J. Chem. SOC., Faraday Trans. I, 1982, 78, 197-211 Calculations on Ionic Solvation Part 6.-Structure-making and Structure-breaking Effects of Alkali Halide Ions from Electrostatic Entropies of Solvation. Correlation with Viscosity B-coefficients, Nuclear Magnetic Resonance B'-coefficients and Partial Molal Volumes. BY MICHAEL H. ABRAHAM* Department of Chemistry, University of Surrey, Guildford, Surrey GU2 5XH AND JANOS LISZI* AND ERZSEBET PAPP Department of Analytical Chemistry, University of Veszprem, 820 1, Veszprem, Hungary Received 9th February, 198 1 The electrostatic entropy of solvation of an ion, AS:, or the contribution to AS: from the co-ordination sphere of the ion, have been shown to be quantitative measures of the structure-making and structure-breaking effects of ions of the alkali halide series in water and in non-aqueous solvents. Both entropy criteria indicate that in water the ions Li+, Na+, Ag+ and F- are net structure-makers, the ions Rb+, Cs+, C1-, Br-, I- and C10; are structure-breakers, and K+ is a borderline case.In the non-aqueous solvents formamide, methanol, N-methylformamide, dimethylformamide, dimethylsulphoxide and aceto- nitrile, all the above ions are structure-makers with the exceptions of the weak structure-breaking ion C10; in formamide and the borderline cases of C10, in methanol and I- in formamide. It is shown that the AS: or AS: II values may be used to assign single-ion B- or B'-coefficients and that for water and several non-aqueous solvents there are good linear correlations between the entropy values and the single-ion coefficients.There are also good linear correlations between the entropy values and single-ion Vo values when the latter are based on V" (H+, aq, 1 mol dm-3) = -5.4 cm3 mol-' and when values of To in non-aqueous solvents are assigned by the correspondence method. It is further shown that the general conclusions reached do not depend on any particular choice of ionic radii, although the Goldschmidt-Pauling set is preferred, and it is suggested that the derived AS: and AS: I I values are close to 'absolute' values and hence provide an 'absolute' measure of ion-solvent interactions. In Part 3 of this series1 we deduced expressions for the electrostatic entropy of solvation of an ion surrounded by concentric layers of solvent, each with a different dielectric constant, E .In the simplest case of a one-layer model, in which the ion of radius a and dielectric constant unity is surrounded by a solvent layer of thickness b - a and E = E ~ , followed by the bulk solvent with E = E,, eqn (1) holds: For a two-layer model in which the ion is surrounded by a first layer of thickness b - a and E = E ~ , then by a second layer of thickness c- b and E = E,, followed by the bulk solvent, eqn (2) was deduced : In both of these equations, 2 denotes the charge on the ion. The advantage of eqn 197198 CALCULATIONS O N IONIC SOLVATION (1) and (2) over those we used previously2 is that the particular terms of the equations give explicitly the contributions from the layers and the bulk so1vent.l Application of eqn (1) and (2) to the solvation of univalent ions in aprotic solvents resulted in good agreement with the experimental entropie~.~ For most ions E, was quite close to the bulk dielectric constant so that there was little numerical difference between calculations using the one-layer and two-layer models; if E , = E, and hence &,/i3T = &,/aT, then eqn (2) collapses to eqn (1).In the case of hydrogen-bonded solvents, neither eqn (1) nor eqn (2) reproduced the experimental values and we concluded that for these solvents there was an additional very positive contribution to the overall AS: value, which arose from a disordered solvent region in the second layer. We therefore applied eqn (2) to solvation of ions in hydrogen-bonded solvents by calculating the contributions from the first layer and the bulk solvent and then deducing, by difference, the contribution of the second layer.3 For ions in water we briefly discussed the relationship between the entropic contribution of the first and second layers and the so-called structure-making and structure-breaking effects of ions, and in the present work we examine such relationships in more detail.Several workers 4-11 have discussed entropies of ions in terms of their structure-making and structure-breaking tendencies, and there have been attempts to correlate, for example, the standard entropies of hydration of ions with ionic viscosity B-coefficients or with partial molal volumes of ions in water. Both the B-coefficients and the partial molal volumes, especially when the latter are corrected to yield the contribution from electrostriction, es,l2? l3 have been used as probes of ion-solvent interactions, and, indeed, ionic viscosity &coefficients have been taken as a direct indication of the structure-making and structure-breaking effects of ions.l4 Friedman and Krishnanll have calculated the entropic contribution of the second layer around ions in water by estimating the bulk contribution by the Born equation; the first layer contribution was taken as - 12 cal K-l mol-l for all monatomic ions and a correction was applied for loss of translational entropy on transfer from the gas phase at 1 atm to water at unit mole fraction (-20 cal K-l mol-1 for all ions).