Thermodynamics in the limit of irreversible reactions

For many complex real physicochemical systems, the detailed mechanism includes both reversible and irreversible reactions. Such systems are typical in homogeneous combustion and heterogeneous catalytic oxidation. Most complex enzyme reactions include irreversible steps. Classical thermodynamics has no limit for irreversible reactions, whereas kinetic equations may have such a limit. We represent systems with irreversible reactions as the limits of fully reversible systems when some of the equilibrium concentrations tend to zero. The structure of the limit reaction system crucially depends on the relative rates of this tendency to zero. We study the dynamics of the limit system and describe its limit behavior as t→∞. If the reversible systems obey the principle of detailed balance then the limit system with some irreversible reactions must satisfy the extended principle of detailed balance. It is formulated and proven in the form of two conditions: (i) the reversible part satisfies the principle of detailed balance and (ii) the convex hull of the stoichiometric vectors of the irreversible reactions does not intersect the linear span of the stoichiometric vectors of the reversible reactions. These conditions imply the existence of the global Lyapunov functionals and allow an algebraic description of the limit behavior. Thermodynamic theory of the irreversible limit of reversible reactions is illustrated by the analysis of hydrogen combustion.