Solution of Acid-Base Equilibria by Successive Approximations Alejandro C. Olivieri' University of Illinois at Urbana-Champaign, Urbana, IL 61801 When solving equilibrium problems, students are often faced with nonlinear equations or even sets of nonlinear equations for which no analytical solution is possible. As is recognized, they should learn how to deal with this type of problem and should be acquainted with a t least some of the available methods for the numerical solution of nonlinear eauations ( 1 4 ) .I t has been pointed out that the method of ~"ccessive approximations ?also called '.fixed point" or "simple iteration" method) exhibits certain advantagesover other known procedures (5-7).It does not require knowledge of calculus on the student's part, and it uses the equilibrium equation itself rather than an ad hoc one to carry out the iteration that will eventually arrive a t the solution. In spite of this, it does present some limitations. The convergence is slow, the iteration may converge to a chemically unacceptable solution. or mav even diverge from the initial value. When tbeunknown appears in varbusplaces in the equation under studv. there is no simple method for choosing one of them to s t a s a successfully convergent iteration. A perfect iteration scheme would be the one that gives the correct answer quickly and starting with any initial guess. Nonlinear equations may, however, have several different mathematical solutions. but usuallv. onlv. one will be realistic from chemiral conside;ations. It is therefore preferable to use some chemical intuition to find a good "first mess". The nearer this guess is to the correct answer, the greater the chances of finding the latter rapidlv. Students should learn that chemical pr
