A volume of 250 ml of saturated clear solution of (aq) requires 6.0 ml of in acid medium for complet — Ionic Equilibrium Chemistry Question
Question
A volume of 250 ml of saturated clear solution of $\text{CaC}_2\text{O}_4$(aq) requires 6.0 ml of $0.001 \text{ M} - \text{KMnO}_4$ in acid medium for complete oxidation of $\text{C}_2\text{O}_4^{2-}$ ions. What is $K_{sp}$ of $\text{CaC}_2\text{O}_4$?
💡 Solution & Explanation
In the redox titration, the n-factor for $\text{KMnO}_4$ is 5 and for $\text{C}_2\text{O}_4^{2-}$ is 2. Equating equivalents: $n(\text{C}_2\text{O}_4^{2-}) \times 2 = n(\text{KMnO}_4) \times 5$. The moles of $\text{KMnO}_4$ used = $6.0 \times 10^{-3} \text{ L} \times 0.001 \text{ M} = 6.0 \times 10^{-6} \text{ moles}$. Therefore, $n(\text{C}_2\text{O}_4^{2-}) = \frac{5}{2} \times 6.0 \times 10^{-6} = 1.5 \times 10^{-5} \text{ moles}$. The concentration in 250 ml (0.25 L) is $[\text{C}_2\text{O}_4^{2-}] = \frac{1.5 \times 10^{-5}}{0.25} = 6.0 \times 10^{-5} \text{ M}$. In a saturated solution of $\text{CaC}_2\text{O}_4$, $[\text{Ca}^{2+}] = [\text{C}_2\text{O}_4^{2-}] = 6.0 \times 10^{-5} \text{ M}$. Thus, $K_{sp} = (6.0 \times 10^{-5})^2 = 36 \times 10^{-10} = 3.6 \times 10^{-9}$. Therefore, correct answer is A.