Problem 4 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Consider the following reaction: \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g}) ; \mathrm{DH}^{0}=+58 \mathrm{~kJ}\) For each of the following cases ((i), (ii)), the direction in which the equilibrium shifts is : (i) Temperature is decreases (ii) Pressure is increased by adding \(\mathrm{N}_{2}\) at constant \(\mathrm{T}\). (a) (i) towards product, (ii) towards product (b) (i) towards reactant, (ii) towards product (c) (i) towards reactant, (ii) no change (d) (i) towards product, (ii) no change

Step-by-Step Solution

Answer

(c) (i) towards reactant, (ii) no change.

Step 1: Analyze Temperature Change (Part i)

The reaction \[\text{N}_2\text{O}_4(g) \rightleftharpoons 2\text{NO}_2(g) \]is endothermic since \(\Delta H^0 = +58 \text{ kJ}\) is positive. Decreasing temperature will favor the exothermic direction to offset the disturbance. In this reaction, the reverse direction (towards reactants) is exothermic. Therefore, the equilibrium will shift towards reactants when the temperature is decreased.

Step 2: Analyze Pressure Change (Part ii)

Adding \(\text{N}_2\) gas increases the pressure but does not affect the initial equilibrium concentrations of \(\text{N}_2\text{O}_4\) or \(\text{NO}_2\), as \(\text{N}_2\) is not involved in the equilibrium. According to Le Chatelier’s principle, adding \(\text{N}_2\) does not shift the equilibrium in any direction because it doesn't alter the partial pressures of the gaseous reactants or products involved in the equilibrium.

Step 3: Choose the Correct Answer

Based on the analysis: - For (i) temperature decrease, the shift is towards reactants.- For (ii) pressure increase by adding \(\text{N}_2\), there is no change.The correct option is (c) (i) towards reactant, (ii) no change.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that explains how a system at equilibrium responds to external changes. It states that when a system at equilibrium experiences a change in pressure, temperature, or concentration, the system adjusts to counteract that change and restore a new equilibrium. This means the system will shift in the direction that reduces the effect of the change.

Imagine equilibrium as a balance on a seesaw: if you push down on one side, the balance shifts to react to that force. Similarly, in a chemical reaction, the equilibrium shifts to reduce the stress caused by a change in conditions.

• If the concentration of a reactant is increased, the system will shift towards the products to use up the added reactants.
• If the temperature is increased, an endothermic reaction will shift the equilibrium to the right, absorbing the extra heat as it favors the product side.
• If the pressure is increased, the system will shift towards the side with fewer moles of gas.

Understanding this principle allows chemists to predict how a reaction will behave when subjected to different changes in conditions.

Endothermic Reactions

In chemical reactions, energy changes are essential in determining the direction of equilibrium and reaction dynamics. Endothermic reactions are those where energy is absorbed from the surroundings during the reaction process. This means the reaction feels cold and often has a positive enthalpy change \(\Delta H > 0\).

During an endothermic reaction, the products are at a higher energy level than the reactants because the system absorbs this energy to convert reactants into products.

For example, in the reaction \text{N}_2 ext{O}_4(g) \rightleftharpoons 2\text{NO}_2(g)\, the positive enthalpy change \(\Delta H^0 = +58 \text{ kJ}\) indicates that the reaction is endothermic.

• This reaction absorbs heat from its surroundings, which would favor the forward shift to \(\text{NO}_2\) when temperature increases.
• Conversely, reducing temperature will drive the reaction towards the reactants \(\text{N}_2\text{O}_4\) because the system needs to release energy.

This knowledge helps in predicting how temperature changes will influence the position of equilibrium in endothermic reactions.

Effect of Temperature

Temperature changes can significantly influence the equilibrium of a chemical reaction. For endothermic reactions, an increase in temperature adds heat to the system, thus the system will shift towards the products to absorb this heat and achieve a new equilibrium. However, when temperature decreases, the system will shift towards the reactants in an exothermic response to release heat.

Consider the \text{N}_2 ext{O}_4(g) \rightleftharpoons 2\text{NO}_2(g)\ reaction:

• If the temperature is increased, equilibrium will shift to the right, favoring the formation of \(\text{NO}_2\).
• If the temperature is decreased, equilibrium will shift to the left, favoring \(\text{N}_2\text{O}_4\) because the reverse reaction is exothermic.

This concept is crucial in chemical process engineering and laboratory settings, where precise control over reaction conditions can lead to desired reaction outcomes.

Effect of Pressure

The effect of pressure on chemical equilibrium largely depends on the gaseous reactants and products involved. According to Le Chatelier’s Principle, increasing the pressure on a gaseous equilibrium shifts the equilibrium toward the side with fewer moles of gas, reducing the system's pressure. If a reaction has equal moles of gas on both sides, pressure change has less effect.

In scenarios where an inert gas like \(\text{N}_2\) is added, it increases overall pressure but not the partial pressures of the involved reactants or products. Thus, the equilibrium position remains unaffected. This is important to note in the reaction of \text{N}_2 ext{O}_4(g) \rightleftharpoons 2\text{NO}_2(g)\, where adding \(\text{N}_2\) has no impact because \(\text{N}_2\) is not part of the equilibrium.

• Pressure changes influence reactions differing in the number of gaseous moles on each side.
• Adding inert gases do not affect equilibrium when they do not participate directly in the reaction.

Understanding these nuances assists in managing reactions effectively, particularly in industrial applications where pressure considerations are critical.