Quick and Easy Rate Equations for Multistep Reactions


  • Phillip E. Savage University of Michigan


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

Author Biography

Phillip E. Savage, University of Michigan

Phillip Savage is a professor of chemical engineering at the University of Michigan. He received his B.S. from Penn State in 1982 and his M.Ch.E. (1983) and Ph.D. (1986) degrees from the University of Delaware, all in chemical engineering. His research and teaching interests focus on the rates, mechanisms, and engineering of organic chemical reactions. Current research projects deal with renewable energy from biomass and environmentally benign chemical synthesis.