. Nat. Acad. Sci. U.S.A., 1967, 59, 1550. 72, 514. 46 R. Fernandez-Prini, Trans. Faraday SOC., 1968, 64, 2146. 47 E. Pitts, Proc. Roy. SOC., 1953, A , 217, 43. 48 E. Pitts, B. F. Tabor, and J. Daly, Trans. Faradny SOC., 1969, 65, 849. 49 Kai-Li Hsia and R. M. Fuoss, J . Amer. Chem. SOC., 1968, 90, 3055.136 A. D. Pethyhridge arid J . E. Prrir been seriously considered since the advent of the Debye-Hiickel theory of electrolytes in 1923’. A reference50 to a review of the work of C. W. Davies and others seems appropriate. These workers invoked association in inter- preting data for alkali-metal salts of oxyanions, whilst in the latest contribu- tions of Fuoss and co-worker~4~~ 5l it is invoked for dilute (<O*~M) aqueous solutions of the halides.For instance, for potassium chloride A , = 149.90 C2-l cm.2 mol-l, K A = 0-79 1. mole-l, a = 5-65 A. The ion-size parameter is much larger than the Bjerrum distance of 3.5 8, at which the mutual electrical potential energy of a pair of oppositely charged ions is equal to 2kT. Before accepting the need for a third adjustable parameter in fitting conductivity data for alkali-metal halides in water, the examination of the theoretical basis of the equations used and numerical comparison with the Pitts equation are highly desirable. A further surprising feature of Fuoss’s latest papers is the use of the Debye-Huckel limiting law for the activity coefficient of free ions because52 ‘ions in contact are counted as pairs and long-range interactions between free ions cannot depend on the size of ions but only on their charges’.After re-evaluating the coefficient of the c3I2 term in the Fuoss-Onsager treatment, 53 concludes that precise data for I : 1 electrolytes in a wide range of pure and mixed low-dielectric solvents are satisfactorily described by an association treatment with an ion size parameter in both the conductivity equation and the ionic activity coefficient equation equal to the Bjerrum distance. Furthermore, the variation of the association constants so obtained is quantitatively in accord with the traditional Bjerrum expression. Such a treatment may raise problems in connection with the conductance equation, but a similar procedure54 successfully describes the conductivity behaviour of 2 : 2 sulphates in water and a common description can be given of conductimetric, thermodynamic, and spectrophotometric results.In the sulphate cases, and it would be interesting to examine whether this is also true of Justice’s results, the association distance between free and associated ions could be varied considerably (with appropriate adjustment in K A ) ~ ~ ~ and an acceptable fit of the data still achieved. A further problem in studying ion association by conductivity methods is raised by Onsager and Provencher’s papers6 in the P. J. W. Debye memorial issue of the Journal of the American Chemical Society. If the rate constants for association and dissociation are appropriate, an additional mechanism for relaxation of asymmetric charge distribution is provided and the relaxation effect can be reduced by as much as 23 x.50 C. W. Davies, in ‘The Structure of Electrolytic Solutions,’ ed. W. J. Hamer, Wiley, 61 Ying-Chech Chiu and R. M. Fuoss, J . Phys. Chem., 1968, 72, 4123. 52 R. M. FUOSS, Rev. Pure Appl. Chetrr. (Australia), 1968, 18, 125. 53 J.-C. Justice, R. Bury, and C. Treiner, J . Chim. phys., 1968, 65, 1708; J.-C. Justice, 54 (a) W. G. Davies, R. J. Otter, and J. E. Prue, Discuss. Furaday Soc., 1957, 24, 103, 55 R. A. Matheson, J . Phys. Chem., 1968,72, 3330. 5G L. Onsager and S. W. Provencher, J . Amer. Chern. SOC., 1968,90, 3134. New York, 1959, p. 19. personal communication.123; (b) J. E. Prue, ‘Ionic Equilibria,’ Pergamon Press, Oxford, 1966, p. 64.Electrolyte Solirtions 137 The conductivity of tetra-alkylammonium salts continues to be a favourite topic of study in aqueous, non-aqueous, and mixed solvents. Fernandez- Prini4'j has shown that by treating these salts as incompletely dissociated in water a self-consistent analysis can be given of both conductivity and thermo- dynamic properties. The association constants increase with the size of anion for a given cation, which is also found in ethanol and propan01.