The values of for and are and respectively at . If a mixture of these two is washed with water, what — Ionic Equilibrium Chemistry Question

💡 Solution & Explanation

The simultaneous solubility involves two equilibria sharing the $Ca^{2+}$ ion. Let the solubility of $CaCO_3$ be $x$ and $CaC_2O_4$ be $y$. Then $[Ca^{2+}] = x + y$, $[CO_3^{2-}] = x$, and $[C_2O_4^{2-}] = y$. The $K_{sp}$ equations are $x(x+y) = 4.7 \times 10^{-9}$ and $y(x+y) = 1.3 \times 10^{-9}$. Adding both equations gives $(x+y)^2 = (4.7 + 1.3) \times 10^{-9} = 6.0 \times 10^{-9} = 60 \times 10^{-10}$. Thus, $[Ca^{2+}] = x+y = \sqrt{60 \times 10^{-10}} \approx 7.746 \times 10^{-5} \text{ M}$.