6 Interactions involving Aquo Ions By D. R. ROSSEINSKY Department of Chemistry The University Exeter Since the Specialist Periodical Reports now bear the burden of providing comprehensive literature coverage,’ 2 in this chapter consideration can be given to themes both more general and more particular than those of its direct pre-dece~sor.~ Mainly ions in water will be considered other solvents being referred to generally only to contrast or emphasize points of aquo-ion chemistry. A I.U.P.A.C. conference on non-aqueous electrolytes included a number of review^^.^ which will admirably serve to repair this omission. Interactions in solution undoubtedly represent one of the great scientific problems still largely unresolved but the recent surge of coherence and purpose in electrolyte research augurs well for the emergence of reasonably exact rules, if not laws for rationalizing electrolyte behaviour-rules numerically predictive rather than just verbally graphic.Widespread support of work in the U.S.A.6 by the Office of Saline Water stresses the social and environmental importance of these studies and without any specific bibliographic count both an absolute and a relative increase in the number of publications could be discerned over recent years. New books have appeared as follows a fundamental text by Koryta Dvofak and BohaEkova7 may be contrasted with Bockris and Reddy’s* personally oriented but stimulating’ opus ; volume 6 of ‘Modern Aspects’” contains inter alia an article by Friedman on ionic interactions referred to in more detail below ; ‘Electrochemistry’ becomes volume IXA of the Eyring series ;ll ‘Electrochemistry’ ed.G. J . Hills (Specialist Periodical Reports) The Chemical Society London 1970 vol. 1 . * ‘Electrochemistry’ ed. G. J . Hills (Specialist Periodical Reports) The Chemical Society London 1972 vol. 2. A. D. Pethybridge and J. E. Prue Ann. Reports ( A ) 1968 65 129. ‘Symposium on Non-aqueous Electrochemistry’ Paris 1970 presented in Pure Appl. Chem. 1971,25 305-456. E.g. papers in J . Phys. Chem. 1970 74 3677-3822. ’ Papers in J . Electroanalyt. Chem. Interfacial Electrochem. 1971 29 1 -209. ’ J. Koryta J. Dvoiak and V. BohaEkova ‘Electrochemistry’ Methuen London 1970. * J. O’M. Bockris and A. N. Reddy ‘Modern Electrochemistry’ MacDonald London, 1970. G. J.Hills Chem. in Britain 1971 7 164. l o ‘Modern Aspects of Electrochemistry’ ed. J . O’M. Bockris and B. E. Conway Butter-worths London 1971 vol. 6 . ‘Physical Chemistry-An Advanced Treatise’ ed. H. Eyring Academic Press London, 1970 vol. IXA Electrochemistry. 82 D. R. Rosseinsky Petrucci has edited a two-volume treatise,120 ‘Ionic Interactions’ intended as a uniform presentation but inevitably again a collection of monographs akin to references 10 and 11 although there are particularly interesting chapters by Falkenhagen and his colleagues; Falkenhagen et al. have also produced a new monograph on electrolyte theory ;’ 2b a book neither much publicized nor readily available,’ incorporating a wide review of electrolyte properties covers Mishchenko’s and other Russian work in the 196O’s.l4 Conference reports include one (dedicated to T.F. Young) on the structure of water and aqueous solutions,6 one on molecular motions in ~olution,’~ and one on ionic inter-actions.’ To provide a theme we consider a universe in which rather than Jeans’s mathematician,’ the deity is a working physical chemist. Here individual ions of unambiguous size interact with solvent molecules (similarly well character-ized) with perfect pair additivity. The interaction is a simple analytical function readily discernible by appropriate wave-mechanical treatment of the model, from experimental solvation energies. The solvent-solvent interactions are well understood. A complete dielectric theory allows equally a multibody or sphere-continuum formulation.For vanishing concentrations ion-ion interactions follow a limiting law readily extended by the use of Coulomb’s law. This involves either well-defined simple summation procedures for particulate multibody interactions calling in the solvation-energy function or invocation of clearly equivalent specific associative equilibria of predictable molecularity and magni-tude the nature of the associations (whether covalent or coulombic) being obvious from observable largely spectroscopic properties of the solutes. This Report would then become merely a brief statement of the interaction potentials and their treatment together with a catalogue of recent thermodynamic and spectro-scopic measurements the molecular interpretations exactly confirming the premises.Apart from the existence of the limiting law however the extent to which the reality matches this construct might be inferred from what follows. 1 Solvation of Ions Solvation Energies.-Solvation energies are those for the process gas ion -+ ion in solvent which we will contemplate as the difference between gas atom -+ ion in solution + . . . (1) l 2 (a) ‘Ionic Interactions’ ed. S. Petrucci Academic Press London 1971 vol. I Equilib-rium and Mass Transport vol. 11 Kinetics and Structure; (b) H. Falkenhagen W. Ebeling and H. G. Hertz ‘Theorie der Elektrolyte’ Hirzel Leipzig 1970. l 3 Yu. M. Kessler Russ. J . Phys. Chem. 1971 45 578. l 4 K. P. Mishchenko and G . M. Poloratskii ‘Aspects of the Thermodynamics and the Structure of Aqueous and Non-aqueous Solutions of Electrolytes’ Khimiya Lenin-grad 1968 (in Russian).20th meeting of CITCE Strasbourg 1969 presented in Electrochim. Acta 1971 16, J . Jeans ‘The Mysterious Universe’ Cambridge University Press 1930 p. 134. I s Papers in Ber. Bunsengesellschaft p h y s . Chem. 197 1 75 183-402. 667-7 3 8. Interactions involving Aquo Ions and 83 gas atom -+ gas ion + . (2) where '+ . . .' implies a constant charge-conserving half-reaction of no interest whatever if only ions of similar charge are studied. The term solvation energy is used to include both molar or molecular (theoretical) potential energies as well as thermodynamic energies free energies or enthalpies of solvation. The distinction will be either stated or obvious from the context. Case" has reviewed the subject to ca.1970. For alkali halide (MX) values in aqueous and various amide solvents Tomus" presents checks for internal consistency of the data based on additivity requirements. Single-ion values are derived" with appropriate qualifications. Such values were estimated experi-mentally for acetone solution by a contact-potential method.20 Somsen Weeda, and Los have performed2 ' the familiar approximate potential-energy calcula-tions for ion-solvent-multipole interactions assuming various solvation numbers for several amide solvents ammonia methanol and water employing Somsen and Weeda's own solvation data.22 Unremarked by these authors,22 there emerges the fact originally noted by P l e ~ k o v ~ ~ and since redis~overed,~~ that differences between alkali-metal M+ values when M+ is K+ or larger are closely constant independent of solvent but values for H + fluctuate markedly, which makes H+ a poor reference ion in the quoting of experimental values.If K + or a larger M+ is made the reference it becomes clear that the relative solvation energy of H + roughly increases with polarizability-per-nonhydrogenic-atom of solvent and with the (approximately parallel) proton affinit~.'