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

Question

If an inert gas is added in the reaction \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3}\) 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

The equilibrium remains unaffected.

Step 1: Understand the Reaction Setup

We are given the chemical reaction: \(\mathrm{N}_2 + 3\mathrm{H}_2 \longrightarrow 2\mathrm{NH}_3\). This reaction occurs at equilibrium. An inert gas is added, and we are to determine the effect of this addition on the equilibrium of the reaction.

Step 2: Consider the Role of Inert Gas

An inert gas does not react with the reactants or products in the given chemical reaction. It simply increases the total pressure if the volume is constant, since pressure is a function of the total number of gas molecules in a given volume.

Step 3: Effect of Inert Gas at Constant Volume

When the volume is constant, as in this problem, adding an inert gas increases the total pressure but does not change the partial pressures of the reactants and products. This is because the partial pressures depend on the mole fractions, which are unchanged.

Step 4: Impact on Equilibrium Position

Since the partial pressures of the gases involved in the reaction are unchanged, the position of the equilibrium is unaffected. The equilibrium constant remains the same, and thus, the reaction does not shift in the forward or backward direction when an inert gas is added at constant volume.

Key Concepts

Inert Gas Addition

When an inert gas is added to a reaction at constant volume, its primary characteristic is that it does not participate or interfere with the chemical reaction. Inert gases, like noble gases, are chemically non-reactive due to their stable electron configuration. Consequently, they do not form bonds with the reactants or products present in the reaction.

In a closed system where the volume is constant, introducing an inert gas will increase the total number of gas molecules within the container. However, this addition simply raises the overall pressure without altering the nature of the individual chemical components involved in the reaction. Importantly, the partial pressures of the reactants and products, which depend on their mole fractions, remain unchanged by this addition of inert gas. As such, while the total pressure rises, the reaction's equilibrium status stays intact. This is because equilibrium is primarily influenced by concentration changes, which are not affected when an inert gas is added under constant volume conditions.

Equilibrium Constant

The equilibrium constant, often denoted as \(K\), is a vital concept in chemical equilibrium that quantifies the ratio of concentrations of products to reactants at equilibrium. This constant is dependent on temperature and remains unchanged if other conditions, such as pressure or the presence of an inert gas, do not affect reactant or product concentrations directly.

Even when an inert gas increases the total pressure at a constant volume, the equilibrium constant does not change because the mole fractions of the reactants and products are the same as they were before the addition of the inert gas. As a result, the concentrations, which are used to compute \(K\), remain the same. Hence, the equilibrium constant serves as a reliable and stable indicator of the favorability of a chemical process, unaffected by changes in total pressure due to inert gas addition.

Partial Pressure

Partial pressure is a term used to describe the pressure that a single gas contributes to the overall pressure when it's part of a mixture of gases. In our context, partial pressures play a crucial role in determining the equilibrium state of a chemical reaction involving gases.

The concept of partial pressure is founded on Dalton's Law, which states that in a mixture of non-reacting gases, the total pressure is equal to the sum of the partial pressures of individual gases. For gaseous reactions like \(\mathrm{N}_2 + 3\mathrm{H}_2 \longrightarrow 2\mathrm{NH}_3\), monitoring the partial pressures of specific reactants and products helps in evaluating equilibrium.

• Partial pressures influence how reactants interact and proceed to form products.
• In a constant volume system, the addition of inert gas does not affect the partial pressures of reactants and products, as their mole fractions remain the same.

Hence, the reaction remains unaffected in its equilibrium position, because equilibrium relies on the balance of these pressures.