Problem 52 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

For the reaction \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\) at a given temperature, the equilibrium amount of \(\mathrm{CO}_{2}(\mathrm{~g})\) can be increased by [1998 - 2 Marks] (a) adding a suitable catalyst (b) adding an inert gas (c) decreasing the volume of the container (d) increasing the amount of \(\mathrm{CO}(\mathrm{g})\).

Step-by-Step Solution

Answer

Increasing the amount of CO shifts equilibrium to produce more \( CO_2\), so the answer is (d).

Step 1: Understanding the Equilibrium Shift

The given equation represents a dynamic equilibrium. According to Le Chatelier's Principle, if a stress is applied to a system at equilibrium, the system shifts in a direction to counteract the change and re-establish equilibrium.

Step 2: Analyze Impact of Adding a Catalyst

Adding a catalyst does not shift the position of equilibrium. It only speeds up the rate at which equilibrium is reached by lowering the activation energy for both the forward and reverse reactions equally. Therefore, option (a) is not correct.

Step 3: Analyze Impact of Adding an Inert Gas

Adding an inert gas at constant volume does not affect the concentrations of the reactants and products, since it does not change the partial pressures of the reactive gases. Therefore, this does not increase the equilibrium amount of CO2. Hence, option (b) is not correct.

Step 4: Analyze Impact of Decreasing the Volume

Decreasing the volume of the container increases pressure, which would favor the side with fewer moles of gas. In this reaction, the number of moles of gas is the same on both sides (1 mole of CO + 1 mole of H2O ↔ 1 mole of CO2 + 1 mole of H2), so the equilibrium position does not shift. Hence, option (c) is not applicable.

Step 5: Analyze Impact of Increasing CO Amount

Increasing the amount of CO shifts the equilibrium to the right to reduce the stress by consuming more CO, producing more CO2 and H2. Thus, the equilibrium amount of CO2 increases. Therefore, option (d) is correct.

Key Concepts

Le Chatelier's Principle

When a chemical reaction reaches equilibrium, it maintains a balance between the forward and reverse reactions. If something occurs to disturb this balance, the system will attempt to counteract the change. This idea is known as Le Chatelier's Principle. For instance, if a reactant is added to the system at equilibrium, the principle predicts that the reaction will shift to consume the added reactant. This adjustment helps to restore the equilibrium. This principle explains why increasing the amount of CO in the reaction \[ \text{CO(g) + H}_2\text{O(g)} \rightleftharpoons \text{CO}_2\text{(g) + H}_2\text{(g)} \]would cause a shift to the right, producing more CO2 and H2. By recognizing how changes affect a system at equilibrium, you can predict the direction of the shift, which is crucial in many industrial processes to maximize product yield.

Catalysis

Catalysts are powerful tools in chemistry, designed to speed up reactions without undergoing any permanent change themselves. They achieve this by lowering the activation energy required for the reaction to proceed, effectively making it easier for reactants to transform into products. However, it is important to know that while catalysts can accelerate the attainment of equilibrium, they do not alter the position of equilibrium itself. In the context of the reaction \[ \text{CO(g) + H}_2\text{O(g)} \rightleftharpoons \text{CO}_2\text{(g) + H}_2\text{(g)} \], adding a catalyst would simply speed up both the forward and reverse reactions without favoring one over the other. This means that the concentrations of CO, H2O, CO2, and H2 at equilibrium remain unchanged, and thus the amount of CO2 does not increase. Catalysts are therefore beneficial for reaching equilibrium faster, but they do not change the overall outcome of the equilibrium itself.

Gas Laws

Gas laws describe principles related to the pressure, volume, and temperature of gases. In a reaction at equilibrium involving gases, these laws become particularly important when considering changes such as volume or pressure. According to the ideal gas law, the pressure of a gas is inversely related to its volume at constant temperature. Therefore, if we decrease the volume of a sealed container containing a gaseous equilibrium mixture, the pressure inside increases.For the reaction \[ \text{CO(g) + H}_2\text{O(g)} \rightleftharpoons \text{CO}_2\text{(g) + H}_2\text{(g)} \], during such a change, the reaction would tend to shift toward the side with fewer moles of gas as a counteraction. However, since there is an equal number of moles of gas on both sides of the reaction, the equilibrium position remains unaffected by changes in volume. Hence, adjusting the volume under these conditions won't change the concentration of CO2 in the system.

Equilibrium Shift

Equilibrium shift refers to the change in concentrations of reactants and products when a system at equilibrium is disturbed. Understanding equilibrium shifts is essential for predicting how changes influence a reaction. In the case of the reaction:\[ \text{CO(g) + H}_2\text{O(g)} \rightleftharpoons \text{CO}_2\text{(g) + H}_2\text{(g)} \], increasing the concentration of one of the reactants, such as CO, will cause the system to temporarily become unbalanced.According to Le Chatelier’s Principle, the system will respond by shifting the equilibrium position to the right, favoring the production of more CO2 and H2 until a new state of equilibrium is achieved. This adjustment helps in utilizing additional CO, hence increasing the equilibrium concentration of CO2. Such shifts are crucial when optimizing conditions for maximum yield in chemical industries. It's a straightforward yet profound concept that explains how to manipulate reactions to achieve desired product concentrations effectively.