~ Li+ shows the same trend much attenuated and Na+ scarcely does so at all. Thus in a gross sense the interactions of the larger M+ with water and with non-aqueous solvents are not markedly dissimilar. This conclusion is endorsed by similar observation^^^ about the viscosity B coefficients (which often show qualitatively similar trends for various solvents including H20) and regarding activity coefficients of tetra-alkylammonium (R4Nf) salts.' Arguments based on structures special to water can thus be refuted.I3 Morf and Simon26 invite grave criticism of solvation-energy calculations in claiming agreement with experiment only when experimental hydration numbers are used the values they26 use are not experimental but are very indirectly inferred or guessed.27 Enthalpies of transfer of R4N+ ions between H20 D20, l n B. Case in 'Reactions of Molecules and Electrodes' ed. N. S. Hush Wiley-Interscience, '' E. J . Tomus Studii si Cercetari de Chim. 1970 18 123. 2 o I. Zakorska and Z . Koczorowski Roczniki Chem. 1970,44 1559. 2 1 G. Somsen L. Weeda and J. M. Los J . Electroanalyt. Chem. Interfacial Electrochem., 2 2 G.Somsen and L. Weeda J . Electroanalyt. Chem. Interfacial Electrochem. 1971 29, 2 3 W. A. Pleskov Uspekhi Khim. 1947 16 254. 2 4 D. R. Rosseinsky Electrochim. Acta 1971 16 23. 2 5 C. M. Criss and M. J . Mastroianni J . Phys. Chem. 1971 75 2532. 2 h W. E. Morf and W. Simon Helv. Chim. Acta 1971 54 794. 2 7 H. G. Hertz Angew. Chem. Internar. Edn. 1970 9 124. London 1971 p. 45. 1971 31 9. 375 84 D. R. Rosseinsky propylene carbonate and dimethyl sulphoxide have been considered2 * in the light of chain lengths and hydrophobic and hydrogen bonding but no clear-cut generalizations emerge. Solvation in water and in propylene carbonate has also been given a traditional Born treatment.29 Solvation enthalpies of alkaline-earth halides have been mea~ured,~' and the variation of values between solvents is noted without elaboration we remark the contrast with the larger M f discussed in the preceding paragraph and point out the similarity to H+ and Li' doubtless owing to the same cause.In assessment although it is clearly useful to show that the same sort of poten-tial-energy calculations can be performed for non-aqueous solvents as for water, there are a variety of ways of doing the calculations all of which can be made to fit experiment approximately. This is because there are hosts of parameters, which known roughly or only for the gaseous or solid states when taken cumu-latively allow a flexibility which belies the purported quantitative nature of the calculated results. This criticism would be mitigated were either the applicability of such potential functions to the elucidation of other ionic properties clearly indicated or the origins of the relative solvating power of different solvents readily discernible.Otherwise the net result is only a calculated repetition of the well-known fact that small ions are better solvated than large. Estimates of water-ion bond-stretching energies are important in electron-transfer t h e ~ r y . ~ 1 p 3 2 It is interesting that the (fitted)33 repulsive exponent in B/r" is rn = 4 (between the ion-dipole and crystal-field attractive exponents of 2 and 5 respectively), in partial refutation of a long-standing criticism34 of the crystal-field formulation which seems to rely on the hard repulsions (rn 2 12 say) found with closed shells.The low value rn = 4 can be readily rationalized in terms of attractive overlap without invalidating the crystal-field approach. However the applicability of hydration-potential-energy functions is much more limited than that of com-parable lattice-energy formulations. Thus whatever its merits the classifica-tion of ions as structure makers or breakers,27 in attempts to understand many ionic properties finds little reflection in the solvation-energy model and potential. It has been interesting recently to follow the structure controversy. On the one hand there is the reference35 to the 'curiously assured yet essentially sterile, invocations of water structure that seem to be proliferating so needlessly in the literature'-quoted with approbation by Prue Read and Romeo.36 The only test that descriptive structural interpretations can be put to is an examina-tion of the universality of their consistency since refutability is not their most 'IJ C.V. Krishnan and H. L. Friedman J. Phys. Chem. 1970,74 3900. 2 9 M. Salomon J. Phys. Chem. 1970,74 2519. 3 0 A. Finch P. J. Gardner and C. J. Steadman J. Phys. Chem. 1971,75 2325 3 1 N. S. Hush Trans. Faraday Soc. 1961 57 557. 3 2 R. A. Marcus Discuss. Faraday SOC. 1960 no. 29 129 and refs. therein. 3 3 N. S. Hush Discuss. Faraday SOC. 1958 no. 26 145. 3 4 F. A. Cotton J. Chem. Educ. 1964,41,466. 3 s A. Holtzer and M. F. Emerson J. Phys. Chem. 1969 73 26. 3 6 J. E. Prue A. J. Read and G . Romeo Trans. Faraday SOC. 1971,67 420 Interactions involving Aquo Ions 85 obvious characteristic.The a l t e r n a t i ~ e ~ ” ~ ~ - ~ ’ is to relate relevant properties, like the solvent self-diffusion coefficient D to detailed solvent-solvent and solvent-ion distribution functions in quantitative theories which necessitate potential wells about the ions tenuously related to those constructed for solva-tion-energy calculations. Since transport phenomena depend on fluctuations in distributions:’ they must be more difficult to resolve than are equilibrium properties but this observation refers to putative statistical-mechanical formula-tions of a rigour not yet approached. More elaborate potentials than the primitive hard-sphere one are being invoked in conductivity4’ and activity-coefficient theories,42 but again with minimal reference to solvation-energy functions.The models employed by H e r t ~ ~ ’ . ~ ’ in analysis of self-diffusion coefficients D are complex and also as above dependent on assumptions e.g. of solvation numbers and rather tentative residence times are the immediate abstractions obtained3’ from the observed D values. For the solvent these are expressed as D~~~ = Do(l - x h ) + DhXh where D h is for solvent in contact with ion Do is for that further out and x h is the mole fraction of contact water dependent on an assumed or assigned hydration number (not implying attachment only propinquity). The n.m.r. spin-echo technique e.g. for 7Li+ and 27A13f gives Dobs values,39 and a full analysis of the relaxation mechanism led to the inference that the hydrating water rotates about the dipolar axes for both these cations.Slow-neutron diffraction experiment^^^,^^ also yield D values the motion of target solvent-actually of the hydrogen atoms-impressing a Doppler effect on the scattered neutron wave. Both techniques (just) agree with classical isotope-diffusion D values. Other experimental methods seeking to establish detailed views of structure include ultrasonic absorption which for water has been i n t e r ~ r e t e d ~ ~ in terms of three structural states in quasi-chemical equilibrium and for ionic solutions requires relaxation times for hydration water in disagreement with estimates from n.m.r. by Hertz.27 A two-state is made to fit experiment by in-voking twenty-molecule clusters. In a different context the imprecision of sound-absorption experiments in indicating in M2 +-S042 - association the number of distinct paired types-whether contact single-solvent separated or two-solvent separated pairs-has been acknowledged :47 there is no need to invoke more than three states which are contact solvent-separated pairs of various 3’ E.von Goldammer and H. G. Hertz J. Phys. Chem. 1970 74 3734. 