~~ Trialkylsulphonium iodides have been investigatedS8 in water, methanol, and acetonitrile over a temperature range. In non-aqueous solvents they seem to be considerably more associated than tetra-alkylanimonium iodides.The limiting conductances of these organic cations, their effects on solvent vis- cosity, and the temperature coefficients of these properties in a variety of solvents have been lengthily discussed59 in terms of so-called solvent-structure theories. These theories, whilst interesting, are as yet of a qualitative nature and although 'explanations' abound, predictions are rare. It is certainly an interesting experimental fact that, whatever the explanation, large organic ions in aqueous solutions move abnormally slowly and the effect is extremely temperature dependent. Tt is also interesting that such effects disappear with the (HOC2H4)4Nf ion. Shedlovsky and co-workers continue60 an interesting series of papers on the behaviour of acetic acid, sodium acetate, hydrochloric acid, and sodium chloride in alcohol-water mixtures at several temperatures.An extensive series of measurements with a lengthy discussion is reported61 on the conductivity and viscosity over a temperature range of aqueous solutions of hydrochloric acid and of potassium hydroxide, fluoride, and chloride. Transport-number measurements have made possible the calculation of ionic conductances in sulpholane.62 Many groups are studying the properties of electrolyte solutions at elevated temperatures and pressures, and a list of these is given in a review by Mar- ~ha11.~3 The behaviour of aqueous solutions at supercritical temperatures and pressures is of interest to geochemists, steam turbine designers, and those concerned with economic methods for producing potable water from sea water.From the theoretical standpoint it is interesting that the dielectric constant of water varies from unity at supercritical temperatures and low pressure to about 100 at 0"c and 1 kbar. Quist and MarshallM have during the past year reported measurements on aqueous solutions of NaCl, HBr, NaBr, and NH3 at 0-100"c at pressures to 4 kbar. The results can be qualitatively explained by the effect of temperature and pressure on density, dielectric constant, and viscosity. As the density falls it becomes necessary to introduce 57 D. F. Evans and P. G. Gardam, J . Phys. Chern., 1968, 72, 3281. 58 D. F. Evans and T. L. Broadwater, J . Phys. Chem., 1968, 72, 1037. 59 R. L. Kay, G. P. Cunningham, and D. F. Evans, ref. 1, p. 249. 6O M. Goffredi and T.Shedlovsky, J . Phys. Chem., 1967,71, 4436. 61 T. Erdey-Gniz, E. Kugler, and L. Majthknyi, Electrochim. Acta, 1968, 13, 947. 62 M. Della Monica, U. Lamanna, and L. Senatore, J . Phys. Chem., 1968,72, 2124. 63 W. L. Marshall, Rev. Pure Appl. Chem. (Australia), 1968,18, 167. 134 A. S. Quist and W. L. Marshall, J . Phys. Chem., 1968,72, 684, 1545, 2100, 3122.138 A . D. Pethybridge and J. E. Prue association constants even for the alkali halides (e.g. at p = 0.75 g. ~ m . - ~ for NaCl). It seems to be generally true that log KA at any temperature is to a good approximation a linear function of log C H ~ O with an almost temperature- independent slope. This suggests equilibria of the type and Quist and MarshaW5 show that the same procedure has considerable success in representing the variation of equilibrium constants with the composition of mixtures of polar and non-polar solvents at ordinary temp- eratures and pressures. Ritzert and FranckG6 report measurements with an inductively heated cell on solutions of salts with divalent cations [BaC12, Ba(OH)2, and MgS041 as well as new measurements on potassium chloride.The maximum conductance values are lower for the salts with divalent ions. Horne and co-workers discuss the effect of pressure on the conductivity of tetra-alkylammonium halides in water67 and of potassium chloride in water- alcohol mixtures.68 Studies on non-aqueous solutions over a temperature and pressure range are reported for tetra-alkylammonium salts in nitr~benzene~~ and in a~etone.~O Two papers71 discuss the design of suitable conductance cells for high-pressure work.Lown, Thirsk, and Wynne-Jone~7~ report measurements on acetic acid, and show that the results at 25"c can be satis- factorily fitted by treating the change in standard partial molal isothermal compressibility as independent of pressure up to 2 kbar. The method is also tested with literature results for the dissociation of water and the ammonium ion. Thermodynamic Properties.-Single electrolytes. Between thermally isolated adjacent drops of solvent and solution in a closed space saturated with solvent vapuur a temperature difference is established. With careful calibration, this effect can provide a method for determining (Po - p)/po where po and p are the vapour pressure of solvent and solution respectively.Instruments which operate on this principle, known as 'vapour pressure osmometers,' have become commercially available and it seems that they are capable of providing values of osmotic coefficients of useful accuracy at lower molalities than the isopiestic method. Only small quantities of solution are required. The method has been used to supplement isopiestic measurements in this way in studies of aqueous solutions of tri-n-alkylsulphonium halides,73 whose behaviour is similar to that of tetra-alkylammonium salts, and of disulphonic acids and 65 A. S . Quist and W. L. Marshall, J . Phys. Chern., 1968, 72, 1536. 