J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1899-1903 Ionic Partial Molar Volumes in Non-aqueous Solvents Yizhak Marcus,? Glenn Hefter and Teck-Siong Pang School of Mathematical and Physical Sciences, Murdoch University, Murdoch, WA6150, Australia Standard partial molar volume data at 298 K for eight tetra-alkyl or -aryl ions and 13 smaller ions in ten solvents, including water, have been statistically related to diverse ion and solvent properties. The radius cubed is the primary ion property determining the volumes for both kinds of ions, as expected. Secondary effects are due to the polarizability of the large ions and the hydrogen bonding abilities of the smaller ones. The molar volumes of the solvents, modified by their polarizabilities as well as their solubility coefficients are the main solvent proper- ties accounting for the ionic volumes.The effects of solvent compressibility are also explored, but the dipole moment and relative permittivity do not play a role. Standard partial molar volumes, I/', of electrolytes are ther- modynamic quantities of considerable importance in a variety of applications. These include the calculation of the properties of seawater, the buoyancy of marine organisms, the properties of membranes and clays, and the behaviour of non-aqueous high-energy-density batteries. Molar volumes of electrolytes are relatively straightforward to measure by tech- niques such as densitometry and dilatometry. However, in contrast to many thermodynamic quantities, their theoretical interpretation has remained difficult.Such an interpretation is customarily made in terms of a model of the ion and its solvent environment and the interactions that take place between them. The most widely employed model has been that of Frank and Wen' who postulated the molar volume of an ion to be given by: where the subscripts int, dis, cag and el refer to the intrinsic volume, the disordered volume of the solvent associated with void-space effects, the formation of a cage of structured solvent around the ion, and the electrostriction of the solvent by the electric charge of the ions, respectively. The last term in eqn. (1) is negative. The Frank-Wen model has, however, proven to be difficult to quantify exactly and it is generally regarded as, at best, semi-quantitative.It is probably of more relevance to highly structured solvents such as water, for which it was originally developed, than for typical organic solvents [in particular the cisand I/cag terms of eqn. (l)]. More recently, Marcus2 has had some success in describing ionic partial molar volumes in water using a modified Born approach with specific allowance for the existence of a hydra- tion shell around the ion. According to this approach: V'(ion) = Kydr+ Ell + Kl2 + I/str where the subscript hydr pertains to the intrinsic volume of a hydrated but as yet unelectrostricted ion, ell to the electro- striction in the hydration shell, el2 to the electrostriction in the water surrounding this shell and str to the structuring of the water around hydrophobic ions.Despite the success of this model in accounting for ionic volumes in aqueous solutions, its application to non-aqueous solvents has not been attempted. One deterrent is the limited availability of the information (derivatives of the relative per- mittivity and the refractive index with respect to pressure) t Permanent address: Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, Jerusalem 9 1904, Israel. required for the extension of this model to non-aqueous sol- vents. A more fruitful approach appears to be to attempt to identify the major factors that govern vo(ion) values in non- aqueous solvents using a statistical analysis that has been employed for other thermodynamic properties of solutes in a variety of solvents.Examples are the standard molar Gibbs energy of transfer of ions, AtrGe,3 and the (logarithms of) the equilibrium constants for the distribution of organic solutes between water and immiscible solvents, log