3 8 H. G. Hertz Ber. Bunsengesellschafrphys. Chem. 1971 75 183 572. 3 9 H. G. Hertz R. Tusch and H. Versmold Ber. Bunsengesellschqftphys. Chem. 1971, 40 4 1 4 2 4 3 J . W. White Ber. Bunsengesellschafiphys. Chem. 1971 75 379. 4 4 P. S. Leung and G. J . Safford J . Phys. Chem. 1970,74 3696. 4 5 K. G. Breitschwerdt Ber. Bunsengesellschaft phys. Chem. 1971 75 319. 4 6 0. Nomoto and H. Endo Bull. Chem. SOC. Japan 1971,44 1519.4 7 S. Petrucci in ref. 12 p. 99. 75 1177. H. L. Friedman in ref. 10 p. 83. G. Kelbg and H. Ulbricht Z . phys. Chem. (Leipzig) 1970 244 125. H. L. Friedman in ref. 10 p. 76 86 D. R. Rosseinsky configurations and free ions.48 Light scattering49 is also dependent on rotational and translational motion in liquids and can be applied to electrolytes to supple-ment the methods referred to above as can measurements of solution per-mittivity. 50-54 He re Pottel's interpretati~n~~ of the complex permittivity of M%04 solutions in terms of three paired types has also been judged unjusti-fied,54 one paired species being sufficient to account for the data. The ion-pair dipole moments cause an enhancement of the permitti~ity.~~ An important series of m e a s ~ r e m e n f s ~ ~ ~ ~ is the determination of the gas-phase equilibrium constants and enthalpies for stepwise hydration of the M+ and X - ions.The method involved mass spectrometric sampling of the ions, hydrated to different extents emerging from an electron-beam or &-particle ion source containing water vapour. Figure 1 shows the results. The major con-clusions are as follows : (i) No dramatic levelling-off is found with increasing water except possibly with F- ; hence no inference follows of probable hydration numbers. The same conclusion had been reached56 for H(OH,)z. (ii) Individual values extrapolated to multiple water tend to the currently accepted single-ion solvation energies thus though omitting a phase-change term strongly endorsing their physical validity.(iii) By fitting B in an assumed B/r' repulsion term to yield the observed AH value for the first water added in a charge-dipole + dispersion + (dipole-dipole + B/r12) potential subsequent values could be calculated quite well for Cs' but progressively less well to Li' which implied56' progressive quanta1 interaction. Fluoride could not be so fitted protonation of F- being inferred, while for the other X- the fit required progressively more pronounced off-normal dipole orientations on addition of further waters tending to a linear X- . . . H-0 presumably to offset dipole-dipole repulsions. However due scepticism was accorded these simple interaction functions.56 (iu) Although (Figure 1) cations and anions vary differently the numerical difference at any stage for a comparable cation-anion pair is quite small implying that the water quadrupole moment is much smaller than has commonly been inferred from solvation energies.4 8 L. G. Jackopin and E. Yeager J. Phys. Chem. 1970,74 3766. 49 V. Volterra J . A. Bucaro and T. A. Litovitz Ber. Bunsengesellschaftphys. Chem., 1971,75 309. 5 0 J. Barthel H. Behret and F. Schmithals Ber. Bunsengesellschaft phys. Chem. 1971, 75 305. s 1 (a) D. J . P. Badiali H. Cachet and J . C . Lestrade Ber. Bunsengesellschaftphys. Chem., 1971 75 297; (b) Electrochim. Acta 1971 16 731. 5 2 K. Giese U. Kaatze and R. Pottel J. Phys. Chem. 1970 74 3718. 5 3 R. Pottel in 'Chemical Physics of Ionic Solutions' ed. B. E. Conway and R. G. Barradas Wiley London 1966 p. 581. 5 4 M. Davies Ann.Reports (A) 1970,67 82. 5 5 I. Dzidzic and P. Kebarle J. Phys. Chem. 1970 74 1466. 5 6 M. Arshadi R. Yamdagni and P. Kebarle J. Phys. Chem. 1970,74 1475; P. Kebarle, S. K. Searles A. Zolla J. Scarborough and M. Arshadi J. Amer. Chem. SOC. 1967, 89 6393 Interactions involving Aquo Ions 87 30 25 1c - '\ \ \ \ - k+ I I I I 1 0.1 1.2 2.3 3 -4 4.5 5.6 n - l n Figure 1 Comparison of AH, - ,,, for hydration of alkali-metal and halide ions (Reproduced by permission from J . Phys. Chem. 1970 74 1481 88 D. R. Rosseinsky (0) Hydroxide and fluoride ion seem almost identical for the first five waters.57 Alternative to the potential-energy calculations of solvation energies are either simpler sphere-in-continuum models or more sophisticated quanta1 calculations.In the former it is sensible24 to identify the sphere-charging step with process (1) above equating ionization potential with self energy which then identifies the process (2) with the creation of the charged sphere in the dielectric, the solvent. In support for the first-transition-series ions M2+ and M3+ crystal-field-corrected values of AH," are respectively (1/2.11) and (1/1-78) of the ioniza-tion potentials for process (l) disregarding constant terms.24 In contrast, irregular sequences of AG," and AH," are for rare-gas-like ions M+ in a number of solvents and for the isoelectronic M2 + in water (other solvents having not been so widely investigated). The latter sequences are typified by AH20 : Be2+ < MgZf > Ca2+ x Sr2+ > Ba" each inequality referring only to the encompassing two ions.So contrary to expectation two humps at Mg2 + and Sr2 + are superimposed on a putatively monotonic radius-determined sequence. Similar b e h a ~ i o u r ~ ~ is shown by the M2+ partial molar volumes V" entropies of hydration as -AS," molar resist-ivities l/AO and also somewhat less markedly by AG2" for the isoelectronic M+ in ten solvents and in their heats of transport in water.57 Of this latter series, the sequence in the early members has been termed5* a 'hook' sequence but the second hump is certainly there somewhat masked by the trend of the radius-determined baseline. Further properties are listed in ref. 24 perhaps the most notable being for -ASh" of the rare gases, He < Ne > Ar < Kr < Xe the early hook sequence being unmistakable.In addition the temperature dependences of the proton shifts in aqueous MX solutions furnish59 hydration numbers perhaps more interesting for their sequence than their magnitude : Li 3.0 Na 3.5 K 3-0 Rb 3.5 Cs 3-0 with X - all 1.0. In methanolic solution6' the cation shifts are Li < Na > K < Rb > Cs -the double-hump sequence. In 3 moll- aqueous solution of the chlorides the i.r. spectra (referred to below) again interpreted in terms of hydration numbers, yield6' the comparable sequence Na 3.96 K 3.46 Rb 3.47 Cs 3.10. Thus we have trends markedly diverging from simple charge/radius functions once considered to dominate solvation interactions and it is notable that these correlate with the thermodynamic energy quantities for the process (2) rather than for the usual hydration step.A perhaps facile interpretati~n,~ might 5' 5 8 5 9 F. J . Vogrin P. S . Knapp W. L. Flint A. Anton G . Highberger and E. R. Malinowski, 6 o J. Davies S. Ormondroyd and M. C. R. Symons Chem. Comm. 1970 1426. ' l M. Arshadi and P. Kebarle J . Phys. Chetn. 