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 \(\mathrm{C}-\mathrm{C}\) single bonds? Are they shorter than \(\mathrm{C}=\mathrm{C}\) double bonds?

Short answer

The resonance of benzene, with two contributing structures, results in the delocalization of its pi electrons over all six carbon atoms. This delocalization leads to a fractional bond order between single and double bonds, causing equal bond lengths for all six carbon-carbon bonds. The C-C bond length in benzene is approximately 1.40 Å, which is intermediate between single (approximately 1.54 Å) and double (approximately 1.34 Å) C-C bond lengths.

Step-by-step solution

Understanding the concept of resonance in benzene

Benzene is a molecule with six carbon atoms arranged in a hexagonal planar ring. It has alternating carbon-carbon single and double bonds. To understand the equal bond length in benzene, we will apply the concept of resonance. Resonance is the phenomenon where a molecule is represented by two or more Lewis structures, called resonance structures or resonance forms, that contribute to the overall structure of the molecule. Benzene is a classic example of resonance.

Illustrate the resonance structures of benzene

Benzene has two resonance structures that contribute equally to the overall structure of the molecule. Resonance Structure 1: In this structure, the double bonds are located between the 1st and 2nd, 3rd and 4th, and 5th and 6th carbon atoms. Resonance Structure 2: In this structure, the double bonds are located between the 2nd and 3rd, 4th and 5th, and 6th and 1st carbon atoms. These two resonance structures are in rapid equilibrium, making it impossible to distinguish between the two structures experimentally. In reality, the bond lengths and strengths are intermediate between those of single and double bonds.

Explain the equal bond lengths in benzene

The resonance of benzene results in the delocalization of its pi electrons over all six carbon atoms. This delocalization means that each carbon-carbon bond has a fractional bond order between single and double bonds. Due to the rapid equilibrium between the resonance structures, all six carbon-carbon bonds in benzene have the same bond order, leading to equal bond lengths.

Comparing C-C bond lengths in benzene to single and double bonds

(b) Now let's compare the C-C bond lengths in benzene to those of C-C single bonds and C=C double bonds: 1. C-C single bond: A typical carbon-carbon single bond has a bond length of approximately 1.54 Å. 2. C=C double bond: A typical carbon-carbon double bond has a bond length of approximately 1.34 Å. 3. C-C bond in benzene: As mentioned earlier, the bond lengths in benzene are intermediate between single and double bonds. The C-C bond length in benzene is approximately 1.40 Å.

Conclusion

To sum up, the concept of resonance explains why all six C-C bonds in benzene are equal in length. The resonance in benzene results in the delocalization of its pi electrons and an intermediate bond length of approximately 1.40 Å, which is shorter than C-C single bonds and longer than C=C double bonds.

Key concepts

Delocalization of Pi Electrons

Understanding the concept of delocalization of pi electrons in benzene is crucial for comprehending its unique chemical behavior. Normally, pi electrons are located between two atoms, forming a pi bond, such as in a double bond. However, benzene, a hydrocarbon with a hexagonal ring structure, showcases a different scenario where these electrons are not confined to one area between adjacent atoms.

Instead, the pi electrons in benzene are shared across all six carbon atoms in a phenomenon known as electron delocalization. This results in a sort of 'electron cloud' above and below the plane of the carbon atoms, allowing the pi electrons to move freely within this cloud. This delocalization contributes to the stability of the benzene molecule and is responsible for its less reactive nature compared to other, more localized structures.

The implications of electron delocalization are significant. It explains the unexpected chemical properties of benzene and, crucially, it sets the stage for the uniform bond lengths observed within the molecule, as all bonds share the same electron density.

Equal C-C Bond Lengths in Benzene

The notion of equal C-C bond lengths within the benzene molecule can be puzzling at first glance given the alternating single and double bonds represented in its typical structural formula. However, benzene doesn't have distinct single and double bonds; instead, all of its bonds are of equal length due to resonance.

Resonance is like a blending of multiple structures, which in benzene's case, results in the pi electrons being shared evenly across all six carbon atoms. The two resonance structures of benzene are just human representations to understand this concept; the molecule itself is a hybrid of these structures. Consequently, each carbon-carbon bond is identical in length, measured to be approximately 1.40 Å. This uniformity is a direct result of the electron delocalization which spreads electron density evenly across the entire ring structure.

This is an essential concept in organic chemistry, altering our understanding of how molecular structure can influence both the physical and chemical properties of a substance. The equal bond lengths contribute to benzene's highly symmetrical structure, which is also a key factor in many of its reactions.

Comparison of Bond Lengths

When we compare the bond lengths in benzene to those in other hydrocarbons, we find a fascinating anomaly. Typically, C-C single bonds are longer, and C=C double bonds are shorter due to the additional electron density between the two atoms in a double bond. Specifically, a standard C-C single bond measures about 1.54 Å, while a C=C double bond is about 1.34 Å.

However, the C-C bond lengths in benzene are neither typical single nor double bond lengths. Instead, they are intermediate at around 1.40 Å. This unusual length is a testament to the hybrid nature of the bonds in benzene due to the resonance effect. It is longer than a standard double bond but shorter than a single bond, indicating that the actual electron distribution is somewhere in between these extremes.

What this means for the molecule is that it's not as reactive as compounds with pure double bonds, yet it's more rigid and less flexible than those with only single bonds. This perfect balance of bond lengths in benzene is a critical factor that shapes its chemical reactivity and stability. It's a classic example of structure dictating function in chemistry.