TPTB assumption

In order to split the experimentally available Ahydr fE° values dealing with entire electrolytes into the ionic contribution a value must be estimated for just one ion. Conventional values are obtained on setting Ahydr f° (H+) " =0 at all temperatures. The absolute value Ahydrf / (H+, aq)=-1103 7 kJ mor at 298.15 K results (Marcus 1987) according to the TPTB assumption, equating the standard enthalpies of hydration of the tetraphenyphosphonium and tetraphenylborate ions ... 

There exists also the problem in obtaining the required information from experimental data, in that the latter pertain to entire electrolytes, and their application to single ions has some bearing on the meaning of the Kirkwood-Buff integrals. Application of the TPTB assumption (see p. 65) to the splitting of the standard molar Gibbs... 

The uncertainty involved in the application of the TATB method was estimated as 1 kJ moF by Cox and Parker [40]. Indeed, if the TATB assumption is accepted for A,G" at 25°C, at which temperature it is generally applied, there is no good reason for not accepting it at any other temperature, and hence the TATB assumption should be valid also for the A,// of ions. The TPTB assumption has in more recent years replaced to some extent the TATB one, but with hardly any effect on the results. 

S.2.4 Ionic Heat Capacities in Nonaqueous Solvents The standard molar ionic heat capacities in water of the alkali metal, halide, perchlorate, tetraalkylammonium, and tenaphenylonium salts are reported in Table 2.8 and also by Abraham and Marcus [45], based on the TPTB assumption. Based on the same assumption, their C" (I, S) in S=MeOH, EtOH, 1-PrOH, PC, NMF, DMF, MeCN, MeNO, and DMSO are reported by Marcus and Hefter [46]. The reservation expressed in Section 2.3.1.1, that slight differences in the sizes and induced partial charges in the phenyl rings cause a large uncertainty in equating the TPTB ions, applies also to the nonaqueous solutions. The values of C (I, S) are listed as far as available in Table 4.5. 

Table 6.2 shows values of the standard molar enthalpy and entropy for the transfer of ions from water into equimolar aqueous mixtures with cosolvents at 25°C, A, /f or A j5 "(I, W 0.5W-i-0.5S), taken from the compilation by Hefter et al. [13]. Further values for the solvents shown there are available at 0.1 mole fraction steps over the entire composition range. The ionic data were selected from data on electrolytes hsted in these references on the basis of their conformation to the TATB or TPTB assumptions (Section 4.3.1). Data are available in this reference also for many other aqueous solvents (n- and i-PrOH, f-BuOH, glycerol, tetrahydrofuran, 1,4-dioxane, acetone, A,A-dimethylacetamide, and sulfolane) for at least a part (the water-rich part) of the composition range, as well as for some other ions that were not measured atX3=0.5 in the solvents shown in Table 6.2 or that could not be traced to the TATB or TPTB assumptions. This table also includes data for these functions for the transfer of ions into aqueous urea, which, though urea is not a solvenf it behaves in aqueous solutions as if it were a liquid amide. 

The individual ionic thermodynamic quantities for hydration, listed in Table 4.1, are based on two extra-thermodynamic assumptions for the enthalpies, they are based on the tetraphenylphosphonium tetraphenylborate (TPTB), A // (Ph4P ) = A //" BPh and for the entropies on the temperature derivative of the electromotive force of... 

An extensively employed and tested method involves a reference electrolyte, the cation and anion of which are large and of the same size, have globular form with peripheries that are inert to interactions with solvents, and which differ only in the sign of the charge. Approximations to such an electrolyte are TPTB and tetrapheny-larsonium tetraphenylborate (TATB), of which mainly the latter has been widely used. Solubility (s) measurements are generally employed, ignoring the activity coefficients of the only very slightly soluble salts in most solvents. The extra-thermodynamic assumption is that ... 

Replacement of TATB by TPTB yields results within the experimental error of 0.4kJ-mol" . There are two minor problems with this assumption pointed out by Kim [29], one depending on the not exactly equal sizes of the cation and the anion and the other on the (unknown) sign-dependent interactions of the ions with the quadrupole of the solvent. The ratio of the van der Waals radii of the TATB ions is W (Ph4As )/ vdw (BPh4 ) = 1.0122 (it is somewhat nearer unity for the ions of TPTB). This discrepancy causes difference of 1.2 and 2.2% in the electrostatic and nentral Gibbs energies (see the radius dependencies in Sections 4.2.1.2 and 4.2.1.1). Once the A G ° (Ph As, W S) is established by Equation 4.21 or measnrements other than solnbility, the anion transfer A G ° (A", W S) is obtained from... 

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. 

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