Step 1: Understanding the Concept
The Hinsberg test separates primary, secondary and tertiary amines using benzenesulfonyl chloride, \(\text{C}_6\text{H}_5\text{SO}_2\text{Cl}\).
Step 2: What happens
A primary amine gives a sulfonamide that has an acidic N-H, so it dissolves in alkali. A secondary amine gives a sulfonamide with no acidic hydrogen, which is insoluble in alkali. A tertiary amine does not react in the same way.
Step 3: Check the options
(A) \(\text{NaNO}_2\)/HCl is used for the nitrous acid test. (B) Alcoholic \(\text{FeCl}_3\) is a test for phenols. (D) \(\text{CHCl}_3\) and alcoholic KOH is the carbylamine test for primary amines only. (C) Benzenesulfonyl chloride is the Hinsberg reagent.
Final Answer:
Hinsberg's reagent is benzenesulfonyl chloride, option (C).
\[ \boxed{\text{C}_6\text{H}_5\text{SO}_2\text{Cl}} \]