Question

The solubility of $B{a_3}{(As{O_4})_2}$ (formula mass = $690$) is $6.9 \times {10^{ - 2}}g{(100mL)^{ - 1}}$ . What is the ${K_{sp}}$?

Answer 1

Hint: Solubility product of an electrolyte at a specified temperature may be defined as the product of the molar concentration of its ions in a saturated solution, each concentration raised to the power equal to the number of ions produced on dissociation of one molecule of the electrolyte.

Complete answer:
The relationship between the solubility$\left( s \right)$in $mol{L^{ - 1}}$ and solubility product $\left( {{K_{sp}}} \right)$ depends upon the nature of the salt.
For $B{a_3}{(As{O_4})_2}$ ;
$B{a_3}{(As{O_4})_2} \to 3B{a^{2 + }} + 2As{O_4}^{3 - }$
$B{a^{2 + }}$ = $3s$ (there are three $B{a^{2 + }}$ions in the formula of the electrolyte)
$As{O_4}^{3 - }$ = $2s$ (there are two $As{O_4}^{3 - }$ ions in the formula of the electrolyte)
${K_{sp}} = {\left( {3s} \right)^3}{\left( {2s} \right)^2}$
= $108{s^5}$
Solubility of $B{a_3}{(As{O_4})_2}$ is ;
$s = \dfrac{{6.9 \times {{10}^{ - 2}}g{{(100mL)}^{ - 1}}}}{{690g{{(mol)}^{ - 1}}}} = {10^{ - 3}}mol{L^{ - 1}}$
Putting the value of solubility we can find solubility product $\left( {{K_{sp}}} \right)$
${K_{sp}} = 108{({10^{ - 3}})^5}$
$ = 108 \times {10^{ - 15}}$
We write this as;
${K_{sp}} = 1.08 \times {10^{ - 13}}$
Thus, the correct option is B.

Additional Information: Both solubility product and ionic product represent the product of the concentrations of the ions in the solution. But these terms also differ from each other. The term ionic product has a broad meaning and is applicable to all types of solutions, may be unsaturated or saturated. On the other hand, the solubility product has restricted meaning since it applies only to a saturated solution in which there exists a dynamic equilibrium between the undissolved salt and the ions present in solution.

Note:
We have seen that the solubility product of a sparingly soluble salt at a particular temperature can be calculated from a knowledge of the solubility of the salt in water at that particular temperature. While calculating, the number of ions in the formula of the electrolyte should be considered otherwise calculations will go wrong.