Application of the KB theory to electrolyte solutions

The simplest system of electrolyte solution is one solvent, say water (W) and one, completely dissociable solute, say KC1, which we denote by S. It is assumed that S dissociates completely into two fragments 

We stress from the outset that the fragments A and B could be either neutral or ions. 

The above system could be viewed in two equivalent ways. One is to ignore the dissociation (4.118) and view the system as a two-component system of W and S. For such a system, the KB theory as derived in section 4.3 applies simply change notation from A and B in section 4.3 into W and S, and we can use all the results 

The second view is to admit the occurrence of dissociation into fragments (4.118) and to treat the system as a three-component system. Again, all the results of section 4.3 apply here. Specifically the matrix B, for the system of three components, W, A and B, is 

However, when the dissociation of S into fragments (4.118) produces ionic species, say 

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The Kirkwood-Buff (KB) theory is the most important theory of solutions. This chapter is therefore central to the entire book. We devote this chapter to derive the main results of this theory. We start with some general historical comments. Then we derive the main results, almost exactly as Kirkwood and Buff did, only more slowly and in more detail, adding occasionally a comment of clarification that was missing in the original publication. We first derive the results for any multicomponent system, and thereafter specialize to the case of two-components system. In section 4, we present the inversion of the KB theory, which has turned a potentially useful theory into an actually useful, general and powerful tool for investigating solutions on a molecular level. Three-component systems and some comments on the application of the KB theory to electrolyte solutions are discussed in the last sections. 

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