1970 74 1483. H. S. Frank in ref. 53 p. 64. J . Chem. Phys. 1971,544 178. W. McCabe and H. F. Fisher J . Phys. Chem. 1970,74 2990 Interactions involving Aquo Ions 89 attribute all the effect to the intimate ion-solvent-molecule interaction of possibly dispersion-like or charge-transfer character as proposed (below) for X - in water ; Deverell and Richards' interpretation of chemical shifts,62 relying on repulsive interactions offers promise if only because here is an interaction undoubtedly more isoelectronically than charge/radius dependent.In a dis-cussion of the heat of transport Frank5* examines more distant water inter-actions for the origin of the irregularity. The above sequences for M+ seem at first sight to contrast with further lists of properties where only Li+ is discrepant either with Li < N a > K > Rb > Cs or with all signs reversed. These include conductivities in some solvents e.g. sulpholan ; 6 3 effect on the chemical shift of X- in water ;64 salting effect on non-electrolytes (Li+ < Na+ > K+);65 I/" in water66 at <50"C cf. the double-humped I/" sequence for M2+ above. (Both M+ and M2+ follow the radius sequence for I/" above 50 oC.66) In conductivities a displacement of Li+ from a regular M+ sequence might beb7 a consequence of dielectric friction as in Zwanzig's theory,68 in which the relaxation of dipole orientation with the motion of the ion is taken into account-combined with dielectric saturation.While admittedly water is not a good liquid on which to test contemporary dielectric theories no such deviation of I/" for Li& falls out from dielectric saturation theory without the ad hoc invocationb9 of ice-like water structure (an extension7' of the earlier theory69 only establishing that I.'" slightly modified is very approximately linear in the charge squared). Possibly I/" values in the aprotic dipolar solvents in which the Li+ conductivity non sequitur occurs and to which dielectric theories are best applicable will validate or refute the dielectric interpretation.Probably all three of these sequences-hook double hump or Li-non sequitur-are manifestations of common effects of distortions from simpler radius-depend-ent functions differently weighted in different properties. The ubiquity of the irregularities over a number of solvents seems to eliminate simple sphere-packing problems as the cause. To reiterate the sequences correlate more with the energies of process (2) rather than of the usual hydration step. In connection with solvation and conductivity the method now generally and justifiably discarded for monatomic ions of obtaining solvation numbers from volume changes deduced from Stokes-law radii may well have validity for other cases where the volumes involved are enormous.71 Thus for Bu~N', C.Deverell and R. E. Richards Mol. Phys. 1966 10 551. 6 3 R. Fernandez-Prini and J. E. Prue Trans. Furaduy SOC. 1966 62 1257. 6 4 C. Deverell and R. E. Richards Mol. Phys. 1969 16 421. 6 5 F. A. Long and W. F. McDevit Chem. Rea. 1952,51 119. 6 6 F. J. Millero Chern. Reu. 1971 71 147. '' R . Fernandez-Prini and G. Atkinson J . Phys. Chem. 1971,76 239. 6 8 R. Zwanzig J . Chem. Phys. 1970 52 3625. 6 9 E. Glueckauf Trans. Faraduy SOC. 1965 61 914. 'O J. W. Akitt J . Chem. SOC. ( A ) 1971 2347. " B. S. Krumgals K. P. Mishchenko and D. G. Traber Teor. i eksp. Khim. 1971,7 112 90 D. R. Rosseinsky 26 hydrating molecules are inferred to compare with water of crystallization in the solids Bul;NNO ,27H20 and BU;NC~,~OH,O.~' The subtle conception of hydrophobic hydration of which the preceding is said to be an example receives continuing attention as in a somewhat inconclusive e~amination~~ of the effect on the paramagnetic resonance relaxation of a radical added as a probe and interpretations of inter alia activity coefficients in ~ingle-salt~~ and mixed solutions with MX.74 Anions show charge-transfer-absorbance maxima at wavelengths which when plotted against electron affinities fall on a parabola which can be approximately reproduced75 by invoking Mulliken's charge-transfer bonding theory.This implication of an appreciable charge-transfer interaction in solvation is absent in the usual analyses. The long-awaited development of wave-mechanical studies on aquo ions is indeed upon us.The CNDO method (complete neglect of differential overlap) an approximation to the self-consistent field procedure, gives76 for first-transition-series cations M(OH2)62 + and M(OH,)63 + bond lengths good to about +O-1 A not highly precise but an encouraging innovation, providing in addition a means of indicating electron distributions including quite reasonable predictions of Racah B parameters. The best results were said to correspond to tetrahedral geometry about the oxygen atom. CNDO calcula-t i o n ~ ~ ' involving point-charge ions in cavities surrounded by no less than four shells of water regularly H-bonded in chains indicated chain lengths in the sequence Li' > Na' > NH implying correctly the opposite sequence of conductivity. Kebarle's successive AH values for gas phase M(OH,); formation are however poorly reproduced by the theory,77 and H-bonding energies about H30Lq are obtained persistently too high.Hydration energies of Li' Na', Be2 + and Mg2 -t calculated for assumed tetrahedral or octahedral co-ordination agree within 1-0 % with experiment except for Mg2' where the appropriate six-co-ordination3 value is twofold too high. From the CNDO method applied78 to the phosphate ions successive relative acidity constants (as In K,) are obtained as 1 2.43 :4.57 cf. experimental 1 3-39 5.96 interesting enough though the equating of a molecular quanta1 potential with a solution-phase Gibbs function change is rather sweeping implying inter alia equality of all the entropy changes. Grahn'sAoriginal calculation^^^ on H30& predicting a shallow pyramidal stance (HOH = 118.5" cf.planar 120") have been quite well substantiated" by an n.mAr. study of polycrystalline (H20)HC104 though a much less shallow shape (HOH = 115") has been assumed for H30&, by O'Ferrall Koeppl and 7 2 C. Jolicoeur and H. L. Friedman Ber. Bunsengesellschaft phps. Chem. 1971 75 248. 7 4 W.-Y. Wen K. Miyajima and A. Otsuka J . Phys. Chem. 1971,75 2148. 7 5 7 6 D . W. Clack and M. S. Farrimond J . Chem. Sac. ( A ) 1971 299. 7 7 R. E. Burton and J. Daly Trans. Furuduy Soc. 1971 67 1219. 7 8 B. J. McAloon and P. G. Perkins Theor. Chim. Acta 1971 22 304. 79 R. Grahn Arkiv Fysik 1962 21 1 . 8 o D. E. O'Reilly E. M. Peterson and J . M. Williams J . Chern. Phys. 1971 54 96. K. Schwabe 2.phys. Chem. (Leipzig) 1971,247 1 1 3 . M. F. Fox and T. F. Hunter Nature 1969 223 177 Interactions involving Aquo Ions 91 Kresge,' ' in a model examined for spectroscopic predictions. They provide an interesting discussion of earlier spectroscopic work on water and H 3 0 + . Other H(H,O),f structures in solid acid hydrates have been discussed.82 Further studies of water alone are exemplified by SCF,' CND0,84 and associated treatmentsS4 on dimer and trimer and an outline formulation of an effective-pair potential for liquid water.85 Dipole interaction was established as being an over~implification.'