Molecular-Weight Mixtures van Laar Model

The methods of statistical mechanics can be used to derive an equation for AiSconf W assuming that the molecules are placed randomly into cells that are of molecular size and are arranged in the form of a three-dimensional lattice (represented in two dimensions in Fig. 3.3). The white circles in Fig. 3.3 represent solvent molecules and the black ones, solute 

By definition, A/Smix is the difference between the entropy of the mixture and the entropies of the components in unmixed (pure) form. According to our model, only configurational entropies need be considered. Therefore A5mix is equal to ASconf- 

The fundamental relation between the entropy S of an assembly of molecules and the total number of distinguishable degenerate (i.e., of equal energy) arrangements of the molecules is given by the well-known Boltzmann relation  

For ideal mixing of Na molecules of A with iVg molecules of B in a lattice with (Na + Nb) cells, the total number of distinguishable spatial arrangements of the molecules is equal to the number of permutations of Na + Nb) objects consisting of Na identical objects of type A and Nb identical objects of type B, that is, 

It is more usual to write thermodynamic equations in terms of numbers of moles, n, and mole fractions, x, which here are defined by 

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