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First-Order or Second-Order Kinetics? A Monte Carlo Answer
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Abstract
In chemical kinetics, data for the concentration [A] as a function of time can be analyzed by least-squares fitting to the appropriate expression for the integrated rate law. The problem of discriminating between first and second order in such analyses is examined through Monte Carlo computational experiments in which synthetic data are fitted to both the direct expressions for [A](t) and to their linearized versions. For 11 data points spanning two half-lives, with 10% random error, a simple comparison of the sum of weighted squared residuals picks the correct order 
90% of the time, which is better than implied in earlier discussions of this problem. The discriminating ability improves markedly with increasing numbers of data points and reduced experimental error. The article includes a description of procedures that permit students to explore the role of random noise in kinetics data, using the representative data analysis program KaleidaGraph.
Keywords (Audience):
Upper-Division UndergraduateKeywords (Domain):
Laboratory InstructionKeywords (Pedagogy):
Computer-Based LearningKeywords (Subject):
ChemometricsCiting Articles
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This article has been cited by 1 ACS Journal articles (1 most recent appear below).
Error Propagation Made Easy—Or at Least Easier
George H. Gardenier, Feng Gui, and James N. DemasJournal of Chemical Education2011 88 (7), 916-920Error Propagation Made Easy—Or at Least Easier
George H. Gardenier, Feng Gui, and James N. DemasJournal of Chemical Education2011 88 (7), 916-920Complex error propagation is reduced to formula and data entry into a Mathcad worksheet or an Excel spreadsheet. The Mathcad routine uses both symbolic calculus analysis and Monte Carlo methods to propagate errors in a formula of up to four variables. ...
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- Received: August 03, 2009
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