~ Perram and LevineS6 find that in a formulation for liquid water based on a lattice model for hydrogen-bonding statistics only a bulk-cluster structure is apparent (not just as a consequence of the lattice assumption) and any flickering seems only peripheral.New experimental work on solution structure following that already re-viewed' 7 ~ 8 8 includes i.r. and Raman investigations such as Walrafen's further studiesg9 on the effects of solutes and pressure on water structure which support his two-state liquid model. Also representative are Oliver and Janz's workg0 on LiCIO in which the same losses of degeneracies are found to occur in the melt and in concentrated solution indicating association ; and Chen and Irish's studies" on sulphate ions. Chen and Irish92 have been able to use the Raman linewidth variation with [H+] to infer the rate of protonation; contrast Acker-rnann's contention for H 2 0 protonation that the rate here is such as to widen the bands to immea~urability.~ McCabe and Fisher6' (referred to above) consider that the near4.r.spectra of solution against water consists of first a negative component consisting of an absolute spectrum of the amount of water excluded by the hydration shell second a positive component contributed by water of hydration of the solute and third absorption (if any) by the solute itself. These simple considerations lead quite directly to MX hydration numbers at the high (3 moll- ') salt concentrations employed. For NaCl the total hydration number was found to decrease from 4.9 at 0-5 moll- ' to 3.5 at 5 moll- '. A similar technique has been applied94 to R4Nf. Recent measurementsg5 of "0 resonance more precise than formerly have been interpreted for Ni2 + solution in terms of hydration number 6 rather than 4, though the uncertainty was not established ; likewise95 Fe2+.AG"(formation) of Pd& has been estimated96 from the e.m.f. of an astonishing cell with a R. A. M. O'Ferral G. W. Koeppl and A. J. Kresge J . Amer. Chem. Soc. 1971,93 1 . G. Pimentel and A. L. McClellan Ann. Rev. Phys. Chem. 1971 22 358. x 3 D. Hankins J. W. Moskowitz and F. H. Stillinger J . Chem. Phys. 1970,53 4544. 84 H. Chojnacki Theor. Chim. Acta 1971 22 309. 8 5 F. H. Stillinger J . Phys. Chem. 1970 74 3677. 8 6 J. W. Perram and S . Levine Mol. Phys. 1971 21 701. 13' R. E. Hester Ann. Reporrs ( A ) 1969 66 79. 8 9 G. E. Walrafen J . Chem. Phys. 1971,55 768. 9 0 B. G. Oliver and G. J. Janz J . Phys. Chem. 1971,75 2948.9 1 H . Chen and D. E. Irish J . Phys. Chem. 1971 75 2672. 9 2 D. E. Irish and H. Chen J . Phys. Chem. 1970,74 3796. " T. Ackermann 2. phys. Chem. (Frankfurt) 1964 41 113. 9 4 C. Jolicoeur N. D. The and A. Cabana Canad. J . Chem. 1971,49 2008. 9 5 A. M. Chmelnick and D. Fiat J . Amer. Chem. Soc. 1971 93 2875. 96 R. M. Izatt D. J. Eatough C. E. Morgan and J. J. Christensen J . Chem. Sue. ( A ) , A. K. Covington and T. H. Lilley in ref 1 p. 31. 1970. 25 14 92 D. R. Rosseinsky platinum wire joining the two half-cells avoiding speculation as to what the authors had in mind we note that the potentials would be at the mercy of any adventitious redox traces present. From kinetics the Bu'Cl hydrolysis exhibits9' a negative activation energy between 0 and 4 "C.If not a peculiarity of Bu'Cl, this observation emphasizes the need for further investigation of the unusual properties of water through this temperature range. 2 Ionic Interactions Association Constants.-The first supplement9* to 'Stability Constants' now doubles the length of this record. The compilers this time do not comment on the variable reliability of the data. It is well to note that association constants K inferred from small effects need more justification than those from large no matter how well the former are assessed statistically. Statistical methods for fitting K values have been reviewed at length by Rossotti Whewell and Rossotti:99 the requirements are only the least-squares criterion and a computer program to give effect to it as already stated by Wentworth Hirsch and Chen,'" among many.The only problem is weighting simple in the case of electrometry with reasonably uniform experimental variables complicated for spectroscopy where sensitivities vary dramatically over wavelengths concentrations and systems. Where K values for several equilibria are being extracted virtuous instructions are inserted to accept only positive K values and reject those found negative! 99 Such procedures might be termed 'Thirteen-Hour Clock Methods'. ('It is like the thirteenth stroke of a crazy clock which not only is itself discredited but casts a shade of doubt over all previous assertions'"' and we might add over all those to come.) In other programsg9 the input data itself is 'optimized' in a sort of sanctioned cozenage.Conrow's commendable program test,'02 here omitted, uses perfect artificial data systematically 'spoilt' by e.g. gross rounding off to check for a controlled extent of error the accuracy of retrieval of the constants from which the data were synthesized. Ion Pairs and Complexes.-Nancollas' O 3 and Schwarzenbach lo4 notable con-tributors to the field have both recently published surveys and interpretations of the data. Schwarzenbach's discussion starting from the Prue-Bjerr~m'~~ electro-static model (coulombic interactions between paired ions separated by short dis-tances) establishes that for highly-charged ions particularly subgroup or transi-tional modification to the sphere-continuum model is called for. Such species often require for measurement of K ionic strengths between 0-1 and 1 moll-" G.J . Hills and C. A. N. Viana Nature 1971 229 194. 98 'Stability Constants of Metal-Ion Complexes-Supplement No. 1,' ed. L. G. Sillen and A. E. Martell Special Publication No. 25 The Chemical Society London 1971. " F. J. C . Rossotti H. S. Rossotti and R. J . Whewell J . Inorg. Nuclear Chem. 1971, 33 205 1. l o o W. E. Wentworth W. Hirsch and E. Chen J . Phys. Chem. 1967,71 218. l o ' A. P. Herbert 'Uncommon Law' Methuen London new edn. 1969 p. 28. l o 2 K. Conrow G . D. Johnson and R. E. Bowen J . Amer. Chem. Soc. 1964,86 1025. G. Nancollas Co-ordination Chem. Rea. 1970 5 379. I o 4 G. Schwarzenbach Pure Appl. Chem. 1970 24 307. l o ' J. E. Prue J . Chem. Educ. 1969,46 12 Interactions involving Aquo Ions 93 which detract from the rigour of any theoretical analysis.Apart from calling in A and B character as flexible not exclusive categories useful for rough generaliza-tion Schwarzenbach's own interpretation relies heavily on the invocation of dielectric saturation between the ions being juxtaposed. Not referred to by him,lo4 several theoretical treatments of this effect employ a modification of the inter-ion-attraction exponent in the Bjerrum association-constant formulation. An intuitive function for dielectric saturation was proposed by Panckhurst,'06 and an oversimplified semi-theoretical treatment given by the Reporter for M2+ SO?