General relations between solvation thermodynamics and the structure of water

2 General relations between solvation thermodynamics and the structure of water 

We first consider the case of a simple spherical solute s in a very dilute solution in water w. By very dilute, we mean that all solute-solute interactions may be neglected. Formally, this is equivalent to a system containing just one s solute and N water molecules. Also, for convenience, we assume that the system is at a given temperature T and volume V. The Helmholtz energy of solvation of s in this system is 

The solvation entropy of s is obtained by taking the derivative of equation (7.214) with respect to T, i.e., 

The second case of interest is the solvation of a water molecule in pure liquid water. Again, we assume that we have a T, V, N system and we add one water molecule to a fixed position, say Rw. The solvation Helmholtz 

Using the latter equation, we can rewrite the expression (7.221) for A (v, in the simpler form 

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