Question

\(K_c\) for the reaction \([\text{Ag(CN)}_2]^-\rightleftharpoons \text{Ag}^+ + 2\text{CN}^-\) is \(4.0\times10^{-19}\) at \(25^\circ\text{C}\). The equilibrium concentration of silver cation in a solution which was originally \(0.1\) molar in KCN and \(0.03\) molar in AgNO\(_3\) is:

• A. \(7.5\times10^{18}\)
• B. \(7.5\times10^{-19}\)
• C. \(7.5\times10^{19}\)
• D. \(7.5\times10^{-18}\)

Hint:

Large excess of ligand greatly lowers free metal ion concentration.

Answer 1

The Correct Option is D

Step 1: Formation of complex reduces free \(\text{Ag}^+\) drastically due to excess CN\(^-\).
Step 2: Using \[ K_c=\frac{[\text{Ag}^+][\text{CN}^-]^2}{[\text{Ag(CN)}_2^-]} \]
Step 3: Substituting given concentrations and solving gives \[ [\text{Ag}^+]=7.5\times10^{-18}\,\text{M} \]