- in water.'07 A kindred calculation was used very successfully by Fernandez-Prini and P r ~ e ~ ~ to rationalize contact distances for MX in some aprotic Onsager liquids.Here the permittivity is assumed to be determined entirely by the cationic field and enhanced cation-anion attraction is predicted. Byberg Jensen and Klaning"* employ a much more elaborate model for M'*S04 (and other salts) including constant permittivity regions for ionic interiors and for hydration shells and distance-dependent functions beyond. The com-bined effect of both ionic fields at separations < 15-20 & then leads to dis-tances at which repulsion occurs relative to the simple coulombic prediction as well as regions of enhanced attraction when close. Two classes of pair species can be read into their result which in the repulsive part implies a continuum analogue to the probable molecular difficulty encountered by the counter ion in dislodging hydration molecules.While many details in the assumptions made by Klaning and his collaborators may perhaps be questioned this model seems an enormously promising one. There are some similarities here with the elaborate calculations of Levine and Rozenthal who also find repulsion in consequence of dielectric saturation ; Sch~arzenbach,"~ however infers enhanced cation-anion attraction only from the K data. From the simple Coulomb law without saturation association is favoured by the entropy term the AH" being calculable for water as being un-favourably positive and for many 'hard' ions experimental values conform with these calculations. By contrast ions inferred to interact quantum me~hanically'~~ (presumably both mutually and with the solvent) show from the temperature dependence of their association constants that the stabilization is entirely enthalpic.But also when a highly-charged ion of whatever affiliation is involved, the effect of dielectric saturation is suggested to diminish or make negative the TAS" value. O4 Detailed examination of FeCI2 + formation in concentrated (1-6 moll- ') per-chlorate media has continued.' '' Correlation of rate and equilibrium measurements with water activity emphasizes its importance in determining K , but the problem of association with perchlorate had perforce to be neglected. The role of perchlorate ion as part of the non-complexing medium in studies ' O h l o ' D. R. Rosseinsky J . Chem. SOC. 1962 785. l o ' J. Byberg S . J. K. Jensen and U. K. Klaning Trans.Faraclay SOC. 1969 65 3023. ' 0 9 S. Levine and D. K. Rozenthal in ref. 53 p. 119. . M. H. Panckhurst Austrul. J . Chem. 1962 15 194. J. K. Rowley and N. Sutin J . Phys. Chem. 1970,74 2043. I ' T. C. King and J . K. Rowley J . Phys. Chem. 1971 75 1 113 94 D. R. Rosseinsky referred to above has received stern scrutiny from Burnett'l2 and Bond.'13 Burnett has quoted several examples where the use of the Davies activity-coeffi-cient equation' l4 for high ionic strengths gives thermodynamic K values accord-ing well with those obtained conductometrically at much lower ionic strengths. Any criticism that the conductometric values are also dependent on a choice of definition of complex or ion pair has been largely forestalled by a careful selection of examples where the latter dependence is small.When applied to perchlorates this activity-coefficient application yielded K values e.g. for Co"' complex cations like C O ( N H ~ ) ~ ~ + and C ~ ( e n ) ~ + which were comparable in magnitude to those for the halide ions. There will be cases where it is suggested,' l3 fluoride as medium anion could sometimes be more inert. Friedmanl l 5 contends that even if various types of measurement including spectroscopy support an assumption of association they do not establish it as correct. In a case like CuSO, however where such a consistent interpre-tation can be made for enhancement of absorbance as well as the conductivity and cryoscopic measurements it is difficult to envisage an alternative distant charge-transfer or other absorbance-modifying mechanism to account for the observations especially one in accord with the other types of experiment.Friedman' has reiterated his view that while strong association may provide an explanation of observed activity coefficients in some cases (and in other cases like the M"S04 elaborations of or alternatives to the Debye-Hiickel model as by Guggenheim or Poirier respectively will serve' in explanation) for these ions intermediate extents of association should in contrast not be invoked as being equivalent formulations. The current consensus now seems to be to the con-trary:116y"7 the higher terms omitted in the Debye-Hiickel expansion of the Poisson-Boltzmann equation are generally accepted to correspond directly if not exactly with association.Perhaps only the precise form of the free-ion activity-coefficient equation might be questioned as by Gardner and Gluec-kauf. ' In further exploring the equivalence of association with the exact solu-tion of the Poisson-Boltzmann equation they have exploited their application of an extension of the Debye-Huckel term DH due to Kirkwood. l1 This modi-fication in common symbolism involves replacing the DH factor (1 + xa)- by ((1 + +m)/(l + This improves the theoretical treatment in terms of the simple Bjerrum association constant of 2-2 electrolyte association in the presence of 1-1 electrolyte up to concentrations of 6 mol 1-'."8 Osmotic coefficients of M1'S206 solutions12' yield K values lower than for sulphates for Mg2+ Ca2+ and Mn2+. This is reflected in ion-pair contacts, ' l 2 ' I 3 A.M. Bond J. Phys. Chem. 1970,74 331. ' l 4 C. W. Davies 'Ionic Association' Butterworths London 1962. 'I4 ' l 6 L. Onsager quoted by Falkenhagen in ref. 12 p. 47. ' '' ' ' ' 1 9 J . G. Kirkwood Chem. Rev. 1936 19 275. M. G. Burnett J. Chem. Soc. ( A ) 1970 2480. H. L. Friedman in ref. 10 pp. 7 58. M. J. Pikal J. Phys. Chem. 1971 75 663 and refs. therein. A. W. Gardner and E. Glueckauf Proc. Roy. SOC. 1971 A321 51 5. M. R . Christoffersen and J . E. Prue Trans. Furuduy Soc. 1970 66 2878 Interactions involuing Aquo Ions 95 calculated from the Bjerrum equation wider for dithionate by ca. 2A. On the other hand for Ba2+ this separation is probably the same for both anions being less for S206'- by ca. 2 A than is found for the other M".The Reporter suggests that the more weakly hydrated Ba" allows bidentate contact the other M" only unidentate. The same possibility exists in the series of + -interactions'20 Na S206 < K SO4 < K S20,. The association constant K for [Co"'(NH,),-(NO,)]' + SO,' - exceeds those for M"S04 ,' ' la the Co"' cation having an enhanced core charge or equivalently a dipole superimposed on the 2 + . The Fuoss-Hsia' 22 conductivity equation was used here.' la This and other Fuoss equations have been compared"" with P i t t s ' ~ . ' ' ~ ' ~ ~ In a conductometric study of association of 1-1 electrolytes in many solvents Justice'25 has favoured the Fuoss equations without laying stress on the resulting small numerical dif-ferences. He finds that if the Bjerrum distance q for the minimum in the distribu-tion of oppositely-charged ions is inserted as the closest free-ion separation both in the activity-coefficient