Problem 158 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) At constant temperature, forward reaction is favoured by (a) introducing inert gas at constant volume(b) introducing inert gas at constant pressure (c) introducing chlorine gas at constant volume (d) increasing the volume of the container

Step-by-Step Solution

Answer

Increasing the container's volume or adding an inert gas at constant pressure favors the forward reaction, so options (b) and (d) are correct.

Step 1: Understanding the Reaction

The exercise involves the reaction of phosphorus pentachloride (\(\text{PCl}_5\)) dissociating into phosphorus trichloride (\(\text{PCl}_3\)) and chlorine (\(\text{Cl}_2\)) gases. This is an equilibrium reaction which can be shifted by changing external conditions according to Le Chatelier's Principle.

Step 2: Examining the Effect of Changes in Volume and Pressure

In this reaction, \(1\) mole of \(\text{PCl}_5\) produces \(2\) moles of product gases (\(\text{PCl}_3\) and \(\text{Cl}_2\)). An increase in volume results in a decrease in the total pressure of the system, leading the equilibrium to shift towards the formation of more gas molecules to counteract the change. This favors the forward reaction to shift to the right, thus producing more \(\text{PCl}_3\) and \(\text{Cl}_2\).

Step 3: Evaluating the Impact of Adding Inert Gas at Constant Volume

When an inert gas is added at constant volume, the total pressure of the system increases. However, the partial pressures of the reacting gases remain unchanged, as the inert gas does not react. Therefore, the position of equilibrium remains unchanged and the forward reaction is not favored.

Step 4: Evaluating the Impact of Adding Inert Gas at Constant Pressure

Adding an inert gas at constant pressure leads to an increase in the volume of the system (since volume must change to maintain constant pressure given the addition of more gas). As with increasing the container volume, this shifts the equilibrium to the right, favoring the forward reaction to create more products and restore pressure balance.

Step 5: Evaluating the Impact of Adding Chlorine Gas

Adding \(\text{Cl}_2\) gas increases its concentration, shifting the equilibrium according to Le Chatelier's principle to the side that consumes \(\text{Cl}_2\), which is the reverse reaction. Thus, the forward reaction is not favored in this scenario.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is an essential concept for understanding chemical equilibrium. It helps us predict how a system at equilibrium will respond to changes in concentration, temperature, or pressure.
It posits that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will move to counteract the change, thus reestablishing equilibrium.
In chemistry, this principle is applied to predict the direction in which a reaction will shift in response to "stress.">

• Concentration Changes: Adding more reactant or product will shift the equilibrium to favor the consumption of the added substances.
• Temperature Changes: Increasing temperature favors endothermic reactions, while decreasing temperature favors exothermic ones.
• Pressure Changes (via Volume): An increase in pressure favors the side of the reaction with fewer moles of gas.

In the given reaction (\(\text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g)\)), changes in external conditions like volume and the introduction of gases influence which direction is favored.

Gas Laws in Equilibrium

Gas laws play a crucial role in understanding reactions involving gases at equilibrium. These laws describe how gases behave under different conditions, such as changes in pressure, volume, and temperature.
When applying gas laws to chemical equilibrium, consider how changes will affect the system's pressure and volume, thereby influencing the equilibrium position.

• Boyle’s Law: States that pressure is inversely proportional to volume, meaning if volume increases, pressure decreases and vice versa.
• Charles’s Law: Indicates that volume is directly proportional to temperature in Kelvin.

In the context of our reaction, where one mole of \(\text{PCl}_5\) dissociates into two moles of products, an increase in volume reduces the system's pressure, leading the reaction to produce more gas molecules as described in step 2 of the solution.

Effects of Inert Gases on Equilibrium

Inert gases, such as noble gases, don't chemically react with other substances. When added to a system at equilibrium, they can alter the total pressure without affecting partial pressures of the reactants or products.
Adding an inert gas at constant volume doesn't change the equilibrium position because the partial pressures and concentrations of the reacting gases remain the same.
However, introducing an inert gas at constant pressure increases the system's volume.
This change mimics an increase in container volume, thus altering the equilibrium position similarly to increasing the reactor volume. The reaction shifts in favor of producing more moles of gas, which is the forward reaction in this context.

Volume and Pressure Changes in Reactions

Volume and pressure are intimately related when dealing with gaseous equilibria. Changes in either can shift the position of equilibrium, affecting the yield of products and reactants.
An increase in the container's volume decreases the overall system pressure. This tends to shift the equilibrium towards the side with a greater number of gas molecules.

• Increased Volume: For the given equilibrium, \(\text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g)\), where there are more moles of gas on the right, increasing volume promotes more products (\(\text{PCl}_3\) and \(\text{Cl}_2\)).
• Constant Pressure with Added Gas: Adding an inert gas at constant pressure increases the volume, which like increasing the container volume, shifts equilibrium towards the side with more gas molecules.

Thus, understanding these concepts helps in predicting how changes will influence reactions, aiding in balancing industrial chemical processes efficiently.