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Values of Sstruc for the alkali metal and halide ions as well as Ag+ and ClO4- were reported on the unusual mole fraction scale for the solution, with S¡Þ(H+,aq) = -68.2 J K-1 mol-1 on this scale, causing K+ to appear as a structure making ion. Adjustment to the molar scale with S¡Þ(H+,aq)= -22.2 J K-1 mol-1 corrects this unacceptable result. Abraham et al.153 noted the usual linear correlation of their ¦¤Sstruc with the viscosity B¦Ç coefficients as well with the BNMR coefficients (see section 5.2.1) and also with the ionic partial molar volumes or their electrostricted volumes. Bhattacharya199
inverted the correlations of ¦¤Sstruc with B¦Ç and BNMR, with ionic values for the latter two parameters obtained according to his method of splitting electrolyte data into ionic contributions (section 5.2.1), to calculate ionic entropies of hydration, but they did not discuss the effects of the ions on
the water structure from the resulting values.
    Marcus and Loewenschuss200 and Marcus201 suggested yet another model for obtaining ¦¤Sstruc values from ¦¤hydrS¡Þ ones, pointing out that ¦¤hydrS¡Þ, with the standard state of 0.1 MPa for the ideal gaseous ions and 1 mol dm-3 for the aqueous ones, includes an irrelevant entropy of compression of ¦¤compS =-26.7 J K-1 mol-1 that ought to be removed from the absolute ¦¤hydrS¡Þ values (based on S¡Þ(H+,aq)=-22.2 J K-1 mol-1). The electrostatic effect beyond the first hydration shell was obtained as above, ¦¤Sel =(NAe2/8¦Ð¦Å0)z2(r +dW)-1¦År-1(∂ ln ¦År/∂T)P, from the Born expression. However, within this hydration shell the n water molecules are translationally immobilized, having to move together with the ion Xz, with a concomitant reduction of their entropy. This contribution
¦¤tr imS(Xz)=1.5R ln[M(X(H2O)n/M(X)]-26.0n         (16)
where the first term denotes the change of translational entropy due to the larger mass (M) of the hydrated ion and 26.0 is the molar translational entropy of water in its liquid form, does not pertain to the water structural effects either.The value of n= A|z|/(r/nm) with A = 0.355 was obtained
empirically, so as to yield
¦¤Sstruc(Na+)=¦¤hydrS¡Þ(Na+)-¦¤compS-¦¤Sel(Na+)-¦¤tr imS(Na+)=0    (17)
  on the supposition that sodium ions are indifferent with respect to the water structure making and breaking. In view of the cumulative errors incurred in such calculations, only values of ¦¤Sstruc(Xz)/J K-1 mol-1 > 6 were construed as indicating the ion Xz to be definitely water structure breaking, values < -6 were construed as indicating it to be structure
making, and in between values were construed to be borderline cases, including those for Na+, Ag+, and Cl-. The assignments201 of ions to such classes generally conformed to assignments by other methods, such as the signs of B¦Ç and BNMR.
  Other models and approaches for obtaining the water structural effects of ions from the entropies of hydration, such as those of Uhlich, Ryabukhin, and Friedman andKrishnan,were briefly reviewed by Marcus and Loewenschuss and need not be detailed here.
  A final development of this concept for ¦¤Sstruc that indicates the water structural effects of ions is due to Marcus,resembling more that of Abraham et al. than his own previous one. It is based on a model common for
various thermodynamic functions of ion hydration, with the key quantity being ¦¤r, the width of the electrostricted hydration shell, where the water molecules have a volume ¦ÐdW3/6 rather than VW/NA. Thus, ¦¤r is obtained from the volume of the hydration shell with n water molecules:
(4¦Ð/3)[(r+¦¤r)3-r3]=n¦ÐdW3/6                            (18)
with n= A|z|/(r/nm) as before, A=0.36 being slightly different, and dW= 0.276 nm. Then the structural entropy is obtained from
¦¤Sstruc=¦¤hydrS¡Þ-[¦¤Snt+¦¤Sel 1+¦¤Sel 2]                      (19)
Here the term ¦¤Snt takes care of the entropic effect of the creation of a cavity in the water to accommodate the ion¦¤Sn as well as the compression term ¦¤compS of the previous models. It is evaluated from the entropies of
hydration of small neutral molecules or rare gas atoms, interpolated for a radius r the same as that of the ion: ¦¤Snt =-3 - 600(r/nm) J K-1 mol-1. In analogy with eq 15, the electrostatic effects are
¦¤Sel 1=(NAe2/8¦Ð¦Å0)z2[¦¤r(r+¦¤r)-1]¦Å-2(∂¦Å/ ∂ T)P           (20a)
¦¤Sel 2=(NAe2/8¦Ð¦Å0)z2(r+¦¤r)-1¦År-2(∂¦År/ ∂ T)P                    (20b)
The former of these two expressions (eq 20a) pertains to the electrostricted hydration shell, where the permittivity and its temperature derivative are assumed to have the infinitely large field value of
¦Å¡ä =nD2= 1.776 and (∂¦Å¡ä/∂T)P = 2(∂nD/∂T)P = -1 ¡Á 10-4 K-1 at 25 ¡ãC, where nD is the refractive index of water at the sodium D line. This treatment could be applied to nearly 150 aqueous cations and anions,
monatomic and polyatomic, with charges -4 e z e 4. Sodium and silver cations now reverted to the structure making category and chloride to the structure breaking one, but the borderline region is widened to (20 J K-1 mol-1. The linear correlation with the viscosity B¦Ç (except for
tetraalkylammonium cations) is
¦¤Sstruc/J K-1 mol-1=20(z2+|z|)-605(B¦Ç/dm3 mol-1)             (21)
Values of ¦¤Sstruc of representative ions obtained according to the treatments of Krestov as reported in ref 196 and by Abraham et al. and Marcus are shown in Table 7, adjusted where applicable to the M scale for the entropies of hydration and based on their absolute values with
S¡Þ(H+,aq)= -22.2 J K-1 mol-1.
  A treatment based on the same model, but dealing with the structural heat capacity, ¦¤CP struct, contribution of the effects of ions on the water structure was also repotted by Marcus. Here CP replaced S in eqs 19 and 20a, ¦¤CP nt =-48 + 1380(r/nm) J K-1 mol-1, and T(∂2¦Å¡ä/∂T2)P and T(∂2¦År/
∂T2)P replaced the corresponding factors in eqs 20a and 20b. A negative bias occurred in ¦¤CP struct calculated in this manner, due to the choice of CP
¡Þ(H+,aq)= - 71 J K-1 mol-1, and in order to show the structure making andbreaking properties of the ions, 175z J K-1 mol-1 are added here, to yield the values shown in Table 7, with positive values for structure making ions and negative ones for structure breaking ones, but allowing for a wide borderline region of (60 J K-1 mol-1.

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