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The molar solubility i mol. ${lit}^{- 1}$ of a sparingly soluble salt ${MX}_{4} is S .$ The corresponding solubility product $K_{Sp}$ is given by the relation

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$S = {(K_{Sp} / 128)}^{\frac{1}{4}}$

$S = {(256 K_{Sp})}^{\frac{1}{5}}$

$S = {(218 K_{Sp})}^{\frac{1}{4}}$

$S = {(K_{Sp} / 256)}^{\frac{1}{5}}$

answer is D.

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Detailed Solution

$MX ⇌ M^{+ 4} + 4 X^{-}$

S 4S

$K_{Sp} = S {(4 S)}^{4} = S \times 256 S^{4} = 256 S^{5}$

$\Rightarrow S {(\frac{K_{Sp}}{256})}^{\frac{1}{5}}$

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