x mg of $\mathrm{Mg}(\mathrm{OH})_2($ molar mass $=58)$ is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ________ mg. (Nearest integer)
(Given : $\mathrm{Mg}(\mathrm{OH})_2$ is assumed to dissociate completely in $\mathrm{H}_2 \mathrm{O}$)

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{pH}=10 \ & \mathrm{pOH}=4 \ & {\left[\mathrm{OH}^{-}ight]=10^{-4}} \end{aligned}$ no. of moles of $\mathrm{OH}^{-}=10^{-4}$ no. of moles of $\operatorname{Mg}(\mathrm{OH})_2=\frac{10^{-4}}{2}=5 	imes 10^{-5}$ $\begin{aligned} 	ext {mass of } \mathrm{Mg}(\mathrm{OH})_2 & =5 	imes 10^{-5} 	imes 58 	imes 10^3 \mathrm{mg} \ & =2.9 \end{aligned}$

x mg of $\mathrm{Mg}(\mathrm{OH})_2($ molar mass $=58)$ is required to be dissolved in 1.0 L of water to…

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