A water-soluble salt X reacts with dilute H_2SO_4 to release a gas...

The gas $Y$ evolved with dilute $\text{H}_2\text{SO}_4$ having a rotten egg smell is hydrogen sulphide ($\text{H}_2\text{S}$). This indicates the presence of sulphide ($\text{S}^{2-}$) ions in the salt $X$.

As a confirmatory test, when an aqueous solution of a sulphide salt is treated with sodium nitroprusside ($\text{Na}_2[\text{Fe}(\text{CN})_5\text{NO}]$), a purple-coloured complex is formed due to the formation of sodium thionitroprusside.

$\text{S}^{2-} + [\text{Fe}(\text{CN})_5\text{NO}]^{2-} \rightarrow [\text{Fe}(\text{CN})_5\text{NOS}]^{4-}$

Thus, the purple complex $Z$ is $\text{Na}_4[\text{Fe}(\text{CN})_5\text{NOS}]$.

Answer: $Y = \text{H}_2\text{S}$, $Z = \text{Na}_4[\text{Fe}(\text{CN})_5\text{NOS}]$