Notions of Microscopic Thermodynamics

The aim of this appendix is to gather together a few statistical thermodynamics notions and, in particular, to establish the expression of equilibrium constants using partition functions, which is useful in the activated complex theory. 

Molecule distribution between tbe different energy states 

Here consider a group of N molecitles that are chemically identical. Among the molecules, N has an energy of 8i, A2 an energy of 62 [...] and N an energy of i. The mtmber of possibihties W (number of complexions) by which to distribute N molecitles in the way thus described is  

The most probable state is the one for which W (or InW) is at its maximum when it obeys to the following condition  

To solve the system formed by eqnations [A2.9], [A2.10] and [A2.12], we will apply Lagrange s method. To do so, we mnltiply relations [A2.10] and [A2.12] by nndefined constants a and P, respectively. The system of three eqnations becomes  

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