9 - Numerical simulation of chemical kinetics

Summary

Introduction

In most of the examples used in the preceding chapters, a closed-form solution was available to describe the phenomenon considered, and the spreadsheet was used either to visualize the resulting behavior, or to manipulate and analyze consequent, experimental data. However, more often than we care to admit, we can formulate a problem in mathematical terms, but cannot find a corresponding, mathematical solution. That usually leaves us with two options: either simplify the mathematical model until it becomes solvable, or use a computer to find a numerical solution. Neither option is ideal. In simplifying a mathematical model, there is always the risk that one or more important aspects of the problem will be missed. On the other hand, numerical solutions apply only for the specific parameter values used, and the results may therefore be difficult to generalize. Still, more and more problems in science and technology are solved by numerical simulation, including the design of camera lenses, cars, and jet airplanes. In this short chapter we will use the rate expressions of chemical kinetics to illustrate how one can use spreadsheets for the numerical simulation of differential equations.

Much of chemistry involves kinetics. The equilibrium behavior we discussed in chapters 4 and 5 can only be observed because the underlying chemical reactions are sufficiently fast. In other cases, however, the reactions involved may be relatively slow, and their rates can be observed and measured.