Problem 164 - Arihant Objective Approach to Organic Chemistry for IIT JEE and NEET all Medical Entrances Part 4

Question

In benzene, all the six \(\mathrm{C}-\mathrm{C}\) bonds have the same length because of: [KCET 1998] (a) isomerism (b) chain isomerism (c) resonance (d) hybridisation

Step-by-Step Solution

Answer

(c) resonance

Step 1: Understanding the Molecular Structure of Benzene

Benzene ( C_6H_6 ) is a planar, cyclic compound where each carbon atom is sp2 hybridized. The molecular formula reveals that benzene consists of six carbon atoms forming a hexagonal ring, where each carbon is bonded to one hydrogen atom.

Step 2: Concept of Bond Length Variation

Typically, single ( C-C ) and double ( C=C ) carbon-carbon bonds have different lengths. A single bond is longer than a double bond, generally around 1.54 Å for single bonds and 1.34 Å for double bonds.

Step 3: Exploring Resonance in Benzene

Benzene features resonance, meaning it can be represented by multiple equivalent structures where the double bonds are in different positions. This results in the electron cloud being delocalized across the entire molecule.

Step 4: Conclusion: Homogenization of Bond Lengths

Due to resonance, the C-C bond lengths in benzene are not distinct single or double bonds. Instead, they average out to an intermediate length (approximately 1.39 Å), making all the bonds equivalent.

Key Concepts

Molecular Structure of Benzene

Benzene, with the molecular formula \( \text{C}_6\text{H}_6 \), is a unique compound in organic chemistry. It is classified as an aromatic hydrocarbon, which means it comes with a cyclic, planar structure. This six-carbon atom ring forms a perfect hexagon, with each carbon being bonded not only to its neighboring carbons but also to a single hydrogen atom. This geometric arrangement is not just about its shape but also plays a critical role in the compound's stability and chemical behavior.

Benzene's structure is stabilized further by its delocalized electrons, meaning that the electrons are spread out across the entire ring. This delocalization creates an even distribution of electron density and results in each of the carbon-carbon bonds within benzene holding the same energy and length. Such a unique structure is what gives benzene its characteristic resistance to reactions that would break the aromatic ring.

Key points about benzene's molecular structure include:

• Six carbon atoms in a planar hexagonal arrangement
• Each carbon atom forms three sigma bonds (two with carbon, one with hydrogen)
• Delocalized \pi-electrons over the ring

Understanding benzene's molecular structure provides insight into why its carbon-carbon bonds exhibit the properties they do.

Carbon-Carbon Bond Lengths

In typical organic compounds, carbon-carbon bonds can exist as single, double, or even triple bonds, each with different lengths. Single bonds are usually the longest, approximately 1.54 Å, while double bonds are shorter, approximately 1.34 Å. However, benzene deviates from these norms.

Due to the unique electron delocalization in benzene, all the carbon-carbon bonds are neither purely single nor purely double. Instead, they share characteristics of both, leading to intermediate bond lengths averaging about 1.39 Å. This particular bond length is consistent across all six bonds in benzene, resulting in a uniform structure. This equality in bond length is a direct consequence of the resonance within the benzene ring.

Key factors affecting bond length in benzene include:

• Resonance—the phenomenon where electrons are shared across bonds, stabilizing the structure
• Delocalized electrons—the equal spread of electrons throughout the carbon framework
• Planarity and symmetry of the benzene ring, contributing to equal bond distribution

This consistent bond length is crucial for benzene's stability and its role as a fundamental compound in aromatic chemistry.

sp2 Hybridization

The concept of sp2 hybridization in benzene is essential to its structure and stability. Each carbon atom in benzene undergoes sp2 hybridization. This process involves the mixing of one \( s \) orbital and two \( p \) orbitals from the carbon atom to form three equivalent sp2 hybrid orbitals.

These hybrid orbitals are arranged in a trigonal planar geometry around each carbon, allowing for the bond angle of approximately 120° between each bond. This arrangement is responsible for creating the planar, hexagonal shape of benzene. The remaining \( p \) orbital, which is not involved in hybridization, overlaps with adjacent \( p \) orbitals to form a delocalized \pi-electron cloud above and below the ring.

Key aspects of sp2 hybridization in benzene include:

• Formation of three equivalent sp2 hybrid orbitals per carbon
• Trigonal planar arrangement leading to a planar ring
• Contribution to the delocalized \pi-electronic structure throughout the aromatic ring

Understanding sp2 hybridization helps explain why benzene's structure is so stable and its electrons are evenly distributed, contributing to the characteristic bond lengths and resonance in the molecule.