2025 H2 Chem P1 Q13 — Solubility Solution

The answer is B (\(1.8 \times 10^{-5}\) mol \(\text{dm}^{-3}\)).
\(\text{Zn(OH)}_2\text{(s)} \rightleftharpoons \text{Zn}^{2+}\text{(aq)} + 2\text{OH}^-\text{(aq)}\)
Let the solubility be \(s\) mol \(\text{dm}^{-3}\): \([\text{Zn}^{2+}] = s\) and \([\text{OH}^-] = 2s\).
\(K_\text{sp} = [\text{Zn}^{2+}][\text{OH}^-]^2 = s(2s)^2 = 4s^3\)
\(s = \sqrt[3]{\dfrac{2.3 \times 10^{-14}}{4}} = 1.79 \times 10^{-5} = 1.8 \times 10^{-5}\) mol \(\text{dm}^{-3}\)
• A is wrong: \(4 \times (1.1 \times 10^{-5})^3 = 5.3 \times 10^{-15}\), not \(2.3 \times 10^{-14}\).
• C is wrong: \(4 \times (2.3 \times 10^{-5})^3 = 4.9 \times 10^{-14}\), not \(2.3 \times 10^{-14}\).
• D is wrong: \(2.8 \times 10^{-5}\) is \(\sqrt[3]{K_\text{sp}}\), which treats \(K_\text{sp}\) as \(s^3\) and ignores the 2 : 1 ratio of \(\text{OH}^-\) to \(\text{Zn}^{2+}\).