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 \(C-C\) bond lengths in benzene shorter than \(C-C\) single bonds? Are they shorter than \(C=C\) double bonds?

Short answer

(a) In benzene, there are two resonance structures with alternating single and double bonds. The true structure of benzene is a hybrid of these resonance forms, with the electron density of the double bonds spread evenly across the molecule. As a result, all six C-C bond lengths in benzene are equal and intermediate between single and double bonds. (b) The C-C bond lengths in benzene are shorter than C-C single bonds but longer than C=C double bonds, as they are intermediate representations in the resonance hybrid structure.

Step-by-step solution

Understanding the Benzene Structure

Benzene is a cyclic compound consisting of 6 carbon atoms (denoted by C) and 6 hydrogen atoms (denoted by H). Each carbon atom forms a single covalent bond with a hydrogen atom, and the remaining bonds between carbon atoms can be represented by alternating single and double bonds in the ring.

Resonance in Benzene

Resonance structures are used to represent molecules where more than one Lewis structure can be written for a species, which differ only in the arrangement of electrons. In benzene, we can draw two resonance structures with alternate single and double bonds: 1. Single bond between C1 and C2, double bond between C2 and C3, single bond between C3 and C4, double bond between C4 and C5, single bond between C5 and C6, and finally a double bond between C6 and C1. 2. Double bond between C1 and C2, single bond between C2 and C3, double bond between C3 and C4, single bond between C4 and C5, double bond between C5 and C6, and finally a single bond between C6 and C1. These two resonance structures can be drawn easily by interconverting the single and double bonds.

Explaining Equal Bond Lengths using Resonance

Both resonance structures of benzene contribute equally to the overall structure. Benzene does not alternate between these two resonance forms; instead, its true structure is a hybrid of these resonance forms. In this hybrid (resonance) structure, each carbon-carbon bond is identical and intermediate between single and double bonds. The C-C bond lengths in the resonance hybrid are equal because the electron density of the double bonds is spread evenly over the entire molecule, making all the C-C bond lengths equal.

Comparing Bond Lengths in Benzene with Single and Double Bonds

(b) Now, we need to compare the bond lengths in benzene with single and double bonds. A C-C single bond is longer (and weaker) than a C=C double bond. As we have just seen, the C-C bonds in benzene are intermediate between single and double bonds. Therefore, the C-C bond lengths in benzene are shorter than C-C single bonds but longer than C=C double bonds.

Key concepts

Chemical Bonding in Benzene

Understanding chemical bonding is fundamental when studying molecules like benzene. In benzene, a cyclic compound with a unique hexagonal structure, each carbon atom bonds to two other carbons and one hydrogen atom. Normally, we would expect alternating single and double carbon-carbon bonds, but benzene challenges this notion.

Chemical bonds are the force that holds atoms together in a molecule. They vary in strength and length, with single bonds generally being the longest and weakest, and double bonds being shorter and stronger. In the case of benzene, the key to its stability and equal bond lengths lies within a concept called resonance.

Resonance is the phenomenon where the actual structure of a molecule is an average of multiple theoretical structures (known as resonance structures). These structures differ only in the placement of electrons, not the arrangement of atoms. Thus, the resonance in benzene leads to a distribution of electron density across the ring in a way that all the bond lengths become equal, neither truly single nor double, but somewhere in between. This contributes to benzene's stability and unique chemical behavior.

Lewis Structures and Benzene's Resonance

To comprehend the resonance in benzene, one must first be familiar with Lewis structures. Lewis structures are diagrams that represent the bonding between atoms of a molecule and the lone pairs of electrons that may exist. They are foundational for visualizing the arrangement of electrons in chemical species.

In benzene, Lewis structures reveal that there can be more than one way to arrange the pi electrons in the carbon-carbon bonds. By drawing the two possible arrangements of bonds—as seen in the resonance structures—we discover the electrons are delocalized. This means that instead of being confined to one specific location, the electrons are spread over the entire molecule. The delocalization is central to the concept of resonance, explaining how all carbon bonds in benzene maintain equal lengths and strengths.

The step-by-step solution mentioned before provides primary understanding, but to fully grasp the concept, students should practice drawing these Lewis structures. By doing so, they familiarize themselves with visualizing electron sharing and better understand molecular geometry in compounds similar to benzene.

Bond Length Comparison in Benzene

When comparing bond lengths, one must remember that a typical carbon-carbon (C-C) single bond is longer than a carbon-carbon double (C=C) bond. Benzene, with its resonance structures, falls into an interesting category. The C-C bonds in benzene are intermediate in length and strength; they are shorter than typical single bonds but longer than double bonds.

This intermediate nature arises due to the electron delocalization throughout the benzene ring. It is as if all the bonds are one-and-a-half bonds, rather than some being single and some being double. Understanding this can clarify why benzene has unusual chemical properties compared to other hydrocarbons. The bond length comparison is a brilliant example of the distinctiveness of benzene among hydrocarbons, with all bonds in the benzene ring being of the same length and strength, contributing to the molecule's symmetrical shape and stability.

By understanding these concepts, students can see the broader implications of resonance on molecular structure and stability. Not only does it explain the bond lengths in benzene, but it also underscores the importance of delocalized electrons in determining the physical and chemical properties of a molecule.