Q. What is the value of $pH$ of saturated solution of $Mg\left(\right.OH\left(\left.\right)_{2}?\left(\right.K_{sp}$ for $Mg\left(\right.OH\left(\left.\right)_{2}$ is $8.9\times 10^{- 12}$ )

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A

$9.4$

B

$11.2$

C

$10.4$

D

$9.8$

Solution:

$Mg\left(\right.OH\left(\left.\right)_{2}\rightleftharpoons\underset{s}{\left(Mg\right)^{2 +}}+\underset{2 s}{2 \left(OH\right)^{-}}$
$4s^{3}=8.9\times 10^{- 12}$
$s=1.3\times 10^{- 4}m$
$\therefore \left[\right.OH\left]\right.=2\times 1.305\times 10^{- 4}$
$pOH=3.58832$
$pH=10.4168$ .

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