J . Chem. SOC., Faraday Trans. I, 1986,82, 233-242 The Hydration Entropies of Ions and their Effects on the Structure of Water Yizhak Marcus Department of Inorganic & Analytical Chemistry, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel The conventional entropies of hydration are interpreted in terms of con- tributions from conversion to the absolute scale, compression from the gas to the solution standard states, long-range electrostatic interactions, immobilization of the solvent near the ion, and water-structural effects. A simple but effective method for the estimation of the entropy of solvent immobilization is presented. Correlations between the entropy of hydration of ions and various measures of the effects of ions on the structure of water, applied in the past mainly to monoatomic ions, are extended to polyatomic ones.Water differs from most other liquids by having a pronounced degree of structure, due to the extended three-dimensional network of hydrogen bonds. This structure is affected by solutes,' including ions that result from the dissociation of dissolved electrolytes. Some ions are known to enhance the 'structuredness' of the water, in whatever manner this might be defined, and others are known to break this structure down. To the latter, structure-breaking category belong large ions of low charge, such as Cs+ or I-, and to the structure-making category belong ions having a strong electrostatic field, such as Li+, Mg2+, or La3+. The structure-affecting properties of the ions are manifested in such properties of their aqueous solutions as the viscosity 2, (structure-breaking ions lower it), the rate of exchange of water molecules4 (structure-breaking ions lower its energy of activation), and the longitudinal relaxation rate of the water molecules, measured by n.m.r.5 (structure-breaking ions increase it).Another property of solutions of electrolytes that has been related to the effect of ions on the structure of water is the standard partial molar entropy of the ions. Since these include intrinsic entropies of the ions, a better measure of their structural effects is their entropy of hydration. The conventional standard molar entropy of hydration of an ion Xz is Ahyd con So(xz) = s&m(xz, as) - so(x*, g) (1) where z is the charge on the ion, S:on(XZ, as) is its conventional standard partial molar entropy in the aqueous standard state, and So(Xz,g) is its standard molar entropy in the gaseous standard state.The former standard state is the hypothetical ideal 1 mol dmP3 aqueous solution, with the convention that S&(H+, aq) = 0 at all temperatures, and the latter standard state is the ideal gas at 0.1 MPa pressure. This pressure and the temperature of 298.15 K are understood to prevail in all the systems to be discussed here. It was realized by Franks and Evans2 that even Ahydcon So(Xz) involves contributions extraneous to the structural effects: uiz. from the change in the volume at the disposal of the ions in the two standard states, from the coordination of water molecules to the ion, and that arising from electrostatic interactions. Frank and Evans,2 as well as the authors who followed considered practically only the monoatomic alkali metal and halide ions in their deliberations. It is instructive to demonstrate that these considerations pertain also to polyatomic ions, and that the water-structural entropy effects for these ions also correlate with the viscosity, exchange rate, and longitudinal 233234 Hydration Entropies of Ions relaxation rate, where known.The present paper considers the available $E,,(X*, aq) and So(Xz, g) data for a large set of ions, and specifies the compression, immobilization, and electrostatic contributions to Ahyd s"(Xz), obtained by the conversion of the conventional values of the standard molar entropies of hydration to the absolute scale in an appropriate manner.After subtraction of the contributions listed above from the absolute standard molar entropy of hydration, the water-structural entropy effects of the ion are obtained as the difference, as is commonly done, there being no direct method for their estimation. Data Employed Conventional standard partial molar entropies of the ions considered here are available in the NBS Tables.12 The standard molar entropies of the gaseous monoatomic ions are calculated by the Sackur-Tetrode equation, which for 298.15 K and the 0.1 MPa standard state pressure takes the numerical expression So(X&onoatomic,g) = 12.4715 In M,+ 108.85 J K-l mol-1 where M , is the relative atomic mass of the ion. The standard molar entropies of the gaseous polyatomic ions considered here are from Loewenschuss and Marcus.13 These data are shown in table 1, as are