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.

Short 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-by-step solution

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.

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.