Based on the Rate-Controlled Constrained-Equilibrium (RCCE) theory [Keck and Gillespie, Combust. Flame 17:237-241 (1971)], a thermochemistry algorithm for characterizing partially equilibrated reacting systems is developed that, given the identity of the equilibrated reactions, determines (regardless of any linear dependencies among the reactions) a reduced reaction mechanism for the system, identifies the constraints and their dependence on this mechanism, and determines the thermodynamic state of the system by minimizing its free energy subject to instantaneous values of the constraints. This algorithm can be combined with any routine integrating the governing equations of the given system to construct programs capable of simulating the evolution of the system using fully rate controlled, partially equilibrated, or fully equilibrated chemistry as required. This is illustrated here by combining this algorithm with an ordinary differential equation solver and using the resulting one-dimensional flow program to predict the quenching of CO in cooled combustion streams, using partial equilibrium chemistry.