66 G. Ritzert and E. U. Franck, Ber. Bunsengesellschaft Phys. Chem., 1968, 72, 799. 67 R. A. Horne and R. P. Young, J . Phys. Chem., 1968,72, 1763.68 R. A. Horne, D. S. Johnson, and R. P. Young, J . Phys. Chem., 1968,72,866. 69 F. Barreira and G. J. Hills, Trans. Faraday SOC., 1968,64, 1359. 70 W. A. Adams and K. J. Laidler, Canad. J . Chem., 1968,46, 1977, 1989, 2005. 71 (a) D. A. Lown and Lord Wynne-Jones, J. Sci. Znstr., 1967, 44, 1037; (b) A. B. 72 D. A. Lown, H. R. Thirsk, and Lord Wynne-Jones, Trans. Faraday SOC., 1968, 64, 73 S. Lindenbaum, J . Phys. Chem., 1968, 72, 212. Gancy and S . l3. Brummer, J . Electrochem. SOC., 1968, 115, 804. 2073.Electrolyte Solutions 139 their salts with divalent cati0ns.7~ An activity coefficient of 1457 for uranyl perchlorate in water at a molality of 5.5 has been quoted75 as an example of extreme behaviour. This value was determined by the isopiestic method, but a recent study76 of the distribution of uranyl perchlorate between aqueous solution and carbon tetrachloride containing trialkyl phosphate gives an approximate value for the activity coefficient of 3.9 at a molality of 5.5.The value was confirmed by sedimentation equilibrium in the ultracentrifuge. It is suggested that the abnormally high isopiestic value is probably due to hydrolysis of the cation which increases the number of solute particles in soh tion. A heating-curve method was used by Garnsey and P r ~ e ~ ~ for the precise cryoscopic determination of osmotic coefficients of alkali-metal salts in dimethyl sulphoxide and in sulpholane (tetrahydrothiophen 1,l-dioxide). Although the dielectric constants of the two solvents are similar, the ionic solvating power of dimethyl sulphoxide is much greater than that of sul- pholane, which results in opposite sequences of osmotic coefficients for the alkali-metal perchlorates, and striking differences in degrees of ion association in the two solvents, particularly for lithium chloride. The results for lithium chloride in dimethyl sulphoxide are in fair agreement with earlier cryoscopic measurements by a different technique, but activity coefficients calculated from both sets of results do not agree with those obtained from e.m.f.mea- surement~.~~ The discrepancy awaits explanation. A recent contribution to the theory of the subject is a preliminary note by Rasaiah and Friedman79 proposing a model which superposes on the Coul- ombic potential between rigid non-polarisable ions a square-topped well or mound over the distance r to r + 2w where r is the sum of the crystallographic radii and w the radius of a water molecule.With a mound of height $kT they claim a surprisingly good description of the activity coefficient behaviour of aqueous sodium chloride. The relationship of the model to hydration effects is obvious. A semi-empirical equation has recently been suggesteds0 which is based on treating a concentrated solution by a so-called ‘two-structure’ model, one part following Debye-Hiickel behaviour, the other that of a randomised fused salt. A three-parameter equation is derived which, like the conventional power series in I s , fits data up to a molality of 2, but has the additional virtue that two of the parameters are functions only of the charge type of the electro- lyte. 74 0.D. Bonner, C. Rushing, and A. L. Torres, J. Phys. Chem., 1968,72, 4291. 75 R. A. Robinson and R. H. Stokes, ‘Electrolyte Solutions,’ 2nd Ed., Butterworths, 76 K. Schwabe, R. Kretschmer, R. Gartner, and R. Rottenbach, 2. phys. Chem. 77 R. Garnsey and J. E. Prue, Trans. Faraday SOC., 1968, 64, 1206. 78 W. H. Smyrl and C. W. Tobias, J . Electrochem. Soc., 1968, 115, 33; J. N. Butler, 79 J. C. Rasaiah and H. L. Friedman, J . Phys. Chem., 1968, 72, 3352. 80 M. H. Lietzke, R. W. Stoughton, and R. M. FUOSS, Proc. Nut. Acad. Sci. U.S.A., 1959, p. 218. (Leipzig), 1968, 238, 391. private communication. 1968, 59, 39.140 A. D . Pethybridge and J. E. Pule Studies of free energies and enthalpies of transfer of electrolytes between solvents continue.81 Those concerned with the resolution of free energies and enthalpies into ionic contributions by some kind of extrathermodynamic assumption will be interested in five recent papers.82 Morriss2e also discusses the present position regarding the ionic radii of alkali-metal and halide ions.There has been marked activity in the determination of apparent molar volumes and their concentration dependence. At sufficiently low concentra- tions the behaviour agrees with Debye-Huckel predictions and the zero- concentration values should eventually further our understanding of ion- solvent interaction. Dunns3 has continued his work with precise results by a dilatometric method for 1 : 1 and 2: 1 salts over a temperature range. Franks and Smiths4 have reported results for sodium and potassium chlorides and tetra-alkylammonium halides obtained with a magnetic float apparatus capable of measuring densities to one part in lo6 (at which point salt impurities become the factor limiting accuracy and reproducibility).Ellis85a, has reported measurements for several electrolytes at temperatures up to 2Oo0c, which have been discussed by Gluecka~f.