Example. The solubility product for aluminum hydroxide, AI(OH)₃, is K_sp = 5 X 10^-33. What is the solubility of aluminum hydroxide in pure water, in moles liter^-1?

Solution. Let the solubility be x. The dissociation reaction is

and the solubility-product expression is

The two ion concentrations will be

Hence we can write

Solubility-product calculations rarely are worth carrying beyond one or two significant figures, because of inaccuracies in K_sp. They also are accurate mainly for dilute solutions, since the equilibrium-constant expressions contain hidden assumptions that the ions in solution do not interact with one another, and that their behavior depends only on how many of them there are.

POSTSCRIPT: ACID-BASE CATALYSIS

One of the reasons given at the beginning of this chapter for an interest in acids and bases was their widespread use as catalysts for chemical reactions. We distinguish between heterogeneous catalysis, in which the substrate molecules diffuse to a catalytic surface, and homogeneous catalysis, in which the catalysts are ions dissolved in the same solution as the reactants. H⁺ and OH^- are among the best of the homogeneous catalysts.

When rates of reaction began to be studied carefully at the end of the last century, one of the most studied reactions was the hydrolysis (literally "cleaving by water") of ethyl acetate into ethanol and acetic acid:

This is typical of many other hydrolysis reactions, including the dissolving of fats in soapmaking, and the digestion of proteins. It received a lot of attention because its equilibrium constant is close to 1.00, making the accurate measurement of concentrations of reactants and products at equilibrium easy. Another attraction is the dramatic effect that is produced on this reaction by catalysts.