In their paper “Using a Graphing Calculator to Determine a First-Order Rate Constant when the Infinity Reading is Unknown”, Cortés-Figueroa and Moore (1) offer ingenious solutions to a common vexing problem (2). The authors use the graphing calculator to estimate the infinity reading from linearized kinetics data, and then they use linearized semi-log data to determine the first-order rate constant. If students are limited to graphing calculators for their data analysis, then the authors present an elegant solution to the problem. However, many students have access to data analysis software such as Excel, Mathematica, Mathcad, or TableCurve, and plotting software like DeltaGraph, SigmaPlot, or Kaleidagraph. All of these programs offer nonlinear curve fitting that for several reasons is preferable to linearizing nonlinear raw data.

The point has been made in this Journal that unless weighting factors are used carefully, linearizing nonlinear raw data often yields inaccurate results (3, 4). With the computer software that is currently available in most colleges and universities and in many high schools (5), it is no longer necessary to linearize data. Direct fitting of nonlinear raw data has the advantage that it is both simpler (students deal only with plots of the raw data) and more accurate (3, 4). As pointed out by McNaught (4), “the standard deviations in the derived parameters are as important as the parameters themselves”. Without uncertainties, the reader has no idea how precise the results are. For example, Cortés-Figueroa and Moore quote slopes and intercepts with 10-11 significant figures, and rate constant values with six significant figures. Considering uncertainty in the linear regression, their k values should have three, or at most four significant figures. Mathematica, TableCurve, and Kaleidagraph all return not only values for the fitted parameters, but also uncertainties in these fitted values. Expedient use of Excel’s Solver function (6), also allows estimation of uncertainties in fitted parameters. For all of these reasons, if the relevant software is available, it is worthwhile to teach our students to use nonlinear curve fitting in their analysis of nonlinear data.

Literature Cited

1. Cortés-Figueroa, J. E.; Moore, D. A. J. Chem. Educ. 2002, 79, 1462-1464.
2. Hemalatha, M. R. K.; NoorBatcha, I. J. Chem. Educ. 1997, 74, 972.
3. Logan, S. R. J. Chem. Educ. 1995, 72, 896-898.
4. McNaught, I. J. J. Chem. Educ. 1999, 76, 1457.
5. Kantardjieff, K. A.; Hardinger, S. A.; Van Willis, W. J. Chem. Educ. 1999, 76, 694-696.
6. Harris, D. C. J. Chem. Educ. 1998, 75, 119-121.

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