the derived conventional standard molar entropies of hydration, obtained by means of eqn (1).A few comments on the data shown in table 1 are in order here. The uncertainties of the SzOn(Xz, aq) values follow the convention of being 8-80 times the unit of the last digit reported.12 Those of the So(Xz,g) values follow the code of being 2-10 times the unit of the last digit reported. The values of Sz,,[(CH,),N+, aq] and $~,,[(C,H,),N+, as], not reported in the NBS Tables,12 are from Johnson and Martin.14 For two of the ions in table 1, AuBr; and Hg(CN)i-, the values of So(Xz, g) are not from Loewenschuss and Marcus,13 but have been calculated in the present study.The former of these two complex anions is square planar, having an Au-Br distance of 0.257 nm and a complete set of vibration frequencies given by Goggin and Mink.15 The latter of the two anions is tetrahedral, having an Hg-C distance of 0.222 nm (and the C-N distance taken as 0.11 5 nm)16 and a complete set of vibration frequencies given by J0nes.l' Both sets of frequencies were fully assigned by the authors, i.e. were accompanied by the pertinent degeneracies, including estimates of the frequencies of non-observed vibrations. The entropies of the gaseous ions were calculated according to the manner described previously. l3 Calculation of the Structural Entropy Effect The conventional standard molar entropies of hydration are converted to the corres- ponding absolute values by the addition of z times the absolute standard partial molar entropy of the aqueous hydrogen ion: This quantity was estimated by various methods, as reviewed and discussed by Conway,lS who recommended the value - 22.2 & 1.2 J K-l mol-l for P(H+, aq).The derived absolute standard molar entropies of hydration of the ions considered here are also shown in table 1. The change in the volume at the disposal of the ion, when it is transferred in the process of hydration from its gaseous standard state to its solution standard state, the so-called 'compression term' is: Acomp So = R In (1 dm3 mo1-I x 0.1 MPaIRT) = - 26.7 J K-l mol-1 (4) for all ions. (The volume in the ideal gas is RTIO.1 MPa; in solution it is 1 dm3.) Others have suggested different values, as discussed in the Discussion section below.c3 3 u s s; E8- IA 16- m L- 9z - m OP - 62- I € - I PI - 9E 8s LS - L9 - 2 - 1 9 91 6 PI E E l - S I - Z- S s1- 1- 1 1- 691 - 08 - 82- ( S L ) 8E 61 E LP - 6 I I - EZ S - 82 8Z 61 0 (81) PEI- OLI- 89 - 88 - SL - LS - LS - sz - IP- oz - E 621- 291 - 9E - PE - OE - 61 - 92- ZZ - t E - 211- 09 - PP- IP- 9s - LP - I E - SP - S61- 011- SL- 19- I- PZ- 6E - I01 - ZPI - OPI - 9E - 08 - €2- 62- 8E - PL - €01 - os.'nJ75v *osPAqv OLI - 982- WI - 991 - I Z I - I6- 16- 85 - 5L- EL- ES - 181 - 002- I L - 69 - w- ES - 09- LS - 99 - Wl- 56 - 08 - 9L - 16- 28 - 99 - 222 - WI - Z l l - 221- 9E - 65 - SL- LEI - 602- soz - ZL- L I I - 6S - 59 - PL- I l l - ZPI - on - OSPhSV 1'261 - 8'PLE - Z'ZIZ- 2-2!3- 0991 - 0 E l I - 0 E l I - E'08- 6'96- 8'LI I - 0'16- Z'IEZ- 8'PPZ - L'26- 016- 9'98 - O'EL - 5-28 - 0'6L - 0'88 - 8.69 I - O'LI I - 0.201 - 9'86 - €'El 1 - €'pol - E'88 - 9'201 - 0'002 - 0'22 1 - 9'68 - L'99 1 - 1'8S- 2'18- 6'96 - 9'65 I - 0'59 1 - 8'09 I - 8'6P - 9L.P6- IK9E - 16'2P- I'ZS- 0.68- 9'61 1 - osuoJpAqv L'8LZ 8'69P S'Z8P 8'WP S'OLP S'P82 S'P82 E'91P KE9E L'6LC 0' I PE P'182 9X92 1.962 5'882 8'LLZ O'L62 I 'Z8Z O'E92 6'L92 2'882 L'8LZ E'WL Z'SPZ E'9EZ Z'ZIZ S'ZEZ L'91 I O'E8P 6'IEE E'981 PI'ZSI 9S.691 LS'E9I OP'E s 1 6S'SPI 6P'S L 1 SE'OL 1 ZE'SLI W'L91 98'69 I I P'P9 I E9'PS I 86'LP I 66'2EI 4.98 0'56 E'OLZ 9'2EZ O'SOF 0'2 L I O'ZL I 0'9EE 6'992 6'192 E'PPZ 2.0s 8'8 I C'IOZ S'L61 2'161 0.2zz 9'66 I O'P8 I 0'08 I 9'81 I L'19I E'Z91 9'9PI O'EZ 1 6'LOI E'PPI I'PI O'E82 0'0 I2 6'96 9'PI - €'I11 P'Z8 S'9S 8'El - S'OI 9'6 S'SZI 89'ZL SO'EEI OS'IZI S'201 0'65 P'E I (be)""&236 Hydration Entropies qf Ions The electrostatic contribution to the entropy is considered to pertain beyond the first hydration shell.Any electrostatic effects that pertain to distances closer to the ion are taken up by the solvent immobilization term. The Born equation is invoked for the calculation of the electrostatic term : ABorn So(Xz) = [Ne2(C1~/2T)p/871~0 c2] z 2 / ( r X + 2r,) (5) where N is Avogadro's constant, e the charge of the proton, E , the permittivity of free space, E the relative permittivity of water and (?E/t)T)p its isobaric temperature coefficient, r x is the radius of the ion and rw is the radius of a water molecule. When the relevant numerical values are inserted, eqn ( 5 ) becomes: (6) ABorn So(Xz) = - 4067 z2[(rx/pm) + 2801 J K-' mol-l where the diameter of the water molecule in the first hydration shell is taken to be 280 pm.It is now