Solvation of completely dissociable solutes

In section 7.2, we introduced 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 

In this section, we generalize this relation to solutes which dissociate in the liquid. The most important solutes of this kind are electrolytes, but the treatment is general and applies to any type of dissociable solutes. 

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 KC1, then A and B are K+ and Cl, respectively. For simplicity, we assume that A and B do not have any internal degrees of freedom. The generalization in the case of multi-ionic solutes and polynuclear ions is quite straightforward. 

The relevant solvation process is depicted in figure 7.9. 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 l 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 at constant T, V is the same quantity as A GAB at constant T, P, provided that the exact volume in the former is equal to the average volume in the latter. 

---