Problem 23 - A Complete Resource Book in Chemistry for JEE Main

Question

A vessel at equilibrium, contains \(\mathrm{SO}_{3}, \mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\), Now some helium gas is added, so that total pressure increases while temperature and volume remain constant. According to Le Chatelier's Principle, the dissociation of \(\mathrm{SO}_{3}\) (a) decreases (b) remains unaltered (c) increases (d) change unpredictably

Step-by-Step Solution

Answer

(b) remains unaltered

Step 1: Understanding Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. In this scenario, the total pressure is increased by adding helium, a noble gas that doesn't participate in the reaction.

Step 2: Reaction Equation and Conditions

The reaction in the vessel is the dissociation of sulfur trioxide: \( 2 \mathrm{SO}_3 (g) \rightleftharpoons 2 \mathrm{SO}_2 (g) + \mathrm{O}_2 (g) \). It involves a change in the number of moles of gas: from 2 moles of \( \mathrm{SO}_3 \) to 3 moles of \( \mathrm{SO}_2 \) and \( \mathrm{O}_2 \). This means a shift towards more moles of gas if the pressure were manually decreased by volume change.

Step 3: Effect of Adding Helium

Adding helium increases the total pressure but does not change the partial pressures of the reactants and products because helium is inert and does not change the concentrations of the involved gases. This is a change in the total pressure rather than a change impacting reaction participants.

Step 4: Equilibrium Position Analysis

Since the volume and temperature remain constant and the increase in pressure is not due to a change in reactant/product concentrations, the equilibrium position remains the same. Helium does not affect the equilibrium concentrations or pressures of \( \mathrm{SO}_3 \), \( \mathrm{SO}_2 \), and \( \mathrm{O}_2 \) in this condition.

Key Concepts

Gas Equilibrium

Gas equilibrium is a state where the rates of the forward and reverse reactions in a closed system are equal. At equilibrium, the concentrations of reactants and products remain constant over time. This doesn't mean the reactions stop; both processes continue at equal rates, maintaining a balance.
In the context of gas equilibrium, changes in external conditions like pressure, temperature, or the addition of inert gases can shift the position of equilibrium. However, certain changes may not affect the equilibrium state.

• Adding an inert gas, like helium, at constant volume and temperature does not alter the equilibrium concentrations or partial pressures of reactants and products.

This is because an inert gas doesn't participate in the reaction and therefore doesn't influence the relative rates of the forward and backward reactions.

Partial Pressure

Partial pressure refers to the pressure exerted by a single type of gas in a mixture of gases. In chemical equilibrium systems, each gas in the reaction contributes to the total pressure proportionally.
In the reaction of sulfur trioxide dissociation, the partial pressures of each gas are important indicators of their concentration in the mixture.

• The addition of an inert gas like helium increases total pressure, but does not affect the partial pressures of the reactants and products, because it doesn't interact with them.

This means while the overall pressure rises, the equilibrium concentrations remain the same as they are determined by the partial pressures, which are unchanged.

Chemical Equilibrium

Chemical equilibrium is reached in a reaction when the forward and reverse reactions occur at the same rate. Consequently, the concentrations of reactants and products remain stable.
Le Chatelier's Principle plays a crucial role in understanding chemical equilibrium. It predicts how an equilibrium system responds to external changes. In the case of adding an inert gas like helium under constant volume and temperature:

• It doesn't alter reactant or product concentrations.
• The equilibrium position stays unchanged.

Such addition changes only the total pressure and does not disturb the balance of the concentration ratios of reactants and products within the equilibrium.

Sulfur Trioxide Dissociation

Sulfur trioxide dissociation involves the reversible reaction where sulfur trioxide (\( \mathrm{SO}_3 \)) decomposes into sulfur dioxide (\( \mathrm{SO}_2 \)) and oxygen (\( \mathrm{O}_2 \)). The balanced reaction is:\[2 \mathrm{SO}_3 (g) \rightleftharpoons 2 \mathrm{SO}_2 (g) + \mathrm{O}_2 (g)\]This reaction results in an increase in the number of gas molecules from two to three. If external conditions were such that a change in volume occurred, we would expect the equilibrium to shift in a way that adjusts to the new volume.
However, adding an inert gas like helium does not influence the equilibrium of this reaction, since it doesn't alter the partial pressures of sulfur trioxide, sulfur dioxide, or oxygen. Thus, the equilibrium position remains steady in this scenario, respecting the principles defined by Le Chatelier.