Why Equilibrium? Understanding Entropy of Mixing

Abstract

To help students understand entropy and the origin of equilibrium, it is useful to explicitly calculate the components of the Gibbs free energy. This can be done if the reaction is a gas-phase reaction at moderate pressure. In this case, reactants and products can be treated as ideal gases. Both reaction enthalpy and the nonmixing contribution to the entropy are then linear functions of reaction progress. As a result of the second law, to establish equilibrium, the Gibbs free energy must have a minimum as a function of reaction progress. This minimum occurs when the entropy of mixing is added to the enthalpy and nonmixing entropy. By choosing a gas-phase reaction with a moderate DGq, the minimum in DG as a function of reaction progress can be determined by inspection. The location of the minimum is determined by DGq for the reaction and the total number of moles of reactants compared to products (i.e., the stoichiometry of the reaction). These concepts are illustrated with an explicit calculation for the ...