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If solubility product of $A l C l_{3}$ is denoted by $" K_{S P} "$ and it's Molar solubility is denoted by $S,$ then which of the following relation between $S$ and $K_{S P}$ is correct

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$S = {(\frac{K_{S P}}{27})}^{1 / 4}$

$S = {(\frac{K_{S P}}{2})}^{1 / 2}$

$S = {(\frac{K_{S P}}{4})}^{1 / 3}$

$S = {(\frac{K_{S P}}{929})}^{1 / 9}$

answer is C.

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Detailed Solution

$A l C l_{3} \to A l^{+ 3} + 3 C l^{-}$

$K_{S P} = (S) {(3 S)}^{3}$

$K_{S P} = (S) {(27 S)}^{3}$

$K_{SP} = 27 S^{4}$

$S = {(\frac{K_{S P}}{27})}^{1 / 4}$

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