Question #45033

This problem tests the competition between the solubility product ($K_{sp}$) and complex formation ($\beta_2$), compounded by the common ion effect.

The 'Hidden Variable' is the coordination number of the \ce{Ag+} (+1 oxidation state, $d^{10}$) complex, which is 2.

This dictates the stoichiometric coefficient of \ce{NH3} and requires squaring the ammonia concentration in the denominator.

The 'Chemical Trap' is that students often assume $S$ is negligible and approximate $[\ce{NH3}] \approx 2.4 \text{ M}$ and $[\ce{Cl-}] \approx 0.3 \text{ M}$, leading to an erroneous solubility of $0.48 \text{ M}$.

However, because $K_{eq}$ is relatively large ($0.025$), the depletion of the ligand ($2S$) and the addition to the common ion ($+S$) are highly significant and must be solved via a full quadratic equation.