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The Quasi-Steady-State Approximation: Numerical Validation

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Richard A. B. Bond , Bice S. Martincigh and Janusz R. Mika

University of Natal, Durban 4041, Republic of South Africa

Reuben H. Simoyi

West Virginia University, Morgantown, WV 26506-6045

J. Chem. Educ., 1998, 75 (9), p 1158

DOI: 10.1021/ed075p1158

Publication Date (Web): September 1, 1998

Section:

History, Education, and Documentation

Abstract

The quasi-steady-state approximation (QSSA) of chemical kinetics is a mathematical way of simplifying the differential equations describing some chemical kinetic systems. Originally devised by biochemists on an ad hoc basis, it is now recognized as belonging to singular perturbation theory. Ideally, this theory provides an error estimate for the QSSA, but it is too complicated for general use. Various investigations of special cases, invoking exact solutions, give some indications of the applicability of the QSSA. But further clarification is called for, especially since the QSSA is virtually unavoidable in introductory texts on chemical kinetics, while at the same time it is open to misuse in practice. In this note, we explore first the graphical representation of exact numerical solutions of partially nondimensionalized forms of the kinetic equations of some small systems of pedagogic interest, and thereby show that the QSSA is more widely applicable than is often assumed.Secondly, qualitative discussions of singular perturbation theory and of numerical stiffness are shown to lead to a simple computational test of QSSA validity, which works with intricate and large systems. This procedure is illustrated for the case of the Oregonator.