The values of $K_{sp}$ of two sparingly soluble salts $Ni(OH)_2$ and $AgCN$ are $2.0 \times 10^{-15}$ and $6 \times 10^{-17}$ respectively. Which salt is more soluble? Explain.
(N/A) For $AgCN$: $AgCN \rightleftharpoons Ag^{+} + CN^{-}$. Let solubility be $S_1$. $K_{sp} = S_1^2 = 6 \times 10^{-17}$. Thus,$S_1 = \sqrt{6 \times 10^{-17}} \approx 7.75 \times 10^{-9} \ M$.
For $Ni(OH)_2$: $Ni(OH)_2 \rightleftharpoons Ni^{2+} + 2OH^{-}$. Let solubility be $S_2$. $K_{sp} = (S_2)(2S_2)^2 = 4S_2^3 = 2.0 \times 10^{-15}$.
$S_2^3 = 0.5 \times 10^{-15} = 5 \times 10^{-16}$.
$S_2 = \sqrt[3]{5 \times 10^{-16}} \approx 7.94 \times 10^{-6} \ M$.
Comparing $S_1$ and $S_2$,$S_2 > S_1$,therefore $Ni(OH)_2$ is more soluble.
For $Ni(OH)_2$: $Ni(OH)_2 \rightleftharpoons Ni^{2+} + 2OH^{-}$. Let solubility be $S_2$. $K_{sp} = (S_2)(2S_2)^2 = 4S_2^3 = 2.0 \times 10^{-15}$.
$S_2^3 = 0.5 \times 10^{-15} = 5 \times 10^{-16}$.
$S_2 = \sqrt[3]{5 \times 10^{-16}} \approx 7.94 \times 10^{-6} \ M$.
Comparing $S_1$ and $S_2$,$S_2 > S_1$,therefore $Ni(OH)_2$ is more soluble.
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