Problem 57 - Chemistry: The Central Science in SI Units, Global Edition

Question

True or false: \((\mathbf{a})\) The \(\mathrm{C}-\mathrm{C}\) bonds in benzene are all the same length and correspond to typical single \(\mathrm{C}-\mathrm{C}\) bond lengths. (b) The \(\mathrm{C}-\mathrm{C}\) bond in acetylene, \(\mathrm{HCCH}\), is longer than the average \(\mathrm{C}-\mathrm{C}\) bond length in benzene.

Step-by-Step Solution

Answer

(a) False: All C-C bonds in benzene are the same length, but they have an intermediate length between typical single and double C-C bond lengths due to resonance. (b) False: The C-C bond in acetylene is shorter, not longer, than the average C-C bond length in benzene because it is a triple bond formed by the overlap of sp-hybridized orbitals.

Step 1: Statement A: Benzene C-C bonds are all the same length and correspond to typical single C-C bond lengths

Benzene has a planar, hexagonal ring structure with alternating single and double bonds between carbon atoms. However, due to resonance, the pi electrons in these double bonds are delocalized across all six carbon atoms, resulting in a bond length that is intermediate between a typical single bond and a double bond. Therefore, it's true that all C-C bonds in benzene are the same length, but they do not correspond to typical single C-C bond lengths. As a consequence, statement A is false.

Step 2: Statement B: The C-C bond in acetylene is longer than the average C-C bond length in benzene

Acetylene has a triple bond between its two carbon atoms, which results from the overlap of sp-hybridized orbitals. Triple bonds are shorter and stronger than single or double bonds. So, the C-C bond in acetylene is actually shorter than the average C-C bond length in benzene. Therefore, statement B is false. Both statements A and B are false.

Key Concepts

Benzene

Benzene is a fascinating and unique molecule known for its ring-like structure consisting of six carbon atoms arranged in a hexagonal shape. The core attraction here is how benzene distributes electrons. Unlike simple organic compounds that switch between single and double bonds, benzene has alternating single and double bonds. Yet, the bonds are not straightforwardly single or double. Instead, in benzene, the pi electrons are delocalized across the entire carbon ring. This delocalization makes all the carbon-carbon (C-C) bonds the same length, somewhere between a single and a double bond length. This equality in bond length is a key feature, distinguishing it from other hydrocarbons. Ultimately, benzene's structure offers stability and symmetry thanks to this equal bond length attributed to resonance.

Resonance

The concept of resonance is crucial in understanding molecular structure like that of benzene. Resonance refers to the phenomenon where electrons are not localized to single bonds but can occupy multiple positions in a molecule. In benzene, this means the pi electrons float around the carbon ring freely rather than sticking to one specific bond. The resonance creates a situation where the benzene molecule is best represented not by one single structure but a combination of two or more structures, often called resonance structures.

• Resonance results in lower energy and more stability for the molecule.
• It allows bonds to have an equal length and strength that is intermediate between two extremes.

Understanding resonance in benzene highlights why the carbon-carbon bonds are not strictly single or double bonds, but a blend of the two.

Triple Bond

Triple bonds are something special in chemistry, recognized for their strength and shortness compared to single and double bonds. Acetylene is one of the simplest molecules that showcases a triple bond. In acetylene, a triple bond occurs between two carbon atoms, indicating that three pairs of electrons are shared.

• One pair of electrons forms a sigma bond via the overlap of sp-hybridized orbitals.
• The other two pairs create pi bonds through the overlap of unhybridized p orbitals.

This configuration explains why triple bonds are exceptionally stronger and shorter compared to other types of C-C bonds. This makes the acetylene bond considerably shorter than those found in benzene, demonstrating a noteworthy comparison between bond lengths affected by different bonding orders.

C-C Bond Length

When discussing the C-C bond length, it's crucial to consider both the types of bonds and their electronic structures. The bond length generally decreases as the bond order increases because more electrons are pulling the atoms together with greater force. In hydrocarbons like benzene, the C-C bond length is intermediate due to resonance, making it not quite as short as a typical double bond but far shorter than a usual single bond length.

• Single C-C bonds are the longest and appear in many basic organic structures.
• Double C-C bonds are shorter due to additional shared electrons.
• Triple C-C bonds are the shortest, evident in acetylene, showcasing tightly held atoms

This hierarchy helps to explain why the bonds in benzene are uniform in length, standing apart from structures reliant on fixed single or double bond configurations.