Question

(a) Use the concept of resonance to explain why all six \(\mathrm{C}-\mathrm{C}\) bonds in benzene are equal in length. (b) Are the \(\mathrm{C}-\mathrm{C}\) bond lengths in benzene shorter than \(\mathrm{C}-\mathrm{C} \mathrm{sin}-\) gle bonds? Are they shorter than \(\mathrm{C}=\mathrm{C}\) double bonds?

Short answer

In benzene, all six C-C bonds have equal lengths due to the molecule being a resonance hybrid of two different structures. This causes the electrons to be shared equally among the carbon atoms, resulting in a bond length intermediate between a single bond and a double bond. As a result, benzene's C-C bond lengths are shorter than C-C single bonds but longer than C=C double bonds.

Step-by-step solution

(Step 1: Understanding Resonance Structures in Benzene)

Resonance structures are used to describe molecular structures where a single Lewis structure does not fully describe the bonding in a molecule. Benzene, with a chemical formula \(\text{C}_6\text{H}_6\), has two resonance structures. In one structure, benzene has \(\text{C-C}\) single bonds adjacent to \(\text{C} = \text{C}\) double bonds, while the other structure has double bonds adjacent to single bonds. Since neither structure fully describes benzene, the actual molecule is a hybrid of these two resonance structures.

(Step 2: Explaining Equal Bond Lengths in Benzene)

In benzene, all \(\text{C-C}\) bond lengths are equal because the molecule is a resonance hybrid of two different structures. This means that the electrons are shared equally between all the carbon atoms, creating a bond length between a single bond and double bond. The actual structure of benzene is neither of the resonance structures but an intermediate form. This intermediate structure causes all \(\text{C-C}\) bonds to have equal bond lengths.

(Step 3: Comparing Bond Lengths in Benzene to C-C Single Bonds and C=C Double Bonds)

In general, a single bond has a longer bond length than a double bond. This is because double bonds involve more electron sharing between the bonded atoms, pulling them closer together. In benzene, the actual bond length lies between the length of a single bond and a double bond. To answer part (b) of the question, the C-C bond lengths in benzene are shorter than \(\text{C-C}\) single bonds but longer than \(\text{C}=\text{C}\) double bonds. The actual bond length of benzene is an intermediate length between single and double bonds due to the resonance hybrid structure.

Key concepts

Equal Bond Lengths in Benzene

In benzene, all carbon-carbon (C-C) bonds are of equal length, which is quite unique. Unlike typical molecules where bonds vary depending on single or double bond configurations, benzene is special. This uniform bond length occurs due to resonance, a phenomenon in chemistry where a molecule can be represented by two or more valid Lewis structures. In the case of benzene, these structures involve alternating single and double bonds.

However, benzene doesn't constantly switch between these structures. Instead, it exists as a resonance hybrid, where the actual structure is a blend of all possible resonance forms. This hybridization leads to the equal distribution of electron density over the C-C bonds. As a result, each bond has a length that is not purely single or double but rather a consistent intermediate length, making them all identical.

C-C Bond Comparison in Benzene

Benzene's C-C bonds are best understood when compared with standard single and double bonds. In general, single bonds are longer than double bonds because they involve fewer shared electrons. More electrons in a double bond create greater overlap between atomic orbitals, pulling the bonded atoms closer together.

In benzene, the situation is somewhat in between. The C-C bond lengths here are shorter than typical single bonds, which would normally be longer due to lesser electron sharing. However, they remain longer than standard double bonds found in alkenes. This unique bond length in benzene is due to its resonance hybrid form, where no bond is entirely single or double, but an average of both.

The Resonance Hybrid Structure of Benzene

The resonance hybrid structure is a key factor in explaining the unique properties of benzene. While individual resonance structures show clear single and double bonds, the real benzene molecule does not flip between these forms. Instead, it is a resonance hybrid. This hybrid is not an average of two structures but a true continuous state where electrons are delocalized. This delocalization allows the bonds to be shared equally among the carbons.

In this hybrid structure, electrons move freely across the molecule, providing stability and reducing the potential energy. This results in equal bond lengths, setting benzene apart from other compounds exhibiting isolated double or single bonds. The resonance hybrid contributes to benzene's remarkable stability and unique electrical and optical properties.