On passing a gas, '$$X$$', through Nessler's reagent, a brown precipitate is obtained. The gas '$$X$$' is

We need to identify gas $$X$$ that gives a brown precipitate with Nessler's reagent.

Nessler's reagent is an alkaline solution of potassium mercuric iodide ($$K_2[HgI_4]$$). It is a specific test reagent for ammonia ($$NH_3$$) and ammonium ions ($$NH_4^+$$).

When ammonia gas is passed through Nessler's reagent, the following reaction occurs:

$$NH_3 + 2K_2[HgI_4] + 3KOH \rightarrow \underset{\text{(brown ppt)}}{Hg_2ONH_2I} + 7KI + 2H_2O$$

The brown precipitate formed is known as the iodide of Millon's base ($$Hg_2ONH_2I$$).

Let us verify by checking the other options:

• $$H_2S$$ gives a black precipitate ($$HgS$$) with Nessler's reagent, not brown.
• $$CO_2$$ does not react with Nessler's reagent to give a precipitate.
• $$Cl_2$$ does not give a brown precipitate with Nessler's reagent.

Therefore, the correct answer is Option 3: NH$$_3$$.