The problem of integrating the rate equations is often overcome by the use of approximations. The steady-state approximation assumes that the concentration of B remains constant; this assumption leads to analytical solutions to the rate equations. How good this approximation is can be analyzed by a variety of programs (1–7). In general, however, these programs have to be downloaded, sometimes compiled, and then installed, a process that is inconvenient for a large class of students and impractical for students who want to study on their own computers.

An alternative approach to solving the rate equations is to use the pre-equilibrium approximation, that is, A and B are always present in their equilibrium ratios, equivalent to assuming that k₂ is much slower than both k₁ and k_-1.

A Java applet is presented here that allows students to make interactive analyses of reactions of this type and to assess the reliability of the steady-state and equilibrium approximations for themselves. This applet allows students to compare the results of these approximations, and also to investigate the results of applying thermodynamic and kinetic controls. The Java applet has these advantages: it needs no installation (provided a Web browser is available), it is very compact (less than 7 KB) and thus downloads quickly, and the Java applet runs on a variety of different computers.

Figure 1. A view of the applet with the settings k₁ = 1.1, k_-1 = 1.0, and
k₂ = 0.1; [A₀] = 1.0. [B₀] = [C₀] = 0.

Literature Cited

1. Pavlis, R. R. J. Chem. Educ. 1997, 74, 1139.
2. Viossat, V.; Ben-Aim, R. I. J. Chem. Educ. 1993, 70, 732.
3. Miller. S. I. J. Chem. Educ. 1985, 62, 490.
4. Tardy, D. C.; Cater, E. D. J. Chem. Educ. 1983, 60, 109.
5. Volk, L.; Richardson, W.; Lau, K. H.; Hall, M.; Lin, S. H. J. Chem. Educ. 1977, 54, 95.
6. Pyun, C. W. J. Chem. Educ. 1971, 48, 194.
7. DeTar, D. F. J. Chem. Educ. 1967, 44, 193.