Question

Indole smells rather terrible in high concentrations but has a pleasant floral-like odor when highly diluted. It has the following structure: Indole is a planar molecule. The nitrogen is a very weak base, with a \(K_{b}\) of \(2 \times 10^{-12}\). Explain how this information indicates that the indole molecule is aromatic in character.

Short answer

Indole is an aromatic molecule due to its planar structure, weak basicity, and molecular structure which includes a benzene ring and a pyrrole ring. Despite not directly following Hückel's rule, the weak basicity of indole, with a \(K_{b}\) of \(2 \times 10^{-12}\), suggests that the lone pair of electrons on the nitrogen atom is highly delocalized into the ring system, interacting with other pi electrons and conferring aromatic properties to the molecule.

Step-by-step solution

Understanding Molecular Structure

Indole has a planar molecule structure with a fused ring containing a benzene ring (which we know to be aromatic) and a pyrrole ring (which can also be aromatic).

Counting Delocalized Electrons

To identify if a molecule is aromatic or not, we need to find out whether it follows Hückel's rule - having \(4n+2\) delocalized pi electrons, where n is an integer. In indole, there are a total of 7 pi electrons that participate in resonance - 4 on the benzene ring and 3 from the double bond and bent nitrogen atom with a lone pair of electrons in the pyrrole ring.

Applying Hückel's Rule

Hückel's rule indicates that a molecule is aromatic if it has \(4n+2\) pi electrons in the delocalized system. In the case of indole: \(4n+2 = 7\) \(4n = 5\) \(n = 1.25\) Since n is not an integer, this rule cannot be directly applied to determine if indole is aromatic based on electron count.

Weak Basicity of Indole

Indole has a weak nitrogen base, with a \(K_{b}\) of \(2 \times 10^{-12}\). Given this weak basicity, it is very difficult to protonate the nitrogen atom in indole. This difficulty indicates that the lone pair of electrons on the nitrogen atom is predominately delocalized into the ring system and interacts with the other pi electrons. This delocalization makes indole exhibit aromatic properties.

Conclusion

Based on the molecular structure, weak basicity, and the planar structure of indole, we can conclude that indole is an aromatic molecule. The weak basicity of the nitrogen in the ring structure implies that its electrons are highly delocalized into the ring, thereby providing the molecule with aromatic character.

Key concepts

Hückel's Rule

Hückel's rule is a powerful tool used to determine if a planar, cyclic molecule is aromatic. According to this rule, a molecule must have a certain number of delocalized pi electrons—specifically, those that satisfy the formula \(4n + 2\), where \(n\) is an integer. Aromatic compounds are exceptionally stable because of the delocalization of electrons across the molecule's structure.
In the case of indole, the molecule contains 7 delocalized pi electrons. Aromatic systems are generally expected to have \(4n + 2\) pi electrons, where examples include 6, 10, or 14 pi electrons, but the arithmetic for indole leads to an unconventional assessment. Indole doesn't perfectly fit Hückel's rule because 7 electrons do not fit \(4n + 2 = 7\). Nevertheless, its electron delocalization and structural features still contribute to its aromatic characteristics.

Indole Structure

The structure of indole is unique, combining elements of different cyclic systems. It consists of a fused ring system that includes a benzene and pyrrole ring. Both rings contribute to the overall stability and aromatic quality of indole.

• The benzene ring is a classic example of an aromatic system.
• The pyrrole ring introduces a nitrogen atom, which participates in the electron cloud.

The fusion of these two rings in indole enables electron sharing across the extended ring system. This structural arrangement is crucial for the delocalization and stability observed in indole, characteristics typical of aromatic compounds.

Delocalized Electrons

Delocalized electrons play a crucial role in conferring aromaticity. In indole, these electrons are spread over the entire ring system rather than being localized on any specific atom. This distribution occurs because the pi electrons are not confined to single bonds but move around the rings.
In indole, there are 7 pi electrons, which come from double bonds and the nitrogen atom's lone pair. Despite not fitting traditional aromatic electron counts, the distribution of these electrons contributes to its aromatic properties. Delocalization enhances stability and reactivity patterns that are characteristic of aromatic compounds.

Weak Basicity

One distinct property of indole is its weak basicity. The nitrogen atom within the pyrrole ring has a lone pair of electrons that are part of the delocalized pi electron system. This configuration makes indole's nitrogen much less basic than other amines because protonation would disturb the aromatic system.

• The nitrogen’s basicity is given by a \(K_b\) of \(2 \times 10^{-12}\).
• This low value indicates that the nitrogen's electrons are engaged in delocalization, enhancing aromatic stability and demonstrating weak basicity.

Thus, the weak basicity of indole is correlated with its aromatic nature, as the involvement of nitrogen's electrons in the electron cloud prevents the typical protonation seen in non-aromatic amines.

Planar Molecule

For a molecule to be considered aromatic, it must have a planar structure. This planarity allows for the effective overlap of p orbitals, enabling the delocalization of pi electrons across the entirety of the ring system. Indole maintains this requirement, as it is inherently a planar molecule.
Planarity ensures all involved atoms are on the same geometric plane, facilitating the even spread of electrons across the ring structure. The flat configuration ensures that pi electrons are delocalized, which is a characteristic necessary for a substance to exhibit aromatic properties, as seen in indole.