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

The forward reaction is favored by options 3, 4, and 5. (Answer: d)

Step 1: Understand the Reaction and Equilibrium Shift

The reaction \(\mathrm{PCl}_{5} \rightleftharpoons \mathrm{PCl}_{3} + \mathrm{Cl}_{2}\) indicates that one mole of \(\mathrm{PCl}_{5}\) decomposes to form two moles of product gases (\(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\)). According to Le Chatelier's principle, changes in pressure, volume, or concentration will shift the equilibrium to favor the side that opposes the change.

Step 2: Analyze Option 1 - Inert Gas at Constant Volume

Introducing an inert gas at constant volume does not change the partial pressures of the reactants or products, thus it does not favor the forward reaction (no shift in equilibrium as total moles and concentration remain unchanged).

Step 3: Analyze Option 2 - Chlorine Gas at Constant Volume

Adding \(\mathrm{Cl}_{2}\) at constant volume increases the concentration of products, shifting the equilibrium towards the reactants to counteract the change, thus not favoring the forward reaction.

Step 4: Analyze Option 3 - Inert Gas at Constant Pressure

Adding an inert gas at constant pressure effectively increases the volume, decreasing the partial pressures of the gases. According to Le Chatelier's principle, the equilibrium shifts towards the side with more moles—here, towards the products (forward reaction favored).

Step 5: Analyze Option 4 - Increasing Volume

Increasing the volume reduces the pressure, favoring the side of the reaction with more gas moles. Here, the forward reaction produces more moles of gas, so an increase in volume shifts equilibrium towards products, favoring the forward reaction.

Step 6: Analyze Option 5 - Introducing PCl5 at Constant Volume

Adding more \(\mathrm{PCl}_{5}\), a reactant at constant volume, increases its concentration, shifting equilibrium towards the right to favor the formation of products, thus favoring the forward reaction.

Key Concepts

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept in chemical equilibrium. It describes how a system at equilibrium responds to external changes. Consider the reaction \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\). According to Le Chatelier's principle, if we make a change in either the concentration, pressure, or temperature of this equilibrium system, the system will adjust itself to counteract that change and restore a new equilibrium state.

For example, increasing the concentration of one component on the products side causes the system to shift the equilibrium towards the reactants. This is a natural attempt to balance the increase and minimize the disturbance. Similarly, if we introduce more \(\mathrm{PCl}_{5}\), the system compensates by shifting towards the creation of more products, favoring the forward direction of the reaction.

Reaction Shifts

Reaction shifts refer to the direction the equilibrium moves to restore balance after a disturbance. In our given reaction, various scenarios can alter this balance, causing the reaction to shift accordingly.

For instance, if we introduce \(\mathrm{Cl}_2\) gas, the concentration of products increases, prompting a shift towards the reactants to reduce the formed imbalance. Conversely, adding reactants like \(\mathrm{PCl}_{5}\) pushes the equilibrium towards the products, favoring the forward reaction.

• Adding More Reactants: Shifts equilibrium to the right (towards products).
• Adding More Products: Shifts equilibrium to the left (towards reactants).

This dynamic property helps in predicting the outcomes of deliberate changes made to the system.

Effect of Pressure

Pressure is a critical factor influencing the position of equilibrium in gaseous systems. In our scenario, if pressure is altered, the system adapts to minimize this impact.

When an inert gas is added at constant pressure, it leads to an increase in volume, effectively reducing the pressure experienced by reactants and products. According to Le Chatelier's principle, the equilibrium shifts toward the side with more gas moles, which in this case is the products (\(\mathrm{PCl}_{3} + \mathrm{Cl}_{2}\)).

• Decrease in Pressure: Favors the side with more moles of gas.
• Increase in Pressure: Favors the side with fewer moles of gas.

This intricate connection between pressure and equilibrium position is important when predicting reaction behavior under changes in physical conditions.

Effect of Concentration

The concentration of reactants and products can have significant effects on equilibrium, as demonstrated by our equilibrated reaction.

If we increase the concentration of \(\mathrm{PCl}_{5}\), the equilibrium will shift towards the right, favoring the formation of more \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\). This compensating shift seeks to reduce the stress of increased reactant concentration.

• Increase in Reactant Concentration: Shifts equilibrium to right (toward products).
• Increase in Product Concentration: Shifts equilibrium to left (toward reactants).

These changes in concentration effectively guide the direction in which the reaction will proceed, enabling careful control over chemical processes.