Basic Grand Ensemble Equations

We begin by considering, at the BO level, a mixture of solvent (species w, activity z, number of molecules / or L) and a single solute (species a, activity 

Zay number of molecules n or N) in a volume V at temperature ks/P, where is Boltzmann s constant. The grand partition function for this system may be written 

The corresponding correlation function g j, normalized to approach unity when the n solute particles and / solvent particles all are far from each other, is given by the equation 

The procedure in this theory can be discussed in terms of a solution in osmotic equilibrium with a pure solvent phase, as illustrated in Fig. 1. The pressure on the solution phase, designated Pin, is greater than Pout, the pressure on the solvent phase, by the amount necessary to raise the chemical potential of 

Because Si is given by Eq. (27) with Za and selected to match the values in the in region in Fig. 1, and Sout is given by Eq. (27) with the same Zh, but with Za = 0, it follows that Smm is given by a power series in which may be written 

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