Question

$Mg(OH)_{2}(s) \rightleftharpoons \underset{SM}{Mg^{2 +}} + \underset{2SM}{2OH^{-}}$

$\text{Now, }K_{sp} = 4S^{3} \Rightarrow S = \left( \frac{9 \times 10^{- 12}}{4} \right)^{1/3}M$

$\text{Now, }\left\lbrack OH^{-} \right\rbrack = 2S = 2 \times \left( \frac{9 \times 10^{- 12}}{4} \right)^{1/3} = \left( 18 \times 10^{- 12} \right)^{1/3}M $$$\therefore P^{OH} = - {\log\left( 18 \times 10^{- 12} \right)}^{1/3} = 3.58 \Rightarrow P^{H} = 10.42$$