Problem 172 - A Complete Resource Book in Chemistry for JEE Main

Question

Assertion: Adding an inert gas todissociation equilibrium of gaseous \(\mathrm{N}_{2} \mathrm{O}_{4}\) at constant pressure and temperature increases the dissociation. Reason: Molar concentration of the reactants and products decreases on the addition of inert gas.

Step-by-Step Solution

Answer

The assertion and the reason are both correct.

Step 1: Understand the Concepts

First, we need to understand what dissociation equilibrium is. For the reaction \( \mathrm{N}_2\mathrm{O}_4 (g) \rightleftharpoons 2\mathrm{NO}_2 (g) \), dissociation equilibrium involves the breaking of \( \mathrm{N}_2\mathrm{O}_4 \) into \( \mathrm{NO}_2 \).

Step 2: Role of Inert Gas at Constant Pressure

When an inert gas is added to a reaction at constant pressure, the volume of the system increases. Since the inert gas does not react with the components of the system, it dilutes the reactants and products.

Step 3: Analyze the Effect on Concentrations

By adding an inert gas, the partial pressures of the reactants and products decrease, which implies a decrease in molar concentrations. This change affects the equilibrium according to Le Chatelier's Principle.

Step 4: Apply Le Chatelier's Principle

According to Le Chatelier's Principle, if a change is made to a system in equilibrium, the system will adjust to counteract that change. If the concentration of substances decreases, the system shifts to increase concentrations by favoring the side with more moles of gas.

Step 5: Determine Reaction Shift

In the dissociation \( \mathrm{N}_2\mathrm{O}_4 \rightarrow 2\mathrm{NO}_2 \), more moles of gas are produced on the right side. Hence, the equilibrium will shift towards \( 2\mathrm{NO}_2 \) to increase the number of moles to restore balance.

Step 6: Conclusion on Assertion and Reason

The assertion is correct because adding an inert gas increases dissociation. The reason is also valid as lower concentrations drive the reaction towards more moles, perfectly aligning with Le Chatelier's principle.

Key Concepts

Dissociation Equilibrium

In chemical reactions such as the dissociation of dinitrogen tetroxide (\( \mathrm{N}_2\mathrm{O}_4 \)) into nitrogen dioxide (\( 2\mathrm{NO}_2 \)), the term dissociation equilibrium refers to the balance established between these two states at a given temperature. Essentially, this means that the rate at which\( \mathrm{N}_2\mathrm{O}_4 \) molecule breaks down into \( 2\mathrm{NO}_2 \) molecules equals the rate at which \( 2\mathrm{NO}_2 \) molecules combine to reform \( \mathrm{N}_2\mathrm{O}_4 \).
There is a dynamic equilibrium where the concentrations of reactants and products remain constant, even though the actual particles are continuously reacting. This process is highly dependent on temperature, pressure, and the nature of the substances involved.
Understanding dissociation equilibrium is crucial for determining how different conditions, such as the addition of inert gases or changes in temperature, affect the position of equilibrium and the reaction's extent.

Le Chatelier's Principle

Le Chatelier's Principle is a primary guideline for predicting the behavior of a chemical equilibrium when it is subjected to changes. It states that if a system at equilibrium is disturbed by a change in concentration, temperature, or pressure, the system will shift its equilibrium position in a way that counteracts the effect of the disturbance.
In the context of our dissociation equilibrium example, if an inert gas is added to the system at constant pressure, according to Le Chatelier's Principle:

• The system will adjust to lower the pressure increase caused by the added gas by favoring the reaction that produces more moles of gas.
• For the \( \mathrm{N}_2\mathrm{O}_4 \) dissociation, this is the forward reaction, leading to the formation of more \( 2\mathrm{NO}_2 \).

This adjustment helps maintain equilibrium despite the external change, showcasing the principle's central role in predicting the direction of shift in such reactions.

Effect of Inert Gas

Adding an inert gas to a chemical equilibrium can unduly influence the balance of a reaction, but its effects depend on maintaining either constant volume or constant pressure. Since inert gases like nitrogen or argon do not react with substances in the system, they typically do not change the chemical equation's balance directly; however, they do influence the equilibrium indirectly.
At constant pressure, adding inert gas increases the system's total volume, which effectively reduces the molar concentration of reactants and products.

• This reduces partial pressures of gaseous components, according to the equation \( P = \frac{nRT}{V} \), where volume \( V \) has increased.
• The drop in concentration may shift the equilibrium in favor of the reaction that produces more moles of gas as seen with \( \mathrm{N}_2\mathrm{O}_4 \), favoring its dissociation into \( 2\mathrm{NO}_2 \).

In contrast, if the volume were held constant while adding an inert gas, there would be no effect on the equilibrium because the partial pressures would not change. Thus, the understanding of how inert gases can affect dissociation equilibria is crucial for controlling industrial processes where precise manipulations of gas concentrations are required.