Question

The solubility of $AgCN$ in a buffer solution of $pH=3$ is $x.$ The value of $x$ is:
[Assume, no cyano complex is formed]
$K_{sp}\left(AgCN\right)=2.2\times {10}^{-16}$ and $K_a\left(HCN\right)=6.2\times {10}^{-10}$

• A. $0.625\times {10}^{-6}$
• B. $1.6\times {10}^{-6}$
• C. $2.2\times {10}^{-16}$
• D. $1.9\times {10}^{-5}$

Answer 1

The correct option is D $1.9\times {10}^{-5}$

$AgCN\rightleftharpoons A{g}^{+}+C{N}^{-}-xx$

$C{N}^{-}+H^{+}\rightleftharpoons HCNxc--c-xxyc-x+yx-y$

$\therefore \left[C{N}^{-}\right]=y\left[H^{=}\right]=c-x+y\approx c-x\left[HCN\right]=x-y\approx x{K}_{sp}=x\times y$

$\frac{1}{K_a}=\frac{x}{y(c-x)}y=\frac{x\times K_a}{c-x}\therefore K_{sp}=\frac{x^2\times K_a}{c-x}\Rightarrow x=\sqrt{\frac{K_{sp}(c-x)}{K_a}}\because c>>>x\therefore s=\sqrt{\frac{K_{sp}\times c}{K_a}}s=\sqrt{\frac{2.2\times {10}^{-16}\times {10}^{-3}}{6.2\times {10}^{-10}}}\approx 1.9\times {10}^{-5}$