The standard molar enthalpies of formation of cyclohexane(l) and benzene liquid at 25*C are -156 and 49 kj/mol respectively. The standrd enthalpy of hydrogenation of cyclohexene(l) at 25*c is -119kj /mol. Use this data to estimate the magnitude of resonance energy of benzene.

To estimate the resonance energy of benzene using the provided data, we can apply some thermodynamic principles. The resonance energy is a measure of the stability of a molecule due to delocalized electrons, and in the case of benzene, it reflects how much more stable benzene is compared to a hypothetical structure that does not have resonance. Let's break down the calculation step by step.

Understanding the Concepts

First, we need to clarify a few terms:

• Standard Molar Enthalpy of Formation: This is the change in enthalpy when one mole of a compound is formed from its elements in their standard states.
• Enthalpy of Hydrogenation: This refers to the heat released when a compound reacts with hydrogen to form a saturated compound. For cyclohexene, this is the reaction that converts it to cyclohexane.

Given Data

We have the following values:

• Standard molar enthalpy of formation of cyclohexane (C6H12): -156 kJ/mol
• Standard molar enthalpy of formation of benzene (C6H6): 49 kJ/mol
• Standard enthalpy of hydrogenation of cyclohexene: -119 kJ/mol

Calculating the Enthalpy Change for Benzene Hydrogenation

To find the resonance energy, we first need to calculate the enthalpy change for the hydrogenation of benzene to cyclohexane. The reaction can be represented as:

C6H6 + 3H2 → C6H12

The enthalpy change for this reaction can be derived from the enthalpies of formation:

ΔH = [Enthalpy of formation of products] - [Enthalpy of formation of reactants]

Substituting the values, we get:

ΔH = [(-156 kJ/mol)] - [49 kJ/mol] = -156 kJ/mol - 49 kJ/mol = -205 kJ/mol

Relating Hydrogenation to Resonance Energy

The enthalpy of hydrogenation of benzene can be thought of as the energy released when benzene is converted to cyclohexane. However, we need to consider the enthalpy of hydrogenation of cyclohexene as well. The enthalpy of hydrogenation for cyclohexene is given as -119 kJ/mol.

Now, the total enthalpy change for the hydrogenation of benzene can be expressed as:

ΔH (benzene) = ΔH (cyclohexene) + Resonance Energy

Rearranging this gives us:

Resonance Energy = ΔH (benzene) - ΔH (cyclohexene)

Substituting the values we calculated:

Resonance Energy = -205 kJ/mol - (-119 kJ/mol) = -205 kJ/mol + 119 kJ/mol = -86 kJ/mol

Final Thoughts

The magnitude of the resonance energy of benzene is approximately 86 kJ/mol. This value indicates how much more stable benzene is compared to a hypothetical structure that does not have resonance. In essence, the resonance energy is a reflection of the delocalization of electrons in the benzene ring, contributing to its unique stability and aromatic character.