In the Classroom edited by
Overhead Projector Demonstrations
Doris K. Kolb Bradley University Peoria, IL 61625
Simulating Dynamic Equilibria A Class Experiment John A. Harrison Institute of Fundamental Sciences, Massey University, Albany, Auckland, New Zealand
Paul D. Buckley* Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand;
[email protected] Conceptual misunderstanding about dynamic equilibria often remains even when the mathematical skills associated with equilibrium calculations appear to have been mastered (1). Many analogues and simulations to aid in understanding the concept of equilibrium have been suggested (2–18). We have found the following transparent simulation a particularly useful device for introducing dynamic equilibria. The reaction scheme for a first-order reversible reaction is shown to the class on an overhead projector transparency: 1 min−1 2
A
1 min−1 4
B
The students are told that the constants (identified as rate constants if appropriate for the class) shown above and below the arrows will be used to calculate the number of reactants going to products and vice versa at the end of each minute. Twenty-four small coins (we have also successfully used 24 students in front of the class) are placed below A on the overhead projector transparency and none below B, representing the initial concentrations (set as usual by the person doing the experiment). At the end of each minute, half the reactants are converted to products and one quarter of the products are converted back to reactants. A table of the kinetic data recorded in jumps of one minute is drawn up on the board with help from the class as the reaction proceeds (Table 1). Note how at the end of the second minute, since neither 9 nor 15 divides to give a whole number and since the coins cannot be split, an approximation must be made. It is
Table 1. Time Course from Simulation of a Reversible FirstOrder Reaction in Which at the End of Ever y Minute 1/2 of A Has Been Converted to B and 1/4 of B Has Been Converted Back to A Time/min
[A]
0
24
[B] 0
1
12
12
2
9
15
3
8
16
4
8
16
5
8
16
important not to spend much time in class resolving this issue. With larger numbers of molecules the need to approximate does not arise. One straightforward method is simply to ignore any remainder left after division (i.e., round down to give a whole number). Thus in this simulation at the end of the second minute, four A molecules are converted to B molecules while three B molecules are converted to A molecules. This method will work for all simulations described in this paper. The question of what is happening from the third minute onward must then be addressed by the class. The concept of a dynamic equilibrium is dramatically illustrated by this simple simulation. It can be pointed out that provided nothing else is changed, we must continue shifting four objects from left to right and four from right to left each minute until the end of the universe if we wish to simulate a real equilibrium. All sorts of extensions are obvious and have proven fruitful. The data can be plotted as a function of time and the shapes of the graphs discussed and compared to those shown in the opening pages of the chapter on equilibria in any general chemistry text. To determine the effect of changing the initial concentration on the amounts of A and B present at equilibrium, another simulation can be carried out beginning with 48 A and 0 B, to give at equilibrium 16 A and 32 B. The reason why at equilibrium the concentration ratio is the same despite the different initial conditions can be discussed, and this leads to the concept of the equilibrium constant. The effect of perturbing a system initially at equilibrium (Le Châtelier’s principle) can also be simulated. For example, begin at the equilibrium position arrived at in Table 1 and perturb the system by adding a further 6 A coins to the lefthand side. As the new equilibrium position is approached there is a net conversion of A into B as predicted by Le Châtelier’s principle. The simulation will also show that the equilibrium concentration of A at the end is still higher than before the addition of the extra 6 A coins. Some students also notice that the time taken to reach equilibrium is about the same regardless of the initial concentration, and the role of the (rate) constants can be explored. The question of what would happen if the temperature is changed can also be raised. Of course the same simulation can be performed equally well using a calculator or on a spreadsheet (19). This would allow any students unsatisfied with the approximation made during the simulation, because of the small number of indivisible coins that are used, to further explore this idea without approximating.
JChemEd.chem.wisc.edu • Vol. 77 No. 8 August 2000 • Journal of Chemical Education
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In the Classroom
Literature Cited 1. Bergquist, W.; Heikkinen, H. J. Chem. Educ. 1990, 67, 1000–1003. 2. Sorum, C. H. J. Chem. Educ. 1948, 25, 489. 3. Hambly, G. F. J. Chem. Educ. 1975, 52, 519. 4. Battino, R. J. Chem. Educ. 1975, 52, 55. 5. Martin, D. F.; Lothrop, K. L. J. Chem. Educ. 1976, 53, 634. 6. Hernandez, M. L.; Alvarino, J. M. J. Chem. Educ. 1983, 60, 930–932. 7. Schilling, J. W. J. Chem. Educ. 1983, 60, 43–44. 8. Kac, M.; Rota, G.-C.; Schwartz, J. T. In Discrete Thoughts. Essays on Mathematics, Science and Philosophy; Newman, H., Ed.; Birkhauser: Boston, 1985; p 42.
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9. Olney, D. J. J. Chem. Educ. 1988, 65, 696–697. 10. Russell, J. M. J. Chem. Educ. 1988, 65, 871–872. 11. Kac, M. Enigmas of Chance; University of California, Berkeley, 1985; p 117. 12. Cullen, J. F. Jr. J. Chem. Educ. 1989, 66, 1023–1025. 13. Laurita, W.; Grotz, L. C. J. Chem. Educ. 1990, 67, 598. 14. Dickinson, P. D.; Erhardt, W. J. Chem. Educ. 1991, 68, 930–931. 15. Chang, A.; Larsen, R D. J. Chem. Educ. 1991, 68, 297–300. 16. Sawyer, D. J.; Martens, T. E. J. Chem. Educ. 1992, 69, 551– 553. 17. Garritz, A. J. Chem Educ. 1997, 74, 544–545. 18. Wilson, A. H. J. Chem. Educ. 1998, 75, 1176–1177. 19. Marzzacco, C. J. J. Chem. Educ. 1993, 70, 993–994.
Journal of Chemical Education • Vol. 77 No. 8 August 2000 • JChemEd.chem.wisc.edu
