# Simplified Statistical Model for Equilibrium Constant

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Consider a simple chemical equilibrium with equilibrium constant . (This can alternatively be written in terms of the concentrations of and .) The difference in electronic energy for the reaction equals , conveniently expressed in kJ/mol. Let the internal structure of each molecule be idealized as a series of equally spaced energy levels (similar to those of a harmonic oscillator), with the energy increments and . The spacings and relative to are exaggerated in the graphic for easier visualization. The sublevels of each molecular species are assumed to occupy a Boltzmann distribution at temperature . Accordingly, , where , the molecular partition function for , and analogously for . For a mixture of and , a single Boltzmann distribution can be considered to apply for the composite levels of both molecules. This leads to the formula for equilibrium constant in statistical thermodynamics: .

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Contributed by: S. M. Blinder (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: a strongly exothermic forward reaction

Snapshot 2: an endothermic forward reaction enabled by entropy effect

Snapshot 3: effect of higher temperature

Reference

[1] D. A. McQuarrie, *Statistical Mechanics*, New York: Harper & Row, 1976 pp. 142 ff.

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