Solubility Product & the Common-Ion Effect (A2)

The solubility product

For a sparingly soluble ionic solid in equilibrium with its saturated solution, the solubility product $K_{sp}$ is the product of the ion concentrations, each raised to the power of its coefficient:

$$\text{A}_x\text{B}_y(s) \rightleftharpoons x\text{A}^{y+}(aq) + y\text{B}^{x-}(aq)$$ $$K_{sp} = [\text{A}^{y+}]^x[\text{B}^{x-}]^y$$

For example, $\text{BaSO}_4$: $K_{sp} = [\text{Ba}^{2+}][\text{SO}_4^{2-}]$; and $\text{Mg(OH)}_2$: $K_{sp} = [\text{Mg}^{2+}][\text{OH}^{-}]^2$. $K_{sp}$ applies only to saturated solutions of sparingly soluble salts and depends only on temperature.