The solubility of AgCN in a buffer solution of pH = 3 is x . The...

Let, the solubility be $x$

Given that,

${K}_{sp}\left(AgCN\right) = 2 . 2 \times {10}^{- 16}$ and ${K}_{a}\left(HCN\right) = 6 . 2 \times {10}^{- 10}$

$AgCN ⇌ \mathop{{Ag}^{+}}_{x} + \mathop{{CN}^{-}}_{x}{K}_{sp} = 2 . 2 \times {10}^{- 16}$

${H}^{+} + {CN}^{-} ⇌ HCNK = \dfrac{1}{{K}_{a}} = \dfrac{1}{6 . 2 \times {10}^{- 10}}$

${K}_{sp} \times \dfrac{1}{{K}_{a}} = \left[{Ag}^{+}\right]\left[{CN}^{-}\right] \times \dfrac{[ HCN ]}{\left[{H}^{+}\right]\left[{CN}^{-}\right]}$

$2 . 2 \times {10}^{- 16} \times \dfrac{1}{6 . 2 \times {10}^{- 10}} = \dfrac{[ S ] [ S ]}{{10}^{- 3}}$

${S}^{2} = \dfrac{2 . 2}{6 . 2} \times {10}^{- 9}$

${S}^{2} = 3 . 55 \times {10}^{- 10}$

$S = \sqrt{3 . 55 \times {10}^{- 10}}$

$S = 1 . 88 \times {10}^{- 5} ⇒ 1 . 9 \times {10}^{- 5}$