Relation between the thermodynamics and kinetics of a complex reaction system at constant temperature and pressure

Abstract

For complex systems, it is convenient to express both the thermodynamic condition for chemical equilibrium and the rate equation in matrix notation. Chemical equilibrium calculations at constant temperature and pressure are generally made on the assumption that the only constraints on the minimization of the Gibbs energy are the element balances. This can be accomplished in terms of chemical reactions (the so-called stoichiometric formulation of the problem) by the use of any independent set of R reactions that can provide for all possible compositions permitted by the conservation of elements. The rate equation for a complex system is written in terms of a mechanism that may involve a larger or smaller number of reactions. An equilibrium composition can be calculated from the rate equation by integration to infinite time, but this composition may or may not agree with that calculated from thermodynamics on the assumption that the only constraints are the element balances. If the mechanism includes R independent reactions, the equilibrium compositions calculated in these two ways should agree if the forward and reverse rate constants for each step are in agreement with the equilibrium constants for those steps. If the mechanism involves fewer than R independent reactions, amore » different equilibrium composition will be calculated from the rate equation because constraints are implicitly involved in the mechanism. This is illustrated for a system involving polycyclic aromatic hydrocarbons.« less