Statistical Mechanical Expressions for the Solvation Thermodynamic Quantities

Statistical Mechanical Expressions for the Solvation Thermodynamic Quantities 

In this section, we derive some general statistical mechanical expressions for the thermodynamic quantities of solvation which are independent of any assumptions about the model. We shall later examine special cases of these relations for either a molecular model for water (in terms of a model pair potential) or for a specific mixture-model view of liquid water. 

Equation (3.4.1) follows directly from the definition of the process of solvation (see also Appendix G). The expression for the solvation, Gibbs or Helmholtz energy in terms of the process of inserting a particle at a fixed position is quite old, probably due to Kirkwood (1935) and later used in the scaled particle theory [see Sec. 3.8 and also Hill (1960) and Widom (1963,1982)]. 

The quantity P(X ) in (3.4.2) is the probability density distribution for the configurations of the solvent molecules  

Note that, in general, when the solvent is composed of many components, we need to take an average over all molecules in the system except the one placed at Rs. 

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