Question

The solubility of calcium fluoride in saturated solution, if its solubility product is $3.2 \times {10^{ - 11}}$ is,
1) $2.0 \times {10^{ - 4}}\,{\rm{M}}$
2) $12.0 \times {10^{ - 3}}\,{\rm{M}}$
3) $0.2 \times {10^{ - 4}}\,{\rm{M}}$
4) $2.0 \times {10^{ - 3}}\,{\rm{M}}$

Answer 1

Hint: We know that different salts dissolve to different extent in a solvent. Some salts are highly soluble while the others dissolve to a smaller extent. Solubility product constant $\left( {{K_{sp}}} \right)$ is a constant that helps to compare relative solubilities of different salts.

Complete step by step answer:
Let’s discuss the solubility product constant in detail. It is defined as the product of the concentration of ions of the salt in its saturated solution at a given temperature raised to the power the number of ions produced by the dissociation of one mole of salt.
Now, come to the question. The salt given is calcium fluoride \[\left( {{\rm{Ca}}{{\rm{F}}_{\rm{2}}}} \right)\]. The calcium fluoride is dissociated to calcium ions and fluoride ions. The dissociation reaction is as follows:
$CaF_{2}\rightleftharpoons Ca^{2+}+2F^{-}$
At equilibrium, the concentration of ${\rm{C}}{{\rm{a}}^{{\rm{2 + }}}}$ ion is S and the concentration of ${{\rm{F}}^ - }$ is 2S.
The solubility product expression of the above reaction is,
${K_{sp}} = \left[ {{\rm{C}}{{\rm{a}}^{{\rm{2 + }}}}} \right]{\left[ {{{\rm{F}}^ - }} \right]^2}$
Now, we put the concentration of calcium and fluoride ions.
${K_{sp}} = \left[ {{\rm{C}}{{\rm{a}}^{{\rm{2 + }}}}} \right]{\left[ {{{\rm{F}}^ - }} \right]^2}$
$ \Rightarrow {K_{sp}} = S \times {\left( {2S} \right)^2} = 4{S^3}$
Now, we have to put the given value of ${K_{sp}} = 3.2 \times {10^{ - 11}}$ to the above equation.
$ \Rightarrow 3.2 \times {10^{ - 11}} = 4{S^3}$
$ \Rightarrow S = \sqrt[3]{{0.8 \times {{10}^{ - 11}}}} = 2 \times {10^{ - 4}}\,{\rm{M}}$
Therefore, the solubility of calcium fluoride is $2 \times {10^{ - 4}}\,{\rm{M}}$.

Hence, the correct answer is option (1).

Note: Always remember that the ionic product is different from the solubility product. Solubility product relates to the product of ionic concentration only in the saturated solution of the salt. But the ionic product has a wide range since it is applicable to any type of solutions both saturated and unsaturated. Thus the ionic product represents the product of ionic concentration of ions at any concentration of the salt.