Rate-controlled constrained-equilibrium method, firmly based on the second law of thermodynamics, is applied to the expansion of combustion products of methane during the power stroke of an internal combustion engine. The constraints used in this study are the elemental oxygen, hydrogen, carbon and nitrogen together with other four dynamic constraints of total number of moles, moles of DCO (CO+HCO), moles of free valence and moles of free oxygen. Since at chemical equilibrium, the mixture composition is dominated by H/O, CO/CO2, and a few other carbon-containing species, almost independent of the fuel molecule, the set results in accurate predictions of the kinetic effects observed in all H/O and CO/CO2 compounds and temperature history. It is shown that the constrained-equilibrium predictions of all the species composed of the specified atomic elements can be obtained independent of a kinetic path, provided their Gibbs free energies are known.