necessary to specify the ionic radius r x to be used. For the monoatomic ions the Pauling crystal ionic radii (coordination number 6), as given by Shannon and Prewitt,lg are employed. For the polyatomic ions the thermochemical radii, as given by Jenkins and Thakur,20 are employed as far as they are available. In the other cases, the distance between the central atom and the peripheral atom that has been used13 for the calculation of the rotational contribution to the entropy of the gaseous ion is scaled by a factor obtained from the known thermochemical radii of isostructural ions.These factors are 1.60 for triatomic, 1.33 for tetra-atomic, 1.53 for tetrahedral and 1.41 for octahedral ions. The electrostatic contributions, according to eqn (6), and the radii rx used in parentheses, are shown in table 1 . An interim quantity, Ahyd So*, results when Acomp So and ABorn S o ( X r ) are subtracted from the absolute standard molar entropy of hydration of the ion : A,,, So* = Ahyd So(Xr) - Acomp So - ABorn So(Xz). (7) For monoatomic ions, both those included in table 1 and all the others for which the relevant data are available, AhydSo* is a more or less smooth function of lzl/rx, see fig. 1. This is interpreted as arising from the two remaining contributions to the entropy of hydration: the translational immobilization of the solvent in the first hydration shell of the ion and the effect of the ion on the structure of the water, and in particular from the first.The translational immobilization of the water is due to its coordination to the ion in the first hydration shell around the bare ion, containing n molecules of water on the (8) average : Xr(bare, aq) + n H,0(1) + X(H,O)Z, (aq). From the initial n+ 1 particles participating in reaction (8) only one, the hydrated ion, retains translational freedom. If it is assumed that the non-translational degrees of freedom of the water molecules are not affected, then the amount nS&ns,(H,O,l) of entropy is lost in reaction (8), and a small amount of translational entropy is gained, owing to the increase in the mass of the hydrated ion, compared with the bare one: (3/2) R In (M[X(H,O),]/M(X)).The translational entropy of water in the liquid is taken to be: (9) The standard molar entropy of water in the liquid and gaseous states is from the NBS Tables,12 and the translational entropy of the gaseous water is obtained from eqn (2). The translational immobilization entropy of the solvent is thus Atrim So(Xz) = = 12.4715 In (M[X(H,O],]/M(X))-26.0 n J K-I mol-*. (10) It remains to specify the number n of water molecules that are translationally immobilized by the ion. In view of the behaviour shown in fig. 1, and accepting as a fact S&nsl(H20, 1) = S0(H20, 1) - [So(H20, g) - StOransl(H20, g)] = 26.0 J K-l mol-l.Y. Marcus 237 I I I I I V 4 e OHf Zr I I I I 1 0 0.01 0.02 0.03 0.04 0.05 0.06 I z l/(r/pm) Fig.1. Difference between the hydration entropies of ions and the sum of the compression and electrostatic contributions thereof, Ahyd So*, plotted against the field strengths of the ions, lzl/rx, for monoatomic ions (e, cations, 0, anions). that the sodium ion is neither structure-making nor structure-breaking89 21 the following empirical relationship is proposed: n = 355 Izl/(rX/pm). (1 1) This value of n, together with eqn (10) above and (12) below, produce the value of AstrucSo(Na+) = 0 as specified. Finally, AtrimSo(XZ) is subtracted from Ahy9So*, and the difference is taken to represent the entropic results of the effect of the ion on the structure of the water: The values of the quantities appearing in eqn (12) are presented in table 1, those of n obtained according to eqn (11) being shown in parentheses after the value of Negative values of Astrue So(Xz) denote structure-making properties of the ions whereas positive values denote structure-breaking properties.The quantitative data of table 1 are translated into these qualitative terms (- for structure-making, + for structure-breaking ions) in table 2, for the sake of comparison with the results from other approaches. Since Astrue So(Xz) has considerable cumulative errors from all the terms that come into its calculation [estimated at k4(1+z2)4 J K-l mol-'1, values that are between -6 and +6 J K-l mol-l are denoted by in table 2, signifying that they are borderline cases. Atr im So(XZ)* Correlation with Other Aspects of Ionic Effects on the Structure of Water Table 2 presents, again in a qualitative manner, the results from other lines of investigation concerning the effects of ions on the structure of water.To the ions in table 2 must be added a long list of other ions, all multiply charged and not very big, that are assigned to the structure-making