Question

The precipitate of $Ca{{F}_{2}}$ $({{K}_{sp}}=1.7\times {{10}^{-10}})$ is obtained when equal volumes of which of the following are mixed?
A. ${{10}^{-4}}MC{{a}^{^{+2}}}+{{10}^{-4}}M{{F}^{-}}$
B. ${{10}^{-2}}MC{{a}^{+2}}+{{10}^{-3}}M{{F}^{-}}$
C. ${{10}^{-5}}MC{{a}^{+2}}+{{10}^{-5}}M{{F}^{-}}$
D. ${{10}^{-3}}MC{{a}^{+2}}+{{10}^{-5}}M{{F}^{-}}$

Answer 1

Hint: Precipitates are obtained when the ionic product of salt is greater than solubility product.

Complete step-by-step answer:
Overall reaction is:
$Ca{{F}_{2}}\to C{{a}^{2+}}+2{{F}^{-}}$

The precipitates will be obtained when the ionic product of a salt is greater than the solubility product of salt.
The solubility product of $Ca{{F}_{2}}$ is $1.7\times {{10}^{-10}}$. So the ionic product should be greater than this.
Ionic product is calculated by:
$ionic product=[C{{a}^{2+}}]{{[{{F}^{-}}]}^{2}}...........(1)$
On keeping the value of option a ${{10}^{-4}}MC{{a}^{^{+2}}}+{{10}^{-4}}M{{F}^{-}}$ in equation ionic product comes out $1\times {{10}^{-12}}$ which is less than solubility product so the salt of this concentration will not be precipitated.
On keeping the value of option b ${{10}^{-2}}MC{{a}^{+2}}+{{10}^{-3}}M{{F}^{-}}$ in equation ionic product came out $1\times {{10}^{-8}}$ which is more than solubility product therefore salt will precipitate at this concentration.
On keeping the value of option c ${{10}^{-5}}MC{{a}^{+2}}+{{10}^{-5}}M{{F}^{-}}$ in equation ionic product came out $1\times {{10}^{-15}}$ which is less than solubility product so the salt of this concentration will not be precipitated.
On keeping the value of option d ${{10}^{-3}}MC{{a}^{+2}}+{{10}^{-5}}M{{F}^{-}}$ in equation ionic product came out $1\times {{10}^{-13}}$ which is less than solubility product so the salt of this concentration will not be precipitated.
Thus option b i.e. ${{10}^{-2}}MC{{a}^{+2}}+{{10}^{-3}}M{{F}^{-}}$ ionic product of salt is greater than solubility product. The correct option is B.

Note: Precipitation happens when solubility product is less than ionic product. Solubility is the characteristic of solute to dissolve in solvent which is denoted by ${{K}_{sp}}$ and ionic product is product of ions raised to their respective powers. So, in order to dissolve a solute in solvent, the ionic product should be greater than the solubility product. Ideally if the concentration of both the elements is same in compound then its solubility product is more than ionic product.