Type: MCQ

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

[Assume: No cyano complex is formed; $K_{sp}(\text{AgCN}) = 2.2 \times 10^{-16}$ and $K_a(\text{HCN}) = 6.2 \times 10^{-10}$]

(a) $0.625 \times 10^{-6}$
(b) $1.6 \times 10^{-6}$
(c) $2.2 \times 10^{-16}$
(d) $1.9 \times 10^{-5}$

Show Answer

Let solubility be $x$. $\text{AgCN} \rightleftharpoons \text{Ag}^+ + \text{CN}^-$

$\text{H}^+ + \text{CN}^- \rightleftharpoons \text{HCN}$; $K = \frac{1}{K_a} = \frac{1}{6.2 \times 10^{-10}}$

$K_{sp} \times \frac{1}{K_a} = [\text{Ag}^+][\text{CN}^-] \times \frac{[\text{HCN}]}{[\text{H}^+][\text{CN}^-]}$

$S^2 = \frac{2.2 \times 10^{-16}}{6.2 \times 10^{-10}} \times 10^{-3} \approx 3.55 \times 10^{-10}$

$S = \sqrt{3.55 \times 10^{-10}} \approx 1.88 \times 10^{-5} \approx 1.9 \times 10^{-5}$