Which of the following amines does not undergo benzoylation?

N,N-Dimethylethanamine

The answer is 3. \(N,N\)-Dimethylethanamine.

Benzoylation is the reaction of an amine with benzoyl chloride to form an amide. This reaction occurs with primary and secondary amines, but not with tertiary amines. This is because tertiary amines do not have a reactive hydrogen atom on the nitrogen atom.

Here are the reactions of the given amines with benzoyl chloride:

1. \(N\)-Methylethanamine: \(CH_3NH_2 + C_6H_5COCl \rightarrow CH_3NHC=OC_6H_5 + HCl\)

2. \(N\)-Ethylethanamine: \(CH_3CH_2NH_2 + C_6H_5COCl \rightarrow CH_3CH_2NHC=OC_6H_5 + HCl\)

3. \(N,N\)-Dimethylethanamine: \((CH_3)_2NH + C_6H_5COCl \rightarrow \text{No reaction}\)

4. \(N\)-Methylbenzenamine: \(C_6H_5NHCH_3 + C_6H_5COCl \rightarrow C_6H_5NHC=OC_6H_5 + HCl\)

Therefore, the only amine that does not undergo benzoylation is \(N,N\)-Dimethylethanamine.