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Solubility Product

For which of ...

Question

For which of the following sparingly soluble salt, the solubility $(S)$ and solubility product $(K_{s p})$ are related by the expression:
$S = {[\frac{K_{s p}}{4}]}^{\frac{1}{3}}$

B a S O_{4}

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C a_{3} (P O_{4})_{2}

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H g_{2} C l_{2}

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A g_{3} P O_{4}

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Solution

The correct option is C $H g_{2} C l_{2}$
$a) B a S O_{4} ⇌ B a^{2 +} S + S O_{4}^{2 -} S$
$K_{s p} = S^{2} \Rightarrow S = [K_{s p}]^{\frac{1}{2}}$

$b) C a_{3} (P O_{4})_{2} ⇌ 3 C a^{2 +} 3 S + 2 P O_{4}^{3 -} 2 S$
$K_{s p} = (3 S)^{3} \times (2 S)^{2} = 108 S^{5} \Rightarrow S = {[\frac{K_{s p}}{108}]}^{\frac{1}{5}}$

$c) H g_{2} C l_{2} \to H g_{2}^{2 +} S + 2 C l^{-} 2 S K_{s p} = [H g_{2}^{2 +}] [C l^{-}]^{2} = [S] [2 S]^{2} = 4 S^{3} \Rightarrow S = {[\frac{K_{s p}}{4}]}^{\frac{1}{3}}$

$d) A g_{3} P O_{4} ⇌ 3 A g^{+} 3 S + P O_{4}^{3 -} S K_{s p} = (3 S)^{3} (S) = 27 S^{4} \Rightarrow S = {[\frac{K_{s p}}{27}]}^{\frac{1}{4}}$

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