Question

Would you expect the value of \(\Delta H_{\mathrm{f}}^{\circ}\) for benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\) computed from tabulated bond energies, to be very close to the experimentally measured value of \(\Delta H_{\mathrm{f}}^{\circ}\) ? Justify your answer.

Short answer

The value of \(\Delta H_{\mathrm{f}}^{\circ}\) for benzene computed from tabulated bond energies is not expected to be very close to the experimental value, because the bond energies do not account for the resonance stabilization in benzene.

Step-by-step solution

Understand the Concept of Heat of Formation

The heat of formation, \(\Delta H_{\mathrm{f}}^{\circ}\), is defined as the heat change associated with the formation of one mole of a compound from its elements in their standard states. Theoretical values can be calculated using bond energies, which are average values of the energy required to break each type of bond in a molecule.

Consider the Limitations of Bond Energies

Bond energies are average values derived from a variety of different molecules and do not account for the specific molecular environment. In benzene, the resonance stabilization and the delocalized pi-electron system can make the actual bond energies different from the tabulated average bond energies.

Assess the Expectation for Benzene

Given that bond energies are averages and do not account for the unique stabilization in benzene, we would not expect the calculated \(\Delta H_{\mathrm{f}}^{\circ}\) for benzene to be very close to the experimentally measured value. The experimental value for benzene will likely be lower (more negative) than the theoretical value calculated from average bond energies due to the resonance energy.

Key concepts

Bond Energies

Understanding bond energies is crucial when evaluating chemical reactions and predicting the energy changes involved. In essence, bond energy is a measure of the strength of a chemical bond and is defined as the average amount of energy required to break one mole of bonds in their standard state.

However, when it comes to complex molecules, like benzene, these average bond energies might not accurately reflect the true energy requirements for bond-breaking. This discrepancy occurs because these average values are drawn from an array of different molecules and do not consider the unique electronic interactions present in a particular molecule. In the case of benzene, the ring structure with its alternating double bonds leads to a more stable configuration that is not accounted for by simple summation of average bond energies.

Therefore, if one were to calculate the heat of formation of benzene using these average values, the resulting figure would be an approximation that neglects the stabilization brought about by the molecule's specific structure and electronic arrangements.

Resonance Stabilization

What is Resonance Stabilization?

Resonance stabilization plays a pivotal role in understanding the stability of certain molecules, such as benzene. It refers to the phenomenon where the true structure of a molecule is represented as a hybrid of multiple Lewis structures (resonance structures). These structures differ only in the position of electrons, not the position of nuclei.

For benzene, the resonance stabilization arises from the equal distribution of electrons over the six carbon atoms. This delocalization of electrons leads to a structure that is more stable than any conceivable individual Lewis structure with localized electrons. As a consequence, the molecular stability, and thus the energy associated with benzene, is significantly higher than one would predict based solely on average bond energies. When calculating the heat of formation, failing to consider resonance effects can result in a theoretical value that is higher (less negative) than what is observed experimentally.

Pi-electron System

The Delocalized Pi-electron System in Benzene

The concept of a pi-electron system is central to the stability and unique chemical properties of aromatic compounds like benzene. In these systems, pi electrons, which are found in p orbitals above and below the plane of the atoms, can delocalize over the entire molecule. This electron delocalization is a key factor contributing to the resonance stabilization mentioned previously.

In benzene, the six pi electrons are not confined to individual double bonds as they would be in isolated alkenes, but rather spread out equally over the entire ring. This results in a type of electron cloud that provides extra stability. From a bond energy perspective, this means that the strength of the carbon-carbon bonds in benzene lies somewhere between a single and a double bond, defying assignment to any single set of average bond energy values. The delocalized pi-electron system is a significant aspect that influences the heat of formation and makes the experimental value for benzene more negative than theoretical calculations relying on discrete bond energies would suggest.