* They concluded that the ions Li+ and F- are structure-making ions, the ion Na+ has no structure-making or -breaking effect, and the larger ions such as K+, Rb+, Cs+, NH;, Cl-, Br-, I- and C10; were structure-breaking ions.We felt that any structure-making or structure-breaking effects of ions in a given solvent should be reflected either in the electrostatic term AS: or in the entropic contribution of the first and second layers AS: I1 = ASP + We therefore, as before,2 divided the experimental ionic solvation entropy, AS:, into a neutral and electrostatic part, eqn (3), AS: = AS: + AS: (3) calculated the neutral part, AS:, again exactly as before,2 and thus obtained the electrostatic part, AS:, by difference. The electrostatic solvation entropy is then written as the sum of the contributions from the first layer, ASP, the second layer, ASIOI, and the bulk solvent, AS:, as in eqn (4), We calculate the ASP and AS: terms uia eqn (2) and then obtain the AS: term by difference.Although the numerical values of AS: depend on the standard states adopted for the gas phase and solution, the values of AS: are independent of standard * 1 cal = 4.184 J. AS: = AS: + AS:I + AS:.M. H. ABRAHAM, J. L I S Z I A N D E. P A P P 199 states because of cancellation between the AS: and AS: terms. The AS," term, eqn (3) and (4), contains not only the electrostatic effect but also the effect of any disordered layer; we shall continue to denote the overall (AS: - AS:) term as AS,", following our previous nomenclature.2 The above procedure [cf. ref. (1 l)] will yield a comparative set of entropies for a series of cations or a series of anions, but any comparison between the two series or any attempt at quantitative estimations of structure-making or structure-breaking effects will depend on the division of the AS: (M++X-) values into cationic and anionic contributions and also on the ionic radii used.We have previously2 obtained a set of AS: (M+) and AS: (X-) values that was compatible with the Goldschmidt- Pauling (GP) radii we had used,15 and was derived from Noye9 data. Most other sets of ionic radii are quite close to the GP radii except for that suggested by Adrian and Gourary" (AG). In order to examine the possible effects of different sets of ionic radii and AS: values, we have carried out calculations using both GP and AG radii and with the sets of single-ion AS: values that are compatible with these sets of radii.In all calculations, values of E,, a ~ ~ / a T ' , and the solvent radius, r, were those used l5 we took b = (a+ r ) and c = (b+ r ) = (a+ 2r), and values of cl = 2.0 and aEl/aT = - 1.6 x l5 As K-l. TABLE 1 .-SINGLE-ION VALUES OF AS:, AS:, AS: 11, B- AND B-COEFFICIENTS AND Po IN WATER AT 298 K BASED ON GOLDSCHMIDT-PAULING RADP ASSO AS: AS,qII B B P /cal K-l /cal K-l /cal K-l /dm3 /dm3 /cm3 ion a/W mol-1 mol-1 mol-l mol-1 mol-l mol-l H+ Li+ Na+ Ag+ K+ Rb+ Cs+ F- c1- Br- I- c10, - 0.90 1.05 1.13b 1.33 1.43 1.66 1.33 1.81 1.95 2.20 2.45 - 42.3 - 44.6 -36.8 - 38.6 -28.7 - 25.9 - 25.2 -37.1 - 23.3 - 19.3 - 14.3 - 13.0 - - 32.8 - 19.7 - 19.0 - 3.7 1 .o 5.1 - 12.1 8.6 14.0 21.7 25.6 - 0.096 - 30.4 0.174 - 17.4 0.1 10 - 15.7 0.115 - 1.5 0.0 17 3.1 -0.006 7.1 -0.021 - 9.9 0.072 10.6 -0.031 15.9 -0.066 23.5 -0.092 27.3 -0.089 0.09 -5.4 0.17 -6.3 0.09 -6.6 0.09 -6.1 0.02 3.6 - 0.0 1 8.7 - 0.02 15.9 0.1 1 4.2 - 0.04 23.2 - 0.07 30.1 -0.1 1 41.6 -0.1 15 49.5 Data from references in the text, except where shown.Single-ion values assigned as detailed in the text. Ref. (19). DISCUSSION RESULTS FOR WATER SOLVENT In table 1 are results based on GP radii. Both the calculated AS: and AS: values indicate that all the listed ions are net structure-breakers (AS," and AS: I I > 0) except for Li+, Na+, Ag+, K+ and F- which are net structure-makers (AS: and AS: I I < 0). In order to compare our conclusions with those based on single-ion viscosity B- coefficients, some method of assignment of these single-ion values is necessary; unfortunately there is no generally accepted method of so doing.l49 l8 We have assigned single-ion B-coefficients so that in a plot of AS: or AS: II against B points for both cations and anions lie on the same curve or line.The B-coefficients are derived from200 CALCULATIONS O N IONIC SOLVATION results collected by Nightingale14 and by Engel and Hertz.lg In the event, there are excellent linear correlations between AS: and AS: I I and the single-ion B-coefficients. In particular, all ions for which AS: and AS: II are positive have negative B-coefficients (structure-breakers) and all ions for which AS: and AS; I I are negative have positive B-coefficients (structure-makers). Engel and Hertzlg have studied structure-making and structure-breaking effects of ions through measurement of proton relaxation rates in water and also in some non-aqueous solvents. They obtain the solvent proton relaxation rate in the absence (Go) and presence (q) of electrolyte at a concentration C, and write an equation analogous to the Jones-Dole viscosity equation : (l/Tl)/(l/T;) = 1 +B’C+C‘C2 The coefficient B’ is a measure of the structure-making (B’ > 0) and structure-breaking (B’ < 0) effect of an electrolyte on the solvent.Again, B has to be separated into single-ion values; Engel and Hertzlg used the convention14 that B (K+) = B (Cl-) but we preferred to use the same procedure that we adopted for the division of B-coefficients into single-ion quantities. There is an excellent linear correlation between the single-ion B’ values in table 1 and the AS: and AS: quantities, with an exact agreement between the signs of AS: and AS: II and the signs of the B- and B’-coefficients.Structure-making and structure-breaking effects of ions should influence not only the B- and B-coefficients but also the partial molal volumes, Vo, of ions. In this case, not only must single-ion values be assigned, but it would also be useful to obtain an estimate of the electrostriction effect, Vgs, because it is this quantity that is closely related to structure-making or structure-breaking effects. We find that single-ion values of To assigned on the basis8 that To (H+, aq) = - 5.4 cm3 mol-1 need no further adjustment, and that there are again quite reasonable linear correlations between AS: or AS; II and the single-ion To values in table 1 11, 2o There have been numerous methods suggested for subtracting out from the single-ion Vo values the intrinsic molar volume of ions En so as to leave the contribution due to electrostriction.The simplest method is merely to calculate the volume of an ion, 4/3na3N, which is given by the formula 2.52a3 when a is in A and To in cm3 mol-l. Mukerjee21 applied a correction to this formula yielding 4.48a3 as the intrinsic volume, and this was later used by Surdo and Millero.22 Several other methods of calculation Kn have been put forward, but Hirata and A r a k a ~ a ~ ~ have suggested that all the various methods are more or less approximations of a more general equation for cavity formation obtainable through scaled-particle theory.For water at 298 K, Hirata and A r a k a ~ a ~ ~ deduced eqn (6) En = 2.52a3+4.310a2+2.187a+0.639 (6) where Kn is in cm3 mol-1 and a is the Pauling ionic radius in A. A much more complete analysis has recently been given by M a t t e ~ l i , ~ ~ who not only included the s.p.t. cavity calculation but also took into account non-electrostatic ion-solvent interactions. Values of Ks deduced using various formulae are in table 2, together with correlation coefficients, p, for plots of AS: I I against the KS values. Because the sets of Ks values vary so widely in numerical values, it is not easy to assess any quantitative connection between AS: or AS; II and Es. The most recently calculated values of Matte01i~~ are reasonably well-correlated with AS: or ASEI1 ( p = 0.974), however, so we feel that such a connection, if not established, is at least indicated.We thought it useful to recalculate all our results using the AG set of radii, and the various sets of values are summarised in table 3. The correlations are detailed in table 4, both for results calculated using GP radii as well as for those using the AG set.M. H. ABRAHAM, J. LISZI AND E. PAPP 20 1 TABLE 2.-vALUES OF THE ELECTROSTRICTIVE CONTRIBUTION, Cs, IN WATER CALCULATED USING VARIOUS METHODS, IN cm3 mo1-1 AT 298 K BASED ON GOLDSCHMIDT-PAULING RADII ion vo U b C d Li+ Na+ K+ Rb+ c s + F- c1- Br- 1- Ag+ c10, - 6.3 - 6.6 -6.1 3.6 8.7 15.9 4.2 23.2 30.1 41.6 49.5 0.949 0.976 -8.1 - 9.5 - 9.7 - 2.3 1.3 4.4 - 1.7 8.2 11.4 14.7 12.4 0.952 0.973 - 9.6 - 14.2 -11.8 - 17.2 - 12.6 - 18.4 - 6.9 - 13.5 - 4.4 - 11.3 - 4.6 - 11.8 - 12.2 - 12.9 - 18.4 - 10.5 -21.8 - 9.9 - 33.0 - 11.6 - 53.5 - 18.7 - 0.670 0.297 -0.710 0.322 - 28 - 24 -21 - 14.2 - 11.7 -7.1 - 14.2 - 5.2 - 4.0 -2.7 -2.1 0.974 0.962 a Es = 8O-2.52~~.Matteoli's method. cs = TO-4.48~~. cs = Po- Tion, the latter calculated via eqn (6). Correlation constant for S: I I plotted against To or V&. f Correlation constant excluding the point for Li+. Also given are values of p. A noteworthy feature is that the regression line for correlations involving B- or B'-coefficients passes quite close to the origin, hence the one-to-one correspondence between the sign of AS: or ASP, I1 and the sign of the B- or B'-coefficients.There are not very substantial differences between results based on AG radii and those based on the GP set of radii, although the former set leads to K+ as a weak structure-breaker whereas the latter set leads to K+ as a weak structure-maker. In general, the results in tables 1 and 3 are in agreement with conclusions reached by many 11, 1 4 9 l9 An exception is the infrared study of Bonner and Jumper,25 who concluded that all anions, even F, were structure-breakers and who listed structure-makers in the order Ag+ > Li+ > Cs+ > Rb+ > K+ > Na+. Jackson and Symons26 have criticised these conclusions, and our results support the latter workers views. The single-ion AS: values in table 1 correspond to so (H+, aq, 1 mol dmP3) = - 8.3 cal K-l