Quick and Easy Rate Equations for Multistep Reactions

Abstract

Students rarely see closed-form analytical rate equations derived from underlying chemical mechanisms that contain more than a few steps unless restrictive simplifying assumptions (e.g., existence of a rate-determining step) are made. Yet, work published decades ago allows closed- form analytical rate equations to be written quickly and easily for arbitrarily large multistep reaction mechanisms (catalyzed or uncatalyzed) that meet a few common criteria. This approach to writing general rate equations was developed by using linear algebra to solve the set of n simultaneous algebraic equations that arise from application of the quasi-stationary-state approximation to the n reactive intermediates in the reaction system. This article describes the methods, illustrates their application, and discusses the author’s experience teaching these techniques. Key words: kinetics, catalysis, mechanisms, reaction engineering