Problem 38 - A Complete Resource Book in Chemistry for JEE Main

Question

For the reaction \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) the forward reaction at constant temperature is favoured by 1\. introducing an inert gas at constant volume 2\. introducing chlorine gas at constant volume 3\. introducing an inert gas at constant pressure 4\. increasing the volume of the container 5\. introducing \(\mathrm{PCl}_{5}\) at constant volume (a) \(1,2,3\) (b) 4,5 (c) \(2,3,5\) (d) \(3,4,5\)

Step-by-Step Solution

Answer

(d) 3, 4, 5 favor the forward reaction.

Step 1: Identify the Reaction Type

The given reaction \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) is a reversible decomposition reaction, and it occurs in the gaseous state. There is an increase in the number of moles of gas from reactants to products, implying it is an equilibrium where volume changes can shift the balance.

Step 2: Analyze Option 1

When introducing an inert gas at constant volume, the total pressure increases but the partial pressures of the reactants and products do not change. Therefore, this has no effect on the equilibrium position.

Step 3: Analyze Option 2

Introducing chlorine gas at constant volume increases the partial pressure of \(\mathrm{Cl}_{2}\), shifting the equilibrium position towards the left (the reverse reaction is favored). Hence, the forward reaction is not favored.

Step 4: Analyze Option 3

Introducing an inert gas at constant pressure decreases the partial pressures of all gases in the system due to the increase in total volume. This will affect the equilibrium position by shifting it towards the side with more moles of gas, i.e., the right side, thus favoring the forward reaction.

Step 5: Analyze Option 4

Increasing the volume of the container decreases the overall pressure, which according to Le Chatelier's Principle will shift the equilibrium to the side with more moles of gas (the products), favoring the forward reaction.

Step 6: Analyze Option 5

Introducing \(\mathrm{PCl}_{5}\) at constant volume increases the concentration of the reactant. More reactant shifts the equilibrium position towards the products, hence favoring the forward reaction.

Step 7: Select Correct Combo

Based on the analysis: Options 3, 4, and 5 all favor the forward reaction by either altering pressure or adding reactants. Therefore, the correct answer is (d) \(3,4,5\).

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemical equilibrium. It states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change and restore balance. This principle helps us predict how a reaction will respond when conditions such as pressure, concentration, or temperature are altered.

In the context of gas reactions, like the one given with \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\), changes in volume and pressure significantly impact the equilibrium.

• When pressure increases by decreasing the volume, the equilibrium shifts towards the side with fewer gas moles to minimize the change.
• If the volume increases, the pressure drops, favoring the side with more gas moles.
• Introducing or removing reactants or products shifts equilibrium according to the direction that will counter the concentration changes. Adding \(\mathrm{PCl}_{5}\) favors the forward reaction as it shifts the equilibrium toward producing more products.

Understanding this principle is crucial for manipulating chemical processes, as it predicts the direction of shift in equilibrium.

Reversible Reactions

Reversible reactions are processes where the reactants form products, which can themselves react to regenerate the original reactants. This is indicated by a double arrow, \(\rightleftharpoons\), in reaction equations. Such reactions can reach a state of equilibrium where both the forward and reverse reactions occur at the same rate, resulting in constant concentrations of reactants and products.

In the exercise provided, \(\mathrm{PCl}_{5}\) decomposes into \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\), and these products can recombine to regenerate \(\mathrm{PCl}_{5}\). This dynamic balance is characterized as equilibrium, where concentration of products and reactants remain unchanged over time despite the ongoing reactions.
This reversibility emphasizes the need for understanding equilibrium manipulation for optimizing yields, as both sides compete to reach a stable state. The effect of changes like pressure adjustments or concentration alterations are better understood in light of this continuous state of interaction.

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature, volume, and pressure. In the context of chemical reactions, understanding these laws is essential for predicting how a reaction's position of equilibrium will shift.

Key gas laws include:

• **Boyle's Law**: Increased pressure decreases volume, which for reactions with gases means the shift in equilibrium depends on mole count.
• **Charles's Law**: Increase in volume with temperature can affect reaction conditions.

In the exercise, increasing container volume favors the side with more moles of gas due to decreased pressure, aligning with Boyle's Law implications. Also, when introducing an inert gas at constant pressure, the effective volume increases, favoring reactions like the one where more moles are formed. The toolset of gas laws aids chemists in precisely predicting these shifts.

Mole Concept

The mole concept is fundamental in chemistry for quantifying substances in reactions. One mole corresponds to \(6.022 \times 10^{23}\) entities, such as atoms or molecules. In reversible reactions at equilibrium, the stoichiometry indicated by moles is crucial for predicting changes and outcomes.

In the given reaction, as one mole of \(\mathrm{PCl}_{5}\) decomposes, it produces one mole of \(\mathrm{PCl}_{3}\) and one mole of \(\mathrm{Cl}_{2}\). This implies an increase in the number of gas moles when the forward reaction proceeds.

• Increased moles resulting from volume expansion shifts equilibrium to favor more products.
• The contribution of each component at equilibrium can be numerically analyzed using mole ratios.

This quantitative basis not only aids in equilibrium calculations but also serves as a bridge to other chemical principles, such as conservation of mass and predictability of reaction yield.