The concept of local composition in a solution

In reality, the exchange energy has consequences for the local distribution of the molecules. Indeed, it is easy to see that if there is a stronger foree of attraction between a molecule of A and a molecule of B than there is between two molecules of A or between two molecules of B, then a molecule of A will tend to be siuroimded by molecules of B, and therefore the composition of the immediate enviromnent of the molecule of A will not be the same as the overall eomposition of the solution - it will be richer in molecules of B. The opposite effect would be observed if the two moleeules A and B had a lesser foree of attraction than two molecules of A and two molecules of B. This is the concept of local composition, first expressed by Wilson. 

In order to describe this concept of local composition, we use a nomenclature that enables us to clearly distinguish, every time, between the central molecule and its closest neighboring molecules. 

Nij denotes the number of molecules of i around a molecule of j, and we define the conditional probability Py that a molecule of i will be located in the environs of a molecule of j by the expression (where N denotes the number of components in the solution)  

Note that this probability also represents the local molar fiactioiL Evidently, we have  

We shall suppose that it is always possible to define a weighting factor ky such that the local composition is the overall composition weighted by that 

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