category by all the methods. These include both monoatolnic cations, such as Mg2+, Ca2+, Zn2+, Hg2+, La3+, Zr4+, etc. and polyatomic anions, such as Cog-, SO:-, PO:-, etc. as far as they have been studied by the methods considered in table 2. The picture arising from table 2 (and the added list of ions238 Hydration Entropies of Ions Table 2. Water structure-affecting properties of ions" ion S V E N ion S V E N Li+ Na+ K+ R b+ cs+ T1+ Ba2+ Pb2+ F- c1- Br- I- S2- NH; &+ (CH,),N+ (C,H,),N+ N3 CN- SCN- NO, NO; CH,CO; ClO, BrO; I 0 3 BF, c10, BrO; 10, MnO; TcO; ReO, Au(CN); AuCl; AuBr; CrOz- Cr20:- Co(CN)i- Fe( CN)g- Fe(CN):- Ag(CN), so:- S @ - Hg(CN):- + + - + + + + + + - + + + + + + + - + + + - + + + + - - + + + + - + - - + + + - a S, from the entropy of hydration, this work.V, from viscosity data, ref. (3), ( 5 ) , (22) and (23). E, from the energy of activation for water exchange, ref. (4). N, from the n.m.r. longitudinal relaxation rate, ref. ( 5 ) . mentioned above) is of general agreement among the methods, with some minor exceptions. Numerical correlations were determined between the quantities expressing the effects of the ions according to the various methods included in table 2.24 The results are: (13) (14) (15) B(n.m.r.) = -0.01 -0.0024A,,,,, So; n' = 28; reor, = -0.936 B(viscosity) = 0.14-0.025A,,,,,So; n' = 27; rcorr = -0.955 E(exchange) = - 0.9 1 - 0.0 1 8Astruc So ; n' = 16; rcorr = - 0.857 where B(n.m.r.) = [(zx/zo) - 11 (n VHzo) is the analogue5 of the Dole-Jones B(viscosity) coefficient3 (both in dm3 mol-l), E is the activation energy for water exchange from the immediate vicinity of the ion with the bulk water (in kJ mol-l), n' is the number of pairs of data, and r,,,, is the correlation coefficient for the linear regression.The correlations of these three measures of the effects of ions on the structure of water with the structural entropy contribution obtained by eqn (12) in this work are as good as they are among themselves. In all Ae cases there are items that fall very far from the linear regression curve, and these items have been excluded from correlations (13E(15). The more important qualitative discrepancies noted in table 2 are the apparent positive structural entropy changes (structure-breaking properties) obtained for Li+ and S2-, which are known or expected to be structure-making, and the negative structural entropy change (structure-making property) obtained for NHZ, which other methods assign to the opposite category.In the case of Li+ the fault may rest with the overlarge value of n, the number of waterY. Marcus 239 molecules immobilized, which is larger than the usual coordination number of 4. If this is taken to be the value of n applicable in eqn (lo), then the translational immobilization term becomes Atrim S"(Li+) = - 74 J K-l mol-1 and the structural entropy change becomes Astrue So(Li+) = - 30, as expected for this structure-breaking ion.In the case of S2- the fault may rest with the unrealistically small radius used for this ion in solution (only 184 pm) compared with the 18 1 pm of the isoelectronic singly charged C1- ion. If the value of the radius is increased by 20% (to the value of the univalent radius), then the Born term is 3 and the immobilization term is 15 J K-l mol-l less negative, yielding for Astrue So(S2-) the smaller positive value of 7 J K-l mol-l, which is more reasonable for such a large, though doubly charged, anion as S2-. Another possible source for the discrepancy could be an incorrect value of Sg,,(S2-,aq), owing to the difficulties encountered with this readily hydrolysed anion.The fault in the case of NH: may be only apparent, and may not be due to a shortcoming of the structural entropy method. The ammonium cation may not be structure-breaking, as the other methods lead one to think, since it fits so well into the structure of the water itself that it cannot be discerned by X-ray diffraction studies of aqueous solutions of ammonium salts. The negative value of Astruc S"(NH;) is, therefore, to be expected from the fact that the ammonium ion forms four hydrogen bonds with the water molecules surrounding it. Discussion The occurrence of negative values for Ahyd So(Xz), both for the ions appearing in table 1 and for all the others that have ever been examined, is generally interpreted as being due to a summation of contributions, most of which are negative.It is also generally accepted that electrostatic effects, alone or in combination with a 'neutral term' (accounting for the change in the standard states on hydration, among other effects), are inadequate for explaining the entire negative magnitude of the entropy of hydration. They are accepted, however, as accounting for