A brown ring is formed in the ring test for \(NO_3^-\) ion. It is due to the formation of:

\([Fe(H_2O)_5(NO)]^{2+}\)

The correct answer is (2) \([Fe(H_2O)_5(NO)]^{2+}\)

The brown ring test for the nitrate ion \((NO_3^-)\) involves adding iron(II) sulfate to a nitrate solution and then slowly adding concentrated sulfuric acid such that the acid forms a layer below the aqueous solution. A brown ring will be formed at the junction of the two layers, indicating the presence of the nitrate ion.

The brown ring is due to the formation of a complex ion, \([Fe(H_2O)_5NO]^{2+}\). This complex ion is formed by the reaction of iron(II) ions with nitric oxide \((NO)\), which is produced by the reduction of nitrate ions. The reaction is as follows:

\(NO_3^- + 3Fe^{2+} + 4H^+ \longrightarrow NO + 3Fe^{3+} + 2H_2O\)

\(NO + Fe^{2+} \longrightarrow [Fe(H_2O)_5NO]^{2+}\)

The brown color of the complex ion is due to the absorption of light in the visible region of the spectrum.

The ring test for nitrate ion is a sensitive test and can detect even small amounts of nitrate ion. It is a common test used in analytical chemistry.