Problem 53 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

For the reaction : $$ \mathrm{PCl}_{5}(\mathrm{~g}) \rightarrow \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) $$ The forward reaction at constant temperature is favoured by (a) introducing an inert gas at constant volume (b) introducing chlorine gas at constant volume (c) introducing an inert gas at constant pressure (d) increasing the volume of the container (e) introducing \(\mathrm{PCl}_{5}\) at constant volume

Step-by-Step Solution

Answer

Option (d) - Increasing the volume of the container favors the forward reaction.

Step 1: Understand the Reaction

The given reaction is \( \mathrm{PCl}_{5}(\mathrm{~g}) \rightarrow \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \). This is a gaseous decomposition reaction where one mole of \( \mathrm{PCl}_5 \) decomposes into one mole of \( \mathrm{PCl}_3 \) and one mole of \( \mathrm{Cl}_2 \). Thus, pressure and volume changes can impact the reaction's equilibrium.

Step 2: Analyze Effect of Introducing Inert Gas at Constant Volume

Adding an inert gas at constant volume does not change the partial pressures of the reactants or products since the total volume remains the same. Therefore, this change does not affect the equilibrium of the reaction.

Step 3: Analyze Effect of Introducing Chlorine Gas at Constant Volume

Adding \( \mathrm{Cl}_2 \) gas will increase its partial pressure, causing a shift of the equilibrium to the left according to Le Chatelier's principle to counteract the change. This disfavors the forward reaction.

Step 4: Analyze Effect of Introducing Inert Gas at Constant Pressure

Introducing an inert gas at constant pressure increases the total volume of the system. This effectively decreases the concentrations (partial pressures) of the reactants and products. For this gaseous reaction, the equilibrium can be shifted to the right to increase moles of gas and restore pressure.

Step 5: Analyze Effect of Increasing Volume of Container

Increasing the container volume decreases the pressure and shifts the equilibrium towards the side with more gas molecules to increase pressure. In this reaction, more moles of gas are on the product side, so increasing volume favors the forward reaction.

Step 6: Analyze Effect of Introducing PCl5 at Constant Volume

Introducing more \( \mathrm{PCl}_5 \) increases its concentration, thereby shifting the equilibrium to the right to counteract the increase, thus favoring the forward reaction.

Step 7: Conclusion: Identify the Correct Answer

From the analysis, both increasing the volume of the container (option d) and introducing \( \mathrm{PCl}_5 \) at constant volume (option e) favor the forward reaction. However, since only one option is to be chosen, we highlight the typical response: (d) increasing the volume of the container.

Key Concepts

Equilibrium Shifts

When a chemical reaction reaches equilibrium, it doesn't mean the reaction stops. Instead, the forward and reverse reactions occur at the same rate, resulting in constant concentrations of reactants and products. However, various actions can "shift" this equilibrium. This is where Le Chatelier's principle comes into play.

If a system at equilibrium is disturbed by changing the concentration, pressure, or temperature, the system will shift its equilibrium position to counteract the effect of that disturbance. For example:

• Adding more reactants or products will cause a shift in the equilibrium to oppose the change.
• Changing the volume or pressure can make the reaction favor the side with fewer or more gas molecules, depending on the scenario.

Let's consider the reaction of \( \text{PCl}_5 \) decomposing into \( \text{PCl}_3 \) and \( \text{Cl}_2 \): increasing the volume of the container leads to a shift to the side with more gas molecules, favoring the decomposition of \( \text{PCl}_5 \).

This concept is crucial in predicting the direction of the equilibrium shift and thereby controlling the yield of reactions.

Gaseous Reactions

Gaseous reactions are unique due to the compressible nature of gases. In these reactions, volume and pressure play significant roles in influencing reaction behavior. The decomposition of \( \text{PCl}_5 \) into \( \text{PCl}_3 \) and \( \text{Cl}_2 \) is one such gaseous reaction.

These reactions can be easily affected by changes in pressure and volume, due to the dependence of gas concentrations on these variables. According to the ideal gas law, \( PV = nRT \), the pressure and volume are directly related to the number of moles and temperature. Thus:

• If you increase the volume (or decrease the pressure), the equilibrium shifts towards the side with more gas molecules to balance the pressure.
• Introducing inert gases at constant volume doesn't change partial pressures of the reacting components, leaving the equilibrium position largely unchanged.

Understanding these principles helps in controlling and predicting outcomes in industrial and lab-scale reactions.

Reaction Equilibrium Factors

Several factors influence the equilibrium state of a reaction. In gaseous reactions like the decomposition of \( \text{PCl}_5 \), understanding these factors helps us control the yield and efficiency.

Key factors include:

• Concentration of Reactants and Products: Changes in concentration can shift the equilibrium to either produce more products or reactants, depending on where the addition happens.
• Pressure and Volume: As seen, changes in these can shift the equilibrium towards more or fewer moles of gas.
• Temperature (though not explicitly explored here): It can affect equilibrium by favoring either endothermic or exothermic reactions.
• Presence of Inert Gases: When added at constant volume, they don't affect equilibrium but can at constant pressure due to changing volume dynamics.

By manipulating these factors, chemists can optimize conditions to favor the production of desired products, making processes more efficient and cost-effective. Knowing how and why these factors affect a reaction allows for precise control in chemical manufacturing.