Water with Two or More Simple Solutes, Hydrophobic Interaction HI

Water with Two or More Simple Solutes. Hydrophobic Interaction (HI) 

The limiting dilute ideal solution is characterized by the complete absence of solute-solute interaction. From the molecular point of view, the properties of such systems are determined by the behavior of a system of one solute in a solvent, a topic dealt with in Chapter 7. The next natural system to be studied is that of two solutes in a solvent. In a formal way, the situation is analogous to the case of a low-density gas, for which we can write the virial expansion 

Similarly, for dilute solutions of a solute S, we write the virial expansion for the osmotic pressure as 

The complete analogy between various expansions in the total density in the gaseous phase, and expansions in the solute density in solution, has been developed by McMillan and Mayer (1945). In this chapter, we will be interested in the expansion (8.2) up to only the second-order term. For this purpose, we use the statistical mechanical expression for as obtained from the Kirkwood-Buff theory in Section 4.9  

The corresponding expression for the second virial coefficient in the gaseous phase is 

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