A student attempts to synthesize the tetraamminecopper(II) complex ion, \([\text{Cu(NH}_3)_4]^{2+}\text{(aq)}\), by combining \(0.100 \text{ mol}\) of \(\text{Cu(NO}_3)_2\text{(s)}\) and \(0.400 \text{ mol}\) of \(\text{NH}_3\text{(aq)}\) in sufficient water to make \(1.00 \text{ L}\) of solution, according to the target reaction below:

\[ \text{Cu}^{2+}\text{(aq)} + 4\,\text{NH}_3\text{(aq)} \rightarrow [\text{Cu(NH}_3)_4]^{2+}\text{(aq)} \]

During the procedure, an undesired competing side reaction occurs in which some of the dissolved copper(II) ions precipitate as copper(II) hydroxide, \(\text{Cu(OH)}_2\text{(s)}\), according to the following equation:

\[ \text{Cu}^{2+}\text{(aq)} + 2\,\text{NH}_3\text{(aq)} + 2\,\text{H}_2\text{O(l)} \rightarrow \text{Cu(OH)}_2\text{(s)} + 2\,\text{NH}_4^+\text{(aq)} \]

Assuming both reactions proceed to completion and a small amount of \(\text{Cu(OH)}_2\text{(s)}\) precipitate forms, which of the following correctly identifies whether \(\text{Cu}^{2+}\text{(aq)}\) or \(\text{NH}_3\text{(aq)}\) remains in excess in the final solution, along with the correct justification?