~~c Other papers report the results of studies of the apparent molar volumes of tetra-alkylammonium halides in water (over a temperature range), g6 in ethanol-water mixtures,87 and in deuterium oxide.8s The differences between the limiting values in deuterium oxide and in water are negative for sodium halides but positive for tetra- alkylammonium bromides. Mixed electrolytes.When studying the thermodynamic properties of solutions of mixed electrolytes there are two basic aims; firstly the prediction of the properties of mixtures from the properties of single electrolytes and secondly the determination of functions suitable for the interpolation of results at intermediate concentrations. Osmotic coefficients (4) of the solvent are usually obtained from isopiestic measurements and activity coefficients(y) of solutes calculated from these by means of the equations of Scatchard or of McKay and Perring. Activity coefficients calculated by the two methods usually agree quite well: the former involves rather cumbrous equations and the latter an unreliable graphical integration from zero concentration. Alternatively, activity coefficients are determined from potentiometric meas- urements on suitably designed cells.81 (a) H. P. Bennetto, D. Feakins, and K. C. Lawrence, J . Chem. Soc. ( A ) , 1968, 1493; (b) J. H. Stern and J. Nobilione, J . Phys. Chem., 1968,72, 1064, 3937. 82 (a) R. G. Bates, ref. I , p. 49; (b) H. P. Bennetto and D. Feakins, ref. 1 , p. 235, and ref. 81(a); (c) C. L. de Ligny, M. Alfenaar, and N. G. Van der Veen, Rec. Trau. chim., 1968, 87, 585; ( d ) W. A. Millen and D. W. Watts, J . Amer. Chem. SOC., 1967, 89, 6051; ( e ) D. F. C. Morris, Structure and Bonding, 1968, 4, 63. 83 L. A. Dunn, Trans. Faraday SOC., 1968, 64, 2951. 84 F. Franks and H. T. Smith, Trans. Faraday Soc., 1967, 63, 2586. 85 (a) A. J. Ellis, J . Chem. SOC. (A), 1968, 1138; (b) A. J.Ellis and I. M. McFadden, 86 (a) F. J. Miller0 and W. Drost-Hansen, J. Phys. Chem., 1968,72, 1758; (b) R. Gopal 87 I. Lee and J. B. Hyne, Canad. J . Chem., 1968,46,2333. 88 B. E. Conway and L. H. LalibertC, J . Phys. Chem., 1968,72,4317. Chem. Comm., 1968, 516; ( c ) E. Glueckauf, Trans. Faraday SOC., 1968, 64,2423. and M. A. Siddiqi, J . Phys. Chem., 1968,72, 1814.Electroly f e Soliltions 141 Isopiestic measurements on mixed electrolytes are made on sets of solutions of selected mole fractions of solutes B and C but whose ultimate total concen- tration is fixed by the criterion that all solutions must at equilibrium have the same vapour pressure. A single-electrolyte solution is included with each set for calibration purposes. The results are fitted to a suitable smoothing function and + and y calculated at various solute mole fractions of B and C and rounded values of the total ionic strength, the upper limit of this usually being fixed by a limit of solubility.It is often difficult to compare different measurements on the same system because individual workers select different solute mole fractions and ionic strengths. Typical of this kind of work are the isopiestic measurements of Wu, Rush, and ScatchardS9 on the four pairwise mixtures containing a common ion of NaCl, Na~S04, MgC12, and MgS04 in water at 25”c. These workers analysed their results by Scatchard’s method and found that all components obey within experimental error the linear relationship (6) known as Harned’s Rule up to a total ionic strength of 6 mole kg.-l.The rule states that log YB(C) = log yS(0) - %BC XC I (6) where YB(C) is the activity coefficient of salt B in a mixed solution of total ionic strength Icontaining a mole fraction x c of salt C, log yB(0) is the activity coefficient of B alone at the same ionic strength and aBC is a constant deter- mined by B and C and the total ionic strength. Platford has confirmed these results for mixtures of NaC1-MgC1zg0 and NaCl-Na2S04.91 He treated his results by both methods outlined above and obtained similar conclusions from each. Butler and co-workers have also obtained confirmatory results for the activity coefficient of one component of these mixtures from potentio- metric measurements on cells of the typeg2 Na(Hg) INaf, M2+, C1-, HzO IAgCl, Ag where M = Mg or Ca, andg3 Pb(Hg), PbSO, INa+, SO,2-, C1-, H20 I Na glass electrode.Unfortunately, the actual e.m.f.’s of this second cell are not reported, but only the calculated activity coefficients. The theoretical background of the subject is discussed in a recent book by Harned and RobinsonY4 and in a chapter of a bookg5 and in a paperg6 by 89 Y . C. Wu, R. M. Rush, and G. Scatchard, J . Phys. Cliei~i., 1968,72,4048. R. F. Platford, J. Phys. Chem., 1968, 72, 4053. 