Calculate the solubility of () in a solution given the complex formation constant of is . — Ionic Equilibrium Chemistry Question
Question
Calculate the solubility of $AgI$ ($K_{sp} = 8.5 \times 10^{-17}$) in a $0.010 \text{ M } KCN$ solution given the complex formation constant of $[Ag(CN)_2]^-$ is $K_f = 1/K_{instability} = 1 / (1.9 \times 10^{-19})$.
Answer: A
💡 Solution & Explanation
$K_{eq} = K_{sp} \times K_f = (8.5 \times 10^{-17}) / (1.9 \times 10^{-19}) \approx 447$. Eq: $AgI + 2CN^- \rightleftharpoons [Ag(CN)_2]^- + I^-$. $K_{eq} = S^2 / (0.010 - 2S)^2 = 447$. $\sqrt{447} \approx 21.1$. $S / (0.01 - 2S) = 21.1 \implies S \approx 5 \times 10^{-3} \text{ M}$.
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