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A Streamlined Approach to Solving Simple and Complex Kinetic Systems Analytically

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John Andraos

Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada

J. Chem. Educ., 1999, 76 (11), p 1578

DOI: 10.1021/ed076p1578

Publication Date (Web): November 1, 1999

Abstract

The use of Laplace transforms and integration techniques for the solution of simultaneous differential equations is demonstrated for obtaining the analytical solutions of simple and complex kinetic systems well known to students of the chemical sciences. These techniques learned in core first- and second-year mathematics courses provide a firm grounding in students' ability to understand the derivation of various rate expressions, and illustrate the value of cross-disciplinary approaches to education between the chemical and mathematical sciences.

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Physical Chemistry

Keywords (Pedagogy):

Problem Solving / Decision Making

Keywords (Subject):

Kinetics

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Citing Articles

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This article has been cited by 9 ACS Journal articles (5 most recent appear below).

Kinetic Analysis of Parallel-Consecutive First-Order Reactions with a Reversible Step: Concentration–Time Integrals Method
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Journal of Chemical Education2009 86 (3), 390
- Kinetic Analysis of Parallel-Consecutive First-Order Reactions with a Reversible Step: Concentration–Time Integrals Method
  A. E. Mucientes and M. A. de la Peña
  Journal of Chemical Education2009 86 (3), 390
  The concentration–time integrals method has been used to solve kinetic equations of parallel-consecutive first-order reactions with a reversible step. This method involves the determination of the area under the curve for the concentration of a given ...
  Abstract | Hi-Res PDF | PDF w/ Links
A Convenient Tool for the Stochastic Simulation of Reaction Mechanisms
Nikolaos Bentenitis
Journal of Chemical Education2008 85 (8), 1146
- A Convenient Tool for the Stochastic Simulation of Reaction Mechanisms
  Nikolaos Bentenitis
  Journal of Chemical Education2008 85 (8), 1146
  The article introduces the stochastic simulation of chemical reactions with Chemical Kinetics Simulator, CKS, a free, easy-to-use, and powerful program. After familiarizing themselves with the Monte Carlo method of stochastic simulation and CKS, students ...
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Gas-Phase Hydration of U(IV), U(V), and U(VI) Dioxo Monocations
Garold L. Gresham, Anita K. Gianotto, Peter de B. Harrington, Libo Cao, Jill R. Scott, John E. Olson, Anthony D. Appelhans, Michael J. Van Stipdonk, and Gary. S. Groenewold
The Journal of Physical Chemistry A2003 107 (41), 8530-8538
- Gas-Phase Hydration of U(IV), U(V), and U(VI) Dioxo Monocations
  Garold L. Gresham, Anita K. Gianotto, Peter de B. Harrington, Libo Cao, Jill R. Scott, John E. Olson, Anthony D. Appelhans, Michael J. Van Stipdonk, and Gary. S. Groenewold
  The Journal of Physical Chemistry A2003 107 (41), 8530-8538
  The formation of adduct ions consisting of uranium oxycations and water was studied using an ion trap-secondary ion mass spectrometer. The U(IV) and U(V) species [UO(OH)]+ and [UO2]+ were produced by bombarding the surface of UO3 using molecular primary ...
  Abstract | Full Text HTML | Hi-Res PDF
Resolution of the Non-Steady-State Kinetics of the Two-Step Mechanism for the Diels−Alder Reaction between Anthracene and Tetracyanoethylene in Acetonitrile
Kishan L. Handoo, Yun Lu, and Vernon D. Parker
Journal of the American Chemical Society2003 125 (31), 9381-9387
- Resolution of the Non-Steady-State Kinetics of the Two-Step Mechanism for the Diels−Alder Reaction between Anthracene and Tetracyanoethylene in Acetonitrile
  Kishan L. Handoo, Yun Lu, and Vernon D. Parker
  Journal of the American Chemical Society2003 125 (31), 9381-9387
  The DielsAlder reaction between anthracene and tetracyanoethylene in acetonitrile does not reach a steady-state during the first half-life. The reaction follows the reversible consecutive second-order mechanism accompanied by the formation of a ...
  Abstract | Full Text HTML | Hi-Res PDF
Quantification and Optimization of Dynamic Kinetic Resolution
John Andraos
The Journal of Physical Chemistry A2003 107 (13), 2374-2387
- Quantification and Optimization of Dynamic Kinetic Resolution
  John Andraos
  The Journal of Physical Chemistry A2003 107 (13), 2374-2387
  A complete and exact kinetic analysis of the phenomenon of dynamic kinetic resolution is presented. This analysis is applicable to reactions of stable stereoisomeric substrates whose ratios can be controlled and is valid for any set of kinetic conditions ...
  Abstract | Full Text HTML | Hi-Res PDF