An aqueous solution of an unknown metal salt is subjected to...

The qualitative analysis of cations relies on selective precipitation based on solubility products. Group II cations (such as $\text{Cu}^{2+}$ and $\text{Pb}^{2+}$) precipitate as sulphides when $\text{H}_2\text{S}$ is passed in an acidic medium. Since no precipitate is formed in the acidic medium, Group II cations are absent.

Group IV cations (such as $\text{Co}^{2+}$, $\text{Ni}^{2+}$, $\text{Mn}^{2+}$, and $\text{Zn}^{2+}$) require a higher concentration of sulphide ions to precipitate. This is achieved by passing $\text{H}_2\text{S}$ in an alkaline medium (using $\text{NH}_4\text{OH}$ and $\text{NH}_4\text{Cl}$). Since a precipitate forms under these conditions, the cation belongs to Group IV.

Among the given options, $\text{Co}^{2+}$ is a Group IV cation. $\text{Ba}^{2+}$ belongs to Group V and does not precipitate as a sulphide in either medium.

Answer: $\text{Co}^{2+}$