Chemistry - Liquid Solution Question with Solution | TestHub

The dissociation of ${\mathrm{CaCO}}_3$ is given by:

${\mathrm{CaCO}}_3(s)\rightleftharpoons {\mathrm{Ca}}^{2+}(aq)+{\mathrm{CO}}_3^{2-}(aq)$

Let the solubility of ${\mathrm{CaCO}}_3$ be $S$. Then the concentrations of the ions are:

$[{\mathrm{Ca}}^{2+}]=S$

$[{\mathrm{CO}}_3^{2-}]=S$

The solubility product $K_{sp}$ is:

$K_{sp}=[{\mathrm{Ca}}^{2+}][{\mathrm{CO}}_3^{2-}]=S\times S=S^2$

Given $S=7\times 10^{-5}\mathrm{mol}{\mathrm{dm}}^{-3}$, substituting this value:

$K_{sp}=(7\times 10^{-5}{)}^2$

$K_{sp}=49\times 10^{-10}=4.9\times 10^{-9}$

Answer: $4.9\times 10^{-9}$