Problem 171 - A Complete Resource Book in Chemistry for JEE Main

Question

Assertion: The equilibrium of \(\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})\) is not affected by changing volume of the system. Reason: \(\mathrm{K}_{\mathrm{c}}\) for the reaction does not depend on volume of the container.

Step-by-Step Solution

Answer

The assertion is false, but the reason is true.

Step 1: Understand the Assertion

The assertion claims that the equilibrium of \( \mathrm{A} \rightleftharpoons \mathrm{B} + \mathrm{C} \) is not affected by changes in the system's volume. This implies that altering volume does not shift the equilibrium position of the reaction.

Step 2: Analyze the Reason

The reason states \( \mathrm{K}_{\mathrm{c}} \) for the reaction does not depend on the volume of the container. \( \mathrm{K}_{\mathrm{c}} \), the equilibrium constant in terms of concentration, is indeed independent of container volume, as it is a ratio of concentrations.

Step 3: Equilibrium Shift Due to Volume Change

For gaseous reactions, if the number of moles of gas is different on either side of the equation, a change in volume will affect equilibrium due to changes in pressure. The reaction \( \mathrm{A} \rightleftharpoons \mathrm{B} + \mathrm{C} \) has different moles on each side (1 mole \(\rightarrow\) 2 moles), meaning equilibrium will shift with volume changes to counteract pressure changes.

Step 4: Evaluate the Truth of Assertion and Reason

The assertion is incorrect because the equilibrium will shift with volume changes due to differing moles of gas. The reason, however, is true because \( \mathrm{K}_{\mathrm{c}} \) is unaffected by volume itself. Thus, the reason does not correctly explain the assertion.

Key Concepts

Equilibrium Constant

The equilibrium constant, often represented as \( K_c \), is a fundamental concept in chemical equilibrium. The equilibrium constant is a number that expresses the relationship between the concentrations of reactants and products at equilibrium for a reversible chemical reaction.

For a general reaction like \( aA + bB \rightleftharpoons cC + dD \), the equilibrium constant \( K_c \) is defined by the equation: \[ K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \] This equation shows that \( K_c \) is the ratio of the concentrations of the products raised to the power of their stoichiometric coefficients to those of the reactants. The value of \( K_c \) is constant at a given temperature, meaning it doesn't change if the concentration of reactants or products changes.

• \( K_c \) provides insights into the position of equilibrium: large \( K_c \) indicates that the products are favored at equilibrium, while a small \( K_c \) suggests reactants are favored.


• The equilibrium constant is unaffected by changes in volume or pressure, although these can influence the position of equilibrium in some reactions.

It's critical to note that while \( K_c \) gives valuable information on equilibrium, it does not depend on concentrations or amounts; rather, it reflects a ratio at equilibrium.

Volume Effects on Equilibrium

Volume changes in a closed system can significantly impact chemical reactions, particularly those involving gases. This is because volume changes affect the pressure and concentration of gaseous reactants and products.

According to Le Chatelier’s Principle, altering the volume of a container can shift the equilibrium position if the number of moles of gas is different on the reactant and product sides of a reaction. For example, in the reaction \( \mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g}) + \mathrm{C}(\mathrm{g}) \), there are more moles of gas on the right side (2 moles) than on the left (1 mole).

• Reducing the volume increases pressure, causing the system to adjust. The equilibrium shifts towards the side with fewer moles of gas to reduce pressure.
• Conversely, increasing the volume decreases pressure, prompting the shift towards the side with more moles of gas to increase pressure.

The assertion from the exercise that volume does not affect equilibrium is incorrect here. This is because a change in volume does change the pressure, leading to a shift in equilibrium when there is a discrepancy in moles on either side of the equation.

Gaseous Reactions

Gaseous reactions are particularly sensitive to changes in volume and pressure, more so than reactions involving only solids or liquids. This sensitivity is due to the highly compressible nature of gases, which means that volume and pressure are inversely related in a closed container.

In the context of equilibria involving gases, adjustments in the volume of the reaction vessel can cause significant shifts in equilibrium, as changes in volume directly affect the pressure of the gases involved. For example, if a reaction involves the production of additional gas moles on one side, decreasing the volume will increase pressure, potentially shifting equilibrium to reduce gas production in an attempt to decrease pressure. This behavior is predictably guided by Le Chatelier's Principle.

• Gaseous reactions are often studied using the ideal gas law, \( PV = nRT \), which relates pressure \( P \), volume \( V \), and moles \( n \).
• Understanding how these quantities interact is key to predicting how changes in the conditions will affect gaseous equilibrium positions.

Therefore, for gaseous reactions, any change in volume very likely leads to a shift in equilibrium, unless the moles of gas are equal on both sides of the reaction equation.

Le Chatelier's Principle

Le Chatelier's Principle is a crucial guideline for predicting how a chemical equilibrium will respond to changes in concentration, temperature, or pressure. This principle states that if a change is imposed on a system at equilibrium, the system will adjust itself to counteract the change and re-establish equilibrium.

In terms of volume effects on gaseous equilibria, when the volume of the container is changed:

• Decreasing volume (increasing pressure) causes equilibrium to shift towards the side with fewer gas molecules, reducing the pressure.
• Increasing volume (decreasing pressure) shifts equilibrium towards the side with more gas molecules, as the system tries to increase pressure.

Le Chatelier's Principle helps predict these shifts, showing how the system dynamically adjusts. In reactions where the number of moles of gas differs on either side, this principle is indispensable in understanding the resultant shifts in equilibrium due to volume changes.
Additionally, while it doesn't provide specific quantitative predictions, it offers a clear qualitative understanding of equilibrium shifts.