some part of it. In order to allow for a positive contribution to the entropy of hydration for ions known to be structure-breakers, there must exist some major negative contribution to the entropy of hydration other than the electrostatic term. The present study proposes the notion of the translational immobilization of solvent (water) molecules around the ion to take this into account.Of the many authors who concerned themselves with the interpretation of the entropy of hydration of 6 - 1 1 ~ 2 5 ~ 26 most have implicitly or explicitly taken approaches similar to the present one, but have emphasized different aspects. The entropy changes that occur when an ion is first coordinated by a certain number of water molecules and the resulting hydrated ion is subsequently dissolved in water were calculated.6* i v 26 The results of these quite complicated calculations, based on unverifiable assumptions and arbitrary choices of parameters, did not give impressive agreement with the experimental entropies of hydration, even for the monoatomic alkali-metal and halide ions. The number of water molecules coordinated to the ions in these calculations was fixed arbitrarily67' or was left open as a free parameter with a wide range of values.26 The other approaches are, essentially, variants of two lines.The approach of Frank and Evans,2 adopted with slight changes by Friedman and Krishnan,* regarded the (absolute) entropy of hydration of an ion as the sum of the same four contributions as considered in the present study : compression, electrostatic, immobilization, and structural contributions (though not necessarily under the same names). Frank and Evans2 used the unit mole fraction standard state for the solute ion in the solution, which is an unreasonable It was, indeed discarded by Friedman and Krishnan,s who employed the molal concentration scale and the hypothetical ideal 1 mol kg-l standard state for the ion in the solution.Owing to the nearness of the density of water at 298.15 K to unity, in terms of kg dm-3, the compression term of these latter240 Hydration Entropies of Ions authors is the same as that used in the present work. Their electrostatic term is also the same as that used here, being applied beyond the distance of the Pauling radius plus the diameter of a water molecule. The translational immobilization of the solvent near the ion was set in the approaches used by the authors named above as a constant coordination number (four) times one half of the entropy lost by a mole of water on freezing (at 298.15 K). These are arbitrary choices that lead operationally to the value of Astruc So(Xz) obtained as the difference.Other choices, such as complete freezing, have been made,lo9 22 and by ignoring any structural contributions to the entropy have led to operationally defined hydration numbers. Krestov and Abrozimovg used a similar approach, but lumped the compression term and the translational immobilization of the solvent term together, in a term called by them AS;. This is obtained by allowing the ion to retain the same fraction of its (translational) entropy in the gas phase after its transfer into the solution as does a rare gas atom on the average (without regard to the size of the latter). The remainder of the entropy of hydration, called includes electrostatic and structural contributions (long- and short-range entropy effects), but their individual evaluation has not been specified.The results of this approach concerning the effects of the ions on the structure of water are limited to monoatomic ions, and are in qualitative agreement with the results of the present work, as shown in table 2. again limited their considerations to univalent ions and mainly to monoatomic ones [the ions (CH,),N+, (C,H,),N+, CN-, and C10; were included in some of their tables]. They developed the electrostatic interaction approach to a multilayer model. The ‘compression term’ was replaced by a ‘neutral term’, obtained from the average entropy of solution of gaseous non-polar solutes of the same size as the ion. This seems to take care of some of the solvent immobilization too, since Asoln So of the rare gases in water (from the 0.1 MPa to the 1 mol dm-, standard states) is considerably more negative than - 26.7 J I C 1 mol-l.However, neither a single-layer model nor a two-layer one accounted satisfactorily for the electrostatic contribution to the entropy of solvation, obtained as the difference between the total ionic entropy of solvation and the neutral term, in the cases of hydrogen-bonded solvents in general and water in particular. For the two-layer model, the electrostatic contribution for the second layer was obtained as the difference between