Problem 193 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider an endothermic reaction \(\mathrm{X} \longrightarrow \mathrm{Y}\) with the activation energies \(\mathrm{E}_{\mathrm{b}}\) and \(\mathrm{E}_{\mathrm{f}}\) for the backward and forward reactions, respectively. In general \([\mathbf{2 0 0 5}]\) (a) \(\mathrm{E}_{b}<\mathrm{E}_{\mathrm{f}}\) (b) \(E_{b}>E_{f}\) (c) \(E_{b}=E_{f}\) (d) there is no definite relation between \(\mathrm{E}_{\mathrm{b}}\) and \(\mathrm{E}_{\mathrm{f}}\)

Step-by-Step Solution

Answer

(a) \(E_{b}

Step 1: Understand Reaction Type

The reaction \( \mathrm{X} \longrightarrow \mathrm{Y} \) is given as endothermic, meaning it absorbs heat from the surroundings.

Step 2: Define Activation Energies

Activation energy is the minimum energy required to initiate a chemical reaction. Here, \( E_f \) is the activation energy for the forward reaction (\( \mathrm{X} \rightarrow \mathrm{Y} \)), and \( E_b \) is the activation energy for the backward reaction (\( \mathrm{Y} \rightarrow \mathrm{X} \)).

Step 3: Analyze Endothermic Reaction

For an endothermic reaction, the forward activation energy \( E_f \) is always greater than the backward activation energy \( E_b \) because the forward reaction absorbs energy to proceed.

Step 4: Conclude the Relation

Since the reaction is endothermic, the relationship \( E_b < E_f \) holds true. Thus, option (a) \( \mathrm{E}_{b}<\mathrm{E}_{f} \) is correct.

Key Concepts

Activation Energy

Activation energy is a crucial concept in chemistry, helping us understand why some reactions happen faster than others. Simply put, activation energy is the minimum energy that reactant molecules must possess for a reaction to commence. Imagine it as a barrier the reactants need to overcome for a reaction to occur.
Think of it like rolling a ball over a hill; you need to push the ball with enough energy to get it over to the other side. Similarly, in a chemical reaction, molecules must be provided with sufficient energy to surpass this barrier.
A higher activation energy indicates that a lot of energy is required to initiate the reaction, making the reaction slower. Conversely, a lower activation energy means the reaction can start more easily and usually proceeds faster. Understanding activation energy is key to controlling reaction speeds in chemical processes.

Forward Reaction

In a chemical reaction, the forward reaction is the process where reactants are transformed into products. Using the example given, in the reaction \( \mathrm{X} \rightarrow \mathrm{Y} \), the conversion from \( \mathrm{X} \) to \( \mathrm{Y} \) is the forward reaction.
During an endothermic forward reaction, energy is absorbed from the environment. This energy absorption is needed to overcome the activation energy barrier and allows the reaction to move forward.

• The forward reaction rate is largely dependent on factors such as temperature, concentration, and particularly, the activation energy \( E_f \).
• A higher \( E_f \) in the forward reaction implies more energy is required, often making these reactions slower compared to exothermic reactions where energy is released.

Recognizing the pathway and energy requirements of the forward reaction is essential to understanding how new compounds are formed.

Backward Reaction

The backward reaction refers to the process of converting products back into reactants. In the provided reaction \( \mathrm{X} \rightarrow \mathrm{Y} \), the reverse path would be \( \mathrm{Y} \rightarrow \mathrm{X} \), which constitutes the backward reaction.
For many reactions, especially reversible ones, backward reactions play a vital role in the concept of dynamic equilibrium, where both forward and backward reactions occur at the same rate, maintaining a balance.
In an endothermic reaction context, the activation energy for the backward reaction \( E_b \) is usually lower than for the forward reaction. This is because energy is released when products revert to reactants, contrasting the energy absorbed in the forward direction. This dynamic helps explain why \( E_b \) is less than \( E_f \) in endothermic reactions. Understanding backward reactions allows chemists to manipulate reaction conditions for desired end results.

Previous

Problem 192

Next

Problem 195

Other exercises in this chapter

Problem 191

What is the equilibrium expression for the reaction [2004] \(\mathrm{P}_{4}(\mathrm{~s})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{P}_{4} \mathrm

View solution

Problem 192

The equilibrium constant for the reaction, \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\) At temperatu

View solution

Problem 195

An amount of solid \(\mathrm{NH}_{4} \mathrm{HS}\) in placed in a flask already containing ammonia gas at a certain temperature and \(0.50\) atm pressure. Ammon

View solution

Problem 196

The exothermic formation of \(\mathrm{ClF}_{3}\) is represented by the equation \(\mathrm{Cl}_{2}(\mathrm{~g})+3 \mathrm{~F}_{2}(\mathrm{~g}) \rightleftharpoons

View solution

Key Concepts

Activation Energy

Activation energy is a crucial concept in chemistry, helping us understand why some reactions happen faster than others. Simply put, activation energy is the minimum energy that reactant molecules must possess for a reaction to commence. Imagine it as a barrier the reactants need to overcome for a reaction to occur.
Think of it like rolling a ball over a hill; you need to push the ball with enough energy to get it over to the other side. Similarly, in a chemical reaction, molecules must be provided with sufficient energy to surpass this barrier.
A higher activation energy indicates that a lot of energy is required to initiate the reaction, making the reaction slower. Conversely, a lower activation energy means the reaction can start more easily and usually proceeds faster. Understanding activation energy is key to controlling reaction speeds in chemical processes.

Forward Reaction

In a chemical reaction, the forward reaction is the process where reactants are transformed into products. Using the example given, in the reaction \( \mathrm{X} \rightarrow \mathrm{Y} \), the conversion from \( \mathrm{X} \) to \( \mathrm{Y} \) is the forward reaction.
During an endothermic forward reaction, energy is absorbed from the environment. This energy absorption is needed to overcome the activation energy barrier and allows the reaction to move forward.

• The forward reaction rate is largely dependent on factors such as temperature, concentration, and particularly, the activation energy \( E_f \).
• A higher \( E_f \) in the forward reaction implies more energy is required, often making these reactions slower compared to exothermic reactions where energy is released.

Recognizing the pathway and energy requirements of the forward reaction is essential to understanding how new compounds are formed.

Backward Reaction

The backward reaction refers to the process of converting products back into reactants. In the provided reaction \( \mathrm{X} \rightarrow \mathrm{Y} \), the reverse path would be \( \mathrm{Y} \rightarrow \mathrm{X} \), which constitutes the backward reaction.
For many reactions, especially reversible ones, backward reactions play a vital role in the concept of dynamic equilibrium, where both forward and backward reactions occur at the same rate, maintaining a balance.
In an endothermic reaction context, the activation energy for the backward reaction \( E_b \) is usually lower than for the forward reaction. This is because energy is released when products revert to reactants, contrasting the energy absorbed in the forward direction. This dynamic helps explain why \( E_b \) is less than \( E_f \) in endothermic reactions. Understanding backward reactions allows chemists to manipulate reaction conditions for desired end results.