Standard entropy of transfer

We shall discuss now the variation of the three main thermodynamic functions with solvent composition for the case of n-Bu4NBr-water-acetone system and shall extend this discussion to the n-Bu4NBr-water-THF system. Figure 4 and Table IV present the results obtained. The figure was constructed as follows first the standard enthalpy of transfer AH°t, obtained by Ahluwalia and co-workers (12) from pure water to Z2 = 0.30, was used in order to get the standard entropy of transfer function from the relation ... 

Here EgEn° and BEN° are the standard potentials of the Ag-AgI electrode in ethylene glycol and the solvent on the mole-fraction scale. The standard entropy of transfer, ASt°, was calculated from... 

A glance at the expressions (7.61) and (7.62) for ASs(x-proccss) and ASs (m-process) shows that both contain the solvent density plB under the logarithm sign. Thus, for a series of solvents with decreasing densities, both A Ss (x-process) and ASs(m-process) will diverge to infinity, clearly an undesirable feature for a quantity that is presumed to measure the solvation entropy of a molecule s. On the other hand, AS tends to zero as the solvent density decreases to zero, as it should In addition to this unacceptable behavior of ASs(x-process) and ASs(m-process), all of these standard entropies of transfer contain the term kTotlp — k, which is irrelevant to the solvation process of the molecule s. 

Tab. 2.6 Standard Gibbs energies, enthalpies, and entropies of transfer of ions from water to non-aqueous solvents (25 °C)1 ...

Table IV. Standard Free Energy, Enthalpy, and Entropy of Transfer of n-Bu4NBr from Water to Water—Acetone Mixtures at 298.15°K...

Table 4 Standard Free Energies, Enthalpies, and Entropies of Transfer of Singly Charged Ions from Water to Dipolar Aprotic Solvents (kcal moD1)... 

Harris FE, Rice SA (1954) A chain model for polyelectrolytes. Int J Phys Chem 58 725-732 Heller GT, Marcus Y, Waghorne WE (2002) Enthalpies and entropies of transfer of electrolytes and ions from water to mixed aqueous organic solvents. Chem Rev 102 2773-2836 Helgeson HC, Kirkham DH, Flowers GC (1981) Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures tmd temperatures IV. Calculation of activity coefficients, osmotic coefficients, and apparent moled and standard and relative partial moM properties to 600 °C and 5 kb. Am J Sci 281 1249-1516 HeplerLG, Hovey JK (1996) Standard state heat capacities ofaqueous electrolytes and some related undissociated species. Can J Chem 74 639-649... 

The chapter reviews the existing experimental data for standard enthalpies and entropies of solution of pure substances in various solvents and gives derived entropies of transfer of molecules, ions, and groups from one solvent to another and from the gas phase to water. The data are summarized in 22 tables and cover both Inorganic and organic substances, electrolytes and non electrolytes. There are 146 references to the literature. 

Another, quite empirical, method assumes that Aj5 (I , W- S) = fl(5) -i- (5)5°° (I, W), that is, a linear function of the standard molar entropy of the aqueous ion with different coefficients a and b for each solvent, proposed by Criss et al. [44]. This requires estimates ofAt5"(I, W->S) from other sources to establish a and b for a given solvent and may be used, for this solvent, for ions for which only 5 (I, W), but not the entropy of transfer, is known. There being no theoretical basis for the linear relationship, this linearity has to be reestablished for each new solvent. 

The entropies of transfer, Aj5 (I, W -> S), are shown in Table 4.4 and were adapted from the aforementioned compilations [41] and [42]. It should be noted that the former were obtained from several extra-thermodynamic assumptions that were acceptable but the latter invariably from the TPTB one. Therefore, there are some inconsistencies (within 10 J K mol" ) and the later values should be preferred. The entropies of transfer from water to nonaqueous solvents are negative for small ions and positive only for the largest, hydrophobic, ions Bu4N, Ph P Ph As, and BPh T It should be noted that for the alkali metal cations, the magnitudes of AjN" (I, W -> S) show a most negative value somewhere in the middle of the series, but for the tetraalkylammonium and halide ions, the values are monotonous with the ionic sizes. On the whole, the standard molar entropies of small ions, whether cations or anions and irrespective of the charge and sign, show a pronounced uniformity. 

TABLE 4.4 Ionic Standard Partial Molar Entropies of Transfer from Water into Nonaqueous Solvents, A S (I-, W S)/J K mol at 25°C"... 

Thermodynamic properties of ions in nonaqueous solvents are described in terms of the transfer from water as the source solvent to nonaqueous solvents as the targets of this transfer. These properties include the standard molar Gibbs energies of transfer (Table 4.2), enthalpies of transfer (Table 4.3), entropies of transfer (Table 4.4) and heat capacities of transfer (Table 4.5) as well as the standard partial molar volumes (Table 4.6) and the solvation numbers of the ions in non-aqueous solvents (Table 4.10). The transfer properties together with the properties of the aqueous ions yield the corresponding properties of ions in the nonaqueous solvents. 

Heat of Precipitation. Entropy of Solution and Partial Molal Entropy. The Unitary Part of the Entropy. Equilibrium in Proton Transfers. Equilibrium in Any Process. The Unitary Part of a Free Energy Change. The Conventional Standard Free Energy Change. Proton Transfers Involving a Solvent Molecule. The Conventional Standard Free Energy of Solution. The Disparity of a Solution. The E.M.F. of Galvanic Cells. 

Entropy changes were estimated with Eq. 4 assuming that V, is equal to the total stationary phase volume existing in the column. Therefore, these values reflect more properly the relative differences in entreaties of transfer instead of the standard molar entropies that would require to use the volume of the active stationary phase. 

It has been shown recently (1) that the transfer of urea from water to water-rich water-tetrahydrofuran (THF) mixtures is an entropy-controlled phenomenon (T AS°t > AH°t ), but from water to water-THF mixtures of mole fraction Z2 > 0.20 it is an enthalpy-controlled phenomenon ( AH°t > T AS°t ) moreover, the transfer is energetically favorable in the former case and unfavorable in the latter. A minimum in the standard free energy transfer... 

Vitha, M. F., and P. W. Carr, The chemical meaning of the standard free energy of transfer Use of van der Waals equation of state to unravel the interplay between free volume, volume entropy and the role of standard states , J. Phys. Chem. B, 104,5343-5349 (2000). 

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