Correct option is (2) 1.9 × 10–5
Let solubility is x
\(AgCN \rightleftharpoons \underset {x} {Ag^+} +\underset {x}{CN^-}\)
\(H^+ + CN^- \rightleftharpoons HCN\)
\(K_{sp} = 2.2 \times 10^{-16}\)
\(K = \frac 1 {K_a} = \frac 1 {6.2\times 10^{-10}}\)
\(K_{sp} \times \frac 1{K_a} = [Ag^+][CN^-] \times \frac{[HCN]}{[H^+][CN^-]}\)
\(2.2 \times 10^{-16} \times \frac1{6.2 \times 10^{-10}} = \frac{[S][S]}{10^{-3}}\)
\(S^2 = \frac{2.2}{6.2} \times 10^{-9}\)
\(S^2 = 3.55 \times 10^{-10}\)
\(S = \sqrt{3.55 \times 10^{-10}}\)
\(S = 1.88 \times 10^{-5}\)
\(S = 1.9\times 10^{-5}\)
