Preferential Solvation in a Two-Component System

In the previous subsection we discussed the theory of preferential solvation of a solute 5 in a two-component system. In the traditional concept of solvation thermodynamics, only very dilute solutions could be treated. Therefore, the minimum number of components required for such a study is three a solute and two solvents. 

However, the question of PS can also be asked in a /wo-component system, say of A and B. At any composition Xa, we may focus on one A molecule and ask what is the PS of with respect to the two components, A and B, in its immediate vicinity. Likewise, we may focus on one B molecule and ask the same, but independent, question of the PS of B with respect to the two components A and B. In this sense, the treatment of the two-component system is a generalization of the corresponding three-component system. 

Since our mixture may have an arbitrary composition, the last two questions concerning the PS of A and B could not be dealt with within the traditional concept of solvation. Fortunately, the theoretical treatment can be easily extended to the entire range of compositions. In a two-component system, we define the average number of A and B molecules around an A molecule by [note Eq. (6.17.7)] 

For any radius Rc, we define the local mole fraction of -molecules around an A-solvaton by 

Next we define the PS of an -solvaton with respect to -molecules simply by the deviation of the local from the bulk composition, i.e.. 

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