The question asks which ion forms a precipitate upon the addition of \(NH_4OH\) (ammonium hydroxide) and \(H_2S\) (hydrogen sulfide). To solve this, we need to understand how these reagents react with the given ions:
- Ammonium hydroxide (\(NH_4OH\)) is a weak base. It is often used to precipitate metal hydroxides from solutions.
- Hydrogen sulfide (\(H_2S\)) can precipitate metal sulfides from solutions.
We will now examine how each ion behaves with these reagents:
- \(Pb^{2+}\): Lead forms a precipitate of lead sulfide (\(PbS\)) when reacted with \(H_2S\), but it does not form a specific precipitate with \(NH_4OH\).
- \(Mn^{2+}\): Manganese forms manganese hydroxide (\(Mn(OH)_2\)) when reacted with \(NH_4OH\) and manganese sulfide (\(MnS\)) with \(H_2S\). In dilute solutions, \(MnS\) precipitates easily.
- \(Cu^{+}\): Copper(I) ions typically form copper(I) hydroxide (\(Cu_2O\)) with \(NH_4OH\), but CuS is not readily precipitated by \(H_2S\).
- \(Fe^{3+}\): Iron forms iron hydroxide (\(Fe(OH)_3\)) with \(NH_4OH\) and iron sulfide (\(Fe_2S_3\)) with \(H_2S\), but the reaction with the sulfide is less distinct under these conditions.
The key here is to find the ion that consistently forms a precipitate with both reagents. In this context:
- \(Mn^{2+}\) is known for forming a sulfide precipitate with \(H_2S\) and a hydroxide precipitate with \(NH_4OH\).
Hence, the correct answer is \(Mn^{2+}\).