mol-l and those based on AG radii in table 3 correspond to so (H+, aq, 1 mol dm-3) = -6.3 cal K-l mol-l.Both of these values are quite close to the generally accepted 8 l l1 absolute value of - 5 to - 6 cal K-l mol-l. Furthermore, the single-ion Vo value in table 1, Vo (H+, aq) = - 5.4 cm3 mol-l, is exactly that suggested89l1 as the absolute value for H+(aq) and the value in table 3 , Vo(H+, aq) = + 1.8 cm3 mol-', is not too far away. We therefore feel that the various single-ion values listed in table 1 (especially) and table 3 must be quite close to absolute values. If this is so, then the conventions that B(K+) = B(Cl-) and B'(K+) = B'(C1-) are not too unrealistic, although a better division would rank Cs+ and C1- as equivalent. Very recently, K r ~ m g a l z ~ ~ has reassigned single-ion partial molal volumes using the method of Conway et a1.28 This method leads to Vo(H+, aq) = -6.0 cm3 mol-l, almost identical to the value in table 1 and to the value suggested by Criss and Salomon,8 by Friedman and Krishnan'l and by Millero.20202 CALCULATIONS O N IONIC SOLVATION TABLE 3.-sINGLE-ION VALUES OF As:, As:, AS: 11, B- AND B'-COEFFICIENTS AND To IN WATER AT 298 K BASED ON ADRIAN-GOURARY RADII~ H+ Li+ Na+ K+ Rb+ cs+ F- c1- Br- I- Ag+ ClO, - - - 40.3 - 0.94 -42.6 -29.4 -27.0 1.17 -34.8 -13.9 -11.6 1.13b -36.6 -17.0 -14.7 1.49 - 26.7 1.1 3.3 1.63 - 23.9 6.1 8.2 1.86 - 23.2 9.2 11.2 1.16 -39.1 -18.5 -16.2 1.64 -25.3 4.8 6.8 1.80 -21.3 10.5 12.5 2.05 - 16.3 18.1 20.0 2.30b - 15.0 22.0 23.8 0.077 0.155 0.09 1 0.096 - 0.002 - 0.025 - 0.040 0.091 -0.012 - 0.047 - 0.073 - 0.070 0.07 1.8 0.15 0.9 0.07 0.6 0.07 1.1 0.00 10.8 -0.03 15.9 - 0.04 23.1 - 0.02 16.0 - 0.05 22.9 - 0.09 34.4 -0.095 42.3 0.13 -3.0 a Units and references as in table 1.S. Ahrland (Pure Appl. Chem., 1979,51, 2019) gives, for ionic radii based on a scale closely related to the AG scale, values of a(Ag+) = 1.12 and a(C10,) = 2.30 A. We conclude that the single-ion values in tables 1 and 3 are near to absolute values, and that the calculated AS: and AS:, II values may be taken as quantitative measures of the structure-making and structure-breaking effects of univalent ions in water. The cations Li+, Na+ and Ag+ are powerful structure-making ions, K+ is a weak structure-maker or perhaps a borderline case and Rb+ and Cs+ are structure-breaking ions.The anions are all quite strong structure-breakers except for F- which is a structure-making ion. Although values of AS: are known for a number of large polyatomic univalent ions,ll we have not carried out any detailed calculations because of the difficulty in estimating ionic radii of the ions. We confirmed, however, that CN- (a = 1.86 A) is a strong structure-breaker, being placed in order between Br- and I-. Finally, we point out that although values of AS: (tables 1 and 3) are well-correlated with B, B' and Vo values, little can be deduced from these correlations about the net structure-making and structure-breaking effects of ions. Only by separating out the AS: or ASIqI1 terms can any quantitative estimates be made. RESULTS FOR NON-AQUEOUS SOLVENTS There are not so many solvents for which sufficient AS:, B, B and To values are known to explore correlations as in the case of water.However, for methanol the required AS: values are known,2 and there are a sufficient number of B-coefficients r e p ~ r t e d ~ ~ - ~ l to enable a set of single-ion values to be constructed. Engel and Hertzlg have determined #-coefficients for several electrolytes in methanol, and Criss and Salomon8 have tabulated To values based on Vo(H+, methanol) = - 16.6 cm3 mol-l; additional To values are also available.20* 3 2 9 33 Results of calculations of AS: and AS: II based on GP radii are in table 5 . Quite unlike the case of solvent water, our calculations indicate that all these inorganic ions, with the possible exception of ClO, as a borderline case, are structure-making ions in methanol; this is in complete agreement with the conclusions of Engel and Hertz.lg After reassignment of single-ion B- and H-coefficients using the method used for aqueous solutions, there are obtained good linear correlations between AS: or ASFI1 and either of the sets ofM.H. ABRAHAM, J. LISZI A N D E. PAPP 203 TABLE 4.-REGRESSION EQUATIONS FOR PLOTS OF As: OR AS: 11 AGAINST B, B' OR To VALUES AT 298 K function plotted no.a mb CC Pd water using GP radii AS: against B 11 -204.3 2.4 0.992 ASP ,, against B 11 -200.7 4.4 0.992 AS,.' against B 11 -192.9 1.0 0.986 ASP ,, against B 11 -189.7 3.1 0.986 AS," against Vo 11 0.893 -13.8 0.950 AS: against Vo 11 0.877 - 11.4 0.949 water using AG radii AS: against B 11 -208.6 2.5 0.991 AS;,, against B 11 -206.3 4.6 0.991 AS,.' against B 11 -194.8 1.0 0.988 ASP against B 11 -192.6 3.1 0.988 AS: against To 11 1.049 - 16.3 0.936 AS: against Vo 11 1.036 -14.0 0.935 AS: against B 8 -54.5 - 1.3 0.965 AS: against B' 9 -149.0 -8.2 0.966 AS: ,, against B 9 -143.1 -3.3 0.966 AS,.' against Vo 10 0.688 -24.8 0.983 AS: ,, against V' 10 0.660 -19.2 0.983 methanol using GP radii AS:,, against B 8 -52.5 5.8 0.965 methanol using AG radii AS: against B 8 -72.0 