Entropy Changes in Ionic Reactions

In the last few sections we have been using simple electrostatic models to compute the contribution to the free energy changes of the electrical interactions of charged particles. From the relations AaS = — [d(AF)/dT]i , = AF + T AS, ACp = [d AH)/dT]p, and AV = [d AF)/dP)T it is possible from the same models to compute these other thermodynamic properties as well. The two types of interaction of interest are the ion-ion and ion-solvent interactions of these, the latter is much the larger. 

By using the continuum model of the solvent, we have calculated the Free energy of separation of a pair of spherical charges and 2b8 [Eq. (XV. 10.5)] in a dielectric constant D as 

This continuum model predicts that all of these thermodynamic properties should preserve their sign and increase in magnitude as D is decreased. This is, of course, subject to the behavior of the derivatives (din D/d In T) and (din D/d In F) as D changes. In the case of weak electrolytes this is qualitatively the observed behavior. Some values are given in Table XV.7 for the dissociation of HaO and acetic acid in water-dioxane mixtures. Since the derivatives of D and F are not the same as the values in pure HaO, the values cannot be expected to follow D in any simple fashion. However, it is seen that qualitative agreement is obtained. If one uses Eqs. (XV.12.2) to (XV.12.5) and the experimental values of the derivatives for water, it is possible to calculate AFp from the experimental values of each of the thermodynamic quantities in turn. For acetic acid the values are 4.7 Kcal from AS, 0.3 Kcal from AH, 5.5 Kcal from ACp, and 5 Kcal from AF. Except for AH, this can be considered quite good correlation compared to AFion = 6.5 Kcal observed directly. For H2O the values are 4 Kcal from AS, 6 Kcal from ACp, 33 Kcal from AH, and 

5 Kcal from AF. The comparison with AF = 19.1 is much poorer, indicating the crudeness of the continuum model at least as applied to these covalent compounds. We have already seen that for ion pairs the model is much better (Table XV.5).  

20% dioxane 45% dioxane 70% dioxane 82% dioxane 10% CHsOH 20% CHsOH HC2H8O2 

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