The solubility of AgCN in a buffer solution of pH = 3 is x. The value of x is:
$[Assume : No cyano complex is formed : K_{sp} (AgCN) = 22 x 10^{- 16} and K_{a} (HCN) = 6 .2 x 10^{- 10}]$

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$0.625 \times 10^{- 6}$

$1.9 \times 10^{- 5}$

$2.2 \times 10^{- 16}$

$1.6 \times 10^{- 6}$

answer is B.

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Detailed Solution

$\begin{array}{l} A_{g} C N ⇌ A_{g}^{\oplus} + C N^{Θ} H^{\oplus} + C N^{Θ} ⇌ H^{+} + C N^{Θ} \\ K_{s p} \times \frac{1}{K_{a}} = [A_{g}^{+}] [C N^{Θ}] \times \frac{[H C N]}{[H^{+}] [C N^{Θ}]} \\ 2.2 \times 10^{- 16} \times \frac{1}{6.6 \times 10^{- 10}} = \frac{Δ . Δ}{10^{- 3}} \\ Δ^{2} = \frac{10^{- 8}}{30} Δ = 1.9 \times 10^{- 5} \end{array}$