Question

What is the pH of a saturated solution of Mg(OH)${}_2$?
$(K_{sp}$ for $Mg(OH{)}_2=1.8\times {10}^{-11})$

• A. 3.5
• B. 10.1
• C. 10.9
• D. 10.5
• E. 9.2

Answer 1

The correct option is D 10.5

The expression for the solubility product $\left(K_{sp}\right)$ for $Mg(OH{)}_2$ is

$\left(K_{sp}\right)=\left[M{g}^{2+}\right][O{H}^{-}{]}^2=S(2S{)}^2=4S^3$

But $\left(K_{sp}\right)=1.8\times {10}^{-11}$

Substitute values in the above expression.

$1.8\times {10}^{-11}=4S^3$

Hence, $S=1.65\times {10}^{-4}$

$\left[O{H}^{-}\right]=2S=2\times 1.65\times {10}^{-4}=3.3\times {10}^{-4}$

$pOH=-log\left[O{H}^{-}\right]=-log(3.3\times {10}^{-4})=3.5$

$pH=14-pOH=14-3.5=10.5$