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Sum of Product of Binomial Coefficients

A3B2 is a spa...

Question

$A_{3} B_{2}$ is a sparingly soluble salt of molar mass M $(g m o l^{- 1})$ and solubility x g $L^{- 1}$ . The solubility product satisfies $K_{S P} = a {(\frac{x}{M})}^{5}$ . The vlaue of a is ______(Integer answer).

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Solution

$A_{3} B_{2} (s) ⇌ 3 A_{(a q)}^{2 +} + 2 B_{(a q)}^{3 -}$

3S 2S

$K_{s p} = {(3 S)}^{3} {(2 S)}^{2}$

$K_{s p} = 108 S^{5}$
$S = (\frac{Solubility in g/L}{Molar mass of A_{3} B_{2}})$

$K_{s p} = 108 {(\frac{x}{M})}^{5} . . . . (1)$

$K_{s p} = a {(\frac{x}{M})}^{5} . . . . . (2)$
Comparing (1) and (2), we get,
a = 108.

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