Calcium ion present in water supplies is easily precipitated...

Calcium ion present in water supplies is easily precipitated as calcite $\left(\mathrm{CaCO}_{3}\right)$ : $$ \mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{CaCO}_{3}(s) $$ Because the $K_{\mathrm{sp}}$ decreases with temperature, heating hard water forms a calcite "scale," which clogs pipes and water heaters. Find the solubility of calcite in water (a) at $10^{\circ} \mathrm{C}\left(K_{\mathrm{sp}}=4.4 \times 10^{-9}\right)$ and (b) at $30^{\circ} \mathrm{C}\left(K_{\mathrm{sp}}=3.1 \times 10^{-9}\right)$

Calcium ion present in water supplies is easily precipitated as calcite $\left(\mathrm{CaCO}_{3}\right)$ :
$$
\mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{CaCO}_{3}(s)
$$
Because the $K_{\mathrm{sp}}$ decreases with temperature, heating hard water forms a calcite "scale," which clogs pipes and water heaters. Find the solubility of calcite in water (a) at $10^{\circ} \mathrm{C}\left(K_{\mathrm{sp}}=4.4 \times 10^{-9}\right)$ and (b) at $30^{\circ} \mathrm{C}\left(K_{\mathrm{sp}}=3.1 \times 10^{-9}\right)$

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Key Concepts

Equilibrium Dissolution of Sparingly Soluble Salts

This concept involves the reversible process where a solid salt dissolves into its individual ions in water until a dynamic equilibrium is reached. At equilibrium, the rate of dissolution equals the rate of precipitation. For salts that dissociate in a 1:1 ratio into its ions, the solubility can be directly related to the square root of the Ksp.

Temperature Dependence of Solubility

The solubility product constant (Ksp) is not fixed at all temperatures; it can change with temperature due to the endothermic or exothermic nature of the dissolution process. In some cases, like with calcite, a decrease in Ksp upon heating results in lower solubility, leading to precipitation and scale formation in water systems.

Solubility Product (Ksp)

This constant represents the product of the equilibrium concentrations of the ions produced when a sparingly soluble salt dissolves. It quantifies the extent to which the salt can dissolve in water, with lower Ksp values indicating lower solubility. The equilibrium expression derived from the salt's dissolution is fundamental to calculating the ion concentrations in a saturated solution.

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