Concept:
According to Huckel’s rule, a compound is aromatic if:
• it is cyclic,
• planar,
• fully conjugated,
• contains \((4n+2)\pi\) electrons.
Step 1: Cyclopropenyl cation.
It contains:
\[
2\pi \text{ electrons}
\]
For:
\[
n=0
\]
\[
4n+2 = 2
\]
Hence aromatic.
Step 2: Naphthalene.
Naphthalene contains:
\[
10\pi \text{ electrons}
\]
For:
\[
n=2
\]
\[
4(2)+2=10
\]
Hence aromatic.
Step 3: Cyclopentadiene.
Cyclopentadiene contains one:
\[
sp^3
\]
hybridized carbon atom.
Therefore conjugation is interrupted.
Hence it is non-aromatic.
Step 4: Azulene.
Azulene is fully conjugated and contains:
\[
10\pi \text{ electrons}
\]
Thus it satisfies Huckel’s rule and is aromatic.
Therefore aromatic compounds are:
\[
I,\ II,\ IV
\]