A student places \(0.10 \text{ mol}\) of \(\text{AgCl}(s)\) into \(1.0 \text{ L}\) of distilled water at \(298 \text{ K}\) and stirs until equilibrium is established. A noticeable amount of undissolved \(\text{AgCl}(s)\) remains at the bottom of the flask. The relevant chemical equations and equilibrium constants at \(298 \text{ K}\) are given below.

\[\text{AgCl}(s) \rightleftharpoons \text{Ag}^+(aq) + \text{Cl}^-(aq) \quad K_{sp} = 1.8 \times 10^{-10}\]

\[\text{Ag}^+(aq) + 2\,\text{NH}_3(aq) \rightleftharpoons [\text{Ag}(\text{NH}_3)_2]^+(aq) \quad K_f = 1.7 \times 10^7\]

The student then adds several drops of concentrated \(\text{NH}_3(aq)\) to the mixture at constant temperature with negligible change in total volume. Which of the following correctly predicts and explains the effect of adding \(\text{NH}_3(aq)\) on the amount of solid \(\text{AgCl}\) in the flask?