Question

Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids. a. \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) b. \(\mathrm{Al}(\mathrm{OH})_{3}\) c. \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Short answer

a. Dissolution reaction: \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(\mathrm{s}) \rightleftharpoons \mathrm{Ag}^{+}(\mathrm{aq}) + \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}(\mathrm{aq})\); \(K_{sp} = [\mathrm{Ag}^{+}][\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}]\) b. Dissolution reaction: \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Al}^{3+}(\mathrm{aq}) + 3\mathrm{OH}^{-}(\mathrm{aq})\); \(K_{sp} = [\mathrm{Al}^{3+}][\mathrm{OH}^{-}]^{3}\) c. Dissolution reaction: \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{s}) \rightleftharpoons 3\mathrm{Ca}^{2+}(\mathrm{aq}) + 2\mathrm{PO}_{4}^{3-}(\mathrm{aq})\); \(K_{sp} = [\mathrm{Ca}^{2+}]^{3}[\mathrm{PO}_{4}^{3-}]^{2}\)

Step-by-step solution

Write the balanced dissolution reaction

For each solid, write down the balanced dissolution reaction. This involves breaking up the solid into its constituent ions. a. For \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(\mathrm{s}) \rightleftharpoons \mathrm{Ag}^{+}(\mathrm{aq}) + \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}(\mathrm{aq})\) b. For \(\mathrm{Al}(\mathrm{OH})_{3}\), \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Al}^{3+}(\mathrm{aq}) + 3\mathrm{OH}^{-}(\mathrm{aq})\) c. For \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\), \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{s}) \rightleftharpoons 3\mathrm{Ca}^{2+}(\mathrm{aq}) + 2\mathrm{PO}_{4}^{3-}(\mathrm{aq})\)

Write the solubility product expressions

For each balanced dissolution reaction, write the solubility product expression, \(K_{sp}\), as the product of the concentration of its constituent ions raised to their respective stoichiometric coefficients in the balanced dissolution reaction. a. For \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), \(K_{sp} = [\mathrm{Ag}^{+}][\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}]\) b. For \(\mathrm{Al}(\mathrm{OH})_{3}\), \(K_{sp} = [\mathrm{Al}^{3+}][\mathrm{OH}^{-}]^{3}\) c. For \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\), \(K_{sp} = [\mathrm{Ca}^{2+}]^{3}[\mathrm{PO}_{4}^{3-}]^{2}\) These expressions represent the solubility product constants for the given solids. Each term shows the product of concentrations of the ions in the dissolution reaction raised to their stoichiometric coefficients, which can be used to quantify the solubility of these solids in water.