Question

The enthalpy of hydrogenation of benzene is \(-51.0\) kcal/mol. If enthalpy of hydrogenation of 1,4 -cyclohexadiene and cyclohexene is \(-58 \mathrm{kcal} / \mathrm{mol}\) and \(-29 \mathrm{kcal} / \mathrm{mol}\), respectively, what is the resonance energy of benzene? (a) \(29 \mathrm{kcal} / \mathrm{mole}\) (b) \(36 \mathrm{kcal} / \mathrm{mole}\) (c) \(58 \mathrm{kcal} / \mathrm{mole}\) (d) \(7 \mathrm{kcal} / \mathrm{mole}\)

Short answer

The resonance energy of benzene is \textbf{(b) 36 kcal/mol}.

Step-by-step solution

Understanding the concept of resonance energy

The resonance energy of a compound is the difference in the energy between the real molecule and the energy of the most stable contributing structure, which is often hypothetical and does not exist. In the case of benzene, the resonance energy represents the stabilization it experiences due to the delocalization of electrons within its ring structure.

Calculating the hypothetical enthalpy of hydrogenation of benzene

Assuming that benzene undergoes hydrogenation in a similar fashion to 1,4-cyclohexadiene, the theoretical enthalpy of hydrogenation for benzene, if it had three isolated double bonds as in cyclohexatriene, would be three times the enthalpy of hydrogenation of cyclohexene. That is, it would be \( 3 \times -29 \mathrm{kcal} / \mathrm{mol} = -87 \mathrm{kcal} / \mathrm{mol} \).

Calculating the resonance energy

The resonance energy of benzene can be calculated by subtracting the actual enthalpy of hydrogenation of benzene from the hypothetical enthalpy of hydrogenation calculated in Step 2. So, resonance energy = hypothetical enthalpy - actual enthalpy = \( -87 \mathrm{kcal} / \mathrm{mol} - (-51.0 \mathrm{kcal} / \mathrm{mol}) = -87 + 51 = -36 \mathrm{kcal} / \mathrm{mol} \). Since energy released is being considered positive in this context, the positive sign of the resonance energy indicates the resonance stabilization of benzene.

Key concepts

Enthalpy of Hydrogenation

The enthalpy of hydrogenation is a thermodynamic quantity that measures the heat released when a molecule undergoes the addition of hydrogen, typically turning unsaturated bonds, like those found in alkenes and alkynes, into single bonds as in alkanes. In simpler terms, it's the energy change that occurs when double or triple bonds in a hydrocarbon are converted into single bonds with the addition of hydrogen atoms.

For benzene, a molecule with a ring structure and alternating double bonds, the enthalpy of hydrogenation is a vital indicator of its chemical stability. The value for benzene's hydrogenation is lower than expected when compared to similar non-conjugated systems, hinting at its special stability. Through calculations, we are able to discern the energy content from this process and further understand the molecular stability and resonance energy which is an intriguing property of benzene and other aromatic compounds.

Delocalization of Electrons

Delocalization of electrons is a concept central to the understanding of the chemical stability of molecules like benzene. Normally in hydrocarbons, electrons are shared between two atoms to form a bond. However, in benzene, the electrons are not localized between individual carbon atoms. Instead, they are spread out or 'delocalized' over the entire ring of carbon atoms.

Imagine electrons in benzene like a fluid, in a ring-shaped container, constantly moving around, rather than being stuck between two atoms. This distribution of electronic charge over the entire structure contributes to the extraordinary stabilization of benzene, which reflects in the lower than expected enthalpy of hydrogenation. Through delocalization, the electrons in benzene are able to evenly distribute the energy throughout the molecule, leading to an even distribution of charge and increased stability.

Stabilization Energy

Stabilization energy, in the context of benzene, refers to the additional stability that benzene experiences due to the delocalization of its electrons. It's a bit like extra savings in energy that benzene has compared to what we would expect if it were just a typical hydrocarbon with localized bonds.

Calculating stabilization energy involves comparing the actual enthalpy of hydrogenation of benzene with the hypothetical value calculated for a non-delocalized structure (cyclohexatriene), assumed to have similar bonding without electron delocalization. The resonance energy, which is a form of stabilization energy, signifies how much more stable benzene is as compared to what we would predict without considering the delocalization. The significant disparity between the expected and observed enthalpies of hydrogenation underlines the concept of resonance energy and by extension, stabilization energy, as a measure of 'extra stability' granted by the electron cloud being shared over the whole molecule.