# Simplified Statistical Model for Equilibrium Constant

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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: .

[more]
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.

## Permanent Citation

"Simplified Statistical Model for Equilibrium Constant"

http://demonstrations.wolfram.com/SimplifiedStatisticalModelForEquilibriumConstant/

Wolfram Demonstrations Project

Published: March 7 2011