Question

Write the equilibrium equations on which the following \(K_{\mathrm{sp}}\) expressions are based. (a) \(\left[\mathrm{Pb}^{4+}\right]\left[\mathrm{O}^{2-}\right]^{2}\) (b) \(\left[\mathrm{Hg}^{2+}\right]^{3}\left[\mathrm{PO}_{4}^{3-}\right]^{2}\) (c) \(\left[\mathrm{Ni}^{3+}\right]\left[\mathrm{OH}^{-}\right]^{3}\) (d) \(\left[\mathrm{Ag}^{+}\right]^{2}\left[\mathrm{SO}_{4}^{2-}\right]\)

Short answer

Question: Write the equilibrium equations for the given solubility product (\(K_{sp}\)) expressions. (a) \(K_{sp}=\left[\mathrm{Pb}^{4+}\right]\left[\mathrm{O}^{2-}\right]^{2}\) (b) \(K_{sp}=\left[\mathrm{Hg}^{2+}\right]^{3}\left[\mathrm{PO}_{4}^{3-}\right]^{2}\) (c) \(K_{sp}=\left[\mathrm{Ni}^{3+}\right]\left[\mathrm{OH}^{-}\right]^{3}\) (d) \(K_{sp}=\left[\mathrm{Ag}^{+}\right]^{2}\left[\mathrm{SO}_{4}^{2-}\right]\)

Step-by-step solution

(a) Identify the ions and write the dissociation equation of the ionic compound

In this case, the ions are \(\mathrm{Pb}^{4+}\) and \(\mathrm{O}^{2-}\). The corresponding ionic compound is \(\mathrm{PbO}_2\). The dissociation equation is: \(\mathrm{PbO}_2 \xrightleftharpoons[]{} \mathrm{Pb}^{4+} + 2\,\mathrm{O}^{2-}\)

(a) Write the equilibrium equation

The equilibrium equation for the given \(K_{sp}\) expression is: \(K_{sp}=\left[\mathrm{Pb}^{4+}\right]\left[\mathrm{O}^{2-}\right]^{2}\)

(b) Identify the ions and write the dissociation equation of the ionic compound

In this case, the ions are \(\mathrm{Hg}^{2+}\) and \(\mathrm{PO}_{4}^{3-}\). The corresponding ionic compound is \(\mathrm{Hg}_3\left(\mathrm{PO}_4\right)_2\). The dissociation equation is: \(\mathrm{Hg}_3\left(\mathrm{PO}_4\right)_2 \xrightleftharpoons[]{} 3\,\mathrm{Hg}^{2+} + 2\,\mathrm{PO}_{4}^{3-}\)

(b) Write the equilibrium equation

The equilibrium equation for the given \(K_{sp}\) expression is: \(K_{sp}=\left[\mathrm{Hg}^{2+}\right]^{3}\left[\mathrm{PO}_{4}^{3-}\right]^{2}\)

(c) Identify the ions and write the dissociation equation of the ionic compound

In this case, the ions are \(\mathrm{Ni}^{3+}\) and \(\mathrm{OH}^{-}\). The corresponding ionic compound is \(\mathrm{Ni}\left(\mathrm{OH}\right)_3\). The dissociation equation is: \(\mathrm{Ni}\left(\mathrm{OH}\right)_3 \xrightleftharpoons[]{} \mathrm{Ni}^{3+} + 3\,\mathrm{OH}^{-}\)

(c) Write the equilibrium equation

The equilibrium equation for the given \(K_{sp}\) expression is: \(K_{sp}=\left[\mathrm{Ni}^{3+}\right]\left[\mathrm{OH}^{-}\right]^{3}\)

(d) Identify the ions and write the dissociation equation of the ionic compound

In this case, the ions are \(\mathrm{Ag}^{+}\) and \(\mathrm{SO}_{4}^{2-}\). The corresponding ionic compound is \(\mathrm{Ag}_2\mathrm{SO}_4\). The dissociation equation is: \(\mathrm{Ag}_2\mathrm{SO}_4 \xrightleftharpoons[]{} 2\,\mathrm{Ag}^{+} + \mathrm{SO}_{4}^{2-}\)

(d) Write the equilibrium equation

The equilibrium equation for the given \(K_{sp}\) expression is: \(K_{sp}=\left[\mathrm{Ag}^{+}\right]^{2}\left[\mathrm{SO}_{4}^{2-}\right]\)