(a) True or false: “solubility” and “solubility-product constant” are the same number for a given compound. (b) Write the expression for the solubility- product constant for each of the following ionic compounds: MnCO \(_{3}, \mathrm{Hg}(\mathrm{OH})_{2},\) and \(\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2} .\)

For a given compound, solubility and solubility-product constant are not the same. Solubility is a measure of the maximum amount of solute that can dissolve in a solvent at a given temperature and pressure, whereas solubility-product constant (Ksp) is the equilibrium constant for the solubility equilibrium of a slightly soluble compound. The Ksp gives us an idea about the extent of how much of the solid will dissolve in the solution at equilibrium, but it is not the same quantity as solubility. Therefore, the statement is false.

To obtain the expressions for the solubility-product constant for each of the given ionic compounds, identify the ions formed when each compound dissolves in water and express the equilibrium in terms of the ion concentrations. 1. For MnCO\(_3\): The dissociation equilibrium can be represented as: MnCO\(_3\)(s) \( \rightleftharpoons \) Mn\(^{2+}\)(aq) + CO\(_3^{2-}\)(aq) The expression for Ksp is then: Ksp = [Mn\(^{2+}\)][CO\(_3^{2-}\)] 2. For Hg(OH)\(_2\): The dissociation equilibrium can be represented as: Hg(OH)\(_2\)(s) \( \rightleftharpoons \) Hg\(^{2+}\)(aq) + 2OH\(^{-}\)(aq) The expression for Ksp is then: Ksp = [Hg\(^{2+}\)][OH\(^{-}\)]\({^2}\) 3. For Cu\(_3\)(PO\(_4\))\(_2\): The dissociation equilibrium can be represented as: Cu\(_3\)(PO\(_4\))\(_2\)(s) \( \rightleftharpoons \) 3Cu\(^{2+}\)(aq) + 2PO\(_4^{3-}\)(aq) The expression for Ksp is then: Ksp = [Cu\(^{2+}\)]\({^3}\)[PO\(_4^{3-}\)]\({^2}\)