Solvation Thermodynamics of Completely Dissociable Solutes

In section 6.13 we defined the process of solvation as the process of transferring a single molecule from a fixed position in an ideal-gas phase to a fixed position in the liquid. For solutes which do not dissociate into fragments, the solvation Helmholtz or Gibbs energy is related to experimental quantities by the equation (see 6.13.15) 

We now wish to generalize this relation to solutes that dissociate in the liquid. The most important solutes of this kind are electrolytes. 

We consider a molecule which is only in a state of a dimer D in the gaseous phase. When introduced into the liquid, it completely dissociates into two fragments A and B. Of foremost importance is the case of ionic solutes—e.g., D may be HCl—then A and B are H and CF, respectively. For simplicity we assume that A and B do not have any internal degrees of freedom. The generalization to the case of multi-ionic solutes and polynuclear ions is quite straightforward. 

The relevant solvation process has been defined in section 6.13. Since the particles are presumed not to possess any internal degrees of freedom, the Gibbs energy of solvation of the pair of ions is simply the coupling work of A and B to the liquid phase / thus 

for simplicity, we shall use below the T, V, N ensemble. Hence we shall derive an expression for AAab- However, it is easy to show that AA b at T, V constant is the same quantity as AG b at T, P constant (see Appendix E). 

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