Step 1:
The reaction described in the question involves the formation of gas X upon treatment with sodium hydroxide. This is typical of ammonia (NH₃), which is released when ammonium salts (like NH₄Cl) react with sodium hydroxide.
Step 2:
Now, gas X (NH₃) reacts with reagent Y. The formation of a brown colored precipitate suggests the reaction with a mercury(I) compound, which is typically represented as K₂HgI₄ (also known as potassium tetraiodomercurate(I)). When ammonia is passed through K₂HgI₄ in the presence of KOH, a brown precipitate of mercury(I) iodide (Hg₂I₂) is formed.
Step 3:
Thus, the gas X is ammonia (NH₃), and the reagent Y is potassium tetraiodomercurate(I) (K₂HgI₄), which, when treated with ammonia, forms a brown precipitate of Hg₂I₂.
Final Answer:
\[ \boxed{X = \text{NH}_3 \text{ and } Y = \text{K}_2\text{HgI}_4 + \text{KOH}} \]