Aromaticity of Pyrrole Furan Thiophene

Aromaticity is a property of cyclic, planar molecules with a conjugated π-electron system that follows Hückel's rule, which states that a molecule is aromatic if it has 

$4n+2$ π-electrons (where $n$ is a non-negative integer).

Let's look at each of the three heterocycles you've mentioned:

1. Pyrrole: Pyrrole is a five-membered ring with four carbon atoms and one nitrogen atom. It has a conjugated π-electron system where the nitrogen atom contributes one lone pair of electrons to the ring's π-system. The ring thus has a total of 6 π-electrons (4 from the double bonds and 2 from the nitrogen lone pair), which follows Hückel's rule ($4n+2$, where $n=1$). Therefore, pyrrole is aromatic.

2. Furan: Furan is another five-membered ring but with four carbons and one oxygen atom. It has a conjugated π-electron system where the oxygen atom contributes two lone pairs (one of which participates in the π-system). The ring has a total of 6 π-electrons (4 from the double bonds and 2 from the oxygen lone pairs), so it also follows Hückel's rule and is aromatic.

3. Thiophene: Thiophene has a five-membered ring with four carbons and one sulfur atom. The sulfur atom contributes two lone pairs, and one of them participates in the π-system. The ring has a total of 6 π-electrons (4 from the double bonds and 2 from the sulfur lone pairs), meeting Hückel's rule, and thus is aromatic as well.

So, all three of these heterocycles—pyrrole, furan, and thiophene—are aromatic