Problem 19 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

What happens when an inert gas is added to an equilibrium keeping volume unchanged? [Main Online April 12, 2014] (a) More product will form (b) Less product will form (c) More reactant will form (d) Equilibrium will remain unchanged

Step-by-Step Solution

Answer

Equilibrium remains unchanged.

Step 1: Identify the Equilibrium Concept

We need to determine how adding an inert gas affects a chemical equilibrium where the volume remains constant. The first thing to consider is the principle of Le Chatelier's principle, which states that if a change is imposed on a system at equilibrium, the system will adjust to counteract that change. However, adding an inert gas with no change in volume may not directly affect the equilibrium concentrations.

Step 2: Understand the Role of Inert Gas

Inert gases do not react with the components of the equilibrium system. For a reaction mixture at constant volume, adding an inert gas increases the total pressure within the container but does not influence the partial pressures of the reacting species, since these are based on their mole fractions and volume.

Step 3: Analyze the Effect on Partial Pressures

Consider that at constant volume, the addition of an inert gas does not alter the partial pressures of the reactants or products because these partial pressures depend on the mole ratio and volume, not the total pressure. Thus, the equilibrium position, determined by the ratio of partial pressures, remains unchanged.

Step 4: Conclude the Equilibrium Behavior

Since the partial pressures of the reactants and products remain constant, the addition of an inert gas under constant volume conditions does not shift the equilibrium either toward the products or the reactants. The position of equilibrium remains unaffected.

Key Concepts

Chemical Equilibrium

Chemical equilibrium refers to a state in a chemical reaction where the rates of the forward and backward reactions are equal. This means that the concentrations of the reactants and products remain constant over time, though they may not necessarily be equal to each other.
For example, in the reaction where A reacts with B to form C and D, the reaction can be written as: \[A + B \rightleftharpoons C + D\] At equilibrium, the rate of formation of C and D from A and B is equal to the rate of formation of A and B from C and D.
It's a dynamic process where molecules continue to react but still maintain a balance in concentration. Understanding equilibrium is essential because many chemical reactions do not go to completion and establish an equilibrium instead. Factors like temperature, pressure, and concentration can shift the position of equilibrium, as described by Le Chatelier's Principle. However, the addition of an inert gas at constant volume is a unique scenario where equilibrium remains unchanged due to unaffected partial pressures of reactants and products.

Partial Pressure

The concept of partial pressure is crucial in understanding the behaviors of gases in mixtures. Partial pressure is the pressure exerted by an individual gas in a mixture, as if it alone occupied the entire volume. It is determined by the mole fraction of the gas and the total pressure of the system.
For instance, in a mixture of gases, the total pressure, P, is the sum of the partial pressures of each gas present. So, for gases A, B, and C in a container, the partial pressures are represented as: \[P_{total} = P_A + P_B + P_C\]Understanding partial pressures is integral when working with gases in chemical reactions, especially in equilibrium. At constant volume, the partial pressures of the gases in a reaction mixture remain fixed even with changes in atmospheric pressure. This is because partial pressures depend on their proportional mole presence in the mixture and volume, not overall pressure. Thus, when an inert gas is introduced into a sealed reaction system at equilibrium and at constant volume, it raises the total pressure without altering partial pressures of the reactive components.

Inert Gas Addition

When an inert gas is added to a system at equilibrium, many students wonder what happens next, especially in terms of pressure and equilibrium. An inert gas, like helium or argon, is non-reactive and does not participate in the chemical reactions of the mixture it is added to.
Under constant volume conditions, the primary effect of adding an inert gas is an increase in the total pressure of the system. However, this increase in total pressure does not translate into a change in the partial pressures of the individual gases already present in the reaction mixture. This is because partial pressures rely on the ratio of moles of each gas to the total volume, which remains unchanged.
Thus, the chemical equilibrium, determined by the balance of reactants and products' partial pressures, persists unaltered. It’s a fascinating outcome where intuition might suggest otherwise, but thanks to Le Chatelier's Principal and the nature of partial pressures, we see no shift in equilibrium position. This concept is especially important in industry and laboratory settings where reactions are carefully controlled, and understanding how inert conditions affect systems can optimize various processes.