91 R. F. Platford, J . Chem. and Eng. Data, 1968, 13, 46. 92 J. N. Butler and R. Huston, J . Phys. Chem., 1967, 71, 4479. 93 J. C. Synott and J. N. Butler, J . Phys. Chem., 1968,72, 2474. 94 H. S. Harned and R. A. Robinson, ‘Multicomponent Electrolyte Solutions,’ 95 E. A. Guggenheim, ‘Applications o f Statistical Mechanics,’ Clarendon Press, 96 E.A. Guggenheim, Trans. Faraday SOC., 1966, 62, 3446. Pergamon Press, Oxford, 1968. Oxford, 1966, p. 165.142 A . D. Pethybridge and J. E. Prue Guggenheim. Scatchard97 derives equations for the excess free energy of mixing and gives a brief, rather personal, review of the historical setting of the various approximations made in the study of the thermodynamic properties of mixed electrolyte solutions. Pan98 has derived a form of the McKay-Perring equation which avoids graphical integration and is quite closely related to Scatchard’s equations. The latter are clarified in papers by Robinson and co-workers on NaC1-KClg9 and KC1-CaCl2lo0 mixtures, and by Rush and Johnsonlo1 who tabulate corrections of the many misprints in Scatchard’s original paper.Rush and JohnsonlOl report isopiestic measurements on pairs of solutes from the trio HC104, LiC104, and NaC104 as well as an extension of measurements on pure NaC104 up to 16 mole kg.-l. They find that Harned’s rule is not obeyed for either salt in the system HC104-NaC104. More interest- ing is the observationlo2 from potentiometric measurements that in binary mixtures of hydrochloric acid with alkaline-earth perchlorates, Harned’s rule is sometimes obeyed by one component of the mixture but not by the other, e.g. obeyed by Sr(C104)~ or Ba(C104)~ but not by HCl. HE GE Guggenheimg6 has shown that the so-called ‘square-cross’ rule for thermo- dynamic functions implies that triplet interactions are negligible, but does not imply small or negligible interactions between ions of the same sign.The square-cross rule for free energies has been recently verifiedlo3 for the system shown in the diagram (the values shown are for a total molality of one); the 97 G. Scatchard, J . Amer. Chem. SOC., 1968, 90, 3124. 98 C. Pan, J . Phys. Chem., 1968,72, 2548. 99 R. M. Rush and R. A. Robinson, J . Tenn. Acad. Sci., 1958,43, 22. loo R. A. Robinson and A. K. Covington, J . Res. Nat. Bur. Stand., Sect. A , 1968, 72, 101 R. M. Rush and J. S. Johnson, J . Phys. Chern., 1968,72, 767. lo2 I. A. Weeks, Austral. J . Chem., 1967, 20, 2367. lo3 A. K. Covington, T. H. Lilley, and R. A. Robinson, J . Phys. Chern., 1968,72,2759. 239.Electrolyte Solutions 143 rule has been previously demonstrated for enthalpies in the same system.With the same assumptions LilleylO4 has shown that the enthalpy and volume changes on mixing equimolar proportions of 1 :1 electrolytes without a common ion can be predicted from experimental data on only one pair of salts with a common cation and one pair with a common anion in conjunction with data for each individual salt. The square-cross rule has also been demon- strated105 for volume changes in the system LiCl, NaCl, Li2SO4, and NazS04. Acid-base equilibria. In their search for a wide range of well defined buffer solutions Bates et al.lo6 report conventional pa^ values for solutions of piperazine phosphate (PzH3P04) over a wide temperature range. The salt is stable and easily purified and the solutions have a high buffer capacity. The pa^ of a 0-05 molal solution at 25"c which contains the species PzHz2+, PzH+, H2P04-, and HP(h2- is 6.26.This value was obtained by extrapolation of measurements on a cell without transference with various quantities of added potassium chloride. As the operational pH is measured in a cell with a liquid junction, values of pH and pa^ will not usually agree. For buffers from acids of type HA, A pa^ - pH m 0, while for HBf, A w 0.013, and for H2B2+, A is even larger. For the piperazine phosphate buffer, A = 0.03 pH units. The same group has published several papers on buffer standards in deuterium oxide and has now investigated107 the relation between the conventional ~ L Z D scale (from cells without a liquid junction) and the operational pD scales (from cells with glass and calomel electrodes with a liquid junction).To obtain readings on the pD scale when the meter has been standardised with an aqueous buffer solution, 0-45 (molal basis) must be added to the observed meter reading for solutions of buffers from acids of the type HA in deuterium oxide. A proposal for a universal pH scale for solutions at different tempera- tures and in different solvents has been made by de Ligny and Alfenaar.lo8 Precise potentiometric measurements of acidity constants and their