Question

Write the equilibrium equation and the \(K_{\mathrm{sp}}\) expression for each of the following. (a) \(\mathrm{AgCl}\) (b) \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}\) (c) \(\mathrm{MnS}_{2}\) (d) \(\mathrm{Mg}(\mathrm{OH})_{2}\)

Short answer

Question: Write the equilibrium equations and the \(K_{\mathrm{sp}}\) expressions for the following compounds: (a) \(\mathrm{AgCl}\) (b) \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}\) (c) \(\mathrm{MnS}_{2}\) (d) \(\mathrm{Mg}(\mathrm{OH})_{2}\) Answer: (a) Equilibrium equation for \(\mathrm{AgCl}\): \(\mathrm{AgCl(s)} \rightleftharpoons \mathrm{Ag^{+}(aq)} + \mathrm{Cl^{-}(aq)}\) \(K_{\mathrm{sp}}\) expression for \(\mathrm{AgCl}\): \(K_{\mathrm{sp}} = [\mathrm{Ag^{+}}][\mathrm{Cl^{-}}]\) (b) Equilibrium equation for \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}\): \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}(s) \rightleftharpoons 2 \,\mathrm{Al^{3+}(aq)} + 3\, \mathrm{CO_{3}^{2-}(aq)}\) \(K_{\mathrm{sp}}\) expression for \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}\): \(K_{\mathrm{sp}} = [\mathrm{Al^{3+}}]^2[\mathrm{CO_{3}^{2-}}]^3\) (c) Equilibrium equation for \(\mathrm{MnS}_{2}\): \(\mathrm{MnS}_{2}(s) \rightleftharpoons \mathrm{Mn^{4+}(aq)} + 2\, \mathrm{S^{2-}(aq)}\) \(K_{\mathrm{sp}}\) expression for \(\mathrm{MnS}_{2}\): \(K_{\mathrm{sp}} = [\mathrm{Mn^{4+}}][\mathrm{S^{2-}}]^2\) (d) Equilibrium equation for \(\mathrm{Mg}(\mathrm{OH})_{2}\): \(\mathrm{Mg}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{Mg^{2+}(aq)} + 2\, \mathrm{OH^{-}(aq)}\) \(K_{\mathrm{sp}}\) expression for \(\mathrm{Mg}(\mathrm{OH})_{2}\): \(K_{\mathrm{sp}} = [\mathrm{Mg^{2+}}][\mathrm{OH^{-}}]^2\)

Step-by-step solution

(a) Equilibrium equation for \(\mathrm{AgCl}\)

For the dissolution of silver chloride, the equilibrium equation can be written as: \(\mathrm{AgCl(s)} \rightleftharpoons \mathrm{Ag^{+}(aq)} + \mathrm{Cl^{-}(aq)}\)

(a) \(K_{\mathrm{sp}}\) expression for \(\mathrm{AgCl}\)

The solubility product constant, \(K_{\mathrm{sp}}\), for this reaction is given by: \(K_{\mathrm{sp}} = [\mathrm{Ag^{+}}][\mathrm{Cl^{-}}]\)

(b) Equilibrium equation for \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}\)

The equilibrium equation for the dissolution of aluminum carbonate is: \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}(s) \rightleftharpoons 2 \,\mathrm{Al^{3+}(aq)} + 3\, \mathrm{CO_{3}^{2-}(aq)}\)

(b) \(K_{\mathrm{sp}}\) expression for \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}\)

The solubility product constant expression, \(K_{\mathrm{sp}}\), for this reaction is given by: \(K_{\mathrm{sp}} = [\mathrm{Al^{3+}}]^2[\mathrm{CO_{3}^{2-}}]^3\)

(c) Equilibrium equation for \(\mathrm{MnS}_{2}\)

The equilibrium equation for the dissolution of manganese(IV) sulfide is: \(\mathrm{MnS}_{2}(s) \rightleftharpoons \mathrm{Mn^{4+}(aq)} + 2\, \mathrm{S^{2-}(aq)}\)

(c) \(K_{\mathrm{sp}}\) expression for \(\mathrm{MnS}_{2}\)

The solubility product constant expression, \(K_{\mathrm{sp}}\), for this reaction is given by: \(K_{\mathrm{sp}} = [\mathrm{Mn^{4+}}][\mathrm{S^{2-}}]^2\)

(d) Equilibrium equation for \(\mathrm{Mg}(\mathrm{OH})_{2}\)

The equilibrium equation for the dissolution of magnesium hydroxide is: \(\mathrm{Mg}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{Mg^{2+}(aq)} + 2\, \mathrm{OH^{-}(aq)}\)

(d) \(K_{\mathrm{sp}}\) expression for \(\mathrm{Mg}(\mathrm{OH})_{2}\)

The solubility product constant expression, \(K_{\mathrm{sp}}\), for this reaction is given by: \(K_{\mathrm{sp}} = [\mathrm{Mg^{2+}}][\mathrm{OH^{-}}]^2\)