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JAMESP. BIRK Arizona State University Tempe, AZ 85287-1604
Bits and Pieces, 50 Guidelines for Authors of Bits and Pieces appeared in July 1986. Bits and Pieces authors who describe programs will make available listings andlor machine readable versions of their Droerams. Please read each descriotion carefully to determi& compatibility with your own computing environment before reauestiue materials from anv of the authors.
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Computer Simulations of Chemical Kinetics L. Kraig ~teffen'and Patrick L. Holt Trinity University 715 Stadium Drive San Antonio. TX 78212
We have found era~hicallvbased modeline software to be an extremely &e&l tool "for stimulating student interest in chemical kinetics. There are a number of commercial modeling programs available for both the Macintosh and DOS platforms that are suitable for teaching kinetics a t any level. We are currently using Stella I1 (High Performance Systems, Inc.), aMacintosh-based dynamics modeling program, in our physical chemistry and advanced organic chemistry courses. In the classroom, we have used this program to do real-time demonstrations of simple and complex kinetie systems that enable students to observe concentration changes as the reactions develop. Setting up models is straightforward and we have students work through several models on their own. We encourage students to investigate rate phenomena by manipulating rate constants, concentrations, and rate expressions. With little difficulty, students are able to develop kinetic schemes ranging from simple first-order through complex sequences such as chain reactions, explosions, enzyme-substrate reactions. and oscillatine reactions. Bv . exolorine these systems st"dents lcarn a l i t of interestingchemistG and thev have fun doina it. We believe the Interactive visual enGronment enhances students'ability to understand kinetic phenomenon in much the same way that exceptional lecture demonstrations enhance student appreciation for chemical reactivity ( I ) . In the following sections, we describe the Stella environment and give examples of some of the models we have developed in our courses.
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The Stella Environment A Stella model for a simple reaction is depicted in Figure 1. The fundamental unit in the Stella environment is the rectangular icon called a Stock and its attached flow pipes; this unit is used to model the dynamic behavior of an individual species in a reaction. Stocks represent the concentrations of the species involved. The direction of the pipe arrow indicates whether the pipe is inflow or outflow. Circular icons represent constants or expressions. Users enter
'~amilleand Henry Dreyfus Postdoctoral Fellow.
Figure 1. Graphical model of the dimerization of cyclopentadiene, a simple second-orderDielpAider reaction. the rate expression for the appearance or disappearance of a species in the circular icon attached to the appropriate flow pipe. Circular icons may also be used to define mathematical relationships such as the reciprocal of the starting material concentration, and these relationships can arrows then be dotted as a function of time. Sinele-line .. connect related icons. For example, the arrows connecting the niclo~cntadienestock and the circle labeled Rate Constant to ihe Rate of CP Loss circle indicate that the flow rate depends on these two quantities. ARer initializing all icons (initial concentrations are entered in the Stocks),the user may run a simulation of,the reaction system over a suitable time interval. The program integrates rate equations numerically using either Euler's method (2) or RungeKutta techniques (3).Of these two, Euler's method is faster and is the default technique. The program may then be used to plot concentrations of selected species as a function of time. Data may also be tabulated and saved in text format for future use in other applications. Simple Reactions First-order reactions are very simple to model. Reactanffproduct concentration curves, the linear relationship between the natural log of the concentration and time, and the concept of a half-life are all easily demonstrated. A simple second-order reaction, the dimerization of cyclopentadiene, is modeled in Figure 1. The relationships defined correspond to the second-order rate law
A flow control for the rate of dimer formation is needed to account for the 2:1 stoichiometry of reactants and products. Reactant and product concentrations for the reaction simulation are shown in Figure 2. As expected for a secondorder reaction, a plot of ln(cyc1opentadiene)versus time is nonlinear whereas the line for the reciprocal of the starting Volume 70 Number 12 December 1993
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Figure 2. Simulated dimerization of cyclopentadiene. 0 Cyclopentadlene A Dcycopentao ene 0 1 [cpJ- 1 [cp],,..A pot ofme natural og of the cyclopentadlene concenrrarlon 1s non near material concentration versus time is linear. As students run the simulation the 2:l stoichiometry between reactants and products is immediately obvious since the final concentration of product is seen to approach half of the initial starting material concentration. The half-life of the reaction can be shown to be a direct function of the initial concentration. We can easily incorporate increasing complexity, such as the competing reaction of cyclopentadiene with another dieneophile, by adding extra flowcontrollers and rate constants. Steady-State Approximation Frequently students are taught how to use the steadystate a~~roximation with too little consideration eiven to the cor%tions under which it is applicable. conse
