Step 1: Understanding the Hinsberg Test
Benzene sulphonyl chloride (\(\text{C}_6\text{H}_5\text{SO}_2\text{Cl}\)) is used in the Hinsberg test to differentiate primary, secondary, and tertiary amines.
- Primary amines (\(\text{RNH}_2\)) react with benzene sulphonyl chloride to form a sulphonamide (\(\text{RNHSO}_2\text{C}_6\text{H}_5\)), which dissolves in alkali.
- Secondary amines (\(\text{R}_2\text{NH}\)) form an insoluble sulphonamide (\(\text{R}_2\text{NSO}_2\text{C}_6\text{H}_5\)), which does not dissolve in alkali.
- Tertiary amines (\(\text{R}_3\text{N}\)) do not have an available hydrogen on nitrogen, so they do not react with benzene sulphonyl chloride.
Step 2: Identifying the Type of Amines
- Option (A) \( (\text{C}_2\text{H}_5)_3\text{N} \) (Triethylamine): Tertiary amine → No reaction.
- Option (B) \( \text{C}_2\text{H}_5 - \text{NH}_2 \) (Ethylamine): Primary amine → Reacts.
- Option (C) \( (\text{C}_2\text{H}_5)_2\text{NH} \) (Diethylamine): Secondary amine → Reacts.
- Option (D) (Aniline): Primary aromatic amine → Reacts.
Step 3: Conclusion
Since tertiary amines do not react with benzene sulphonyl chloride, the correct answer is (A) \( (\text{C}_2\text{H}_5)_3\text{N} \).