Problem 12 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The reaction \(X \rightarrow Y\) is an exothermic reaction. Activation energy of the reaction for \(\mathrm{X}\) into \(\mathrm{Y}\) is \(150 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Enthalpy of reaction is 135 \(\mathrm{kJ} \mathrm{mol}^{-1}\). The activation energy for the reverse reaction, \(\mathrm{Y} \rightarrow \mathrm{X}\) will be : (a) \(280 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(285 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(270 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(15 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-Step Solution

Answer

The activation energy for the reverse reaction is 285 kJ/mol.

Step 1: Understand the Concepts

In an exothermic reaction, energy is released, hence the enthalpy change (\(\Delta H\)) is negative. The activation energy for the reverse reaction is given by the sum of the activation energy of the forward reaction and the magnitude of the enthalpy change of the forward reaction.

Step 2: Define Known Values

Given: Activation energy for the forward reaction \(X \rightarrow Y\) is \(E_{a}(forward) = 150 \ \text{kJ/mol}\). The enthalpy of the reaction \(\Delta H = -135 \ \text{kJ/mol}\) (since it's exothermic).

Step 3: Calculate Activation Energy for Reverse Reaction

The formula to find the activation energy for the reverse reaction \(Y \rightarrow X\) is: \[ E_{a}(reverse) = E_{a}(forward) - \Delta H \]Substitute the known values:\[ E_{a}(reverse) = 150 \ \text{kJ/mol} - (-135 \ \text{kJ/mol}) \]\[ E_{a}(reverse) = 150 \ \text{kJ/mol} + 135 \ \text{kJ/mol} \]\[ E_{a}(reverse) = 285 \ \text{kJ/mol} \]

Step 4: Conclusion

Based on the calculations, the activation energy for the reverse reaction \(Y \rightarrow X\) is \(285 \ \text{kJ/mol}\).

Key Concepts

Exothermic Reaction

An exothermic reaction is a chemical reaction that releases energy into its surrounding environment, usually in the form of heat. This release of energy causes the products to have less energy content compared to the reactants. In essence, the energy that was stored in the bonds of the reactants is greater than the energy needed to form the products. A simple example of an exothermic reaction is combustion. When wood burns, it releases heat and light, making it an exothermic process. Important points to remember about exothermic reactions:

• They release energy, thereby warming up the surroundings.
• The change in enthalpy (\(\Delta H\)) for exothermic reactions is negative because the system loses energy.
• They often occur spontaneously since they increase the entropy of the surroundings by releasing energy.

Understanding these characteristics helps students grasp why energy release is critical in determining the spontaneity and heat dynamics of chemical reactions.

Enthalpy Change

Enthalpy change (\(\Delta H\)) refers to the difference in energy content between the products and reactants of a chemical reaction. For exothermic reactions, like the one in the exercise (\(X \rightarrow Y\)), the enthalpy change is negative. This means the products have lower energy than the reactants, resulting in the release of energy as the reaction proceeds.To understand how enthalpy change impacts a reaction, consider the following facts:

• A negative \(\Delta H\) indicates that the reaction releases energy, making it exothermic.
• A positive \(\Delta H\) suggests an endothermic reaction where energy is absorbed.
• Knowing the enthalpy change allows chemists to predict the thermal behavior of reactions, crucial in energy management and safety measures.

In general, enthalpy change provides deep insights into the energy transformation and conservation principles inherent in chemical reactions.

Reverse Reaction

When discussing chemical reactions, mentioning the reverse reaction is crucial. A reverse reaction (\(Y \rightarrow X\)) refers to the backward process where the products convert back to the original reactants. Understanding the reverse reaction helps in determining the equilibrium state of a chemical process.In exothermic reactions, if the forward reaction releases energy, the reverse reaction will require that same amount of energy to proceed. This is why the exercise mentions that the activation energy for the reverse process is the sum of the forward reaction’s activation energy and the magnitude of the enthalpy change.Key points on reverse reactions:

• The reverse reaction requires energy input if the forward reaction is exothermic.
• Activation energy for the reverse reaction typically exceeds that of the forward reaction, especially in exothermic processes.
• Understanding both directions of a reaction helps in calculating equilibrium constants and reaction yields.

By exploring reverse reactions, students learn about the energy dynamics and the conditions under which a reaction's balance can shift, which is crucial for processes like metabolic pathways and industrial synthesis.