Application of a two-structure model TSM

In this section, we discuss the application of an exact two-structure, mixture-model (MM) approach to aqueous solutions of simple solutes. 

Consider a system of Nw water molecules and Ns solute molecules at a given temperature T and pressure P. We shall be interested only in very dilute solutions. Ns Nw We henceforth assume that T and P are constants, and therefore omit them from our notation. 

Let Ni and Nh be the average number of L-cules and H-cules obtained by any classification procedure (Sec. 2.3). For the purpose of this section, we need not specify the particular choice of the two species therefore, our treatment will be very general. For concreteness, one may think of a two-structure model (TSM) constructed from the vector xcn (see Sec. 2.3), i.e. 

Examples of such studies are Frank and Quist (1961),Namiot (1961), Grigorovich and Samoilov (1962), Yashkiraga (1962), Ben-Naim (1965a), Mikhailov (1968), Mikhailov and Ponomareva (1968), and Frank and Franks (1968). We shall start in the next section with the two-structure model and then proceed with the more general MM approach. 

Any extensive thermodynamic quantity can be viewed either as a function of the variables T,P,Nuj,Ns) or the variables T,P,Ni,Nh,Ns). The equilibrium condition for the conversion between L and H is 

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