Simulation of First-Order Kinetic Mechanisms S. W. Orchard and M. 0 . Mooiman
University of the Witwatersrand Johannesburg, 2001. South Africa We have developed two programs for the APPLE I1 PLUS microcomputer that are designed to serve as learning aids for students taking a first course in kinetics. The program KINDES serves only to explain the operation of the primary program, KINCALC, to new users. KINCALC simulates the kinetic behavior of the system k
~
A-B-C I*.*
tk
on APPLE I1 PLUS (48K). Documentation includes listing, flowchart, student notes and reproduction of CRT display of sample output. Documentation $2.50; documentation with program on APPLE I1 floppy disk, $15 (we provide disk). Send correspondence to Dr. S. W. Orchard, Chemistry Department, University of the Witwatersrand, Jan Smuts Avenue, to ChemJohanneshure 2001. South Africa. Checks oavahle . . istry Department. We thank Professor L. Glasser for valuable advice and the National Institute for Metallurgy for a bursary to M.B.M.
q
tic,,
for anv selected values of the four rate constants and initial concentrations of reactants. The program carries out simple machine integration of the differential rate equations for A, B, and C, and provides output on the monitor screen in the form of plots of the reactant concentrations versus time. The plots are carried out during the course of the calculation, so that the student has the benefit of actually seeing the timedevelopment of the system, rather than being presented with the end result (21 ). Although this four-reaction system may a t first sight seem to be rather restrictive, it is in fact capable of simulating a surprising number of first- and pseudo first-order kinetic systems, including irreversible, reversible, competing, and consecutive reactions: comoosite radioactive decav of two nuclides, low pressure fall-;ff in the rate constant 6r a unimolecular reaction and enzvme kinetics follow in^.the Michaelis-Menten mechanism. The calculation requires values for various parameters, including the rate constants, starting concentrations, time scale and scale expansion factors for the reagent concentrations. These are initialized by the program itself and the operator may then alter them as required before the calculation and plot commence. The operator may also test the effect of changing any of the variables by electing to superimpose the plots on those of the previous run. We have written a set of student notes that give suggestions for carrying out simulation runs to illustrate the various types of hehavior. While students should in many cases be able to decide for themselves what rate constants and other parameters are appropriate, in certain instances, such as the illustration of unimolecular fall-off, they require fairly detailed instructions. In the illustrations presented here the labeling has been
Figure 1 The approach to e q u i b r u m of the system A 7B - C (All rate j', y-axs is concentraton: x-axs s time Full scale an constants = 5 X 10 time axis is 10's) The labels A, 8. and C have been added by hand. The computation and plot take about 35 sec to complete in this case.
>
-- --
C A to 'equilibrium." Figure 2. The approach of the system A * B shown during the development of the screen display. (Rate constants and axes as in Fig. 1.)
- - -
B C A, which approaches cyclic ;ystem (22) A "equilibrium" in an oscillatory fashion. (A minor editing step, explained in the student notes, is required for the latter simulation.) Figure 3 is designed to illustrate the value of transient measurements as opposed to steady-state measurements in
to the steadv-state is sensitive to the values of kan ..- and k ~ n . as illustrated (23). We have also written a similar vroeram for the HP9810Al . 9862A calculator-plotter combination, hut for instructional ourooses the APPLE proeram, being more interactive and
Figure 3.
Translent behavior of the system A
-B
C, starting with pure A.
For clarity. A has been omitted from the plot. The different behavior of jB1 in the transient region is cleariy illustrated. (Upper curves (Band C): k,. = k,, = lo3 Lower curves (5' and C): k,, = k,, = 5 X l o 2 s-'; ke = 10 s-' for all curves: full scale on time axis is 5 X 10@ s.) SF':
Volume 58 Number 5
May 1981
409
