Reaction rates as virtual constraints in Gibbs energy minimization

The constrained Gibbs energy method has been developed for the use of immaterial entities in the formula conservation matrix of the Gibbs energy minimization problem. The new method enables the association of the conservation matrix with structural, physical, chemical, and energetic properties, and thus the scope of free energy calculations can be extended beyond the conventional studies of global chemical equilibria and phase diagrams. The use of immaterial constraints enables thermochemical calculations in partial equilibrium systems as well as in systems controlled by work factors. In addition, they allow the introduction of mechanistic reaction kinetics to the Gibbsian multiphase analysis. The constrained advancements of reactions are incorporated into the Gibbs energy calculation by using additional virtual phases in the conservation matrix. The virtual components are then utilized to meet the incremental consumption of reactants or the formation of products in the kinetically slow reactions. The respective thermodynamic properties for the intermediate states can be used in reaction rate formulations, e.g., by applying the reaction quotients.