Chemical Equilibria: Systematic Approach to Equilibrium Calculations

Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.

The first step is to identify all the chemical reactions involved, The next is to formulate their corresponding equilibrium constant expressions. The third step is to write the equilibrium mass balance equations, which are based on the law of conservation of mass. These equations relate the total amount of a species in the solution in different forms (equilibrium concentration of the species) to the total amount of that species initially added to the solution (analytical concentration of the species). There may be more than one mass-balance equation for a given set of equilibria. Furthermore, for equilibria with charged species, a charge balance equation is required based on the principle of electroneutrality, which states that the total charge concentration of the positively charged species in the solution must equal that of the negatively charged species. For a given set of equilibria, only one charge-balance equation can be written. After mass-balance and charge-balance equations are written, the number of independent equations obtained is counted. If it equals or exceeds the number of unknowns involved in the equilibria, the equations can be solved for the unknowns. After solving for the unknowns, the validity of the approximations needs to be checked because approximations of the relative concentrations of species are often introduced in the mass-balance equations or charge-balance equations to simplify the calculations.