Formulation of the Problem for a Three-Component System

Consider a mixture of two components, molecules of A and Nb molecules of B, at some temperature T and pressure P. In such a system, the composition measured by the mole fraction Xa = Na/ Na + Nb), will be the same at any point Ro within the system. 

We shall refer to Xa as the bulk composition of the system. Next, consider a very dilute solution of a solute S in our two-component mixture. (In principle, we could have discussed also high concentrations of S in the system. However, this will require consideration of three components, 5, A, and B in the surroundings of S. For simplicity, we treat only the case of very dilute solutions, so that S sees practically only s and Bs.) 

The question we now ask is the following What is the composition of the liquid in the immediate vicinity of the solute 5 Clearly, since the affinity of 5 to might be different from its affinity to B, we should expect that the composition near the solute S will differ from the bulk composition Xa.  

The main question that will concern us in this section is how to define the local region in the vicinity of S in which the composition is expected to be affected by the presence of S. Once we have defined the region, we shall provide a method of measuring the composition in this region. 

Consider first a simple spherical solute, say argon, in a two-component solvent, say water and ethanol. Let = dx dy dz be an element of volume at a distance R from the center of S. The average number densities of A and B in this element of volume will be 

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