Question

The solubility of a saturated solution of calcium fluoride is $2\times {10}^{-4}{\text{mol L}}^{-1}$. Its solubility product $\left({\text{in mol}}^3{\text{L}}^{-3}\right)$ is:

• A. $22\times {10}^{-11}$
• B. $14\times {10}^{-4}$
• C. $2\times {10}^{-2}$
• D. $32\times {10}^{-12}$

Answer 1

The correct option is D $32\times {10}^{-12}$

For $Ca{F}_2$, decomposition is as follows:
$$\begin{array}{cccc}& Ca{F}_2& \to C{a}^{2+}& +2F^{-}\\ & & s& 2s\end{array}$$
$\therefore K_{sp}=\left[C{a}^{2+}\right][F^{-}{]}^2$
$\Rightarrow K_{sp}=s\times (2s{)}^2$
$\Rightarrow K_{sp}=4s^3$
$\Rightarrow K_{sp}=4\times (2\times {10}^{-4}{)}^3$
$\Rightarrow K_{sp}=32\times {10}^{-12}{\text{mol}}^3{\text{L}}^{-3}$