Step 1: Recall Gabriel phthalimide synthesis.
Gabriel phthalimide synthesis is a method used for the preparation of
primary aliphatic amines
It involves the reaction of potassium phthalimide with an alkyl halide followed by hydrolysis.
Step 2: Identify the type of amines formed.
This method successfully prepares:
\[
R-NH_2
\]
where \(R\) is an alkyl group.
It does not prepare:
Aromatic amines
or
secondary/tertiary amines
Step 3: Analyze the given options.
Option (1): Aniline
Aniline is an aromatic amine:
\[
C_6H_5NH_2
\]
Gabriel synthesis does not work efficiently for aryl halides.
Option (2): Pyrrolidine
Pyrrolidine is a cyclic secondary amine, not obtained by Gabriel synthesis.
Option (3): Triethylamine
Triethylamine is a tertiary amine, which is not prepared by Gabriel synthesis.
Option (4): Ethylamine
Ethylamine is a primary aliphatic amine:
\[
C_2H_5NH_2
\]
Hence, it can be prepared by Gabriel phthalimide synthesis.
Step 4: Final conclusion.
Therefore, Gabriel phthalimide synthesis is used for the preparation of
\[
\boxed{\text{Ethylamine}}
\]