A student mixes \(100.0 \text{ mL}\) of \(0.200 \text{ M } \text{Pb(NO}_3)_2\text{(aq)}\) with \(100.0 \text{ mL}\) of \(0.300 \text{ M } \text{KI(aq)}\), resulting in the formation of a yellow precipitate according to the balanced net ionic equation below.

\[\text{Pb}^{2+}\text{(aq)} + 2\,\text{I}^-\text{(aq)} \rightarrow \text{PbI}_2\text{(s)}\]

Assuming the reaction goes to completion, how many moles of the excess reactant remain unreacted?