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Chemical Education Today
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Letters
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Don't Be Tricked by Your Integrated Rate Plot: Reaction order Ambiguity
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Sue Le Vent
Department of Chemistry, University of Manchester Institute of Science and Technology, Manchester M60 1QD, United Kingdom
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January 2004
Vol. 81 No. 1
p. 32
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In the article “Don’t Be Tricked by Your Integrated Rate Plot” (1), E. T. Urbansky draws attention to the dangers of determining reaction (partial) order by use of integrated rate equation plots when the reaction has been followed to insufficient extent, particularly when there may be substantial random error in concentration. I would accept the key point that reactions must be followed to substantial extent if, solely, integrated rate equation plots are to be used to determine reaction order; indeed, I would always make that point strongly myself to students in laboratory courses. Urbansky illustrates the problem with a specific numerical problem, using synthesized first order data, based upon chosen rate constant and initial reactant concentration. I would agree that use of specific data is probably sensible to get over the ambiguity problem to undergraduate students, particularly those at an early stage of higher education, but here I want to draw attention to a more general algebraic method of presenting the argument. Integrated rate equations (for constant reaction volume) may be given in terms of relative reactant concentration, C (= concentration/initial concentration) and relative time, T (= time/half-life); in these forms, the equations are independent of rate constants and initial concentrations. The equations, stated here for three functions of C (not merely those giving a linear plot against T) are restricted to orders 0, 1, and 2. They are not difficult to prove from conventional integrated forms (and consequent expressions for half-life) and can be extended to non-integral orders. Zeroth order: C = 1 – T/2 | ln(C) = ln(1 – T/2) | 1/C = 1/(1 – T/2) |
First order: C = 2–T | ln(C) = –T ln(2) | 1/C = 2T |
Second order: C = 1/(1 + T) | ln(C) = –ln(1 + T) | 1/C = 1 + T |
With the obvious requirement that linearity of the function of C with T will automatically imply linearity of the same function of concentration [or strictly, for the logarithmic function, concentration/(a concentration unit)] with time, one can easily see which three of the above nine equations give linear plots, namely, those with right sides linear in T. Furthermore, for the purpose of Urbansky’s paper, one can see by plotting the other six right sides against T, how non-linear are these functions and to what value of T one should ideally follow a reaction to obtain an unambiguous order. Literature Cited- Urbansky, E. T. J. Chem. Educ. 2001, 78, 921.
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| More Information |
 Citation |
Le Vent, Sue. J. Chem. Educ. 2004 81 32.
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Keywords |
Introductory / High School Chemistry; Kinetics; Mechanisms of Reactions; Teaching / Learning Aids; Textbooks
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History |
Created:
Last Updated: |
December 8, 2003
February 18, 2005
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