## Criterion of Chemical Equilibrium

As in any system constrained to constant temperature and pressure, the equilibrium of a chemical reaction is attained when the free energy is a minimum. Specifically, this means that dG = 0, where the differential of G is with respect to the composition of the mixture. In order to convert this criterion to an equation relating the equilibrium concentrations of the reactants and products, the chemical potentials are the essential intermediaries. At equilibrium, Eq (7.27) provides the equation:

where ni is the number of moles of species i and the summation includes all reactants and product species. The equation applies to an equilibrium involving multiple phases. If more than one reaction occurs, Eq (7.27) applies to each.

In order to further develop Eq (7.27) into a usable form, it is applied to generic reaction (9.5), yielding:

The changes in the mole numbers are related to each other by the balancing numbers in Eq (9.5). For example, for every mole of A consumed, b/a moles of B disappear and c/a and d/a moles of C and D, respectively, are produced. These stoichiometric restraints yield the following:

The equilibrium condition for the generic reaction becomes:

The general version of the above equation is:

reactants products where Vi are the balancing numbers in the chemical reaction.

There remains only to express the chemical potentials in terms of the concentrations, which will then lead to the law of mass action.

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