Problem 39 - A Complete Resource Book in Chemistry for JEE Main

Question

For the reaction \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})=\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\) at a given temperature, the equilibrium amount of \(\mathrm{CO}_{2}(\mathrm{~g})\) can be increased by (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

Increase the amount of \( \text{CO(g)} \) to increase the amount of \( \text{CO}_2 \) at equilibrium.

Step 1: Analyze the Reaction

The given reaction is: \[ \text{CO(g)} + \text{H}_2\text{O(g)} \rightleftharpoons \text{CO}_2\text{(g)} + \text{H}_2\text{(g)} \] This is a gas-phase equilibrium reaction. We want to increase the concentration of \( \text{CO}_2 \) at equilibrium.

Step 2: Consider the Role of Catalysts

Adding a catalyst increases the rate at which equilibrium is reached but does not shift the position of the equilibrium. It affects the speed of the reaction equally in both forward and backward directions. Therefore, a catalyst will not increase the amount of \( \text{CO}_2 \) at equilibrium.

Step 3: Evaluate the Addition of an Inert Gas

Adding an inert gas at constant volume does not change the partial pressures of the reactive gases. Consequently, it does not affect the equilibrium position. Therefore, adding an inert gas will not increase \( \text{CO}_2 \) production.

Step 4: Assess the Impact of Volume Change

Decreasing the volume of the container would increase the pressure of the system. According to Le Chatelier’s principle, the reaction shifts in the direction which decreases pressure. Both sides of the equilibrium have the same number of moles of gas (2 moles), so a change in volume/pressure does not affect the position of the equilibrium specifically for this reaction.

Step 5: Analyze Increasing Reactants

Increasing the amount of \( \text{CO(g)} \), a reactant, shifts the equilibrium towards the production of more products, based on Le Chatelier’s principle. As a result, increasing \( \text{CO(g)} \) will increase the amount of \( \text{CO}_2 \), more specifically, the equilibrium amount of \( \text{CO}_2 \) will increase.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is crucial in understanding how a chemical system at equilibrium responds to external changes. The principle states that if a change in conditions is applied to a system at equilibrium, the system will adjust itself to counteract the effect of that change.
In simple terms, the system shifts in the direction that helps minimize or mitigate the change. For instance, if you add more of one reactant, the equilibrium will shift to produce more products, balancing the surplus reactants and bringing the system back towards equilibrium.

• Addition of reactants results in shifting the equilibrium to the right (towards product formation).
• Addition of products will shift the equilibrium to the left (towards reactants).
• Changing pressure or temperature can also impact equilibrium according to this principle.

In the context of the given gas-phase equilibrium reaction, increasing the quantity of CO(g) shifts the equilibrium towards more CO₂(g) production.

Catalysts in Chemical Reactions

Catalysts are substances that speed up the rate of chemical reactions without being consumed in the process. They provide an alternative reaction pathway with a lower activation energy, allowing more reactant molecules to effectively collide and react.
However, catalysts have an essential characteristic regarding equilibrium reactions: they do not affect the position of the equilibrium. Catalysts will hasten both the forward and reverse reactions equally, meaning the balance between reactants and products remains unchanged at equilibrium.
This is important to note in any chemical reaction analysis because, while catalysts are useful for reaching equilibrium faster, they do not alter the concentrations of reactants or products once equilibrium is reached. Hence, for the reaction of CO(g) and H₂O(g) to produce CO₂(g) and H₂(g), adding a catalyst will allow us to reach equilibrium more quickly, but not result in an increased amount of CO₂(g) at equilibrium.

Gas-phase Equilibrium

In gas-phase reactions, equilibrium involves gases existing under certain pressures and conditions where the rates of the forward and reverse reactions are equal. These reactions are particularly sensitive to changes in conditions such as pressure, temperature, and concentration.
Gas-phase equilibria require special attention because changes in any of these factors can cause shifts according to Le Chatelier’s Principle. Unlike reactions in other phases, gas-phase reactions are directly influenced by changes in volume or pressure, given the presence of gases that occupy space and exert pressure.

• Changes in pressure can shift equilibrium, depending on the total number of moles of gas on either side of the reaction.
• Adding an inert gas does not shift equilibrium unless the volume is allowed to change.

In our example reaction, the number of moles of gas is equal on both sides of the equation, which means a change in volume or pressure without a corresponding change in other conditions does not shift equilibrium.

Equilibrium Shift

Understanding equilibrium shifts is integral when predicting how reactions will respond to various changes in conditions. An equilibrium shift means the balance between reactants and products changes - favoring either the right side (more products) or the left side (more reactants).
Factors that influence equilibrium shift include:

• Concentration changes: Adding or removing reactants/products can push the equilibrium in the opposite direction.
• Pressure/volume changes: These primarily affect gaseous equilibria and depend on the number of gas moles.
• Temperature changes: Increasing/decreasing temperature shifts equilibrium depending on whether the reaction is exothermic or endothermic.

In the given reaction of CO and H₂O, adding CO shifts equilibrium towards more CO₂(g) production.
This shift occurs because the system seeks to balance the increased CO concentration by converting it into more products, specifically CO₂ and H₂, in line with Le Chatelier’s Principle.