Fluctuation Theory in Chemical Kinetics

Abstract

In this research, we study the stability properties of chemical reactions of arbitrary orders. In a given chemical experiment, we focus on the formation of a chemical equilibrium by optimizing the reaction rate. Under infinitesimal simultaneous variations of the concentrations of reacting species, the binary component equilibrium is achieved when either one of the orders or concentrations of reactants vanishes. The chemical concentration capacities of the components are calculated to describe the local stability of the equilibrium. The correlation between the components is obtained as the mixed second-order derivative of the rate with respect to concentrations. The global stability analysis is performed by introducing a symmetric matrix with its diagonal components as the chemical capacities and off-diagonal components as the local correlation. We find that the local chemical stability requires the orders of the reactants to be either negative or larger than unity. The corresponding global stability requires the positivity of a cubic factor over the orders of the reactants. In short, our consideration illustrates how a chemical reaction takes place by attaining its activation state and asymptotically approaches the equilibrium when two components are mixed with arbitrary orders. Qualitative discussions are provided to support our analysis towards the formation of an optimized equilibrium. Finally, along with future directions, we discuss verification of our model towards the formation of carbon-based reactions, formation of organic/inorganic chemical equilibria and catalytic oxidation of C O − H 2 mixtures in presence of Pt.

Keywords

• chemical stability
• reaction rate
• chemical equilibria
• fluctuation theory
• kinetic theory