The dynamical evolution of a chemically reacting system is governed by the equations of chemical kinetics, which exhibit a wide range of time scales thus giving rise to stiff equations. In the rate-controlled constrained equilibrium method (RCCE), the dynamical evolution of the system is governed by the kinetics of the species associated with the slower timescales (kinetically controlled), while the remaining species are calculated via a constrained minimisation of the Gibbs free energy of the mixture. This permits the derivation of a general set of differential-algebraic equations, which apply to any reduced system given a particular selection of kinetically controlled species. In this paper, it is shown how the differential-algebraic formulation of RCCE can be derived from first principles, in the form of an extension of the computation of chemical equilibrium via miminisation of the free energy. Subsequently, RCCE is employed to reduce a comprehensive combustion mechanism and to calculate the burning velocity of premixed H
-air flames under a range of pressures and equivalence ratios.