Question

(a) Do the \(\mathrm{C}-\mathrm{C}\) bond lengths in benzene alternate shortlong-short-long around the ring? Why or why not? (b) Are \(\mathrm{C}-\mathrm{C}\) bond lengths in benzene shorter than \(\mathrm{C}-\mathrm{C}\) single bonds? (c) Are \(\mathrm{C}-\mathrm{C}\) bond lengths in benzene shorter than \(\mathrm{C}=\mathrm{C}\) double bonds?

Short answer

(a) No, the C-C bond lengths in benzene do not alternate short-long around the ring. They are equivalent due to the delocalized pi electron cloud giving the bonds an intermediate character between single and double bonds. (b) Yes, C-C bond lengths in benzene (1.39 Å) are shorter than C-C single bond lengths (1.54 Å). (c) No, C-C bond lengths in benzene (1.39 Å) are slightly longer than C=C double bond lengths (1.34 Å), due to the intermediate bond character.

Step-by-step solution

(a) Analyzing the molecular structure of benzene

Benzene (C6H6) is an aromatic compound that has a hexagonal ring structure with carbon atoms (C) at the vertices and a hydrogen atom (H) attached to each carbon. Each carbon atom is sp2 hybridized and forms three sigma bonds, one with each of its two neighboring carbon atoms, and one with a hydrogen atom. Additionally, there is a delocalized pi electron cloud above and below the plane of the hexagonal ring, formed by the overlapping p orbitals of the carbon atoms.

(a) Understanding the C-C bond lengths

Due to the delocalized pi electron cloud, the carbon-carbon bonds in benzene are neither purely single bonds nor double bonds. Instead, it is a resonance hybrid of its Kekulé structure, where the pi electrons are shared equally among all six carbon atoms. This gives the C-C bonds in benzene an intermediate character between a single and a double bond, resulting in equivalent bond lengths all around the ring rather than alternating short-long bond lengths.

(b) Comparing C-C bond lengths in benzene and single bonds

A carbon-carbon single bond (C-C) has a bond length of approximately 1.54 Å, while the C-C bond length in benzene is found to be around 1.39 Å. So, the C-C bond lengths in benzene are shorter than C-C single bond lengths due to the presence of the delocalized pi electron cloud that leads to a partial double bond character.

(c) Comparing C-C bond lengths in benzene and double bonds

Carbon-carbon double bonds (C=C) have a bond length of approximately 1.34 Å. Comparing this to the C-C bond length in benzene (1.39 Å), we notice that the bond lengths in benzene are slightly longer than C=C double bond lengths. The reason for this difference is that the delocalized pi electrons in benzene contribute to the intermediate character between a single and a double bond, rather than a pure double bond.

Key concepts

Aromatic Compounds

Aromatic compounds are a unique and fascinating class of organic molecules characterized by their ring-shaped chemical structure. Benzene is one of the most well-known examples, playing a central role in the study of aromaticity. Typically, these compounds contain a planar, cyclic array of atoms, usually carbon, which participate in the phenomenon of resonance. This resonance involves the delocalization of electrons across the structure, contributing to the unique stability and reactivity of aromatic molecules.

Benzene, with its formula of C₆H₆, exhibits equal bond lengths and angles due to its aromatic nature. This means all carbon-carbon bonds in benzene are of equal length, unlike non-aromatic rings that may show varying bond lengths. Aromatic compounds are highly stable, making them resistant to reactions that would typically disrupt non-aromatic rings, such as hydrogenation under mild conditions. Understanding aromatic compounds opens a window to comprehend how nature utilizes aromatic systems, from DNA bases to crucial vitamins.

Resonance Hybrid

The concept of resonance hybrid is essential in understanding the structure of benzene and many other aromatic compounds. In simple terms, a resonance hybrid is a way to depict a molecule where multiple forms or "structures" can be drawn, and the actual molecule is an average of these forms.

In the case of benzene, it is commonly drawn using two alternating "Kekulé structures". In these structures, single and double bonds swap positions around the ring. However, the true nature of benzene is a resonance hybrid of these forms, meaning that all C-C bonds in benzene are of equal length and character. This equality results from the delocalization of electrons, which prevents the bonds from being purely single or purely double. The resonance hybrid effectively captures this unique electron sharing, giving benzene its balanced and stable structure.

Carbon-Carbon Bonds

Carbon-carbon bonds are fundamental linkages that form the backbone of organic chemistry. In benzene, these bonds are neither typical single ( C-C) bonds nor double ( C=C) bonds. Instead, due to the resonance hybrid structure of benzene, the carbon-carbon bonds have a length and strength that falls intermediate between a single and a double bond.

In quantitative terms, a standard C-C single bond length is about 1.54 Å (angstroms), and a double bond is approximately 1.34 Å. Benzene's carbon-carbon bonds measure roughly 1.39 Å, showing this intermediate distance. This bond length reflects neither the full characteristics of a single bond nor those of a double bond. The intermediate nature of these benzene C-C bonds showcases the impact of electron delocalization, making them unique.

Delocalized Pi Electrons

Delocalized pi electrons are at the heart of the chemistry of benzene and other aromatic compounds. These electrons are not confined to a single bond or a lone pair of atoms but instead hover above and below the plane of the benzene ring, covering all the carbon atoms.

Think of delocalized pi electrons as a shared cloud of electrons that help evenly distribute charge across the molecular structure of benzene. This delocalization stabilizes benzene and contributes to its resistance to reactions typically seen in non-aromatic compounds. Instead of there being distinct "pi bonds" between specific pairs of atoms, the electrons are shared equally, resulting in the observed bond equalization and intermediate bond lengths in benzene. Understanding the role of these delocalized pi electrons helps explain much of benzene's distinct chemical behavior and structural properties.