Identify what Nessler's reagent tests for

Nessler's reagent is used for the detection of ammonia or ammonium ions.

It is an alkaline solution of potassium tetraiodomercurate(II), often written as $\mathrm{K_2[HgI_4]}$ in the presence of excess $\mathrm{KOH}$.

Reaction with ammonia

When ammonia is passed through Nessler's reagent, it gives a brown precipitate (or reddish-brown coloration), due to formation of a mercury-amido-iodide type compound.

Hence, if a gas gives a brown precipitate with Nessler's reagent, that gas must be ammonia.

Check the options

• A: $\mathrm{Cl_2}$ — does not give the characteristic brown precipitate with Nessler's reagent.
• B: $\mathrm{CO_2}$ — does not give this test.
• C: $\mathrm{NH_3}$ — gives brown precipitate with Nessler's reagent.
• D: $\mathrm{H_2S}$ — does not give the Nessler brown precipitate test.

Conclusion

Therefore, the gas $\mathrm{X}$ is $\boxed{\mathrm{NH_3}}$

So the correct option is C.