K: .4 Data Millero5 included some 20 years ago in his extensive review of partial molar volumes of electrolytes and ions the limited amount of data then available for non-aqueous solvents. No major review of this area has since been published, although Marcus6 listed ionic volumes of transfer from water into a number of nonaqueous solvents, as has Krumgalz.' A more comprehensive review of the available vodata at 298 K has recently been completed by Pang and Hefter,* and the data used for regression analysis in the present paper have been taken from that source.The splitting of the voof electrolytes into their ionic contributions has been made according to the reference electrolyte meth~d,'.'~ specifying I/'(Ph,P') -P'(BPh,-) = 2 cm3 mol-' for all solvents. This sets a precision limit to the ionic volumes of +_2 cm3 mol-', that is considered realistic, in view of the inherent difficulties in split- ting electrolyte volumes into their ionic constituents.' Included in the database (Table 1) submitted to the statistical analysis were Poof those ions in those solvents [water, meth- anol (MeOH), ethanol (EtOH), ethane-1,2-diol (EG), N-methylformamide (NMF), propylene carbonate (PC), N,N-dimethylformamide (DMF), cyanomethane (MeCN), nitro- methane (MeNO,), and dimethyl sulfoxide (DMSO)] for which the required ionic and solvent properties are known.Some other ions, such as trifluoromethylsulfonate, for which these are unknown but vo are available, could not be included. Calculations and Results The stepwise multivariable linear least-squares regression method was applied to the ionic standard molar volumes in order to relate them to ionic and solvent properties. This method selects sequentially those properties that explain most the variance of the data, the procedure ending accord- ing to provided statistical criteria. The criteria chosen were Fisher's F = 2 for variables to enter or exit. The regression was forced through zero, i.e., no constant term was allowed, since such a term would not have a physical meaning.In principle, three approaches could have been used: (i) regress J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Ionic volume, I/', database" ion H,Ob MeOH EtOH EG NMF PC DMF MeCN MeNO, DMSO ~ Li -6.4 -18.5 -18.7 -8.7 -8.2 -8.6 -9.9 -16.2 -17.6 -5.3+ Na+ -6.7 -18.2 -9.1 -3.6 -3.5 -4.5 -1.5 -16.0 -12.6 2.9 K+ 3.5 -7.4 -0.7 6.2 4.8 2.4 6.0 -5.0 -8.3 11.2 Rb + 8.6 -3.0 5.2 11.8 (8.6) 6.8 10.1 -1.7 ( -3.4) 17.2 cs + 15.8 3.4 13.1 20.0 14.6 13.4 16.6 5.0 2.0 22.6 NH,+ 12.4 3.3 8.6 10.2 11.5 4.5 F-4.3 -0.9 -13.8 6.2 (6.0) (-5.2) (-15.1) (-26.4) 13.0 -1.3 c1-23.3 13.9 13.4 24.5 25.9 17.6 7.4 1.2 13.8 11.4 Br-30.2 22.0 15.4 31.0 31.2 23.8 9.7 6.8 21.2 16.7 1-41.7 29.2 26.3 40.4 40.9 36.4 23.6 20.6 34.1 31.1 NO,-34.5 29.5 24.4 36.8 18.7 25.5 SCN -41.2 46.0 41.9 24.7 c10, -49.6 39.8 46.3 46.0 32.1 42.8 Me,N 84.1 66.9 76.1 78.9 80.9 83.0+ Et," 143.6 125.9 138.0 137.7 139.3 142.2 140.9 134.8 140.0 Pr,N+ 208.9 196.8 206.9 206.2 210.2 21 1.4 2 12.5 206.2 211.0 Bu,N 270.2 263.6 274.5 275.3 279.3 280.2 282.1 274.5 282.0+ Pe,N+ 333.7 337.5 341.2 349.7 343.9 344.0 Ph4P+ 285.8 263.1 263.3 285.9 286.5 287.9 284.0 274.4 284.9 289.3 Ph,As+ 295.2 269.0 290.9 290.4 29 1.9 283.1 294.3 BPh,-283.1 261.1 261.3 283.9 284.5 285.9 282.0 272.4 282.9 287.3 a The data are from ref.8 and individual ionic volumes are based on the assumption that P'(Ph,P+) -ao(BPh,-) = 2 cm3 mol- l, except where noted.One decimal place is retained, although the values are known only to within k2 cm3 mol-', in order to avoid rounding-off errors. Values in parenthesis are not included in the calculations, but have been subsequently predicted. These data are from ref. 2. first with respect to the ionic properties, then regress the coef- ficients obtained with respect to the solvent properties; (ii) regress first with respect to the solvents, then regress the coef- ficients obtained with respect to the ions; (iii) first form binary products of all the ion and the solvent properties, then