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: Identify Le Chatelier's Principle Application

According to Le Chatelier's Principle, if an external change is applied to a system at equilibrium, the system will adjust itself to counteract the effect of the applied change and restore a new equilibrium. Since the temperature is constant, only pressure changes affect equilibrium.

Step 2: Determine the Effect of Adding Helium

The addition of helium gas increases the total pressure but doesn't change the partial pressures of the reacting gases \(\mathrm{SO}_{3}, \mathrm{SO}_{2}, \mathrm{O}_{2}\). Helium is inert and doesn't react with these gases, thus it doesn't affect the reaction directly but only adds to the total pressure.

Step 3: Analyze Reaction Direction for Pressure Change

The reaction for dissociation of \(\mathrm{SO}_{3}\) is \(2\mathrm{SO}_{3}(g) \rightleftharpoons 2\mathrm{SO}_{2}(g) + \mathrm{O}_{2}(g)\). Increasing pressure by adding helium doesn't lead to a shift in reaction because the number of moles of gaseous products and reactants are the same.

Step 4: Apply Le Chatelier's Principle to Predict Reaction Shift

Since the moles of gas on each side are identical, changes in total pressure due to inert gas addition have no effect on the equilibrium position. Therefore, the dissociation of \(\mathrm{SO}_{3}\) remains unchanged.

Key Concepts

Chemical Equilibrium

In chemistry, equilibrium refers to a state where the rates of the forward and reverse reactions are equal. Thus, the concentration of reactants and products remain constant over time. This doesn't mean they are equal, but that they are not changing. When we say a reaction is at chemical equilibrium, it implies that the system is in a balanced state and any small changes like temperature or pressure might cause the system to "react" to maintain this balance.

In our reaction involving \(\mathrm{SO}_3\), \(\mathrm{SO}_2\) and \(\mathrm{O}_2\), the equilibrium state is crucial for predicting how the system will behave under different conditions. If an outside influence like changes in pressure or temperature occurs, the system might adjust itself to find a new equilibrium or return to the original state. This balance is the focus of Le Chatelier's Principle, which helps us understand and predict such adjustments.

Reaction Shift

Le Chatelier's Principle plays a key role when predicting the behavior of a chemical reaction in response to various changes. When a system at equilibrium is disturbed by a change in concentration, temperature, or pressure, the system will shift its position to counteract the disturbance and restore equilibrium.

In the case of the reaction with \(\mathrm{SO}_3\), if we look at the balanced equation \(2\mathrm{SO}_3(g) \rightleftharpoons 2\mathrm{SO}_2(g) + \mathrm{O}_2(g)\), the principle would predict a shift in the reaction to either the left or right if there was a change. However, because adding inert gases like helium increases total pressure without affecting partial pressures of the individual reactants or products, the position of equilibrium does not shift. Thus, the dissociation of \(\mathrm{SO}_3\) remains unchanged. This is because Le Chatelier's principle is more about changes that affect the concentration or pressure of the reactive species.

Pressure Changes

Pressure changes can notably influence chemical equilibria in systems involving gases. According to Le Chatelier’s Principle, a system will respond to pressure changes by shifting the equilibrium in a direction that reduces the effect of the change.

In our scenario, the addition of helium gas increases the total pressure but does not affect the partial pressures of \(\mathrm{SO}_3\), \(\mathrm{SO}_2\), or \(\mathrm{O}_2\), since helium is inert. The reaction equation shows equal numbers of moles on both sides (\[ 2\mathrm{SO}_3(g) \rightleftharpoons 2\mathrm{SO}_2(g) + \mathrm{O}_2(g)\]), meaning that a change in overall pressure from an inert gas does not prompt a reactive shift. The pressures that matter are those of the reacting gases, not the overall pressure contributed by an inert substance. This scientific understanding confirms that there is no shift in equilibrium, i.e., the dissociation of \(\mathrm{SO}_3\) remains unaltered.