temperature dependence have been made for the dibasic piperazinium ion,l09 and for alkylammoniumllOu and hydroxysubstituted alkylammonium ions.llob A spectrophotometric technique has been usedlll to study the dissociation of a large number of substituted phenols and anilines over a temperature range.The references cited contain references to earlier work. Measurements of the acidity constants of molecules in electronically excited states continue; e.g. for the lowest x-x* state of aromatic carboxylic acids the acidity constant is T. H. Lilley, Trans. Faraday SOC., 1968, 64, 2947. Io5 (a) H. E. Wirth and W. L. Mills, J . Chem. and Eng. Data, 1968, 13, 102; (6) H. E. 106 H. B. Hetzer, R. A. Robinson, and R. G. Bates, Analyt. Chem., 1968,40,634. lo7 A. K. Covington, M. Paabo, R. A. Robinson, and R. G. Bates, Analyt. Chem., lo8 C. L. de Ligny and M. Alfenaar, Rec. Trao. chim., 1967, 86, 1182, 1185. log H. B. Hetzer, R. A. Robinson, and R. G. Bates, J . Phys. Chem., 1968,72, 2081. 110 (a) M. C. Cox, D. H. Everett, D. A. Landsman, and R.J. Munn, J. Chem. SOC. (B), 111 P. D. Bolton and F. M. Hall, Austral. J . Chem., 1968,21, 939; P. D. Bolton, F. M. Wirth and A. LoSurdo, ibid., 226. 1968, 40, 700. 1968, 1373; (b) B. A. Timimi and D. H. Everett, ibid., 1380. Hall, and J. Kudrynski, ibid., 1541.144 A. D. Pethybsidge and J. E, Prire decreased by a factor of about 104 compared with the ground-state value.ll3 An extensive review of titrations and acid-base equilibria in non-aqueous solvents has been published,l13 and several accounts of measurements with dimethyl sulphoxide have been reported.l14 An important and scholarly review of the equilibrium properties of acids and bases in amphiprotic mixed solvents has appeared.82a Relevant to the state of solvation of the proton in methanol-water mixtures are studies115n by mass spectrometry on the com- petitive solvation of the hydrogen ion in the gas phase.In mixtures of methanol and water vapour the hydrogen ion is solvated preferentially by MeOH in small clusters and by H2O in the larger ones. For example, when the vapour phase contains only 5 % MeOH, the clusters L4Hf, L5Hf, and L6Hf, where L is ligand, contain 80,65, and 55 % of MeOH respectively. The trend towards preferential solvation by water in large clusters suggests that the same will occur in liquid mixtures, although Wellsllsb does not agree with this interpre- tation. Electrodes.-Two very interesting reviews have been published. ‘Bio- electrodes’l16 consists of a series of articles on various applications of potentio- nietry to biological systems.Many articles are of interest to a physical chemist, particularly those on silver-silver chloride, glass, and ion-selective electrodes. More detailed information on ion-selective electrodes is included in a review by Toren.l17 These electrodes are based on a ‘membrane’ of some kind which may be of glass, ion-exchange resin (solid or liquid), a precipitate embedded in a matrix, or a single crystal. Ideally the membrane selectively transports ions of a single kind, and the successful development of such electrodes will obviously vastly increase the range of potentiometric studies. Much recent work shows that electrodes of this type show a theoretical response over a limited concentration range and are often subject to specific interference by other ions.One hopes that manufacturers will be able to resist the temptation to make excessive claims for their products in advertising literature. One of the best ion-selective electrodes is a single, doped crystal of lanthanum fluoride cemented into a tube containing a reference electrolyte and electrode. Several workers have shown that this electrode shows a theoretical response to fluoride ions down to a concentration of 10-4~. The electrode has been used to rein- vestigate the acidity constant of hydrofluoric acid and the stability constant of the complex HF:,ll8 and to study the fluoride complexes of t i n ( ~ ~ ) . l l ~ 112 E. Vander Donckt and G. Porter, Trans. Faraday SOC., 1968, 64, 3215. 113 G. A. Harlow and D. H. Morman, Analyt. Chem., I968,40,418R. 114 I .M. Kolthoff, M. K. Chantooni, jun., and S. Bhowmik, J . Amer. Chem. SOC., 1968, 90, 23; C. D. Ritchie and R. E. Uschold, ibid., 2821; I. M. Kolthoff and M. K. Chantooni, jun., ibid., 5961. 115 (a) P. Kebarle, R. N. Haynes, and J. G. Collins, J . Amer. Chem. SOC., 1967, 89, 5753; (b) C. F. Wells, ref. 1 , p. 224. 