regress with respect to these products. In practice, only the first approach could be used, since the ionic volumes are not sufficiently sensitive to the solvent properties.Only after the data have been normalized with respect to the ionic properties could the variability with respect to solvent properties be studied. The following ionic properties were offered to the program: the radius (r),the radius cubed (r3),the reciprocal of the radius (r-'), the polarizability (ai),the softness (o),12 and the hydrogen-bonding ability [aKT for cations, /?KT for anions, collectively designated by (HB)]. The intrinsic volume is proportional to r3, the ionic field to r-l, and the subscript KT refers to the Kamlet-Taft H-bond donation and electron- pair donation abilities. The values employed and their sources are shown in Table. 2. The softness and H-bonding ability are not known for the 'large' (i.e. tetraalkylammonium and the tetraphenyl) ions, hence these were treated separately from the 'small' ions (all the other ions, cations and anions together). For the small ions, because of the limited range of the radii, r is correlated (correlation coefficient R > 0.9 for the linear relationship) with r3 and with r-', hence either r or r3 must be used in the regressions.The latter was chosen, since it can be better justified physically and its correlation with r-is not as good. Also, aiis correlated (R > 0.9) with r3 (and r) and with 0, hence it should enter only when the latter are absent. For the large ions all the variables are cor- related to some extent, and it was difficult to chose orthog- onal variables. The following solvent properties were employed in the program : the molar volume (V,), isothermal compressibility (K~),solubility parameter (a), polarizability (us), relative per- mittivity (E~), dipole moment (p), the Kirkwood dipole angular correlation parameter (g), the Kamlet-Taft H-bond donation (cIKT) and electron-pair donation (PKT) abilities.Essentially all the solvents considered are nearly equally 'hard' (except cyanomethane, which is moderately soft), so that 'softness' was not inc1uded.l6 The values employed and their sources are shown in Table 3. Among the solvent properties, only V, and a, have R > 0.9, all the other variables are less well correlated and all could be employed in the regressions. For the large ions, r3 was the first parameter chosen for all solvents, and it explained >95% of the variability.This is understandable, in view of the success of the Conway-Jolicoeur plots of vous. the relative molecular weight or the number of carbon atoms in the tetraalkylammonium ions.20*2' The rest of the variance was explained by the ion polarizability, that takes care of the differences between the Table 2 Properties of the ions ion 4 l/rb r3' aid ue (HB)f ~ Li + Na + 0.69g 1.02 1.499 0.980 0.33 1.06 0.03 0.26 -1.02 -0.60 2.07 0.83 K+ 1.38 0.725 2.63 1.07 -0.58 0.85 Rb + 1.49 0.671 3.3 1 1.63 -0.53 0.49 cs + 1.70 0.588 4.9 1 2.73 -0.54 0.47 NH,+ 1.4gg 0.676 3.24 1.20 -0.60 1.00'' F-c1- 1.33 1.81 0.752 0.552 2.35 5.93 0.88 3.42 -0.66 -0.09 2.95 1.00 Br- 1.96 0.510 7.53 4.85 0.17 0.67 1- 2.20 0.455 10.65 7.5 1 0.50 0.30 NO,- 2.00 0.500 8.00 4.13 0.03 0.09 SCN - 2.13 0.469 9.66 6.74 0.85 0.33 c10,- 2.40 0.417 13.82 5.06 -0.30 0.08 Me,N+ 2.80 0.357 22.0 9.08' Et,N+ 3.37 0.297 38.3 17.70' Pr," 3.79 0.264 54.4 24.0' Bu,N + 4.13 0.242 70.4 3 1.5' Pe,N+ 4.43 0.226 86.9 39.0' Ph4P+ 4.24 0.236 76.2 45.w Ph,As+ 4.28 0.234 78.4 45.7' BPh,- 4.21 0.238 74.6 43.1' " In A; from ref.2 and references therein. In k'.'In A3. In lo-,' m3, from Y. Marcus, unpublished compilation, based mainly on molar refractivity data from ref. 11 (with the value for Na+ = 0.65 cm3 mol-'), except as noted. From ref.12 and refer- ffences therein. From ref. 4. These values are preferred, see ref. 13. Estimated value. Ref. 14. j Ref. 15. