An Argument Based on the Kirkwood-Buff Theory

We now apply the Kirkwood-Buff theory to reexpress the rhs of (7.13.4) in terms of molecular distribution functions. The basic relation that we need is (section 6.7) 

Ps + PsGss PsPlGsl PsPhGsh B = PlPsGls Pl + PlGll PlPhGlh 

From here on, we specialize to the limiting case of ps 0. In a formal way, we can write the quantity (7.13.4) for any ps in terms of the Gap- However, the general case is very complicated. Therefore we limit ourselves to very dilute solutions as, indeed, aqueous solutions of inert gases are. 

At the limit ps 0, the partial molar volumes Pi and Vh and the compressibility of the system tend to their values in pure water, with composition Ni and Nh, i.e., 

Note that in (7.13.11) we have the frozen-in part of the compressibility. This is because we are now working in the frozen-in system, where N and Nh are assumed to behave as independent variables. Note also that and Vh are definable only in the frozen-in system, and therefore there is no need to add any superscript to these symbols. 

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