A method to calculate multi-component chemical reaction mixtures as a sequence of time-dependent, intermediate thermochemical states is presented. The method combines the overall reaction kinetics with thermodynamic Gibbs energy minimization. The overall reaction is assumed to proceed according to the Arrhenius rate law. During the time-course of the reaction, the temperature and composition of the reaction mixture are calculated by a thermodynamic subroutine, which minimizes the Gibbs energy of the system. The extent of the overall reaction is algorithmically constrained in the Gibbs energy minimization procedure. During the sequential calculation, the kinetic condition is removed by finite differences. The temperature of each intermediate state is reached by an iterative procedure, which takes into account the heat transfer between the system and its surroundings and the enthalpy changes due to the chemical reactions. Thus, the method allows for the effect of temperature on the reaction kinetics as the reaction evolves. The chemical species present in each intermediate state are virtually independent and there is a chemical potential assigned to each of these species. The gradual chemical change in the thermodynamic system proceeds from the initial state of mixed reactants to the final state of product mixture. Both stationary and transient phenomena may be calculated. The method has been applied to some well-known industrial multi-component reaction systems and a fair agreement between the calculated and measured values has been obtained. The application of the thermochemical algorithm in reaction calorimetry is discussed.