Problem 29 - A Complete Resource Book in Chemistry for JEE Main

Question

If an inert gas is added in the reaction \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightleftharpoons 2 \mathrm{NH}_{3}\) at constant volume, then its equilibrium (a) remains unaffected (b) favours the backward reaction (c) favours the forward reaction (d) increases the dissociation of reactants

Step-by-Step Solution

Answer

(a) remains unaffected

Step 1: Understanding the Reaction Conditions

Consider the equilibrium reaction given: \(\text{N}_{2}+3 \text{H}_{2} \rightleftharpoons 2 \text{NH}_{3}\). Here, the volume is kept constant when the inert gas is added. Adding an inert gas at constant volume does not change the partial pressures of the reactants and products involved in the reaction.

Step 2: Analyzing Effect of Inert Gas

At constant volume, adding an inert gas does not affect the concentrations or partial pressures of the reactants or products. Since the concentrations remain the same, the equilibrium constant (\(K_c\)) or the reaction quotient (\(Q\)) does not change.

Step 3: Evaluating Equilibrium Changes

Since neither the partial pressures nor the concentrations are affected, the position of equilibrium remains unchanged. The equilibrium remains undisturbed by the presence of an inert gas; thus, there is no shift in the direction of the reaction.

Step 4: Conclusion with Equilibrium Properties

Since adding an inert gas at constant volume does not change the equilibrium position, the reaction will remain unaffected. The inert gas does not participate in the reaction or alter equilibrium concentrations, maintaining the established balance.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle helps predict how a chemical equilibrium will react to external changes. Imagine a balanced seesaw; this principle tells us what happens when we try to push down one side. When an external change occurs, such as pressure, concentration, or temperature fluctuation, the reaction will adjust to offset this change and restore equilibrium. This adjustment either increases or decreases the concentration of products and reactants. In situations where volume and pressure are constant, like in the exercise, adding an inert gas does not disturb the balance, as it doesn't participate in the reaction process. Therefore, the principle suggests that the equilibrium will stay put under these conditions.

Reaction Quotient

The reaction quotient, denoted as \(Q\), is a helpful tool for determining the direction of a reaction's shift when it's not at equilibrium. You can think of \(Q\) as a snapshot of the system at any given time. For the reaction \(\text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3\), \(Q\) is calculated using the current concentrations or partial pressures of the reactants and products. To compare, we use the equilibrium constant \(K_c\). If \(Q < K_c\), the reaction shifts to the right to make more products. If \(Q > K_c\), the reaction shifts to the left. However, in the presence of an inert gas at constant volume, \(Q\) remains the same because the concentrations of the involved species don't change, resulting in no shift in equilibrium.

Equilibrium Constant

The equilibrium constant, \(K_c\), is a fixed value at a given temperature for a particular reaction. It shows how far a reaction proceeds before reaching equilibrium. Think of \(K_c\) as a map indicating the destination of the chemical process. It is expressed as the ratio of product concentrations to reactant concentrations, each raised to the power of their coefficients in the balanced equation. For \(\text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3\), \(K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}\). Since \(K_c\) is independent of changes in pressure at constant volume when an inert gas is added, the equilibrium remains unaffected, as the conditions under which \(K_c\) was established aren't altered.

Inert Gases Effect

Inert gases are nature's bystanders—they do not react with other chemicals. If added at constant volume, they won't affect the position of chemical equilibrium. Picture a crowd watching a game; more spectators don't change the game score. Similarly, when an inert gas like argon is added to the reaction \(\text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3\), the concentrations of reactants and products remain constant. Their addition neither appears in nor interferes with the reaction's balanced equation. Consequently, the equilibrium position stays untouched, and neither forward nor backward reaction is favored.