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Q. $A _{3} B _{2}$ is a sparingly soluble salt of molar mass $M \left( g\, mol ^{-1}\right)$ and solubility $x\, g \,L ^{-1}$. The solubility product satisfies $K _{ sp }=a\left(\frac{ x }{ M }\right)^{5}$. The value of $a$ is ___ (Integer answer)

JEE MainJEE Main 2021Equilibrium

Solution:

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$K _{ SP }=(3 s )^{3}(2 s )^{2}$
$K _{ SP }=108 S ^{5} \,\&\, s =( X / M )$
$K _{ SP }=108\left(\frac{ x }{ m }\right)^{5}$
given $K _{ SP }= a \left(\frac{ x }{ m }\right)^{5}$
comparing a $=108$