mg of (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 is ____ mg. (Nearest integer) (Given: is assumed to dissociate completely in ) [2025]

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Solution

Q.
$x$ mg of $M g {(O H)}_{2}$ (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: $M g {(O H)}_{2}$ is assumed to dissociate completely in $H_{2} O$ ) [2025]

Ans.
(3)

$pOH = 14 - pH = 14 - 10 = 4$

$[O H^{-}] = 10^{- pOH} = 10^{- 4} M$

$Moles of hydroxide (n_{O H^{-}}) = [O H^{-}] \times volume$

$= 10^{- 4} M \times 1 L = 10^{- 4} mol$

$Moles of Mg(OH)_{2} (n_{Mg(OH)_{2}}) = \frac{n_{O H^{-}}}{2} = \frac{10^{- 4}}{2} mol$

$Mass of Mg(OH)_{2} = n_{Mg(OH)_{2}} \times M_{Mg(OH)_{2}}$

$= \frac{10^{- 4}}{2} \times 58 = 29 \times 10^{- 4} g = 2.9 mg ≈3 g$

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