Assuming chromium is present as \({\text{C}}{{\text{r}}^{3 + }}\), state an equation for its reaction with hydroxide ions, include state symbols.

State an expression for the solubility product constant, \({K_{{\text{sp}}}}\), for chromium(III) hydroxide.

The solubility product of chromium(III) hydroxide is \(1.00 \times {10^{ - 33}}{\text{ mo}}{{\text{l}}^{\text{4}}}{\text{d}}{{\text{m}}^{ - 12}}\) at 298 K. Calculate the concentration, in \({\text{mol}}\,{\text{d}}{{\text{m}}^{ - 3}}\), of \({\text{C}}{{\text{r}}^{3 + }}\) in the solution, when chromium(III) hydroxide is precipitated.

\({\text{C}}{{\text{r}}^{3 + }}{\text{(aq)}} + {\text{3O}}{{\text{H}}^ - }{\text{(aq)}} \rightleftharpoons {\text{Cr(OH}}{{\text{)}}_3}{\text{(s)}}\)

correct equation;

correct state symbols;

Equilibrium or normal arrows can be used.

\({K_{{\text{sp}}}} = {\text{[C}}{{\text{r}}^{3 + }}{\text{][O}}{{\text{H}}^ - }{{\text{]}}^3}\);

\[1.00 \times {10^{ - 33}} = {\text{[C}}{{\text{r}}^{3 + }}{\text{][O}}{{\text{H}}^ - }{{\text{]}}^{\text{3}}}\] and \({\text{[C}}{{\text{r}}^{3 + }}{\text{]}} = 3 \times {\text{[O}}{{\text{H}}^ - }{\text{]}}\);

\(1.00 \times {10^{ - 33}} = {\text{[C}}{{\text{r}}^{3 + }}{\text{](3[C}}{{\text{r}}^{3 + }}{\text{]}}{{\text{)}}^{\text{3}}} = {\text{ }}27 \times {{\text{[C}}{{\text{r}}^{3 + }}{\text{]}}^{\text{4}}}\)

\({\text{[C}}{{\text{r}}^{3 + }}{\text{]}} = 2.47 \times {10^{ - 9}}{\text{ (mol}}\,{\text{d}}{{\text{m}}^{ - 3}}{\text{)}}\);

Award [2] for correct final answer.

Award [1] for 5.62 \( \times \) 10^–9.

Part (a) was generally done well and the majority of candidates scored 1 or 2 marks here. State symbols were sometimes omitted or incorrect, for example \({\text{C}}{{\text{r}}^{3 + }}{\text{(s)}}\) and \({\text{Cr(OH}}{{\text{)}}_{\text{3}}}{\text{(aq)}}\). Some did not know the formula \({\text{Cr(OH}}{{\text{)}}_{\text{3}}}\) and the coefficient of \({\text{O}}{{\text{H}}^ - }\) (3) was sometimes omitted.

In (b) about half the candidates gave the correct expression for \({K_{{\text{sp}}}}\). Some included the solid in the \({K_{{\text{sp}}}}\) expression and quite a few gave the inverted solubility constant expression; there was a lot of confusion with the \({K_{\text{c}}}\) expression.

In (c) only the best candidates did not have major difficulties calculating the solubility product. Most candidates failed to recognize the \({\text{[O}}{{\text{H}}^ - }{\text{]}}\) is three times that of \({\text{C}}{{\text{r}}^{3 + }}\) when calculating the \({\text{C}}{{\text{r}}^{3 + }}\) concentration.