Question

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

Short answer

(a) False - The C-C bonds in benzene are all the same length, about 1.40 Å, but they do not correspond to typical single C-C bond lengths (1.54 Å) due to the bond order of 1.5. (b) False - The C-C bond in acetylene, HCCH, is shorter (approximately 1.20 Å) than the average C-C bond length in benzene (1.40 Å) due to the presence of a triple bond.

Step-by-step solution

Understand the structure of benzene

Benzene (C6H6) is a flat aromatic hydrocarbon with six carbon atoms and six hydrogen atoms. The carbon atoms form a hexagonal ring, and the C-C bonds within the ring have alternating single and double bonds due to resonance. In reality, the electrons within the double bonds are delocalized, leading to a bond order of 1.5 for each C-C bond in the benzene ring.

Compare benzene C-C bonds to a typical single bond

A typical single C-C bond length is approximately 1.54 Å (angstroms). However, the bond length in benzene is shorter, as it has a bond order of 1.5 due to delocalized π electrons. The C-C bond length in benzene is about 1.40 Å, which is shorter than a typical single C-C bond.

Determine the truth of statement (a)

Statement (a) says that the C-C bonds in benzene are all the same length and correspond to typical single C-C bond lengths. Although it is true that all the C-C bonds in benzene are of the same length, they do not correspond to typical single C-C bond lengths. Therefore, statement (a) is false.

Understand the structure of acetylene

Acetylene (C2H2) is a linear hydrocarbon molecule with a triple bond between the two carbon atoms. This triple bond consists of one σ bond and two π bonds.

Compare acetylene C-C bonds to benzene C-C bonds

The C-C bond in acetylene is a triple bond, which is stronger and shorter than the partial double bond (bond order 1.5) in benzene. The C-C triple bond length in acetylene is approximately 1.20 Å, which is shorter than the C-C bond length in benzene (1.40 Å).

Determine the truth of statement (b)

Statement (b) claims that the C-C bond in acetylene is longer than the average C-C bond length in benzene. This statement is false, as the C-C bond in acetylene is shorter than the C-C bond length in benzene due to the presence of a triple bond. In summary: (a) False - The C-C bonds in benzene are all the same length but do not correspond to typical single C-C bond lengths. (b) False - The C-C bond in acetylene is shorter than the average C-C bond length in benzene.

Key concepts

Resonance in Chemistry

Resonance is a fundamental concept in chemistry that helps explain the stability and structure of certain molecules, including aromatic compounds like benzene. At its core, resonance involves the delocalization of electrons across multiple atoms within a molecule. This means that instead of electrons being solely associated with one atom or a pair of atoms, they are spread out over several atoms.

For example, in benzene (C6H6), the molecule displays resonance as the electrons from the π (pi) bonds—the bonds above and below the plane of atoms—are not confined to a single pair of carbon atoms. Instead, these electrons are shared across all six carbon atoms, creating a delocalized electron cloud. This electron delocalization leads to all C-C bonds in benzene being of equal length and intermediate between a single and double bond, with a bond order of 1.5. As a consequence of resonance, benzene exhibits unique stability and a lower reactivity compared to other unsaturated hydrocarbons.

C-C Bond Length

The carbon-carbon (C-C) bond length significantly influences the physical and chemical properties of molecules. In simple terms, bond length is the distance between the nuclei of two bonded carbon atoms. The length of a C-C bond is determined by the type of bond it is: single, double, or triple.

Let's consider a typical single C-C bond, which has a bond length of around 1.54 Å. In contrast, the delocalized electrons in the benzene ring due to resonance affect the C-C bond length, making it shorter, approximately 1.40 Å, than a typical single bond. Importantly, each of these bonds in benzene is equivalent, contrary to what might be expected if they alternated between single and double bonds without resonance. On the other hand, the bond length of the triple bond in acetylene is even shorter, about 1.20 Å, due to the higher bond order and greater electron sharing between the two carbons, making it more compact and stronger than the bonds in benzene.

Acetylene Molecular Structure

Triple Bonding and Linearity

Acetylene's molecular structure showcases a fascinating aspect of chemical bonding: the triple bond. The triple bond is made up of one sigma (σ) bond and two pi (π) bonds. The sigma bond forms from head-to-head overlap of atomic orbitals, and the pi bonds form from side-by-side overlap. The result is a robust and notably shorter bond compared to single and double bonds.

Implications for Reactivity

The acetylene molecule, being linear and consisting of a triple bond, is quite unique. The linear shape arises because the sp-hybridized carbon atoms in acetylene align to maximize the separation of the two pi bonds, consistent with VSEPR theory, which predicts molecular shapes based on electron pair repulsion. The triple bond also marks acetylene as a highly reactive molecule, capable of undergoing addition reactions with relative ease, as the pi bonds are available to react with other substances. Understanding acetylene's structure explains not only its bond lengths but also its significant role in organic reactions, such as in the synthesis of a vast array of chemical products.