4.5 0.962 AS;,, against B 8 -69.3 8.9 0.963 AS,.' against B 9 -145.9 -8.5 0.954 ASP I I against B 9 -140.1 -3.6 0.954 AS,.' against Vo 10 0.757 -25.4 0.958 AS;, II against To 10 0.724 -19.8 0.957 AS: against B 8 -70.4 - 1.3 0.954 ASe against B 7 -181.4 -3.1 0.947 AS; ,, against B 7 -178.8 - 1.5 0.947 AS," against Vo 8 0.614 -26.3 0.994 AS: against Vo 8 0.605 -24.3 0.994 formamide using GP radii ASi,, against B 8 -69.4 0.3 0.954 N-methylformamide using GP radii AS: against B 7 curved plot obtained ASCII against B 7 curved plot obtained ASe against B 9 -304.0 0.1 0.990 AS;, ,, against B' 9 -296.5 1.0 0.988 NN-dimethylformamide using GP radii AS: against To 8 0.627 -39.6 0.980 AS;, against Vo 8 0.604 -36.1 0.982 dimethylsulphoxide using GP radii AS: against B 9 curved plot obtained AS;,, against B 9 curved plot obtained AS: against Vo 8 0.723 -36.1 0.957 AS: ,, against Vo 8 0.714 -34.5 0.967 AS: against Vo 8 0.645 -35.5 0.954 AS: II against To 8 0.629 -32.1 0.955 acetonitrile using GP radii a Number of points; slope; intercept; correlation constant.204 CALCULATIONS ON IONIC SOLVATION TABLE 5.-sINGLE-ION VALUES OF As:, As: 11, B- AND B'-COEFFICIENTS AND Po IN METHANOL AT 298 K BASED ON GOLDSCHMIDT-PAULING R A D I I ~ ion AS: ASP,,, B B V" H+ Li+ Na+ K+ Rb+ Cs+ F- c1- Br- I- c10, - - 40.4 - 34.4 - 27.4 - 22.8 - 19.1 - 26.4 - 15.1 - 12.1 - 6.4 - 3.7 - - 34.2 -28.7 -21.7 - 17.2 - 13.8 - 20.7 - 9.9 - 7.0 - 1.5 1 .o - 0.63 0.59 0.56 0.44 0.36 __ 0.20 0.18 0.11 - - 0.25 0.14 0.1 1 0.08b 0.07b - 0.05 0.03 0.00 - 0.0 1 - 16.6 - 16.0 - 14.6 - 4.6 - 0.6 5.9 - 2.4 11.3 18.6 26.3 34.9 a Units as in table 1 ; data from references in the text except where noted.Estimated values from ref. (1 9). TABLE 6.-sINGLE-ION VALUES OF As:, As:11, B- AND B'-COEFFICIENTS AND v" IN METHANOL AT 298 K BASED ON ADRIAN-GOURARY R A D I I ~ ion AS: AS:,rI B B V" H+ Li+ Na+ K+ Rb+ cs+ F- c1- Br- I- c10, - - 38.2 -31.6 - 24.3 - 19.4 - 15.8 - 29.6 - 18.3 - 15.2 - 9.4 - 6.7 - - -32.1 0.54 -25.7 0.50 -18.8 0.47 -14.0 0.35 -10.6 0.27 -23.7 - - 12.9 0.29 -10.0 0.27 -4.4 0.20 -1.9 - - -10.6 0.23 -8.0 0.12 -8.6 0.09 1.4 0.06b 5.4 O.OSb 11.9 - 8.4 0.07 5.3 0.05 12.6 0.02 20.3 0.01 28.9 - a Units as in table 1 ; data from references in the text except where noted.Estimated values from ref. (1 9). coefficients (table 4). The regression lines pass reasonably close to the origin so that, again, there will be a correspondence between the sign of AS: or AS: I I and the sign of the coefficients. In the event, for the ions other than ClO;, both entropy quantities are always negative and the B- and B'-coefficients are positive, indicative of structure- making effects.Values of To assigned by Criss and Saloman* are in table 5; without any further adjustment, these values are linearly related to AS: or AS:,, for both cations and anions (see table 4). In order to check whether or not our general conclusions for non-aqueous solvents are affected by choice of single-ion AS! values or of ionic radii, we have repeated all the calculations for methanol using the AG set of radii (table 6). Results are very similar to those in table 5 except that C10; would now be classed as a structure-making ion instead of as a borderline case; the correlations using the GP radii are slightly better than those with AG radii. TheM. H. ABRAHAM, J. LISZI AND E. P A P P 205 single-ion B- and B'-coefficients in tables 5 and 6 are almost equivalent to a convention that sets similar values for Cs+ and Cl-; the recent division of B-coefficients into single-ion values carried out by Krumgalzls leads to appreciably different cation and anioncontributions - to those listed in tables 5 and 6.As pointed out above, the single-ion Vo values in table 5 are those suggested by Criss and Salomon8 and are equivalent to taking To (H+, methanol) = - 16.6 cm3 mol-l, whereas the division in table 6 corresponds to a value of - 10.6 cm3 mo1-l for Yo(H+, methanol). These values are quite remote from Vo(H+, methanol) = + 16.3 cm3 mol-l, a value that corresponds to the single-ion division of K r ~ m g a l z . ~ ~ TABLE 7.-sINGLE-ION VALUES OF As:, AS: B- AND E-COEFFICIENTS AND ro IN FORMAMIDE AT 298 K BASED ON GOLDSCHMIDT-PAULING RADIP Li+ Na+ K+ Rbf cs+ c1- Br- I - c10, - 29.4 - 29.4 - 22.4 - 17.8 - 14.2 - 10.1 -7.1 - 1.4 1.3 - 27.4 - 27.4 -20.5 - 16.0 - 12.5 - 8.4 - 5.4 0.2 2.8 0.353 0.465 0.239 0.217 0.19 0.125 0.083 0.053c - 4.7 0.16 -3.2 0.08 7.7 0.06 11.6 0.07 18.0 0.04 24.3 0.03 31.1b 0.005 43.1 - a Units as in table 1 ; data from references in the text except where noted.Ref. (20). Results of J. M. Notley and M. Spiro (J. Phys. Chem., 1966, 70, 1502) suggest 0.00 for B(1-) on the given single-ion division. The most interesting non-aqueous solvents studied by Engel and Hertzlg were glycerol and ethylene glycol, where it appeared that even inorganic ions could act as structure-breakers. Unfortunately, AS: values are not known for ions in these solvents, but values are available2 for formamide, a solvent that is itself so ordered that structure-breaking effects might be observable.Martinus and Vincent34 have determined B-coefficients