pH of saturated aqueous solution of $B a {(O H)}_{2}$ is 12. Identify the correct statement.

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The solubility product of $B a {(O H)}_{2}$ is $5 \times 10^{- 7} M^{3}$

The solubility of $B a {(O H)}_{2}$ in a buffer solution of $p H = 1 i s 5 \times 10^{- 5} m o l e s / L$

The solubility of $B a {(O H)}_{2}$ in a buffer solution of $p H = 13 i s 5 \times 10^{- 5} m o l e s / L$

The solubility of $B a {(O H)}_{2}$ decreases in presence of $N H_{4} C l$

answer is A, D.

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Detailed Solution

Since $p H = 12$
$∴ p O H = 14 - 12 = 2 [O H^{-}] = 10^{- 2} M$
We know $B a {(O H)}_{2} ⇌ B a^{+ +} + 2 O H^{-}$
$∴ [B a^{+ +}] = \frac{10^{- 2}}{2} M ∴ K_{S P} = [B a^{+ +}] {[O H^{-}]}^{2} = (\frac{10^{- 2}}{2}) \times {(10^{- 2})}^{2} = 5 \times 10^{- 7} M^{3}$