Problem 100 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard molar enthalpies of formation of cyclohexane (1) and benzene (1) at \(25^{\circ} \mathrm{C}\) are \(-156\) and \(+49 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The standard enthalpy of hydrogenation of cyclohexene (1) at \(25^{\circ} \mathrm{C}\) is \(-119 \mathrm{~kJ} /\) mol. Find resonance energy of benzene. (a) \(-152 \mathrm{kJmol}^{-1}\) (b) \(-159 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(+152 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(+159 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-Step Solution

Answer

The resonance energy of benzene is \(-152\,\text{kJ/mol}\).

Step 1: Identify Given Data

We are given the standard molar enthalpies of formation of cyclohexane and benzene as \(-156\,\text{kJ/mol}\) and \(+49\,\text{kJ/mol}\) respectively. The standard enthalpy of hydrogenation of cyclohexene is given as \(-119\,\text{kJ/mol}\). We are to find the resonance energy of benzene.

Step 2: Calculate Theoretical Enthalpy of Hydrogenation of Benzene

If benzene had no resonance stability, it would behave like three cyclohexene rings. As such, the enthalpy of hydrogenation of benzene theoretically would be three times that of cyclohexene: \[-119\,\text{kJ/mol} \times 3 = -357\,\text{kJ/mol}.\]

Step 3: Calculate Actual Enthalpy of Hydrogenation of Benzene

The actual enthalpy of formation of benzene directly to the saturated state (i.e., cyclohexane) can be found by subtracting the enthalpy of formation of benzene from that of cyclohexane: \( \Delta H_{\text{actual}} = -156 \,\text{kJ/mol} - (+49\,\text{kJ/mol}) = -205\,\text{kJ/mol}. \)

Step 4: Determine Resonance Energy of Benzene

The resonance energy is the difference between the theoretical and actual enthalpy of hydrogenation of benzene:\( \text{Resonance Energy} = (-357\,\text{kJ/mol}) - (-205\,\text{kJ/mol}) = -152\, \text{kJ/mol}. \)

Step 5: Choose Correct Answer from Options

The calculated resonance energy of benzene is \(-152\,\text{kJ/mol}\). Thus, the correct answer is option (a) \(-152\,\text{kJ/mol}\).

Key Concepts

Enthalpy of Formation

Enthalpy of formation is a fundamental concept in thermodynamics that describes the heat change when one mole of a compound is formed from its elements in their standard states. It's often represented as \( \Delta H_f^\circ \) and is expressed in kilojoules per mole (kJ/mol).
Understanding enthalpy of formation helps us grasp how energy is stored and released during chemical reactions.
For many compounds, values of enthalpies of formation are well-documented. For example:

• Cyclohexane's enthalpy of formation is \(-156 \, \text{kJ/mol}\).
• Benzene's is \(+49 \, \text{kJ/mol}\).

These values reveal the energy dynamics in reactions involving these substances. A negative value indicates that energy is released during the compound's formation, whereas a positive value shows that energy is absorbed.
Enthalpy of formation plays a critical role in calculating other thermodynamic properties, like enthalpy of reaction, aiding in determining whether reactions are exothermic or endothermic.

Enthalpy of Hydrogenation

Enthalpy of hydrogenation refers to the heat change that occurs when hydrogen is added to a compound. This process usually turns unsaturated compounds into saturated ones by adding hydrogen atoms.
For cyclohexene, the enthalpy of hydrogenation is \(-119 \, \text{kJ/mol}\), denoting the energy released when converting cyclohexene to a fully saturated compound like cyclohexane.
When theorizing benzene’s enthalpy of hydrogenation without resonance, it's treated as having three cyclohexene-like units. The calculation becomes:\[ -119 \, \text{kJ/mol} \times 3 = -357 \, \text{kJ/mol}. \]This theoretical value contrasts with the actual enthalpy of benzene formation, underscoring the concept of resonance energy.
Understanding enthalpy of hydrogenation offers insights into reaction stability and the energetic favorability of hydrogenation reactions.

Chemical Thermodynamics

Chemical thermodynamics is the study of heat and energy in chemical reactions. It encompasses principles like enthalpy, entropy, and free energy, which describe the energetic feasibility of reactions.
Thermodynamics aids in predicting if reactions will occur spontaneously and how conditions like temperature and pressure affect such reactions.
In the context of benzene's resonance energy:

• **Resonance energy** accounts for the extra stability benzene gains through electron delocalization, impacting its thermodynamic behavior.
• The difference between the calculated theoretical and actual enthalpies of hydrogenation illustrates resonance energy, offering a measure of stability in aromatic compounds.

These concepts offer a comprehensive view of how energy dynamics influence the formation, reaction pathways, and stability of chemical substances. Understanding them is essential for exploring organic reactions and designing energy-efficient chemical processes.