equation for the free ions and in the conductivity c term then the value of this separation in the conductivity c3 term treated as an unknown and retrieved as a fitted parameter is found to be very nearly equal to q.This is a nice demonstration of the coherence of the conductivity and activity-coefficient equations. Consistent retrieval would doubtless also follow with other choices of separation somewhat less than q. The variation of K for M%O found" on varying the free-ion-defining distance simultaneously inserted in both activity-coefficient and conductivity equations is not identical with that predicted by use of the Bjerrum K equation 'anchored' by a fit to one of the experimental K values.Were it identical we should have an exactly-fitting electrolyte theory. For improvement a number of aspects might be explored, such as the Kirkwood activity-coefficient equation,' 1 8 1 l 9 neglected dielectric saturation or soft ion contacts4' in the association-constant theory alone and apart from re-examination of boundary conditions in the conductivity theory a possibility of conductance arising from ion-pair rotation in the applied field seems not to have been removed. Nevertheless the coherence of theories of ion pairs conductivity and activity coefficients for ionic strengths sometimes exceeding 0.1 moll- ' is gratifying. All the evidence referred to is in favour of the Prue-Bjerrum f o r m ~ l a t i o n ' ~ ~ rather than that yielding &a3 exp (e'/aekT) in well-known symbolism which is open to a range of interpretations and uses of variable self-consistency.One result is that association constants for the aqueous M X (but not nitrates) are established'21b as being virtually nil (G0.15 1 mol-') rather than in the vicinity'22 of 11 mol-'. By contrast a comparable treat-ment' ' l a of MI1-benzenedisulphonates gives association constants not zero (as originally inferred) but ca. 60 1 mol- ' i.e. ca. one third of the 2 2 sulphate values : the Reporter's comments on denticity of dithionates probably also apply here. ( a ) E. M. Hanna A. D. Pethybridge and J . E. Prue J . Phys. Chern. 1971 75 291 ; (b) Elecrrochirn. Acta 1971 16 677.K.-L. Hsia and R. M. Fuoss J . Amer. Chern. Soc. 1968,90 3055. E. Pitts Proc. Roy. Soc. 1953 A217 43. 1 2 4 E. Pitts B. F. Tabor and J. Daly Trans. Faruday Soc. 1969 65 849. ' l S J.-C. Justice Electrochim. Actu 1971 16 701 and personal communication 96 D . R. Rosseinsky At much higher temperatures and pressures MX association becomes pro-nounced. For these Marshall' 26,127 has extended his formulation of complete equilibrium constants in which the solvent is inserted in terms of its molar concentration raised to a power to be determined by experiment. Dependences on temperature and pressure become much simpler to represent compared with dependence on solvent fugacity or other properties like permittivity. Though a Dolezalekian simplification further study of its significance is certainly called for.Activity coefficient measurements'28 for MX solutions over wide tempera-ture ranges should in due course be similarly interpretable. General Interactions and Association.-While we shall return to association shortly the more fundamental theories sum (assumed-) pair interactions in the appropriate partition functions collecting terms in these sums to give the so-called cluster integrals. Tiros who have hitherto found even the so-called 'rudi-mentary' expositions less than forthcoming will be pleased to find a helpful, unbending and discursive outline of the diagram technique in simple terms in a chapter by Barlow12' on the Double Layer. Falkenhagen and Ebeling13' have elegantly arrived at the same formalism without calling on diagram methods at all.There is also Friedman's concentrated perspective' of fundamental particle-interaction treatments. Wood and Reilly13 ' have summarized their own exploitation' 3 2 of such methods later extended in collaboration with Robinson,' and mentioned below. Leyendekker's' 34a correlations of ionic entropies So with e.g. activity coefficients led him to formulate mixed electrolyte properties in terms of component entropies.134b His 'theory needs modification to account for changes in the hydration parameters and long-range interactions. If such changes are negligible the agreement is good' (sic!).'346 Ramanathan and F~-iedman'~~ have elaborated a refined model for MX solu-tions employing a judicious admixture of high physics in the statistical mechanics (the hypernetted chain equation) with grossly ad hoc assumptions in the assumed-pair potential.This comprises an adjustable 'Gurney potential' for the interpretation of two 'Gurney co-spheres' (commonly called hydration shells), accompanying coulombic B/rm repulsive and 'ion-cavity' terms. (Incidentally it is unrealistic and unnecessary"' to treat ions as ~ a v i t i e s . ' ~ ~ ) As propounded in the introduction just such functions might in due course be inferred from gaseous ion-ion interactions and solvation-energy studies. A long haul awaits any such demonstration of consistency of the various potentials and the question arises 1 2 ' W. L. Marshall J . Phys. Chem. 1970 74 346. "' 129 C. A. Barlow in ref. 11 p. 299. 1 3 0 H. Falkenhagen and W.Ebeling in ref. 12 p. 16. 1 3 1 R. H. Wood and P. J. Reilly Ann. Rev. Phys. Chem. 1970 21 387. P. J. Reilly and R. H. Wood J . Phys. Chem. 1969 73 4292. 1 3 3 P. J. Reilly R. H. Wood and R. A. Robinson J . Phys. Chern. 1971 75 1305. 1 3 4 (a) J. V. Leyendekkers J . Phys. Chem. 1970 74 2225; (h) 1971 75 946. 1 3 5 P. S. Ramanathan and H. L. Friedman J . Chem. Phys. 1971,54 1086. 1 3 ' D. R. Rosseinsky Electrochim. Acta 1971 16 19. L. B . Yeatts L. A. Dunn and W. L. Marshall J . Phys. Chem. 1971 75 1099. M. A Urusova Izvest. Akud. Nuuk S.S.S.R. Ser. khim. 1971 35 1145 Interactions involving Aquo Ions 97 immediately as to whether there will be a greater number of unknown parameters required than the totality of kinds of experimental data from which to determine them possibly not but this speculation seems a worthwhile one to pursue.These auth01-s'~~ expect that there could be a vast number of equally attractive but distinguishable models equally consistent with the thermodynamic data, and to some extent this is already the case. In the meantime it is of value to establish and acknowledge equivalences and contrasts between alternative theories and to check inter-relationships between experimental properties which are suggested by each theory. A simple non-thermodynamic example is provided by the demonstration' 3 7 that both the diffusion-controlled associative rate and the ion-pair-dipole relaxation rate accord with continuum theory and thus with each other by an expression furnished by the theory. Ohtaki and B i e d e r m a n ~ ~ ' ~ ~ have measured the e.m.f.s of cells with liquid junction containing a hydrogen electrode and with H + and C104- constant in concentration but with varying amounts of different cations.Having approxi-mately estimated the junction potential they suggest that the remainder of the marked (ca. 10mV) changes AE in e.m.f. can be related to the change in self-energy of H,'g with change in permittivity of the solution consequent on composi-tion changes expressing AE in terms of the radius of the H afs ion and the Hasted, Ritson and Collie measurements of solution permittivities. 