Nessler's reagent is a chemical reagent used for detecting ammonia. In order to understand which formula corresponds to Nessler's reagent, let's examine the provided options:
$KHgI_3$: This compound contains potassium (K), mercury (Hg), and iodine (I), but it is not the correct formula for Nessler's reagent.
$HgI_2$: This is mercuric iodide, a compound of mercury and iodine, but it is not Nessler's reagent.
$K_2HgI_4$: This is the correct formula for Nessler's reagent. It comprises potassium, mercury, and iodide ions in a specific ratio and is used to detect the presence of ammonia in solutions.
$KHg_2I_2$: This is not the formula for Nessler's reagent. It involves potassium, multiple mercury atoms, and iodide, but in an incorrect formulation for this use.
The correct answer is $K_2HgI_4$, which is the known composition of Nessler's reagent. Nessler's reagent forms a brown precipitate or a yellow coloration in the presence of ammonia, which helps in its detection.
Conclusion: Option $K_2HgI_4$ is the correct choice for the formula of Nessler's reagent, which is used extensively in qualitative analysis for detecting trace amounts of ammonia.
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