Ideal Mixtures of Small Molecules

For a Systran in a givrai state, the entropy is related to the number of distinguishable arrangements the eomponraits in that state can adopt and can be calculated from the Boltzmann law, 5 = k In Q, where Q is the number of statistical microstates available to the Systran. We can begin by considering the mixing of iV, molecules of component 

1 with A 2 molecules of component 2, and this can be assumed to take place on a hypothetical lattice containing (N + N2) = Ng cells of equal size. Although this formalism is not strictly necessary for the analysis, the arrangement of spherical molecules of equal size in the liquid state will, to the first near-neighbor approximation, be similar to a regular lattice structure, and so it is a useful structure to use as a framework for the mixing process. 

The total number of possible ways in which the component molecules can be arranged on the lattice increases when mixing takes place and is equal to (A -1- Aj) = Agl, but as the interchanging of a molecule of component 1 with another molecule component 1, or component 2 with component 2 will be an indistinguishable process, the net number of distinguishable arrangements will be 

The configurational (or combinatorial) entropy can then be derived from the Boltzmann law and 

For large values of Aj, Stirring s approximation can be used to deal with the factorials i.e.. In A = A In A - A, and Equation 8.3 becomes 

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