## Solving Equilibrium Problems with a Graphing Calculator: A Robust Method, Free of Algebra and Calculus

**David K. Ruch(*) and Thomas G. Chasteen(#)**

Department of Mathematics(*) and Department of Chemistry(#), Sam Houston State University, Huntsville, Texas USA

## Journal of Chemical Education, 1993, Vol. 70(7), pages A184-185.

## Abstract

Solving equilibrium problems in chemistry involves solving mathematical equations, frequently of an intimidating nature. Because many of these equations are extremely difficult to solve using purely algebraic methods, other approaches are used. For example the method of successive approximations (MSA) is frequently introduced in freshman chemistry as a means of solving these equations. Although MSA is a powerful technique, it will not work in some problems, and the reasons for why it works requires some calculus background. An alternative approach is to solve the problem graphically. This paper describes a method for solving an equation of the form *f* (x) = 0 by simply graphing y = *f* (x). The intersection point of the curve y = *f* (x) and the x axis gives the solution to the problem. The procedure described is easy to carry out on a graphing calculator or spreadsheet, and students quickly become proficient. An example using a complex K_{sp} problem is presented.