$(20$ pts$)$ Calculate the solubility $(m\frac{g}{m}L)$ of $Mg(OH{)}_2$ in a buffer solution that is $0\mathrm{.}75MN{H}_3$ and $0\mathrm{.}50MN{H}_{4}Cl.$

$K_{sp}$ of $Mg(OH{)}_2$ is $5\mathrm{.}61{10}^{-12}$

$K_b$ of $N{H}_3$ is $1\mathrm{.}8{10}^{-5}$

Molar mass of $Mg(OH{)}_2$ is $58\mathrm{.}3197\frac{g}{m}ol$

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