Systematic Approach To Calculate the Concentration of Chemical Species in Multi-Equilibrium Problems

When two or more simultaneous reactions take place in an aqueous solution, a system of equations should be solved to calculate the concentration of each chemical species at equilibrium, which is particularly challenging for students with insufficient chemical and mathematical skills. The systematic approach suggested here simplifies this calculation, whatever the number of involved reactions or chemical species. There is no restriction in the type of reaction, only the equilibrium constants should be known. The systematic approach is useful for cases where the pH is unknown or in any other situation where the Ringbom approach, based on the use of conditional constants, cannot be applied. However, in cases involving a large number of reactions where one or more experimental conditions are fixed, it can be convenient to combine previously two or more reactions, using the conditional constant of the main reaction instead. Any powerful minimization algorithm can be used to solve the set of equations. In this work, we demonstrate that the Solver option in the Microsoft Excel spreadsheet, based on the nonlinear least-squares routine on the Levenberg-Marquardt algorithm (15, 16), can yield accurate results. Students with a basic knowledge of chemical reactions, of the calculation of the concentration of species at equilibrium, and of the Solver option of the Excel spreadsheet can carry out easily the entire process from start to finish. The approach allows instructors to highlight the importance of establishing balances in equilibrium problems without the obscuring factor of difficult mathematics. The use of a systematic approach to solve the simultaneous equations that describe the equilibrium conditions is important, ut if students are to understand equilibrium systems, they should be able to make reasonable approximations of the concentrations at equilibrium from starting conditions (e.g., initial concentrations and equilibrium constants). This also helps to provide good seeds to initialize the minimization proc ss in the systematic approach. © 2010 American Chemical Society and Division of Chemical Education, Inc.