117 E. C. Toren, Analyt. Chem., 1968, 40, 402R. I l 8 K. Srinivasan and G. A. Rechnitz, Analyt. Cliem., 1968, 40, 509; N. E. Vander- Ann. New York Acad. Sci. (‘Bioelectrodes’), 1968, 148, 1-287. borgh, Talanta, 1968, 15, 1009. F. M. Hall and S. J. Slater, Ausfrul. J . Clienr., 1968, 21, 2663.Electrolyte Solutions 145 Electrodes reversible to calcium ions have been used120 in conjunction with a calomel electrode to measure activity coefficients of calcium chloride in mixtures with sodium and magnesium chlorides. The specificity of the elec- trodes breaks down if the concentration of sodium ions rises above 10-2~, but in the absence of other cations the electrodes show a theoretical response over a wide range of concentration.Amalgam electrodes have also been widely investigated. Feakins and co-workers81a discuss the best technique for making these electrodes and measuring their potentials (a digital voltmeter and automatic data recording cquipment were used). The use of lithium,121 s ~ d i u i n , ~ ~ and calcium12z amalgam electrodes in aqueous media has been described. A lead amalgam electrode has been shown123 to respond reversibly to changes in the hydroxide ion concentration in solutions of high pH. A useful review of electrode potentials in non-aqueous solvents has been p~b1ished.l~~ The behaviour of the lithium electrode in propylene carbonate125 and dimethyl sulphoxide126 has been studied.Smyrl and Tobias127 discuss the effect of diffusion of a sparingly soluble salt on the e.m.f. of cells without transference. This effect is more important for electrodes of the same kind, e.g. Ag-AgC1, in non-aqueous solutions, than in aqueous solutions because the ‘insoluble’ salts are usually more soluble than in water. The Ag-AgC1,128a Ag-AgBr,128b and Cd-CdCl2128C electrodes behave reversibly in formamide. Tetra-alkylaxnmonium Salts.-It has been known for forty years that dilute aqueous solutions of these salts show abnormally large deviations from Debye-Huckel behaviour.Recent work (see, for example, several contribu- tions and references therein in ref. 1) has been partly stimulated by interest in the fashionable concepts of ‘hydrophobic bonding’ and ‘hydrophobic hydration’. It is convenient to discuss these two topics separately, as the first is concerned with solute-solute interaction and the second with solute-solvent interaction alone. ‘Hydrophobic bonding’ or better ‘hydrophobic interaction’ describes the tendency of non-polar groups in the same or different molecules to associate in aqueous solution, thereby reducing the interactions between solute and water.12g The attraction is often considered exceptional because it is charac- terized by AH0 > 0 and T A P > 0. In fact the same is true of ion-pair 120 A. Shatkay, J .Phys. Chem., 1967, 71, 3858. lZ1 R. Huston and J. N. Butler, J . Phys. Chem., 1968, 72,4263. 123 G . Schorsch and N. Ingri, Acta Chem. Scand., 1967,21,2727. lz4 H. Strehlow in, ‘The Chemistry of Non-aqueous solvents,’ ed. J. J. Lagowski, 125 B. Burrows and R. Jasinski, J. Electrochem. SOC., 1968,115, 365. lZ6 D. R. Cogley and J. N. Butler, J . Phys. Chem., 1968,72, 1017. 127 W. H. Smyrl and C. W. Tobias, Electrochim. Acta, 1968, 13, 1581. 12* (a) R. W. C . Broadbank, S. Dhabanandana, K. W. Morcom, and B. L. Muju, Trans. Faraday SOC., 1968, 64, 3311; (b) K. W. Morcom and N. L. Muju, Nature, 1968, 217, 1046; (c) R. W. C . Broadbank, B. L. Muju, and K. W. Morcom, Trans. Faraday SOC., 1968, 64, 3318. J. N. Butler, J . Electroanalyt. Chem. Interfacial Electrochem., 1968, 17, 309.Academic Press, New York, London, 1966, vol. 1, p. 129. G. Ndmethy, Angew. Chem., 1967, 6 , 195.146 A. D. Petlij*bsiclgc and J . E. Priie formation in aqueous solution solely due to coulombic attraction.130 The implication in both cases is that ‘bond’ formation releases solvent from constraint. Hydrophobic interaction between two oppositely charged ions will clearly be enhanced by coulombic attraction and could result in associa- tion between ions unlikely to associate for electrostatic reasons alone; indeed, the larger the ions and the smaller their charge, the stronger will be the hydro- phobic interaction. A clear qualitative discussion of the origin and role of hydrophobic attraction in leading to ion pairing was written by Diamond in 1963.131 With the tetra-alkylammonium halides there is strong quantitative evidence from the variation with concentration of conductivities,46 osmotic coefficient^,^^ and apparent molar volumes132 for ion association which increases with size of cation or anion.Such an effect can, if sufficiently small, be formally described by an abnormally small ion-size pararneter,l33 or in the case of osmotic coefficients by a negative specific interaction ~oefficient.l3~ A of the effect of sodium halides on the solubility of tetrabutyl- ammonium perchlorate reveals the same pattern of behaviour. Orthodox members of the ‘hydrophobic hydration’ school object to the concept of ion pairing between (say) tetrabutylammonium and iodide ions, because these two ions belong in different categories, The former is a ‘structure-maker’, whilst ions such as the latter with small surface charge densities but not con- taining organic groups are characterized