Beyond Traditional Chemical Kinetics Formulas: Group-Theoretic Approach

According to the traditional formulas of chemical kinetics, the rate is proportional to the product of concentrations of reagents. This formula leads to a reasonable description of interactions both in chemistry and in other disciplines (e.g., in ecology). However, in many cases, these formulas are only approximate. Several semi-empirical formulas have been designed to more accurately describe the interaction rate. The problem is that most of these formulas are purely empirical, they lack a convincing theoretical explanation. In this paper, we show that a group-theoretic approach – taking into account natural symmetries of the systems – leads to the desired theoretical explanation for these empirical formulas. 1 Formulation of the Problem Traditional formulas of chemical kinetics. According to the traditional chemical kinetics formulas, the reaction rate is proportional to the product of the concentrations of all the inputs. In particular, for a reaction A + B → X, the rate is proportional to the product of the concentrations a and b of the substances A and B: da dt = g(a, b) and db dt = g(a, b), where g(a, b) = − k · a · b. Chemical kinetics formulas are used to describe interactions beyond chemistry. Similar formulas are used to describe interactions in other areas as well. For example, in the standard Lotka-Volterra model of predator-prey interactions, the presence of predators P causes the decrease of the prey population N which is proportional to N · P : dN dt = − k ·N · P ; see, e.g., [8]. Need to go beyond traditional formulas of chemical kinetics. In the first approximation, chemical formulas accurately describe interaction in chemistry and in other disciplines. However, more accurate measurements revealed