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 3 Properties of the solvents' water 18.1 4.52 47.9 78.4 1.46 1.83 2.57 1.17 0.47 MeOH 40.7 11.95 29.3 32.1 3.26 2.87 2.82 0.98 0.66 EtOH 58.7 11.87 26.0 24.6 5.13 1.66 2.90 0.86 0.75 EG 55.9 3.82 32.4 31.7 5.73 2.28 2.08 0.90 0.52 NMF 59.1 6.27h 31.1 182.4 6.05 3.86 3.97 0.62 0.80 PC 85.2 5.90 21.8 66.1 8.56 4.98 1.23 0.00 0.40 DMF 77.4 6.22 24.1 36.1 7.90 3.86 1.03 0.00 0.69 MeCN 52.9 10.70 24.1 37.5 4.4 1 3.44 0.81 0.19 0.40 MeNO, 54.0 5.9h 25.7 35.8 4.95 3.56 0.92 0.22 0.06 DMSO 71.3 5.20 26.6 46.7 7.99 3.90 1.04 0.00 0.76 FA 39.9 4.0 39.6 111.0 4.23 3.37 2.04 0.7 1 0.48 NMA 77.0 29.4 191.3 7.85 4.39 4.2 1 0.47 0.80 AC 74.0 12.55 22.1 20.7 6.41 2.69 1.21 0.08 0.6 1 HMPT 175.7 7.9 19.1 30.0 16.03 5.54 0.86 0.00 1.05 ' From ref.6, ch. 6; unless oth erwise noted, b ulk data pertain to 25°C. In cm3 mol-'. In 10-l' Pa -'. In 5''' ~m-~". In m3. In Debye (3.335 64 x C m). From ref. 17. From ref. 18 (NMF) and ref. 19 (MeNO,). tetraphenyl ions and the tetraalkyl ions of similar size. It was with an average standard deviation of k0.30; those of (HB) rather difficult to relate the regression coefficients for the varied from -2.57 to -10.29 with an average standard devi- large ions to the properties of the solvents, but V, appeared to ation of & 1.63, both coefficients, thus, being highly signifi- play the primary role.The final results for the large ions are: cant. The former coefficients depended on the 6 and V, of the solvents, whereas for the latter a dependence on V, and a, orVo = (0.146 f0.025)r3[K -(7.1 & 1.4)~~~+ (0.44 f 0.16)6] on xT and g was found. Therefore the final results are: -(0.14 f0.03)0rj[V,-(8.6 & 2.2)aJ (3) Po = (0.08 +_ 0.01)r3[6 + (0.20 +_ 0.06)1/,] That is, the standard molar volumes for up to eight large ions -(0.66 & O.OS)(HB)[ V, -(6.0 O.5)as] (4~)in nine solvents (there are no data for MeNO,) are describ- able by a total of five parameters: two ion properties and vo= (0.08 _+ 0.01)r3[6 + (0.20 & 0.06)V,] three solvent properties.The standard deviations of the fits -(0.88 fo.ll)(HB)[~,-(0.9 k0.5)g-J (4b)vary between k3.5 for water to k18.7 for PC, the mean being k11.2 cm3 mol-' for data ranging from 67 to 350 cm3 The standard partial molar volumes of up to 13 small ions in mol-'. Notable outliers are Me,N+ and Pe,N+ in MeOH, up to 10 solvents were thus described by four parameters Ph4P+ and Ph,B- in EtOH, most ions in PC, Et,N+ in with two ion properties and three (or four, if K, is invoked) DMF, Pe,N+ and Ph,As+ in MeCN and DMSO, and solvent properties. The standard variations of the fits are Bu,N+ in DMSO. These cases were included in the regres- between f4 and k6 cm3 mol-I for Po values ranging from sions and contributed to the overall average standard devi- -20 to 50 cm3 mol-l, but MeOH (f8 cm3 mol-') and ation of the fit.MeNO, (& 12 cm3 mol-') show poorer results. Notable out- For the small ions, r3 was again the first variable chosen by liers are Na' in water, MeOH and MeCN, NH,' in MeOH the program for all solvents (except that for DMF it was on a and DMF, Rb' and Cs' in DMSO, and SCN- in PC. par with the H-bonding ability). Alone it explained from 55% For Rb+ and F-, two spherical ions with rare-gas elec- of the variability of vo(for MeNO,) up to 92.7% (for water). tronic configurations, values of Vo in several solvents are The second variable chosen was (HB): alone it explained a lacking.8 These can be predicted with the aid of the results of minor fraction of the variability of V0,but was more signifi- eqn.(4)coupled with the experimental values for other alkali cant for EG, PC and DMF. Together, r3 and (HB) could metal and halide ions. That is, differences between values explain 80%-96% of the variability of Po,except for MeNO, from the correlations and the experimental values for other (62% only). The coefficients of r3 varied from 2.32 to 4.12, ions in the series were taken into account. These systematics Table 4 Experimental and predicted values of Vo of ions in solvents for which there are no TPTB data FA NMA AC HMPT ion exptl. pred. exptl. pred. exptl. pred. exptl. pred. +Li -2.0 -9.4 -20.8 -29.1 Na -5.2 2.2 3.7 -0.4 -18 -4 -11.6 -8.0+ K+ 5.5 8.3 10.1 5.2 0.2 -2.0 NH,+ 14.5 6.6 Et,N+ 140.9 147.0 128 156 +Pr,N 209.4 208.9 20 1 226 Bu,N ' 277.4 270.3 27 1 29 1 Pe,N+ 350.8 333.7c1-22.5 16.3 -8 9 Br-33.4 28.0 28.2 23.8 21.5 20.1 I-45.0 41.2 38.6 37.0 41.5 38.0 NO,-31.7 28.5 SCN -49.0 37.2 ClO,-17 38 1902 yield for Rb+ in NMF and MeNO, predicted 'experimental' values of 8.6 and -3.4 cm3 mol- ', respectively using eqn.