for electrolytes in this solvent, #-values are available,lg and single-ion vo values have been assigned by Criss and Salomon;s all these values are in table 7. We have carried out calculations only in terms of GP radii, in view of the similar conclusions obtained (above) using the AG set. Our calculated AS: and AS: I I values, table 7, indicate that formamide behaves rather similarly to methanol; only for the largest ions does any structure-breaking effect appear. With the division of B- and #-values into single-ion quantities carried out as described before, the resulting ionic B- and B'-coefficients are reasonably well-correlated with AS: and AS; I I .The cationic and anionic division of B-coefficients (table 7) is very close to that given before,34 the difference being only _+ 0.04 dm3 mol-l. Our conclusions based on AS: or AS: II values are almost exactly the same as those of Martinus and Vincent,34 who found that all the alkali halide ions are structure-makers with the exception of I- which is a weak structure-breaker. The To values of Criss and Salomon (table 7) are also linearly correlated with AS: and AS& but in this case Krumgalz'~~~ division of Vo into single-ion values yields quite different results. Details of all the regression equations for formamide solvent are in table 4. Engel and Hertzlg measured B'-coefficients for a number of electrolytes in N- methylformamide, and there are excellent correlations of our calculated AS: andM. H.ABRAHAM, J. LISZI AND E. P A P P 205 single-ion B- and B'-coefficients in tables 5 and 6 are almost equivalent to a convention that sets similar values for Cs+ and Cl-; the recent division of B-coefficients into single-ion values carried out by Krumgalzls leads to appreciably different cation and anioncontributions - to those listed in tables 5 and 6. As pointed out above, the single-ion Vo values in table 5 are those suggested by Criss and Salomon8 and are equivalent to taking To (H+, methanol) = - 16.6 cm3 mol-l, whereas the division in table 6 corresponds to a value of - 10.6 cm3 mo1-l for Yo(H+, methanol). These values are quite remote from Vo(H+, methanol) = + 16.3 cm3 mol-l, a value that corresponds to the single-ion division of K r ~ m g a l z .~ ~ TABLE 7.-sINGLE-ION VALUES OF As:, AS: B- AND E-COEFFICIENTS AND ro IN FORMAMIDE AT 298 K BASED ON GOLDSCHMIDT-PAULING RADIP Li+ Na+ K+ Rbf cs+ c1- Br- I - c10, - 29.4 - 29.4 - 22.4 - 17.8 - 14.2 - 10.1 -7.1 - 1.4 1.3 - 27.4 - 27.4 -20.5 - 16.0 - 12.5 - 8.4 - 5.4 0.2 2.8 0.353 0.465 0.239 0.217 0.19 0.125 0.083 0.053c - 4.7 0.16 -3.2 0.08 7.7 0.06 11.6 0.07 18.0 0.04 24.3 0.03 31.1b 0.005 43.1 - a Units as in table 1 ; data from references in the text except where noted. Ref. (20). Results of J. M. Notley and M. Spiro (J. Phys. Chem., 1966, 70, 1502) suggest 0.00 for B(1-) on the given single-ion division. The most interesting non-aqueous solvents studied by Engel and Hertzlg were glycerol and ethylene glycol, where it appeared that even inorganic ions could act as structure-breakers. Unfortunately, AS: values are not known for ions in these solvents, but values are available2 for formamide, a solvent that is itself so ordered that structure-breaking effects might be observable.Martinus and Vincent34 have determined B-coefficients for electrolytes in this solvent, #-values are available,lg and single-ion vo values have been assigned by Criss and Salomon;s all these values are in table 7. We have carried out calculations only in terms of GP radii, in view of the similar conclusions obtained (above) using the AG set. Our calculated AS: and AS: I I values, table 7, indicate that formamide behaves rather similarly to methanol; only for the largest ions does any structure-breaking effect appear.With the division of B- and #-values into single-ion quantities carried out as described before, the resulting ionic B- and B'-coefficients are reasonably well-correlated with AS: and AS; I I . The cationic and anionic division of B-coefficients (table 7) is very close to that given before,34 the difference being only _+ 0.04 dm3 mol-l. Our conclusions based on AS: or AS: II values are almost exactly the same as those of Martinus and Vincent,34 who found that all the alkali halide ions are structure-makers with the exception of I- which is a weak structure-breaker. The To values of Criss and Salomon (table 7) are also linearly correlated with AS: and AS& but in this case Krumgalz'~~~ division of Vo into single-ion values yields quite different results.Details of all the regression equations for formamide solvent are in table 4. Engel and Hertzlg measured B'-coefficients for a number of electrolytes in N- methylformamide, and there are excellent correlations of our calculated AS: andM. H. ABRAHAM, J. LISZI AND E. P A P P 205 single-ion B- and B'-coefficients in tables 5 and 6 are almost equivalent to a convention that sets similar values for Cs+ and Cl-; the recent division of B-coefficients into single-ion values carried out by Krumgalzls leads to appreciably different cation and anioncontributions - to those listed in tables 5 and 6. As pointed out above, the single-ion Vo values in table 5 are those suggested by Criss and Salomon8 and are equivalent to taking To (H+, methanol) = - 16.6 cm3 mol-l, whereas the division in table 6 corresponds to a value of - 10.6 cm3 mo1-l for Yo(H+, methanol).These values are quite remote from Vo(H+, methanol) = + 16.3 cm3 mol-l, a value that corresponds to the single-ion division of K r ~ m g a l z . ~ ~ TABLE 7.