Application of an Interstitial Model

We extend here the application of the interstitial model for water to aqueous solutions of simple solutes. The merits of this model are essentially the same as those discussed in Section 6.7 this is the simplest model that contains elements in common with similar models worked out by various authors (Frank and Quist, 1961 Yashkichev and Samoilov, 1962 Bulsaeva and Samoilov, 1963 Ben-Naim, 1965a Malenkov, 1966 Mikhailov, 1968 Mikhailov and Ponomareva, 1968 Frank and Franks, 1968). This is also the only model proposed for water that can be solved exactly, and, therefore, various general results of the mixture-model formalism can be obtained in an explicit manner. 

The basic assumptions of the model have been introduced in Section 6.7. To adapt the model for aqueous solutions, we further assume that Ns solute molecules occupy the interstitial positions in the framework built up by the L-cules. Only one new molecular parameter is introduced in the new model, i.e., the interaction energy between the solute 5 and its surroundings, which we denote by Es- 

The combinatorial factor in (7.62) is the number of ways in which one can place Ng //-cules and Ns solute molecules into NqNj holes. The summation is carried over all possible volumes of the system, which, by virtue of the assumptions of the model, is the same as a summation over all Nj. The condition Ng N N for pure water is replaced by the condition 

As in the case of the one-component system, we take the maximal term in the sum (7.62), from which we obtain the equilibrium condition 

The mole fractions of empty holes, holes occupied by //-cules, and holes occupied by S are 

---

Application of an Interstitial Model for Water to Aqueous Solutions... 

---