Question

Explain how the structure of benzene can be used to explain its unusually high stability compared to other unsaturated cyclic hydrocarbons. (Chapter 21)

Short answer

The unusually high stability of benzene compared to other unsaturated cyclic hydrocarbons can be explained by the resonance structures and delocalization of electrons in its hexagonal ring. The carbon-carbon bonds within benzene are a hybrid of single and double bonds, leading to intermediate bond lengths of approximately \(1.39 \thinspace Å\) and reduced reactivity. This delocalization of electrons results in a more stable, less reactive ring system. The stability is further evidenced by benzene's preference for electrophilic substitution reactions rather than addition reactions, which are typical for unsaturated cyclic hydrocarbons.

Step-by-step solution

1. Introduction to Benzene Structure

Benzene is an unsaturated cyclic hydrocarbon, with a molecular formula of C6H6. It's structure consists of six carbon atoms arranged in a hexagonal ring, where each carbon atom is bonded to two other carbon atoms and one hydrogen atom. The carbon-carbon bonds within the ring are not the same as a regular single or double bond, but rather a hybrid of both, resulting in increased stability.

2. Resonance Structure

In benzene, we observe resonance structures that are the contributing forms of its actual structure. The resonance forms can be represented by two structures where the double bonds are alternating between three carbon-carbon bonds, with the other three being single bonds. It's important to note that these resonance structures are not isolable and do not alternate between each other; they are simply a way for us to represent the delocalized electrons within the benzene ring.

3. Delocalization of Electrons

The concept of resonance suggests that instead of having localized double and single bonds, the electrons within the double bonds are spread out or delocalized evenly across all six carbon atoms. These delocalized electrons are often represented by a circle within the hexagonal ring, to show that they are distributed across all the carbon atoms in benzene. The delocalization of these electrons leads to a less reactive ring system which contributes to its stability.

4. Bond Lengths and Energies

In benzene, the carbon-carbon bond lengths are intermediate between that of a single bond (\(1.54 \thinspace Å\)) and a double bond (\(1.34 \thinspace Å\)). The actual bond length in benzene is approximately \(1.39 \thinspace Å\), which is consistent with the idea that benzene has a hybrid bond structure of single and double bonds. Furthermore, the overall energy of benzene is lower than other unsaturated cyclic hydrocarbons because the electrons are delocalized, leading to the increased stability of benzene.

5. Comparison to Cyclohexatriene

If the structure of benzene was simply a conjugated cyclic system like cyclohexatriene (without resonance and delocalization), then the stability would be lower. If benzene was just cyclohexatriene, it would be expected to readily undergo addition reactions like other unsaturated cyclic hydrocarbons. However, benzene doesn't undergo these typical addition reactions, and instead participates in electrophilic substitution reactions, which further validates its unusually high stability. In conclusion, the structure of benzene involving resonance and delocalization of electrons throughout the hexagonal ring explains its unusually high stability compared to other unsaturated cyclic hydrocarbons. This unique structure results in intermediate bond lengths, reduced reactivity, and increased overall stability.

Key concepts

Resonance Structure

Benzene is often represented by its resonance structures to explain its unique stability. These structures are two theoretical forms where double bonds appear to alternate between carbon-carbon pairs. However, it's crucial to understand that the electrons in the benzene ring are not jumping back and forth but are rather shared equally among all the carbon atoms. This concept of resonance helps chemists visualize the stability that arises from this equal sharing.
Resembling neither perfectly single nor perfectly double, the resonance structures suggest that each carbon-carbon bond in benzene has both double and single bond characteristics. By this clever depiction, we explain benzene's reluctance to participate in reactions typical for compounds with isolated double bonds. Instead, it maintains a stable "resonance hybrid" form, contributing significantly to its chemical durability.

Delocalization of Electrons

The heart of benzene's stability lies in the delocalization of electrons. In most molecules, electrons in double bonds are localized between two specific atoms. However, in benzene, these electrons are not confined to any one bond or atom.
They are spread equally across the six carbon atoms, forming what could be visualized as a cloud of electrons over the ring. This redistribution of electrons decreases the molecule's potential energy, as the electrons are more stabilizing when delocalized. The circle often drawn inside benzene's hexagonal structure represents this delocalized electron cloud, emphasizing that the electrons are not tied to any specific bond.
Thanks to this delocalization, benzene exhibits behavior that is markedly different from other unsaturated compounds, contributing to the molecule's high level of stability and its preference for substitution rather than addition reactions.

Carbon-Carbon Bond Lengths

The intermediate carbon-carbon bond lengths in benzene serve as another indicator of its unique structure. Typically, single bonds have a length of about 1.54 Å and double bonds about 1.34 Å. Benzene's carbon-carbon bonds stand at an intermediate length of roughly 1.39 Å.
This uniform bond length is a physical footprint of benzene's resonance stability. It also indicates that none of the bonds in benzene are outright single or double bonds, but rather a blend of both.
This pattern confirms the resonance theory, where the bonds are neither fully single nor double but share characteristics of both bond types. Thus, the bond lengths add another layer of understanding to benzene's stability, showing physically how its molecular structure allows for even electron distribution, leading to enhanced stability. This, in turn, explains why benzene doesn't easily react like other similar hydrocarbons.