as ‘structure breakers’ (for a defini- tion of terms see ref.59). The ‘hydrophobic hydration’ schooP36 prefer to invoke, although usually without quantitative discussion, pairs between like- charged cations. However, even in dilute solutions the colligative behaviour shows a marked specific dependence on the anion.134 As the concentration rises higher aggregates involving both cations and anions may become important and eventually hydrophobic interaction will induce micelle forma- t i ~ n . l ~ ~ An attempt to clarify the situation by relaxation studies137a of solu- tions of tetra-alkylammonium salts may be complicated by relaxation involving the alkyl chains alone.137* As would be expected, hydrophobic interaction between tetra-alkylammoniuni ions and solutes such as benzene138 or naphthalene139 increases the solubility of such solutes in water. We turn now to ‘hydrophobic hydration’ which is much more closely associated with controversial views about solvent ‘structure’ and in particular I3O J. E.Prue, J . Chem. Educ., 1969, 46, 12. 131 R. M. Diamond, J. Phys. Chem., 1963, 67, 2513. 132 H. E. Wirth, J . Phys. Chem., 1967, 71, 2922. 133 R. L. Kay and D. F. Evans, J . Phys. Chem., 1966,70, 366. 13* J. E. Prue, A. J. Read, and G. Romeo, ref. 1 , p. 155. 135 J. Steigman and J. Dobrow, J . Phys. Chem., 1968, 72, 3424. 136 H. S. Frank in, ‘Chemical Physics of Tonic Solutions,’ eds. B.E. Conway and R . G. 13’ (a) G . Atkinson, R. Garnsey, and M. J. Tait, ref. 1 , p. 161; (6) M. J. Blandamer, 13* (a) H. E. Wirth and A. LoSurdo, J . Phys. Chem., 1968,72,751; (b) J. E. Desnoyers, 139 J. E. Gordon and R. L. Thorne, J . Phys. Chem., 1967, 71, 4390. Barradas, Wiley, New York, 1966, p. 59. M. J. Foster, N. J. Hidden, and M. C. R . Symons, Trans. Faraday Sac., 1968,64, 3247. G. E. Pelletier, and C. Jolicoeur, Canad. J . Chem., 1965,43, 3232.Electrolyte Solutions 147 the structure of water. It seems140 that phrases such as ‘hydrophobic structure making’ refer particularly to three effects : firstly, an increase in the molecular reorientation time of water molecules in the neighbourhood of a non-polar group, evidence for which is provided by n.m.r. measurements, although this has recently been questioned141 as the result of some measurements on di- quaternary ammonium bromides : secondly, an effect on the transport properties (see p. 009) of large organic ions which puts them into a category different from inorganic ions of either small or large surface charge density: thirdly, the hydrophobic effect is thermodynamically characterised1lo3 140 by a decrease in entropy and a large increase in the heat capacity when alkyl chains are inserted into water. It is readily apprehensible that on the introduction of a non-wetting surface into water, in order to reduce the electric field extending into the non-polar environment, the water molecules immediately adjacent to the non-polar surface should become relatively rigidly orientated and hydrogen-bonded to water molecules in the next shell. The larger the surface of the solute the greater will be the effect which may well reduce both the re-orientation time of the water molecules involved and the solute mobility. What is less evident, however, is that an extensive volume of solution around a tetra-alkylammon- ium ion is converted to some kind of ‘iceberg’ or ‘flickering cluster’ (no estimate seems to have been hazarded as to the number of water molecules in such an ‘iceberg’), or what relationship, if any, such regions have to crystalline clathrates of tetra-alkylammonium salts. Too many papers are insufficiently concerned with deciding the minimum number of adjustable parameters consistent with interpretation of a particular set of results, and too often content to conclude that all is in excellent accord with ill-defined notions of the ‘structure’ of water. As Atkin~onl~~ has stressed, in the absence of quantitative theory, ‘structural’ effects can too easily become a repository of collective ignorance. An interesting observation is that tetra-alkylammonium salts, like other salts, depress the temperature of maximum density of water.143 From the discussion in the paper, it is clear that the authors had expected the ‘structure-making’ tetra-alkylammonium salts would have the opposite effect to ‘structure-breaking’ salts because of a tendency to stabilise strongly hydro- gen-bonded, more ‘structured’ and less dense regions. The explanation that this would happen at 25” but not at 4”c because there are insufficient free water-molecules to form ‘flickering clusters’ at the lower temperature, is, to say the least, not particularly convincing. 140 Ref. 1, p. 221-233. 141 D. D. Eley and M. J. Hey, Trans. Farachy SOC., 1968,64, 1990. 142 G. Atkinson, ref. I , p. 269. 143 A. J. Darnell and J. Greyson, J . Phys. Chenr., 1968, 72, 3021.