Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View

Abstract

The aim of the present paper is to check - or better to confirm - the mathematical validity of chemical reaction rate, faced as a set of differential equations. Firstly one - way elementary reactions are considered, in the most general case. Secondly the same thing is done with two-way (opposing) elementary reactions. At this stage, we show that the two – way reaction, as we mean it, is compatible with the reduction of the total Gibbs energy as expected in every natural process. As an example of a two way elementary reaction of a completely solvable problem we give the hydrolysis of sucrose to glucose and fructose, where the “inversion” of sucrose is examined not only with the initial linear reaction of “Wilhelmy” (1850), but also with the two way nonlinear reaction introduced. Finally the validity of the mathematical model is checked for more complex cases such as the Michaelis-Menten mechanism or reactions in solution, where it is found that the two cases, apparently are four – dimensional while in reality are two – dimensional (after the “subtraction” of the constraints of “motion”) and naturally cannot exhibit chaotic behavior. In all cases the treatment is not one-hundred-percent mathematically austere but it has also arbitrary although reasonable hypotheses.