Water with One Simple Solute Particle

The study of very dilute solutions of simple nonpolar solutes is of interest for various reasons. First, these solutions reveal some anomalous properties in comparison with corresponding nonaqueous solutions, and have therefore presented an attractive challenge to scientists. Second, the study of dilute aqueous solutions, viewed as systems deviating slightly from pure water, provides some further information which is helpful in the study of water itself. Finally, understanding the thermodynamics of these systems is a first, indispensable step in the study of the problem of hydrophobic interaction, a topic of prominence especially in biochemical systems and to which we devote the next chapter. 

Regarding the theoretical development of the study of dilute aqueous solutions, one cannot expect the situation to be better than that for pure water. In fact, progress in this field is contingent upon progress in the theory of water. Therefore, it is no wonder that most of the theories developed for these systems are rather speculative. It is difficult to make a critical assessment of the various assumptions and approximations that have been introduced, either explicitly or implicitly, in these theories. 

In this chapter, we survey some of the theories that have been suggested for dilute aqueous solutions. As in the previous chapter, we elaborate on the molecular foundations of each of the approaches, and discuss some of the approximations that are introduced, in order to pursue the theory to the point where thermodynamic results can be computed. 

Consider a dilute solution of Ng molecules (or moles) of solute S and Nw molecules (or moles) of water at a given temperature T and pressure P. In most of this chapter, we use these variables, since they are the most common ones in practice. We assume that the system is macroscopic, but that Ns Ny. Suppose we are interested in the response of the volume of the system to an addition of solute. We write the expansion (r, P, constant) 

We define the partial molar volume at infinite dilution (i.e., at the limit of zero solute concentration) by 

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