Problem 214 - A Complete Resource Book in Chemistry for JEE Main

Question

The energies of activation for forward and reverse reactions for \(\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB}\) are \(180 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(200 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by \(100 \mathrm{~kJ} \mathrm{~mol}^{-1}\). The enthalpy change of the reaction \(\left(\mathrm{A}_{2}+\mathrm{B}_{2} \longrightarrow 2 \mathrm{AB}\right)\) in the presence of catalyst will be (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) [2007] (a) 120 (b) 280 (c) 20 (d) 300

Step-by-Step Solution

Answer

The enthalpy change in the presence of a catalyst is 20 kJ/mol.

Step 1: Define the Activation Energies

The activation energy for the forward reaction is given as 180 kJ/mol, and for the reverse reaction, it is 200 kJ/mol.

Step 2: Calculate the Enthalpy Change without Catalyst

The enthalpy change, ΔH, for the reaction can be calculated using the difference between the activation energies of the reverse and forward reactions: \[ \Delta H = E_a(\text{reverse}) - E_a(\text{forward}) = 200 \text{ kJ/mol} - 180 \text{ kJ/mol} = 20 \text{ kJ/mol}. \]

Step 3: Consider the Effect of Catalyst

In the presence of the catalyst, the activation energy for both the forward and reverse reactions is lowered by 100 kJ/mol, so the new activation energies are: - Forward reaction: 180 kJ/mol - 100 kJ/mol = 80 kJ/mol. - Reverse reaction: 200 kJ/mol - 100 kJ/mol = 100 kJ/mol.

Step 4: Calculate the Enthalpy Change with Catalyst

The enthalpy change of the reaction does not depend on the activation energy and remains the same with the presence of a catalyst. Thus, the enthalpy change \( \Delta H \) is still 20 kJ/mol.

Key Concepts

Enthalpy Change

Enthalpy change, symbolized as \( \Delta H \), represents the total heat absorbed or released during a chemical reaction at constant pressure. It's a crucial concept in thermodynamics and helps us understand whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). In our exercise, the enthalpy change of the reaction \( \mathrm{A}_2 + \mathrm{B}_2 \rightarrow 2 \mathrm{AB} \) is calculated by the difference in activation energies of the reverse and forward reactions.

• Without a catalyst, \( \Delta H = 200 \text{ kJ/mol} - 180 \text{ kJ/mol} = 20 \text{ kJ/mol} \).
• Importantly, \( \Delta H \) remains unchanged even with a catalyst since it only affects the rate-oriented activation energies, not the total energy profile.

This means that the catalyst does not alter the fundamental energy difference of the products and reactants, just the pathway it takes to get there.

Catalysis

Catalysis is a process that increases the rate of a chemical reaction by reducing the activation energy required. Catalysts achieve this by providing an alternative mechanism or pathway that requires less energy. However, they do not affect the overall balance of energy in the reaction—meaning they don't change the enthalpy change, \( \Delta H \).Consider the exercise:

• The catalyst lowers the activation energy for both the forward \( (180 \text{ kJ/mol} \rightarrow 80 \text{ kJ/mol}) \) and reverse reactions \( (200 \text{ kJ/mol} \rightarrow 100 \text{ kJ/mol}) \) by 100 kJ/mol.

The fundamental principle here is that while catalysts speed up a reaction, making it more efficient, they don't alter the underlying thermodynamics. This property makes them indispensable in both industrial settings and biological systems where faster reaction rates are essential to maintain productivity and balance.

Chemical Reactions

Chemical reactions involve breaking and forming bonds between atoms, resulting in the transformation of reactants into products while conserving matter and energy. These reactions are fundamental to chemistry and crucial in various daily and industrial processes. In the exercise, the reaction \( \mathrm{A}_2 + \mathrm{B}_2 \rightarrow 2 \mathrm{AB} \) serves as an example of these dynamic transformations:

• "Forward reaction" refers to the progress from reactants (\( \mathrm{A}_2 \) and \( \mathrm{B}_2 \)) to products (\( 2\mathrm{AB} \)).
• "Reverse reaction" is the conversion of \( 2\mathrm{AB} \) back to reactants (\( \mathrm{A}_2 \) and \( \mathrm{B}_2 \)).

Understanding the energies involved in these reactions, such as the activation energy and enthalpy change, provides insights into how feasible or spontaneous these transformations are. The concept of catalysts illustrates a practical way to manage these processes by enhancing the rate without changing the fundamental energy changes.

Energy Profile

An energy profile is a graphical representation of the energy changes during a chemical reaction. It shows how the energy of the system varies with the progression of the reaction, detailing both the enthalpy change and activation energy. In the exercise, the energy profile would illustrate:

• A peak for the "activation energy," symbolizing the energy barrier needed to start the reaction.
• An initial energy level for reactants and a final energy level for products, with the difference reflecting the enthalpy change, \( \Delta H \).

With the introduction of a catalyst, the energy profile shifts downward, indicating reduced activation energies for both directions of the reaction. However, the heights of the reactant and product energy levels stay the same, graphically depicting why the enthalpy change remains constant. Thus, energy profiles are an essential tool for visualizing and understanding how reactions proceed and how catalysts influence the process.