Chemical-potential balance for a reaction

For a reaction with stoichiometric changes ${\nu }_i$, varying the reaction extent at fixed temperature and pressure givesEquilibrium requires ${\sum }_i{\nu }_i{\mu }_i=0$.

Thermochemical equilibrium requires every chemical reaction to have zero Gibbs free-energy change. For ideal reactants, the equilibrium constant is $K=\exp [-{\Delta }_r{G}^{\circ }/(RT)]$ after standard-state activity factors are included.

At fixed temperature and pressure, a closed reacting system reaches thermochemical equilibrium by minimizing Gibbs free energy over nonnegative species amounts subject to conserved elemental abundances. For an allowed stoichiometric vector $\nu$, an interior minimum has ${\sum }_i{\nu }_i{\mu }_i=0$. More generally the chemical potential vector lies in the row span of the elemental conservation matrix at positive concentrations, with the appropriate one-sided inequalities for absent species. The first law of thermodynamics gives the thermodynamic differential, while the Second law of thermodynamics supplies the minimization direction.

For an elementary reversible reaction, detailed balance gives $k_f{\prod }_r{n}_r^{{\nu }_r}=k_r{\prod }_p{n}_p^{{\nu }_p}$ at equilibrium. Hence the reverse rate coefficient is the forward coefficient divided by the equilibrium constant, with units fixed by the reaction stoichiometry.