the total entropy of hydration and the combined contributions from the first layer (corresponding roughly to the translational immobilization of the solvent in the present work), the bulk solvent (corresponding roughly to the electrostatic term in the present work), and the neutral term (corresponding roughly with the compression term in the present work).Conceptually, therefore, the entropy change due to this second layer could correspond to the structural effects of the ion. However, the detailed calculations of Abraham et a1.l1 produced positive values of this term for all the ions considered, both structure-breaking ones (e.g. Cs+ and I-) and a structure-making one (F-). The term was less positive for F- and more positive for K+, Rb+, Cs+, C1-, Br-, I-, and C10; than for Na+, and was in linear correlation with the Dole-Jones B-coefficient of the viscosity. This was cited” as evidence that this contribution to the entropy from a disordered second layer around the ion did have structural connotations. The arrival at all-positive values, however, depends on the rather arbitrary choices of the parameters that have gone into the calculations of the contributions from the neutral, first layer, and bulk terms.It is seen that the approach to the problem taken by other authors each has its own arbitrary choice of models and parameters. The approach proposed here is not different in this respect. Little can be said against the choices made here regarding the ‘compression term’ and the ‘electrostatic term’, so that any criticism should be pointed against the ‘translational immobilization term’, Atrim So(Xz). There are two main aspects that can be criticized: one concerns the limitation to translational entropy changes, the other concerns the empirical calculation of n, the number of water molecules taken to be translationally immobilized. Abraham etY.Marcus 24 1 Beyond admitting that both lines of criticism are valid, the following arguments can be raised to counter them. The rotational degrees of freedom lost by the coordinated water molecules are expected to be compensated for by degrees of freedom of rotation around the ion-water bond and of libration about it, and by the rotational entropy of the hydrated ion, compared with the lack of it for a monoatomic bare ion. How adequate such a compensation is must be left to very complicated calculations, to which the unsuccessful examples reported so far6y ' 9 26 are a deterrent. The estimation of the translational entropy of water in the liquid by eqn (9) assumes, in essence, that the non-translational degrees of freedom of water are not affected on its condensation from the gaseous to the liquid states.Again, a compensation of positive and negative entropy effects is invoked as a justification. The simple-minded estimation of the number n by eqn (11) could, perhaps, have been improved at the expense of requiring a more complicated expression, but it must be conceded by critics that the resulting values of n, shown in table 1 in parentheses in the column of Atrim So(Xz), are reasonable as hydration numbers. This is true not only for the ions shown in this table but also for those not included there: monoatomic ions, e.g. Mg2+(9.9), Mn2+(8.6), Zn2+(9.5), Hg2+(7.0), La3+( lO.Z), Lu3+(12.4), Fe3+(16.5), and Zr4+( 19.7); and polyatomic ones, e.g.OH-(2.7), H,0+(2.7), P043-(4.5), among others. A different choice of the numerical constant would change these numbers proportionally and cause a shift of the water structure-breaking and structure-making assignments of the ions. For instance, if the numerical constant in eqn (1 1) is set at 240, then potassium becomes the ion to which the structure of water becomes indifferent [ie. Astrue S"(K+) = 01, and sodium and lithium become structure-making [Astruc S"(Na+) = - 22 and (Xstruc S"(Li+) = - lo], but the resulting hydration numbers are then on the low side [e.g. Mg2+(6.7) and H,O+( 1.8)]. The main merit of the present approach is that in spite of its simplicity it yields estimates of the effects of the ions on the structure of water that are in agreement with those obtained by other methods.Another merit is that it can be readily extended to a large number of ions not studied by these methods, but for which S&, (Xz, aq) and So(Xz, g) data are available or can be estimated. These include many complex ions, for which the structural effects can now be predicted. References 1 Y. Marcus and A. Ben-Naim, J. Chem. Phys., 1985, in press. Abs. 7th Intl. Symp. Solute- 2 H. S. Frank and M. W. Evans, J. Chem. Phys., 1945. 13, 507. 3 R. W. Gurney, Ionic Processes in Solution (McGraw-Hill, New York, 1953). 4 0. Ya. 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