(4) with the data for Kf and Cs+. Similarly, for F-in NMF, PC, DMF and MeCN, eqn. (4) and the data for C1- and Br- yield predicted 'experimental' values of 6.0, -5.2, -15.1, and -26.4 cm3 mol- ',respectively. These predictions should be tested by experiment. Further predictions can be made for solvents where the TPTB approximation for splitting the voof electrolytes into the individual ionic values could not be applied directly due to the lack of data.Splitting by other means had to be resorted to, and the data were not included in the database from which eqn. (3) and (4)were derived. Such solvents are formamide (FA), N-methylacetamide (NMA), acetone (AC), and hexamethyl phosphoric triamide (HMPT).* The proper- ties of these solvents are included in Table 3, and the calcu- lated values of voresulting from the application of eqn. (3) and (4)are compared in Table 4 with the experimental data. The agreements are of the same order as for the database used for the derivation of eqn. (3) and (4), except for AC, where there exists a systematic deviation of the calculated values of +22 & 5 cm3 mol-' for both cations and anions (i.e.not due to wrong splitting). The experimental and pre- dicted values for the ions in NMA could have been brought to closer agreement (within 2 cm3 mol-l) if the value of as were 9.2 instead of 7.85 (in m3), noting that the Po data pertain to 35 "C. Discussion The thermodynamics of ion hydration has been studied by one of the authors, in a series of papers for a large number of ions of various charges, sizes, and A model, depending only on the radius r and algebraic charge z of the ions, involving a hydration shell of thickness Ar, that depends on I z I and inversely on r, is It is based on some- what similar models proposed by others previously and was shown to fit these data adequately for the Gibbs energy, enth- alpy, entropy and heat capacity of hydration. Although all these quantities, including partial molar volumes, can be understood in terms of the same general model, involving the cavity in the solvent, in which the ion is located, and the electrostatic interactions of the ion with its environment, the details can be different.The standard partial molar volumes of ions in both aqueous and non-aqueous solutions may, therefore, depend on different ion and solvent properties from those that determine other ionic thermodynamic quantities. The statistical approach adopted here reveals which of several plausible properties play the major role in determin- ing the standard partial molar volumes of ions in a variety of solvents. The present statistical evaluation shows that Po of the large ions is primarily sensitive to their intrinsic volumes, quantities proportional to r3.Because of the correlation of this quantity with r and r-' (and also r2, which is pro- portional to the surface area of the ions), nothing very defi- nite can be made of this fact. On the other hand, the linearity of the Conway-Jolicoeur20*21 plots of vo us. the relative molar weight or the number of carbon atoms per alkyl chain of the tetraalkylammonium cations is consistent with a dependence on the ionic volume. Noting that the tetra-methylammonium cations are outliers in many solvents, this means that the density of a -CH2- segment with its solva- tion shell is independent of the number of such segments per chain, provided it is 22.However, the voof the three tetra- phenyl ions, although in between those of the tetrabutyl-. and tetrapentyl-ammonium ones, fall below the straight line plots us. r3. The higher polarizability, ai, of the tetraaryl ions J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 accounts for this, eqn. (3), expressing the higher 'squeezability' of these ions. However, unquantifiable proper- ties, such as openness of the structure, which would enhance solvent penetration, thus reducing Po,could also account for the non-compliance of the tetraaryl ions with the line pre- scribed by the tetraalkyl ones. The solvent properties associated with the intrinsic volumes of the large ions in eqn.