Degree of rate control and De Donder relations – An interpretation based on transition state theory

Abstract

We describe sensitivities of elementary steps as salient parameters in determining the rate determining character of elementary steps within a reaction network and develop a formalism wherein the overall composite reaction is described by an apparent rate-determining step that is a sensitivity-weighted average of the elementary steps that comprise the reaction network. Reaction parameters—apparent reaction orders, apparent enthalpy and entropy of activation—of the composite reaction network are determined within the framework we develop by application of transition state theory to the apparent rate-determining step. From this formalism we develop methods for determination of surface coverages by measuring only reaction orders, methods for discrimination between proposed mechanisms, a proof that the kinetic degrees of rate control sum to unity, and a proof for the relationship between fractional coverages and thermodynamic degrees of rate control. Two complementary formalisms for identifying rate-limiting transition states are broadly employed in chemical kinetics—De Donder relations based on assessing the thermodynamic driving forces of elementary steps during reaction and degrees of rate control based on knowledge of the kinetics of elementary reaction steps. The formalism developed herein unifies these two strategies to elucidate in the most general case a relationship between the thermodynamic driving forces of elementary steps captured by the reversibilities and the kinetic and thermodynamic degrees of rate control.