-sINGLE-ION VALUES OF As:, AS: B- AND E-COEFFICIENTS AND ro IN FORMAMIDE AT 298 K BASED ON GOLDSCHMIDT-PAULING RADIP Li+ Na+ K+ Rbf cs+ c1- Br- I - c10, - 29.4 - 29.4 - 22.4 - 17.8 - 14.2 - 10.1 -7.1 - 1.4 1.3 - 27.4 - 27.4 -20.5 - 16.0 - 12.5 - 8.4 - 5.4 0.2 2.8 0.353 0.465 0.239 0.217 0.19 0.125 0.083 0.053c - 4.7 0.16 -3.2 0.08 7.7 0.06 11.6 0.07 18.0 0.04 24.3 0.03 31.1b 0.005 43.1 - a Units as in table 1 ; data from references in the text except where noted.Ref. (20). Results of J. M. Notley and M. Spiro (J. Phys. Chem., 1966, 70, 1502) suggest 0.00 for B(1-) on the given single-ion division. The most interesting non-aqueous solvents studied by Engel and Hertzlg were glycerol and ethylene glycol, where it appeared that even inorganic ions could act as structure-breakers. Unfortunately, AS: values are not known for ions in these solvents, but values are available2 for formamide, a solvent that is itself so ordered that structure-breaking effects might be observable. Martinus and Vincent34 have determined B-coefficients for electrolytes in this solvent, #-values are available,lg and single-ion vo values have been assigned by Criss and Salomon;s all these values are in table 7.We have carried out calculations only in terms of GP radii, in view of the similar conclusions obtained (above) using the AG set. Our calculated AS: and AS: I I values, table 7, indicate that formamide behaves rather similarly to methanol; only for the largest ions does any structure-breaking effect appear. With the division of B- and #-values into single-ion quantities carried out as described before, the resulting ionic B- and B'-coefficients are reasonably well-correlated with AS: and AS; I I . The cationic and anionic division of B-coefficients (table 7) is very close to that given before,34 the difference being only _+ 0.04 dm3 mol-l. Our conclusions based on AS: or AS: II values are almost exactly the same as those of Martinus and Vincent,34 who found that all the alkali halide ions are structure-makers with the exception of I- which is a weak structure-breaker. The To values of Criss and Salomon (table 7) are also linearly correlated with AS: and AS& but in this case Krumgalz'~~~ division of Vo into single-ion values yields quite different results.Details of all the regression equations for formamide solvent are in table 4. Engel and Hertzlg measured B'-coefficients for a number of electrolytes in N- methylformamide, and there are excellent correlations of our calculated AS: andM. H. ABRAHAM, J. LISZI AND E. P A P P 205 single-ion B- and B'-coefficients in tables 5 and 6 are almost equivalent to a convention that sets similar values for Cs+ and Cl-; the recent division of B-coefficients into single-ion values carried out by Krumgalzls leads to appreciably different cation and anioncontributions - to those listed in tables 5 and 6.As pointed out above, the single-ion Vo values in table 5 are those suggested by Criss and Salomon8 and are equivalent to taking To (H+, methanol) = - 16.6 cm3 mol-l, whereas the division in table 6 corresponds to a value of - 10.6 cm3 mo1-l for Yo(H+, methanol). These values are quite remote from Vo(H+, methanol) = + 16.3 cm3 mol-l, a value that corresponds to the single-ion division of K r ~ m g a l z . ~ ~ TABLE 7.-sINGLE-ION VALUES OF As:, AS: B- AND E-COEFFICIENTS AND ro IN FORMAMIDE AT 298 K BASED ON GOLDSCHMIDT-PAULING RADIP Li+ Na+ K+ Rbf cs+ c1- Br- I - c10, - 29.4 - 29.4 - 22.4 - 17.8 - 14.2 - 10.1 -7.1 - 1.4 1.3 - 27.4 - 27.4 -20.5 - 16.0 - 12.5 - 8.4 - 5.4 0.2 2.8 0.353 0.465 0.239 0.217 0.19 0.125 0.083 0.053c - 4.7 0.16 -3.2 0.08 7.7 0.06 11.6 0.07 18.0 0.04 24.3 0.03 31.1b 0.005 43.1 - a Units as in table 1 ; data from references in the text except where noted.Ref. (20). Results of J. M. Notley and M. Spiro (J. Phys. Chem., 1966, 70, 1502) suggest 0.00 for B(1-) on the given single-ion division. The most interesting non-aqueous solvents studied by Engel and Hertzlg were glycerol and ethylene glycol, where it appeared that even inorganic ions could act as structure-breakers. Unfortunately, AS: values are not known for ions in these solvents, but values are available2 for formamide, a solvent that is itself so ordered that structure-breaking effects might be observable.Martinus and Vincent34 have determined B-coefficients for electrolytes in this solvent, #-values are available,lg and single-ion vo values have been assigned by Criss and Salomon;s all these values are in table 7. We have carried out calculations only in terms of GP radii, in view of the similar conclusions obtained (above) using the AG set. Our calculated AS: and AS: I I values, table 7, indicate that formamide behaves rather similarly to