Question
At what pH, is the solubility of Zn(OH)2 minimum? What is the minimum solubility?
Zn(OH)2(s) $\rightleftharpoons$ Zn2+ (aq) + 2OH– (aq); Ksp = 1.2 × 10–17
Zn(OH)2(s) + 2OH– (aq) $\rightleftharpoons$Zn(OH)42− (aq); Kf = 0.12
Options
Solution
$s = \left\lbrack Zn^{2 +} \right\rbrack + Zn(OH)_{4}^{-} = \frac{K_{sp}}{\left\lbrack OH^{-} \right\rbrack^{2}} + K_{f}\left\lbrack OH^{-} \right\rbrack^{2}$
For maximum or minimum S, $\frac{dS}{d\left\lbrack OH^{-} \right\rbrack} = 0$
Or, $\frac{- 2K_{sp}}{\left\lbrack OH^{-} \right\rbrack^{3}} + 2K_{f}\left\lbrack OH^{-} \right\rbrack = 0$
$\Rightarrow \left\lbrack OH^{-} \right\rbrack = \left( \frac{K_{sp}}{K_{f}} \right)^{1/4} = 10^{- 4}\text{ M}$
$\therefore P^{H} = 10\text{ and }{\text{S} - 9\text{ M}}_{\min}$
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