Spectroscopic and Thermodynamic Properties of Associated Solutions

We shall use (15.3.7) in the next paragraph to deduce a rather general relation between spectroscopic and thermodynamic properties of associated solutions. 

Let us now consider a given site (which is merely an element of volume of the order of the mean volume per molecule in the solution) and consider the ratio P between the probabilities that this site is occupied by a monomolecule or by a molecule of the solvent. Both molecules being completely equivalent this probability must be given by the ratio of the concentration of the monomers Cax and of the solvent Cb 

On the other hand this ratio may be estimated by constructing the grand ensemble corresponding to the given site. This method is identical to Guggenheim s method for the calculation of the combinatorial factor of polymer solutions described in Ch. Ill, 6 (see also Ch. II, 3). The contribution to the grand ensemble from the occupation by a monomolecule is proportional to 

Using the fact that Aj and B have the same intCTaction with their environments, we get 

Alternatively introducing the activity coefihcient and ys related to the chemical potentials by (1.6.1), we have 

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