Question

The solubility constant ${{K}_{sp}}$ of $Mg{{(OH)}_{2}}$ is $9.0\text{ x 1}{{\text{0}}^{-12}}$. If a solution is 0.010 with respect to $M{{g}^{2+}}$ ion, what is the maximum hydroxide ion concentration which could be present without causing precipitation of $Mg{{(OH)}_{2}}$ ?

Answer 1

Hint: Write the solubility product reaction for $Mg{{(OH)}_{2}}$. Now write the reaction constant at equilibrium. The solubility constant is given to us as well as the concentration of $M{{g}^{2+}}$. Substitute both these values in the reaction constant at equilibrium to obtain the concentration of hydroxide ions.

Complete step-by-step answer:
Solubility is defined as the property of a substance (solute) to get dissolved in a solvent in order to form a solution.
The solubility product constant is the equilibrium constant for the dissolution of a solid solute in a solvent to form a solution. It is denoted by the symbol ${{K}_{sp}}$. We can form an idea about the dissolution of an ionic compound by the value of its solubility product.
The concentration of $\text{M}{{\text{g}}^{\text{2+}}}$ = 0.010 M
Reaction:
$\text{Mg(OH}{{\text{)}}_{\text{2}}}\text{ }\to \text{ M}{{\text{g}}^{\text{2+}}}\text{ + 2O}{{\text{H}}^{-}}$
${{\text{K}}_{\text{sp}}}\text{= }\!\![\!\!\text{ M}{{\text{g}}^{\text{2+}}}\text{ }\!\!]\!\!\text{ }\!\![\!\!\text{ O}{{\text{H}}^{-}}{{\text{ }\!\!]\!\!\text{ }}^{\text{2}}}$
$\text{ }\!\![\!\!\text{ O}{{\text{H}}^{-}}\text{ }\!\!]\!\!\text{ = }\sqrt{\dfrac{\text{9}\text{.0 x 1}{{\text{0}}^{\text{-12}}}}{\text{0}\text{.010}}}$
$[\text{O}{{\text{H}}^{-}}]\text{ = 3 x 1}{{\text{0}}^{-5}}$
The concentration of hydride ions is $3\text{ x 1}{{\text{0}}^{-5}}$.

Therefore, the correct answer is option (D).


Note: The common ion effect describes the effect of adding a common ion on the ​equilibrium of the new solution. The common ion effect generally decreases ​solubility of a solute. The equilibrium shifts to the left to relieve off the excess product formed.
When a strong electrolyte is added to a solution of weak electrolyte, the solubility of weak electrolyte decreases leading to the formation of precipitate at the bottom of the testing apparatus.