Question

The correct equation relating solubility and solubility product for the sparingly soluble salt with the general molecular formula $ AB_{2} $ is

• A. $ S = [4K_{sp}]^{1/3} $
• B. $ S=2^{2/3} [K_{sp}]^{-1/3} $
• C. $ S=[4K_{sp}]^{-1/3} $
• D. $ S=2^{-2/3} [K_{sp}]^{1/3} $

Answer 1

Answer: (D)

$AB_{2}\rightleftharpoons A^{2+}+2B^{-}$
$K_{sp}=(S)\times (2S)^{2}$
$K_{sp}=4S^{3}$
$\Rightarrow S=\sqrt[\frac{1}{3}]{\frac{K_{sp}}{4}}=2 ^{-\frac{2}{3}}\left[K_{sp}\right]^{1 /3}$