For each of the following pairs of solids, determine which solid has the smallest molar solubility. a. \(\mathrm{FeC}_{2} \mathrm{O}_{4}, K_{\mathrm{sp}}=2.1 \times 10^{-7}\), or \(\mathrm{Cu}\left(\mathrm{IO}_{4}\right)_{2}, K_{\mathrm{sp}}=1.4 \times 10^{-7}\) b. \(\mathrm{Ag}_{2} \mathrm{CO}_{3}, K_{<\rho}=8.1 \times 10^{-12}\), or \(\mathrm{Mn}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=2 \times 10^{-13}\)

For each of the two pairs of solids, write balanced dissociation reactions, and their corresponding expressions for the solubility product constant (\(K_{sp}\)). a) For \(\mathrm{FeC}_{2}\mathrm{O}_{4}\): Dissociation reaction: \(\mathrm{FeC}_{2}\mathrm{O}_{4}(s) \leftrightarrows \mathrm{Fe}^{2+}(aq) + 2\mathrm{C}_{2}\mathrm{O}^{2–}_{4}(aq)\) Expression for \(K_{sp}\): \(K_{sp} = [\mathrm{Fe}^{2+}][\mathrm{C}_{2}\mathrm{O}^{2–}_{4}]^2\) For \(\mathrm{Cu}\left(\mathrm{IO}_{4}\right)_{2}\): Dissociation reaction: \(\mathrm{Cu}\left(\mathrm{IO}_{4}\right)_{2}(s) \leftrightarrows \mathrm{Cu}^{2+}(aq) + 2\mathrm{IO}^{–}_{4}(aq)\) Expression for \(K_{sp}\): \(K_{sp} = [\mathrm{Cu}^{2+}][\mathrm{IO}^{–}_{4}]^2\) b) For \(\mathrm{Ag}_{2}\mathrm{CO}_{3}\): Dissociation reaction: \(\mathrm{Ag}_{2}\mathrm{CO}_{3}(s) \leftrightarrows 2\mathrm{Ag}^{+}(aq) + \mathrm{CO}^{2–}_{3}(aq)\) Expression for \(K_{sp}\): \(K_{sp} = [\mathrm{Ag}^{+}]^2[\mathrm{CO}^{2–}_{3}]\) For \(\mathrm{Mn}(\mathrm{OH})_{2}\): Dissociation reaction: \(\mathrm{Mn}(\mathrm{OH})_{2}(s) \leftrightarrows \mathrm{Mn}^{2+}(aq) + 2\mathrm{OH}^{–}(aq)\) Expression for \(K_{sp}\): \(K_{sp} = [\mathrm{Mn}^{2+}][\mathrm{OH}^{–}]^2\)

For each solid, calculate its molar solubility (\(S\)) using the given \(K_{sp}\) values and the expressions for the \(K_{sp}\). a) \(\mathrm{FeC}_{2}\mathrm{O}_{4}\): Let the molar solubility of \(\mathrm{Fe}^{2+}\) and \(\mathrm{C}_{2}\mathrm{O}^{2–}_{4}\) be \(x\) and \(2x\), respectively. \(K_{sp} = 2.1 \times 10^{-7} = x \times (2x)^{2}\) Solve for \(x\) (molar solubility of \(\mathrm{FeC}_{2}\mathrm{O}_{4}\)) \(\mathrm{Cu}\left(\mathrm{IO}_{4}\right)_{2}\): Let the molar solubility of \(\mathrm{Cu}^{2+}\) and \(\mathrm{IO}^{–}_{4}\) be \(x\) and \(2x\), respectively. \(K_{sp} = 1.4 \times 10^{-7} = x \times (2x)^{2}\) Solve for \(x\) (molar solubility of \(\mathrm{Cu}\left(\mathrm{IO}_{4}\right)_{2}\)) b) \(\mathrm{Ag}_{2}\mathrm{CO}_{3}\): Let the molar solubility of \(\mathrm{Ag}^{+}\) and \(\mathrm{CO}^{2–}_{3}\) be \(2x\) and \(x\), respectively. \(K_{sp} = 8.1 \times 10^{-12} = (2x)^{2} \times x\) Solve for \(x\) (molar solubility of \(\mathrm{Ag}_{2}\mathrm{CO}_{3}\)) \(\mathrm{Mn}(\mathrm{OH})_{2}\): Let the molar solubility of \(\mathrm{Mn}^{2+}\) and \(\mathrm{OH}^{–}\) be \(x\) and \(2x\), respectively. \(K_{sp} = 2 \times 10^{-13} = x \times (2x)^{2}\) Solve for \(x\) (molar solubility of \(\mathrm{Mn}(\mathrm{OH})_{2}\))

Compare the molar solubilities calculated in Step 2 to determine which solid in each pair has the smallest molar solubility. a) Comparing the molar solubilities of \(\mathrm{FeC}_{2}\mathrm{O}_{4}\) and \(\mathrm{Cu}\left(\mathrm{IO}_{4}\right)_{2}\), the solid with the smallest molar solubility is ______. b) Comparing the molar solubilities of \(\mathrm{Ag}_{2}\mathrm{CO}_{3}\) and \(\mathrm{Mn}(\mathrm{OH})_{2}\), the solid with the smallest molar solubility is ______.