Question

$K_{sp}$ of $M{\left(OH\right)}_2$ is $5\times {10}^{-16}$ at ${25}^{o}C$. The $pH$ of its saturated solution at ${25}^{o}C$ is ________.

Answer 1

$M(OH{)}_2\to M^{2+}+2O{H}^{-}$

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

$5\times {10}^{-16}=4S^3$

$S=(1.25\times {10}^{-16}{)}^{\frac{1}{3}}$

$S=5\times {10}^{-6}M$

$\left[O{H}^{-}\right]=2S=1\times {10}^{-5}M$

$pOH=-log{10}^{-5}=5$

$pH=14-pOH=14-5=9$