Problem 175 - A Complete Resource Book in Chemistry for JEE Main

Question

In a hypothetical reaction \(\mathrm{X} \rightarrow \mathrm{Y}\), the activation energy for the forward and backward reaction is 15 and \(9 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\) respectively. The potential energy of \(\mathrm{X}\) is \(10 \mathrm{~kJ}\) \(\mathrm{mol}^{-1} .\) Identify the correct statement(s). (a) The threshold energy of the reaction is \(25 \mathrm{~kJ}\). (b) The potential energy \(\mathrm{f} \mathrm{Y}\) is \(16 \mathrm{~kJ}\) (c) Heat of reaction is \(6 \mathrm{~kJ}\). (d) The reaction is endothermic.

Step-by-Step Solution

Answer

Statements (a), (b), (c), and (d) are correct.

Step 1: Understanding Activation Energy

The activation energy for the forward reaction is the energy required to convert X to the transition state. This value is given as 15 kJ/mol. For the backward reaction, from Y to the transition state, the activation energy is 9 kJ/mol.

Step 2: Calculating Threshold Energy

The threshold energy is the energy of the reactants plus the activation energy of the forward reaction. Thus, Threshold Energy = Potential Energy of X + Activation Energy (forward) = 10 kJ/mol + 15 kJ/mol = 25 kJ/mol.

Step 3: Calculating Potential Energy of Y

Since the activation energy for the backward reaction is 9 kJ/mol, Potential Energy of Y = Threshold Energy - Activation Energy (backward) = 25 kJ/mol - 9 kJ/mol = 16 kJ/mol.

Step 4: Determining Heat of Reaction

The heat of reaction (ΔH) is the difference in potential energy between products and reactants. Here, ΔH = Potential Energy of Y - Potential Energy of X = 16 kJ/mol - 10 kJ/mol = 6 kJ/mol.

Step 5: Assessing Reaction Type

Since the potential energy of Y is greater than that of X, the reaction absorbs energy, indicating it is endothermic. The heat of reaction is positive, confirming the reaction is endothermic.

Key Concepts

Activation Energy

In chemical kinetics, activation energy is the minimum energy required for a chemical reaction to occur. This implies that it is the energy barrier that must be overcome for reactants to transform into products. For the hypothetical reaction \[ \mathrm{X} \rightarrow \mathrm{Y} \]the activation energy for the forward reaction is given as 15 kJ/mol, and for the backward reaction, it is 9 kJ/mol.
Activation energy is crucial because:

• It determines the rate at which a reaction proceeds. Higher activation energy means slower reactions, as fewer molecules possess the necessary energy to overcome the barrier.
• It helps in understanding and comparing the energy required for both forward and backward reactions.

Understanding activation energy helps in controlling reaction conditions to achieve the desired products efficiently.

Potential Energy

Potential energy in this context refers to the stored energy of a substance associated with its structural or positional state. It is crucial in predicting the behavior of a reaction. For the given reaction, the potential energy of the reactant, \(\mathrm{X},\) is 10 kJ/mol.
In reaction analysis:

• Potential energy provides insight into the energy stored in molecules due to their position and arrangement. This energy changes as substances undergo chemical reactions.
• It acts as a reference point for determining changes in energy during a reaction, playing a critical role in calculating the heat of reaction.

The difference in potential energy between reactants and products helps determine whether the reaction absorbs or releases energy, leading us to the concept of endothermic and exothermic reactions.

Endothermic Reaction

An endothermic reaction is a type of chemical reaction that absorbs energy from its surroundings, typically in the form of heat. In this process, the products have higher potential energy than the reactants. In the reaction \(\mathrm{X} \rightarrow \mathrm{Y},\) we observe:

• The potential energy of product \(\mathrm{Y}\) is 16 kJ/mol, higher than that of \(\mathrm{X},\) which is 10 kJ/mol.
• The heat of reaction, \(\Delta H,\) is the difference between the potential energy of the products and reactants, calculated as 6 kJ/mol, indicating energy absorption.

The positive value of \(\Delta H\) confirms the reaction is endothermic, as additional energy is required to form the products. This type of reaction is common in processes like photosynthesis and thermal decomposition.

Threshold Energy

Threshold energy is the minimum amount of energy that must be available to reactants to proceed with a chemical reaction. It is essentially the sum of the potential energy of reactants and the activation energy of the forward reaction. Here, the calculation is:

• Potential Energy of \(\mathrm{X} = 10 \mathrm{~kJ/mol}\)
• Activation Energy of forward reaction is 15 kJ/mol.
• Threshold Energy = 10 kJ/mol + 15 kJ/mol = 25 kJ/mol.

This value signifies the total energy that reactants need to transition into the products. It's a critical concept for understanding the energy landscape of a reaction, aiding in predicting how a reaction progresses under various conditions.