methanol; only for the largest ions does any structure-breaking effect appear. With the division of B- and #-values into single-ion quantities carried out as described before, the resulting ionic B- and B'-coefficients are reasonably well-correlated with AS: and AS; I I . The cationic and anionic division of B-coefficients (table 7) is very close to that given before,34 the difference being only _+ 0.04 dm3 mol-l.Our conclusions based on AS: or AS: II values are almost exactly the same as those of Martinus and Vincent,34 who found that all the alkali halide ions are structure-makers with the exception of I- which is a weak structure-breaker. The To values of Criss and Salomon (table 7) are also linearly correlated with AS: and AS& but in this case Krumgalz'~~~ division of Vo into single-ion values yields quite different results. Details of all the regression equations for formamide solvent are in table 4. Engel and Hertzlg measured B'-coefficients for a number of electrolytes in N- methylformamide, and there are excellent correlations of our calculated AS: andM.H. ABRAHAM, J. LISZI AND E. PAPP 209 solvents become less polar and less ordered, so the inorganic ions become even stronger makers of structure, as shown in table 12. Not only do our AS: and AS: I I values provide a quantitative criterion of the effect of an ion on the solvent structure, they also provide a method of inter-relating quantities such as B- and #-coefficients and partial molal volumes of ions. If single-ion B- and #-coefficients are assigned so that in plots against AS: or ASZII points for cations and anions fall on the same line, the resulting single-ion B- and B’-coefficients make up a self-consistent and coherent set of data both for water and non-aqueous solvents. The plots of B or B’ against AS: or AS: I I (see fig. 1) pass almost through the origin so that on one diagram it is possible to indicate the quantitative relationship that exists between B or B’ and AS: or AS: I I in all solvents.All ions appear either in the top left-hand quadrant (AS: negative and B or B positive) as structure-makers or in the bottom right-hand quadrant (AS: positive and B negative) as structure-breakers. 1-0.2 FIG. 1 .-Plot of single-ion viscosity B-coefficients in dm3 mo1-I against single-ion values of AS:. in cal K-I mo1-I for alkali halide ions in @, water; 0, formamide and m, methanol. We have not explored possible relationships between AS: or AS[,, and the temperature variation of ionic viscosity B-coefficients, aB/a T, partly because of lack of experimental data and partly because the aB/aT values have also to be assigned to single ions. However, it seems generally to be the case for the inorganic ions studied that negative values of AS: or AS: I I (structure-making effects) correspond to positive values of B and to negative values of aB/aT, both in water and in non-aqueous solvents.Conversely, at least in water, positive values of AS: or ASFIr (structure-210 CALCULATIONS ON IONIC SOLVATION breaking effects) correspond to negative values of B and to positive values of aB/aT. Although Vo values themselves cannot be used as criteria of ion-solvent structural effects, partial molal volumes must include contributions from such effects. In the event, we find empirically that when Vo values in water are assigned to single ions so that Vo(H+, aq) = - 5.4 cm3 mol-1 and when Vo values in non-aqueous solvents are then assigned to single ions by the correspondence method,* there are excellent linear correlations between AS: or ASCII and the obtained single-ion Vo values.The correspondence method does yield single-ion To values that differ very considerably from those assigned by K r ~ m g a l z . ~ ~ All we wish to say in favour of the former method is that it does result in a set of To values that seems to be compatible with the AS:, ASIqI1, B- and B-coefficients used in the present work. Finally, we point out that our conclusions are almost unaffected by choice of a different set of ionic radii (and associated AS: values) as shown by results in tables 1, 3, 5 and 6. We prefer the GP set of radii, but conclude that our values of AS: and A S t I 1 calculated using either set of radii must be close to 'absolute' values.If this is so, then our single-ion values of B and B in tables 1, 5 , 7, 8 and 10 will also be close to an 'absolute' division. The single-ion values of B and B in cases where only a few values are available (tables 9, 10 and 11) are approximate only; more data are needed to obtain a reliable division. We thank Dr Enrico Matteoli for communicating results prior to publication and for kindly calculating values of Ves using his method. M. H. Abraham, J. Liszi and L. Meszaros, J. Chem. Phys., 1979, 70, 249. M. H. Abraham and J. Liszi, J. Chem. Soc., Faraday Trans. I, 1978, 74, 2858. M. H. Abraham and J. Liszi, J. Chem. Soc., Faraday Trans. I , 1980, 76, 1219. H. S. Frank and M. W.Evans, J. Chem. Phys., 1945, 13, 507. R. W. Gurney, Ionic Processes in Solution (McGraw-Hill, New York, 1953). E. R. Nightingale Jr, J. Phys. 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