Problem 35 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

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 \(-119\) \(\mathrm{kJ} \mathrm{mol}^{-1}\). Use these data to estimate the magnitude of the resonance energy of benzene.

Step-by-Step Solution

Answer

The resonance energy of benzene is 150 kJ/mol.

Step 1: Understand the Problem

We need to calculate the resonance energy of benzene using given enthalpies. Resonance energy is the difference between the experimental enthalpy of benzene and the theoretical enthalpy if benzene behaved like an isolated double bond hydrocarbons.

Step 2: Write the Hydrogenation Reactions

The hydrogenation of cyclohexene to cyclohexane is given as \(-119 \, \text{kJ/mol}\). The hydrogenation of benzene produces cyclohexane. Use these reactions to evaluate the enthalpy change for benzene.

Step 3: Calculate Theoretical Enthalpy of Benzene

The theoretical enthalpy of benzene if it had isolated double bonds can be calculated by multiplying cyclohexene's enthalpy of hydrogenation \(-119 \, \text{kJ/mol}\) by 3 (since benzene would have 3 double bonds in isolated state): \(-119 \, \text{kJ/mol} \times 3 = -357 \, \text{kJ/mol}\).

Step 4: Calculate the Experimental Enthalpy of Benzene

The experimental enthalpy of formation of benzene is given as \(+49 \, \text{kJ/mol}\). To find the experimental enthalpy change when benzene forms cyclohexane, subtract \(-156 \, \text{kJ/mol}\) (enthalpy of cyclohexane): \(+49 \, \text{kJ/mol} - (-156 \, \text{kJ/mol}) = -207 \, \text{kJ/mol}\).

Step 5: Calculate Resonance Energy

The resonance energy of benzene is the difference between the theoretical and experimental enthalpies of benzene: \(-207 \, \text{kJ/mol} - (-357 \, \text{kJ/mol}) = 150 \, \text{kJ/mol}\). Thus, resonance energy is \(150 \, \text{kJ/mol}\).

Key Concepts

Enthalpy of Hydrogenation

The enthalpy of hydrogenation refers to the heat change that occurs when one mole of an unsaturated compound (like alkenes) reacts with hydrogen to become a saturated compound. This process usually involves the formation of single bonds, replacing double or triple bonds. It is typically exothermic, meaning that heat is released and the enthalpy change is negative.

For cyclohexene, the enthalpy of hydrogenation is \(-119 \, \text{kJ/mol}\), because the process of converting it into cyclohexane releases a significant amount of energy. By understanding this value, we can derive theoretical predictions for other molecules, such as benzene. The greater the negative value, the more energy is released in forming the saturated compound.

This enthalpy is a useful way to gauge the stability of unsaturated compounds, as more stable compounds tend to have less negative enthalpy of hydrogenation.

Enthalpy of Formation

Enthalpy of formation is the change in energy when one mole of a compound is formed from its elements under standard conditions. This is often measured in \(\text{kJ/mol}\).

For instance, cyclohexane has an enthalpy of formation of \(-156 \, \text{kJ/mol}\), while benzene's is \(+49 \, \text{kJ/mol}\). These values give insights into the energy required to produce each compound from its basic elements, typically in their most stable form.

Understanding the enthalpy of formation helps predict the stability and reactivity of a compound. A negative value indicates that energy is released, showing the compound is lower in energy and more stable. A positive value, as in benzene, suggests a less stable compound in terms of its elemental formation.

Cyclohexane

Cyclohexane is a saturated, cyclic hydrocarbon with the formula \(\text{C}_6\text{H}_{12}\). It consists entirely of carbon single bonds, forming a closed ring structure.

Due to its saturated nature, cyclohexane is relatively stable. The enthalpy of formation \(-156 \, \text{kJ/mol}\) indicates that cyclohexane is a thermodynamically favorable compound, releasing energy upon its formation.

Cyclohexane serves as the product of hydrogenation reactions involving unsaturated ring compounds, such as cyclohexene and benzene. Its stable nature makes it a crucial comparison point when discussing the stability of other cyclic compounds.

Cyclohexene

Cyclohexene is a cyclic hydrocarbon that contains a single double bond within its six-carbon ring, with the formula \(\text{C}_6\text{H}_{10}\). As an unsaturated compound, it can undergo hydrogenation to form cyclohexane.

The enthalpy of hydrogenation for cyclohexene is \(-119 \, \text{kJ/mol}\), indicating that when it reacts with hydrogen, it forms the more stable cyclohexane, releasing energy in the process.

Cyclohexene plays a significant role in understanding resonance energies, especially when comparing it to benzene. Studying these transformations offers insights into the stability of aromatic hexagonal structures.

Benzene

Benzene is an aromatic hydrocarbon with the formula \(\text{C}_6\text{H}_6\), characterized by a ring structure with alternating double bonds. However, due to resonance, these double bonds are not isolated but rather delocalized, giving benzene its unique stability.

The enthalpy of formation of benzene is positive at \(+49 \, \text{kJ/mol}\), indicating higher energy compared to isolated double bond formations. Calculating benzene's resonance energy involves comparing the actual formation enthalpy to a theoretical value derived from isolated double bonds, revealing an additional stability feature due to resonance.

Benzene's particular stability is a central subject in studies of aromatic chemistry, and assessing its formation angles helps understand its unique properties.

Double Bond Hydrocarbons

Hydrocarbons containing double bonds are known as unsaturated hydrocarbons and can include compounds like alkenes and aromatic rings. The presence of double bonds results in higher reactivity compared to saturated hydrocarbons, which only have single bonds.

These bonds can be "isolated" or "delocalized". Isolated double bonds, like in alkenes, contribute to reactions like hydrogenation, releasing energy to form saturated products.

Aromatic hydrocarbons like benzene have delocalized "pi" electrons across the ring, offering increased stability. The resonance in compounds like benzene leads to less negative values in their enthalpies compared to theoretical isolated bond compounds.

Double bond hydrocarbons are pivotal in chemical synthesis and industrial applications, with their varied reactivities important in forming more complex chemical structures.