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The molar solubility in $m o l . l i t^{- 1}$ of a sparingly soluble salt $M X_{4}$ is S. The corresponding solubility product Ksp is given by the relation.

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$S = (K_{s p} / 128) ¼$

S = (218 $K_{s p}$ )1/4

$S = (256 K_{s p}) 1 / 5$

S = $[\frac{K_{s p}}{256}]^{\frac{1}{5}}$

answer is D.

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Detailed Solution

If S is the solubility of $M X_{4}$ then –

$M X_{4} ⇌ M^{+} + 4 X^{-}$

$K_{s p} = [M^{4 +}] * [X -]^{4}$

$K_{s p} = S * (4 S)^{4}$

$K_{s p} = [\frac{K_{s p}}{256}]^{\frac{1}{5}}$

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