(3) indicate that these ions are 'solvated', at least as far as their voare concerned, since otherwise no solvent-property dependence would be expected. This contrasts with the finding of Kr~mgalz,~~ that these ions are non-solvated in the ordinary sense, but this was based on conductivity data. In fact, the positive depen- dence on the molar volumes of the solvents, V,, modified by a contrary dependence on the polarizability of the solvents, cc,, is due to the exclusion of the centres of the solvent molecules from an annular region around the ion. The larger the solvent molecules and the less they are able to squeeze into confined spaces, the larger is the resulting effective volume of the ion. The further, but weaker, dependence of vo on the solubility parameter, 6, indicates that the more open struc- tures of associated solvents are also reflected in the size of this exclusion shell.A similar rationalization can be made for the solvent properties associated with the polarizability of the ions, ai,in eqn. (3). It is significant to note that for the large ions, none of the solvent properties related to ion4ipole interactions, such as E, p, aKTand BKT,are of importance with respect to Vo. For the small ions, it is seen, eqn. (4), that the intrinsic volume of the ions, proportional to r3, is of importance and explains more than half of the variability of vo.Because of the mutual correlation, a dependence on r (or r2)cannot be excluded, but r-' definitely yields a statistically inferior relationship.It may be recalled that in the case of aqueous solutions, where Po data for many more univalent ions than the 13 considered here, and for ions with charges 21 are available, a dependence on r-' was found for both the intrin- sic hydrated volume, depending on (r + with Ar increas-ing with r-', and the electrostriction, depending on Ar/(r + Ar).2 In the present more restricted case, the inclusion of water in the set of solvents does not require a dependence on r-' for the statistical fit. A major part of the rest of the variability of vois explained by the hydrogen bonding or electron-pair sharing properties of the ions, (HB), i.e. aKTfor the cations and PKTfor the anions. The directional nature of such bonding is possibily responsible for this dependence, but the negative sign of this term indicates it to be related to the electrostriction. This kind of interaction should be related to the field strength of the ion, i.e.to r-', but this dependence is concealed by the r3 dependence for the limited set of ions considered here. In any case, the polarizability, xi, and the softness, 0, of the small ions do not play a significant role in making up their vo. The dependence of voon the properties of the solvents is dominated by the solubility parameter 6, i.e.,by the tendency of self-association of the solvents. This association is still manifested in the solvation shells of the ions that determine their volumes 'before' electrostriction. The molar volumes of the solvents themselves, V,, play a minor role in this respect, eqn.(4). Since solvent polarizability, a,, is fairly well corre- lated with V,, a similar statistical fit is obtained with the former replacing the latter in the first term of eqn. (4),the coefficient increasing from 0.20 to 1.8. The electrostrictive effect on the volume is related to the solvent compressibility, xT,modified slightly by the dipole orientation parameter, g, eqn. (4b). Alternatively, a quantity equal to 33-52% of the molar volume [i.e.V, -6a,, eqn. (4a)l determines the electro- strictive effect on Po. This is less easy to understand than the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 -6 t *\ \* - I *\ \ I .L -12 ' E m EY"1.