Assumptions, extrathermodynamic

Evaluation of the individual contributions requires extrathermodynamic assumptions and analysis of a body of data so as to achieve a self-consistent set of numbers. For this reason, there may be small differences between 8q of Eq. (8-52) and the 8 defined by Eq. (8-43). Table 8-7 gives value of 8, 80, 8j, 8p, 8h for the solvents of Table 8-2." ... 

Without some additional relationship it is impossible to resolve y into and "y. By introducing an extrathermodynamic assumption as this additional relationship, it becomes possible to estimate single ion transfer activity coefficients. A widely used assumption is that the transfer activity coefficients of the cation and anion of tetraphenylarsonium tetraphenylboride, Ph4As BPh4, are equal, i.e.,... 

By combining these ions with other counterions, single ion transfer activity coefficients are calculated. By these techniques transfer free energies or activity coefficients have been determined for many ions and nonelectrolytes in a wide variety of solvents.Parker has discussed the extrathermodynamic assumptions that lead to single ion quantities. 

All ionic values are anchored relative to this, based on the extrathermodynamic assumption in Ref. 73. Ref 73. 

Unfortunately, in many nonaqueous solvents there is no completely unambiguous way of determining half-cell potentials. This ambiguity stems from the fact that the free energies of transfer (AG°) of individual ions from one solvent to another are not knowable. (It should be noted that no ambiguity necessarily exists if one is content with comparing whole-cell potentials in different solvents. This is true because the free energies of transfer of dissolved salts are know-able.) Some type of extrathermodynamic assumption is usually necessary to compare half-cell potentials measured in one solvent to those measured in some other solvent. Popovich has provided excellent... 

The following are the practical procedures for obtaining the Gibbs energies of transfer and transfer activity coefficients of ionic species based on the extrathermodynamic assumptions (i), (ii) and (iii) described above ... 

If we adopt some reasonable extrathermodynamic assumption (37) in order to get the individual free energy of transfer of the ions, we find that AG°t(—) of the bromide ion is positive from water to acetone and that AG°t (+) of the n-Bu4N+ is negative over the whole solvent concentration range. In terms of preferential solvation models we would say that Br is solvated by the water molecules and n-Bu4N+ by the acetone molecules. 

Note that these single ion values were obtained from entirely different extrathermodynamic assumptions elaborate extrapolation procedure in the case of the water-acetone mixtures, and tetraphenylboron assumption for the water-THF mixture. n-Bu4N+ and Br showed similar behavior in the two binary systems studied this might be the consequence of the similarity between the thermodynamic properties of the two aqueous binaries e.g., both are typically aqueous systems with AHE < T ASE. ... 

It is not possible to evaluate k directly, for it appears with the entropy of activation in the temperature-independent part of the rate constant. An estimate of k requires an extrathermodynamic assumption. In two cases of iron(II) spin equilibria examined by ultrasonic relaxation the temperature dependence of the rates was precisely determined. If the assumption is made that all of the entropy of activation is due to a small value of k, minimum values of 10-3 and 10-4 are obtained. Because there is an increase in entropy in the transition from the low-spin to the high-spin states, this assumption is equivalent to assuming that the transition state resembles the high-spin state. There is now evidence that this is not the case. Volumes of activation indicate that the transition state lies about midway between the two spin states. This is a more chemically reasonable and likely situation than the limiting assumption used to evaluate k. In this case the observed entropy of activation includes some chemical contributions which arise from increased solvation and decreased vibrational partition functions as the high-spin state is compressed to the transition state. Consequently, the minimum value of k is increased and is unlikely to be less than about 10 2. 

The thermodynamic functions of transfer of individual ions cannot, of course, be studied experimentally, since only complete electrolytes are thermodynamic components, so that an extrathermodynamic assumption is needed in order to split the measurable quantity into the contributions from the individual ions. A commonly employed assumption is that for a reference electrolyte with large, univalent, nearly spherical cation and anion of nearly equal sizes the measured... 

Table IV. Extrathermodynamic Assumption Based on Scaled Particle Theory Calculations for a Tetrabutylammonium Particle in Water - - Acetone Mixtures at 298.15 Ka 5...

Therefore, knowledge of the solvent properties and ion solvation in such media is essential. Although an exact determination of the solvation energy of individual ions is not possible, extrathermodynamic assumptions have been introduced in order to estimate this parameter. These ideas will be presented before the influence of solvents on equilibrium and kinetic parameters of electrode reactions is discussed. As a basis for this discussion, a brief presentation of the properties of solvents frequently used in electrochemical experiments will be given. 

In order to separate such strictly determined values for electrolytes into ionic parts, some extrathermodynamic assumptions are necessary. In the literature many different types of such assumptions are described which may be divided into three main groups. One of the approaches used in such studies is the measurement of the potential difference, AE, of the following cell ... 

In conclusion, there is no fully satisfactory system for the construction of a unified potential scale which could be used for mixed solvents of different compositions. In fact, the scales used are the same as those applied for pure solvents, but in the case of mixed solvents the extrathermodynamic assumption may be even less strictly obeyed, especially if there are even small preferential interactions of the reference electrode components with one of the solvents of the mixture. In our work we used the Foe /Foe system as a solvent-independent reference electrode. The consequent use of one reference electrode in a series of experiments with mixed solvents of different composition should diminish the error. 

It may forever be impossible to estimate with complete confidence the individual solvent activity coefficients of anions and cations (Kolthoff and Bruckenstein, 1959). However, in an effort to attack this problem, a number of extrathermodynamic assumptions, which are not completely unreasonable, have been suggested. Three of these assumptions have... 

The two extrathermodynamic assumptions used in Table 9 to derive solvent activity coefficients of anions, lead to different values of y cicHsi-)+ The assumption (i) that caesium cation is similarly solvated in methanol and in DMF, suggests that the large rate difference between reaction (27) in methanol and in DMF is as much due to differences in transition state solvation as to differences in solvation of chloride ion. This is the situation shown qualitatively in Fig. 1. On the other hand, the somewhat smaller rate difference between reaction (27) in formamide and in DMF is due entirely to differences in solvation of chloride ion, if the caesium assumption is applied to formamide and to DMF. 

As already noted, more work, along the lines indicated in Tables 4 and 5, is necessary before the implications of Table 9 can be taken too seriously. At this time, it is merely intended to show what the consequences are, to any theory of solvent effects on rate, of adopting two currently popular extrathermodynamic assumptions which lead to the estimation of individual activity coefficients of anions. 

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