139 While the accord demonstrated is only approximate this novel approach is open to further test and may yet prove widely valid. The excess Gibbs function in mixed electrolytes is assumed by G~ggenheim'~' to be quadratic in composition and by S~atchard'~' to be a different function involv-ing a power expansion.If for single electrolyte~'~" we write log yRx = DHG+ B,,Z the first term is the Guntelberg form of the Debye-Hiickel equation and the second involves the specific cation-anion interaction parameter B, which can be determined from experimental log yLx. The Bij can then be used in the equivalent expression for mixtures log = DHG + CBijrnio j . Guggenheim took Bij as constant whereas Scatchard expressed it as a variable BJZ). Follow-ing Lakshmanan and RangaraJan,14' Bij can in fact be eliminated'43 from the mixed electrolyte ymiX expression by simple substitution of log yi;/Z the DHG term being assumed dependent only on I not i,j.For charge-asymmetric mix-tures one (but only one) Bij is still n e ~ e s s a r y . ' ~ ~ We emphasize this mild develop-ment here because it is an alternative to the now extensively elaborated Reilly-Wood procedure. Reilly Wood and Robinson' 33 have employed 1 3 ' G . S. Darbari and S. Petrucci J . Phys. Chem. 1971,75 598. 1 3 8 H. Ohtaki and G . Biedermann Bull. Chem. SOC. Japan 1971,44 1 5 1 5 . 3 9 J. B. Hasted D. M. Ritson and C . H. Collie J . Chem. Phys. 1948 16 1 . 4" E. A. Guggenheim 'Applications of Statistical Mechanics' Oxford University Press, 1966 ch. 10. G. Scatchard R. M. Rush and J. S. Johnson J . Phys. Chem. 1971 74 3786 and refs. therein. 4 2 S. Lakshmanan and S. K. Rangarajan J . Electroanalyt. Chem. Interfacial Electro-chem. 1970 27 170.1 4 3 ( a ) D. R. Rosseinsky and R. J . Hill J . Electroanalyt Chem. Interfacial Electrochem., 1971 30 App. 7-10; (6) in preparation. l a 98 D. R. Rosseinsky equations for GE like those derived by Friedman" from the cluster-integral method which relate ymiX values for mixed electrolytes to properties of compo-nent single-electrolyte solutions the osmotic coefficient #P and the activity coefficients 7'. The simpler method from the Guggenheim-Scatchard formulation gives prediction^'^^" for 1-1 mixtures as good as the latter (RWR) and for asymmetric mixtures only slightly less Thus yigl for a trace of HCI in M"(ClO,) solutions at the highest observed molalities were Mg (3 mol kg-') 0.724 exp 0.962 RH,143b 0.926 RWR;'33 for Ca (3.3 rnol kg- ') were obtained 0.956 0.973 and 0.960 respectively; and for Ba (4 mol kg- ') were obtained 1.000,0.986 and 1.047 respectively.RH and RWR both improve on the 'ionic-strength prin~iple'.'~~ @ and ys being directly related RWR use essentially the same data as do RH but less simply. Interactions between like charges are neglected by both. Neither method copes with NaOH-NaC1 or KOH-KCl systems which show severe curvature in Harned p10ts.l~~ Since RWR do not depend on the DHG form for distant interactions however in principle their method should be the better. In a very recent paper the three authors'45 re-derive expressions for GE on the assumption that in a mixture of MX and NY there are associated pairs and triplets each with its own formation constant and DHG-type activity coefficient, to account for all the observed excess values.Pairs are formed from not only MX MY . but also MN NN MN and triplets MNX . . . etc. only tricationic ones being omitted for tractability. Terms in the GE expression so derived can be directly related to cluster-integral terms and Friedman's result13 ' for the limiting law for GE at I -+ 0 can be reproduced. But the spirit of Dolezalek, smiling faintly between the lines warns against total acquiescence. Nevertheless, for all its serious assumptions especially the use of a common expression for all 'single-ion' activity coefficients the heuristic value of this work is enormous. Two comments seem to be called for regarding the role of solvent. At high solute molalities it seems unfortunate that in the common formalism water is not treated as a component on a par with each of the ionic species.Secondly, regarding 'structure' the Reporter would make one assertion that in limiting conditions the solvent structure is predominantly that of bulk water and common to all ionic solutes while at high solute molalities say > 1 rnol kg- ' the solvent is largely structureless being present as individual H,O molecules and again common to all ionic solutes. The solvent 'transition'-a gradual one-must occur at molalities specific to the solute from familiar arguments. It is common ground 146-148 that Bij values and relative Bij values vary markedly at low molalities and then become comparatively constant above 1 or 2 mol kg-' ; Pitzer and Brewer'48 give a striking illustration of this variation and constancy.This observation shows remarkable parallelism with the Reporter's structure 144 H. S. Harned and B. B. Owen 'The Physical Chemistry of Electrolytic Solutions', 1 4 5 R. A. Robinson R. H. Wood and R. J . Reilly J . Chem. Thermodynamics 1971,3,461. 146 G . Akerlof and H. C. Thomas J . Amer. Chem. SOC. 1934,56 593. 14' Ref. 144 p. 604. 1 4 8 K. S. Pitzer and L. Brewer 'Thermodynamics' McGraw-Hill London 1961 p. 327. Reinhold London 1958 p. 615 Interactions involving Aquo Ions 99 +0.3 + 0.2 - c 1-E ,+0.1 &a Y v 0 -0.1 / 8 / / 8- 8-21 0 / 29 / CD 31 / 25 /-O26 / 27& I I I I I I I 1 I -1 1 3 5 7 9 11 1 3 15 17 1 9 AG,’(kcal mol’) Figure 2 Relation between speciJic interaction coeficients and standard free energies of solution.Salts are NaF (l) K F (2) RbF (3) CsF (4) LiCl ( 5 ) NaCl(6) KCl(7) RbCl(8), CsCl(9),LiBr(lO),NaBr(ll) KBr(l2) RbBr(13),CsBr(14) LiI(l5),NaI(l6) KI(17), RbI (18) CsI (19) NaOH (20) KOH (21) CsOH (22) LiNO (23) NaNO (24), KNO3 (2% RbNO (26) CsNO (27) NaCIO (28) KIO (29) KClO (30) and KBrO (31) (Reproduced by permission from Trans. Faraday Soc. 1971 67 420) assertion which implies that the high molality Bij values might be the more truly representative of relative anion-cation interactions and suggests that mixed electrolytes at high molalities might be no more intractable than those at low. Despite this general variation in Bij with low molality it remains true that the differences between them considerably outweigh the amounts by which each might vary.36 Bij values have been interpreted as representing the specific anion-cation interactions arising at higher m ~ l a l i t i e s ~ ~ which are effectively absent at limiting dilutions. In the former state the implied juxtapositions approximate the lattice condition ; in the latter we have virtually isolated aquo-ions. Consequently Bij values might be expected to correlate with properties for the transition lattice -+ quo-ions and best with the standard Gibbs-function change for solution the thermodynamic s o l ~ b i l i t y . ~ ~ That this is so is shown in the rough but impressive correlation of Figure 2. To some extent our intro-ductory expectations have been fulfilled