-18 4 -24 V" 0 2 4 6 8 10 12 K~/IO-'O Pa-' Fig. 1 The standard molar volumes of transfer of lithium iodide from water to non-aqueous solvents, A,r V0/cm3 mol-', us. the com- pressibilities of the solvents, ~,/10-'O Pa-' dependence on the solvent compressibility. It is noteworthy that for the small ions, as for the large ones, none of the solvent properties related to ion-dipole interactions, p,E, zKT and BKT, are required to explain the variability of vo.This contrasts strongly with the importance of these properties in explaining, for example, the solvent dependence of the Gibbs energies of transfer of ions.3 It is seen above that the standard partial molar volumes of ions in any solvent have as a major constituent the intrinsic volume of the ions, i.e.a quantity that is proportional to r3. The standard molar volumes of transfer, AtrVo,should be less dependent on this qsantity and more on the ion-solvent interactions. It is expected that the dominant ion-solvent interaction is electrostriction. If so, as shown by Hamann and Lirn," AtrV' should depend on solvent compressibility. This was tested for the four alkali-metal ions and three halide ions in the data base for which data are available (Table 4). It turned out that only for Li' among the cations and I-among the anions could linear regressions of AtrVovs. KT be obtained with reasonable correlation coefficients. This means that other solvent properties besides K~ are significantly responsible for the variability of AtrVo.For example, for C1- I903 and Br- Att Vo has some correlation with aKT.Following Hamann and Lim,28 the AtrVo of the electrolyte LiI (rather than of its individual ions) is plotted in Fig. 1 us. K~.The data for HMPT from Table 4 have been included, those of DMF are seen to be outliers, but for no apparent reason. Dr. Brian Clare is thanked for providing help with the sta- tistical calculations. References 1 H. S. Frank and W. Y. Wen, Discuss. Faraday SOC., 1957, 24, 133. 2 Y. Marcus, J. Chem. SOC., Faraday Trans., 1993,89,713. 3 Y. Marcus, M. J. Kamlet and R. W. Taft, J. Phys. Chem., 1988, 92, 3613. 4 Y. Marcus, J.Phys. Chem., 1991,95,8886. 5 F. J. Millero, Chem. Rev., 1971, 71, 147. 6 Y. Marcus, lon Solvation, Wiley, Chichester, 1985.7 B. S. Krumgalz, J. Chem. SOC.,Faraday Trans. I, 1987,83, 1887. 8 T. S. Pang and G. T. Hefter, to be published; from Ph.D. thesis of T. S. Pang, Murdoch University, 1994. 9 G. T. Hefter and Y. Marcus, J. Phys. Chem., 1994, submitted. 10 F. J. Millero, J. Phys. Chem., 1971,75, 280. 11 A. Heydweiler, Phys. Z., 1925, 26, 526. 12 Y. Marcus, Thermochim. Acta, 1986,104,389. 13 Y. Marcus, J. Chem. SOC., Faraday Trans., 1991,87,2995. 14 N. Soffer, M. Bloemendal and Y. Marcus, J. Chem. Eng. Data, 1988,32,43. 15 S. Glikberg and Y. Marcus, J. Solution Chem., 1983. 12.255. 16 Y. Marcus, J. Phys. Chem., 1987,91,4442. 17 Y. Marcus, Chem. SOC. Rev., 1993,22,409. 18 A. J. Easteal and L. A. Woolf, J. Chem. SOC., Faraday Trans. I, 1985,81,2821. 19 1. A. Brodskii and V. S. Libov, Russ. J. Phys. Chem., 1980, 54, 678. 20 B. E. Conway, R. E. Vera11 and J. E. Desnoyers, 2.Phys. Chem. (Leipzig), 1965, 230, 157; Trans. Faraday SOC.,1966,62, 2738. 21 C. Jolicoeur, P. R. Philip, G. Perron, P. A. Leduc and J. E. Des-noyers, Can. J. Chem., 1972,50, 3167. 22 M. H. Abraham and Y. Marcus, J. Chem. SOC.,Faraday Trans. I, 1986,82, 3255. 23 Y. Marcus, J. Chem. SOC., Faraday Trans. I, 1986, 82, 233; Y. Marcus and A. Loewenschuss, Annu. Rev. C, 1985,1984,61. 24 Y. Marcus, J. Chem. SOC., Faraday Trans. I, 1987,83,339. 25 Y. Marcus, Pure Appl. Chem., 1987,59, 1721. 26 Y. Marcus, Biophys. Chem., 1994, in the press. 27 B. S. Krumgalz, J. Chem. SOC.,Faraday Trans. I, 1983,79,571. 28 S. D. Hamann and S. C. Lim, Aust. J. Chem., 1954,7,329. Paper 4/00265B; Received 17th January, 1994