At \(25^{\circ} \mathrm{C}\), the solubility in water of the moderately soluble salt silver acetate, \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) is \(10.6 \mathrm{~g} / \mathrm{L}\). (a) Write the chemical equation for the dissolving of silver acetate in water. (b) Write the \(K_{\mathrm{sp}}\) expression for silver acetate. (c) Calculate the value of \(K_{\mathrm{sp}}\) (show your work).

The balanced chemical equation for the dissolving of silver acetate in water can be written as: \( \mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2(s)} \rightleftharpoons \mathrm{Ag}^{+}_{(aq)} + \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2^{-}}_{(aq)} \) The given reaction shows that silver acetate dissociates into silver ions (Ag+) and acetate ions (C2H3O2-) in water.

The solubility product constant (Ksp) expression for silver acetate can be written as: \( K_{\mathrm{sp}} = [\mathrm{Ag}^{+}][\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2^{-}}] \) Ksp represents the equilibrium constant for the solubility of a slightly soluble ionic compound in water, and it depends only on the concentrations of the ions at equilibrium.

To calculate the value of Ksp, we need the equilibrium concentrations of Ag+ and C2H3O2-. We are given the solubility of silver acetate in water, which is equal to 10.6 g/L. We can use this information to calculate the molar solubility and then the equilibrium concentrations of the ions. 1) Find the molar mass of silver acetate: \( \mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \) = 107.87 (Ag) + 2(12.01) (C) + 3(1.01) (H) + 2(16.00) (O) = 166.92 g/mol 2) Convert the solubility from g/L to mol/L (molar solubility): \( 10.6 \mathrm{g/L} \cdot \frac{1 \mathrm{mol}}{166.92\mathrm{g}} = 0.0634\mathrm{mol/L}\) 3) Since the stoichiometric coefficients are 1:1 in the balanced chemical equation, the equilibrium concentrations of Ag+ and C2H3O2- are equal to the molar solubility: [\(\mathrm{Ag}^+\)] = [\(\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{O}_{2^{-}}\)] = 0.0634 mol/L 4) Calculate the Ksp value using the Ksp expression: \( K_{\mathrm{sp}} = (0.0634) (0.0634) = 4.02 \times 10^{-3}\) The value of Ksp for silver acetate is 4.02 x 10⁻³.