Problem 138 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard molar enthalpies of formation of cyclohexane \((I)\) and benzene \((l)\) are \(-155 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(+49\) \(\mathrm{kJ} \mathrm{mol}^{-1}\) respectively. The standard enthalpy of hydrogenation of cyclohexane \((I)\) at \(25^{\circ} \mathrm{C}-120 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Resonance energy per gram of benzene is approximately _______ kJ.

Step-by-Step Solution

Answer

The resonance energy per gram of benzene is approximately -1.08 kJ/g.

Step 1: Understand the Given Information

We are given the standard molar enthalpies of formation for cyclohexane (given as \( -155 \text{ kJ/mol} \)) and benzene (given as \( +49 \text{ kJ/mol} \)). Additionally, the standard enthalpy of hydrogenation of cyclohexane is \( -120 \text{ kJ/mol} \). We need to find the resonance energy per gram of benzene.

Step 2: Calculate the Enthalpy Change for Benzene Hydrogenation

Hydrogenation of benzene would produce cyclohexane, given by the equation: \[ \text{C}_6\text{H}_6 + 3 \text{H}_2 \rightarrow \text{C}_6\text{H}_{12} \]. The enthalpy change for this reaction corresponds to the difference between the enthalpies of formation of the products and the reactants. This calculates to:\[\Delta H_{\text{hydro}} = \Delta H_f (\text{C}_6\text{H}_{12}) - \Delta H_f (\text{C}_6\text{H}_6) = -155 \text{ kJ/mol} - (+49 \text{ kJ/mol}) = -204 \text{ kJ/mol}.\]

Step 3: Determine the Resonance Energy of Benzene

The resonance energy is the difference between the calculated enthalpy of hydrogenation and the actual enthalpy of hydrogenation:\[ \text{Resonance Energy} = \Delta H_{\text{calculated}} - \Delta H_{\text{actual}} = -204 \text{ kJ/mol} - (-120 \text{ kJ/mol}) =-204 + 120 = -84 \text{ kJ/mol}.\] (The negative sign indicates it's a stabilization energy.)

Step 4: Convert Resonance Energy to Per Gram of Benzene

The molar mass of benzene \(\text{C}_6\text{H}_6\) is 78 g/mol. To find the resonance energy per gram, divide the resonance energy by the molar mass: \[\text{Resonance Energy per gram} = \frac{-84 \text{ kJ/mol}}{78 \text{ g/mol}} \approx -1.08 \text{ kJ/g}.\]

Key Concepts

Enthalpy of Formation

The enthalpy of formation is a fundamental concept in chemistry, particularly in thermodynamics. It refers to the heat change that occurs when one mole of a compound is formed from its elements in their standard state. In this exercise, we are dealing with the enthalpy of formation for cyclohexane and benzene.

• Cyclohexane has an enthalpy of formation of defined as ightarrow -155 ext{ kJ/mol}, indicating that forming cyclohexane releases energy.
• Benzene, on the other hand, has an enthalpy of formation of ightarrow +49 ext{ kJ/mol}, indicating that forming benzene requires energy input.

An important aspect of enthalpy of formation is to standardize the conditions under which these values are measured—typically 298 K and 1 atm pressure—which ensures consistency when comparing different substances.

When you understand that this value reflects the stability of a compound compared to its elements, it becomes clearer why these values are vital in predicting reactions and energy changes.

Hydrogenation

Hydrogenation is a chemical reaction where hydrogen is added to another compound, typically organic, resulting usually in the saturation of the compound. In this context, it refers to adding hydrogen to benzene to form cyclohexane.

Hydrogenation reactions are essential in various industrial applications, such as producing saturated fats from unsaturated oils. The process often requires a catalyst to facilitate the addition of hydrogen atoms to the unsaturated bond.

• The reaction equation for benzene hydrogenation in this exercise is ightarrow ext{C}_6 ext{H}_6 + 3 ext{H}_2 ightarrow ext{C}_6 ext{H}_{12}.
• Theoretical enthalpy change for benzene hydrogenation, derived from enthalpies of formation, indicates the reaction exothermically releases ightarrow -204 ext{ kJ/mol}.
• However, experiment shows a slightly different value: ightarrow -120 ext{ kJ/mol}.

Understanding the hydrogenation process allows us to consider the energy aspects and the molecular changes involved, which are essential for calculating the resonance energy as seen in the exercise.

Molar Mass

Molar mass is an important concept in chemistry, representing the mass of one mole of a substance. In simple terms, it tells you how much a given number of atoms weighs. Knowing the molar mass of substances allows us to convert between grams and moles, which is crucial for stoichiometry calculations.

• For benzene ( ext{C}_6 ext{H}_6 ext{),} the molar mass is calculated as ightarrow 78 ext{ g/mol}.

In the context of resonance energy per gram, understanding molar mass allows us to convert from per-mole quantities, making it possible to express enthalpy values per unit mass rather than per mole.

This conversion is crucial for applications requiring this measure, particularly when dealing with mass-specific energy quantities. It becomes essential when correlating energies with physical samples in a laboratory setting.

Enthalpy Change

Enthalpy change is another pillar of the thermodynamics behind chemical reactions. It represents the heat absorbed or released during a chemical reaction at constant pressure. In our exercise, it plays a key role in each step.

• The enthalpy change for hydrogenation (calculated) is ightarrow -204 ext{ kJ/mol} n an energy release predicted from bonding changes from benzene to cyclohexane.
• The actual measured enthalpy change in experiments is ightarrow -120 ext{ kJ/mol} n differing due to resonance effects.

The difference between calculated and experimental enthalpy changes leads to uncovering resonance energy. It shows how closely theoretical and real situations match up and helps chemists modify approaches to synthesize compounds with desired properties.

Mastering the concept of enthalpy change aids in understanding the energy efficiency of reactions and the stability of compounds involved.