Biphenyl, \(\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{C}_{6} \mathrm{H}_{5}\), has a conjugation energy of 71 \(\mathrm{kcal} / \mathrm{mole}\) (a) Draw an atomic orbital picture of biphenyl, (b) What are its most important resonance contributing structures? (c) Estimate the heat of hydrogenation of biphenyl.

To draw the atomic orbital picture of biphenyl, we need to pay close attention to the structure and bonding pattern of this molecule. Biphenyl consists of two benzene rings connected by a single bond. Here’s the atomic orbital picture of biphenyl: H H // \\ C==C---C==C || || H--C==C C==C--H \\ // H H We can see that the two benzene rings are connected, and the carbon atoms in the benzene rings have a conjugated system of alternating single and double bonds.

Resonance contributing structures are different ways that a molecule can be represented by alternate placements of electrons while maintaining the same skeletal structure. In the case of biphenyl, the two benzene rings are considered aromatic, meaning that the electrons can delocalize around the carbon atoms in the ring. For each benzene ring, we have two resonance contributing structures: Ring 1: 1a) H-C==C-C==C-C==C-C || || || 1b) H==C-C==C-C==C-C \\ || C==C-C Ring 2: 2a) C-C==C-C==C-C==C-H || || \\ 2b) C==C-C==C-C==C-C-H \\ || Since the two rings are connected by a central single bond, we can represent the most important resonance structures for biphenyl by combining both the resonance structures for the two benzene rings. Biphenyl Main Resonance Contributing Structures: 1) 1a connected to 2a 2) 1a connected to 2b 3) 1b connected to 2a 4) 1b connected to 2b

The heat of hydrogenation is the amount of heat released when a molecule undergoes hydrogenation, which is the process of adding hydrogen atoms to unsaturated hydrocarbons to form saturated hydrocarbons. Biphenyl is an unsaturated hydrocarbon with a conjugation energy of 71 kcal/mol. We have two benzene rings in biphenyl, and a single benzene ring has a heat of hydrogenation of about 36 kcal/mol. Thus, if we hydrogenated both the rings, the heat of hydrogenation for biphenyl would be approximately twice that of benzene. Heat of hydrogenation of biphenyl = 2 x 36 kcal/mol ≈ 72 kcal/mol However, since we have a conjugation energy of 71 kcal/mol which contributes to the stability of the biphenyl molecule, we can estimate the heat of hydrogenation more accurately as: Heat of hydrogenation of biphenyl = (2 x 36) - 71 ≈ 1 kcal/mol Thus, we can estimate that the heat of hydrogenation for biphenyl is approximately 1 kcal/mol.