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

Question

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

Step 1: Understanding Equilibrium Reaction

The given reaction is at equilibrium. According to Le Chatelier's Principle, any change to the system will cause the system to adjust in a way that counteracts that change. Our goal is to determine how to increase the amount of \(\mathrm{CO}_2\mathrm{(g)}\) at equilibrium.

Step 2: Considering Option (a): Adding a Catalyst

A catalyst speeds up the rate at which equilibrium is reached but does not affect the position of the equilibrium. Thus, adding a catalyst will not increase the amount of \(\mathrm{CO}_2\) at equilibrium.

Step 3: Considering Option (b): Adding an Inert Gas

Adding an inert gas at constant volume does not change the partial pressures of the reacting gases, so it does not shift the equilibrium position or increase the amount of \(\mathrm{CO}_2\).

Step 4: Considering Option (c): Decreasing the Volume

Decreasing the volume of the container increases the pressure. For a system in which the number of gas moles is the same on both sides of the reaction (1 mole of reactants gives 1 mole of products here), changes in volume do not affect the position of the equilibrium.

Step 5: Considering Option (d): Increasing the Amount of CO

Increasing the amount of \(\mathrm{CO}\) will shift the equilibrium position to the right to consume more \(\mathrm{CO}\) and \(\mathrm{H}_2\mathrm{O}\), thus directly producing more \(\mathrm{CO}_2\) and \(\mathrm{H}_2\). Therefore, option (d) is correct.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a key concept in understanding how a chemical system at equilibrium responds to changes. According to this principle, if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the effect of the disturbance.
For example, if you add more reactant to the system, the equilibrium shifts to produce more product to restore balance. Conversely, removing a product would cause the reaction to shift to produce more of the removed substance. This principle helps predict how changing concentration, temperature, or pressure can affect the outcome of a reaction.

Le Chatelier's Principle is crucial in chemical processes where controlling product yield is important. It allows chemists to manipulate conditions to achieve the desired amount of product.

Equilibrium Position

The equilibrium position in a chemical reaction refers to the ratio of the concentrations of products to reactants at equilibrium. This position shows where the balance of reactants and products lies once the reaction has reached a stable state.
Changes to the system, such as adding or removing substances, can shift this position. According to Le Chatelier’s Principle, the system will adjust to a new equilibrium position by partially counteracting the change.

• If products are removed, the equilibrium shifts to the right to make more products.
• If reactants are added, the system similarly shifts to the right to produce more product.

In our exercise, increasing \( ext{CO}\) shifts the equilibrium to the right, enhancing the production of \( ext{CO}_2\).

Understanding the equilibrium position allows chemists to optimize conditions for desired reaction outcomes.

Effect of Catalysts

Catalysts are used to speed up chemical reactions without being consumed in the process. It's important to note that while catalysts do make reactions proceed faster, they do not affect the equilibrium position. They simply help the reaction reach equilibrium faster.
In the exercise, adding a catalyst will not increase the amount of \( ext{CO}_2\), as it doesn’t shift the equilibrium position. It does accelerate the rate at which equilibrium is achieved, regardless of whether the reaction is moving towards products or reactants.

Because catalysts do not alter the position of equilibrium, their use is mainly beneficial in systems where time is a critical factor in reaching equilibrium quickly.

Effect of Volume Changes

Volume changes in a reaction involving gases can affect the pressure, thereby influencing the equilibrium position according to Le Chatelier's Principle. When volume is decreased, pressure increases, and the system adjusts to reduce this pressure change.
For a gaseous reaction, if the total number of gas molecules on one side of the reaction is different from the other, changes in volume dramatically affect equilibrium. However, in our given exercise, since there is an equal number of gas moles on both sides of the equation, decreasing the volume does not change the equilibrium position.

Understanding how volume affects equilibrium is critical in processes involving gases, as even small changes can significantly impact the reaction's atmosphere and ultimately affect the product yield.