Thermodynamics in the Limit of Irreversible Reactions

TL;DR

This paper explores the thermodynamics of systems with irreversible reactions as limits of reversible systems, establishing conditions for their behavior and extending classical principles to complex chemical reactions.

Contribution

It introduces the extended principle of detailed balance for irreversible reactions as limits of reversible systems and provides a mathematical framework for their analysis.

Findings

Limit systems depend on the rate at which equilibrium concentrations tend to zero.

Extended detailed balance conditions ensure the existence of Lyapunov functionals.

Application to hydrogen combustion illustrates the theory.

Abstract

For many real physico-chemical complex systems 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. The classical thermodynamics has no limit for irreversible reactions whereas the kinetic equations may have such a limit. We represent the systems with irreversible reactions as the limits of the 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 $t \to \infty$. If the reversible systems obey the principle of detailed balance then the limit system with some irreversible reactions must satisfy the {\em 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 alow an algebraic description of the limit behavior. The thermodynamic theory of the irreversible limit of reversible reactions is illustrated by the analysis of hydrogen combustion.