Problem 36 - A Complete Resource Book in Chemistry for JEE Main

Question

For the chemical reaction \(3 \mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g}) \rightleftharpoons \mathrm{X}_{3} \mathrm{Y}(\mathrm{g})\), the amount of \(\mathrm{X}_{3} \mathrm{Y}\) at equilibrium is affected by (a) temperature and pressure (b) temperature only (c) pressure only (d) temperature, pressure and catalyst

Step-by-Step Solution

Answer

Option (a) temperature and pressure.

Step 1: Understanding the Reaction

The chemical reaction given is \(3 \mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g}) \rightleftharpoons \mathrm{X}_{3} \mathrm{Y}(\mathrm{g})\). This is a reversible reaction with gaseous reactants and products.

Step 2: Impact of Temperature

Temperature can affect the position of equilibrium. Depending on whether the forward reaction is exothermic or endothermic, an increase in temperature will either favor the formation of products or reactants. However, without knowing enthalpy changes, it's clear temperature affects equilibration.

Step 3: Impact of Pressure

Since the reaction involves a change in the number of moles of gas (from 4 moles of gas to 1 mole of gas), applying Le Chatelier's principle, increasing pressure will favor the formation of the product \(\mathrm{X}_3 \mathrm{Y}\) as this decreases the pressure.

Step 4: Impact of Catalyst

A catalyst will not affect the equilibrium position; it only speeds up the attainment of equilibrium. Thus, catalysts do not affect the amount of \(\mathrm{X}_3 \mathrm{Y}\) at equilibrium.

Step 5: Selecting the Correct Option

Considering the effects, temperature and pressure both affect the amount of \(\mathrm{X}_3 \mathrm{Y}\) at equilibrium, whereas a catalyst does not alter the equilibrium concentrations. Thus, option (a) is correct.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle helps us predict how a system at equilibrium reacts to external changes. It's like a balancing act for chemical reactions. When the conditions such as concentration, temperature, or pressure of the system change, the system will adjust to counteract that change and re-establish equilibrium.
For example, consider the reaction \(3 \mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g}) \leftrightarrows \mathrm{X}_3 \mathrm{Y}(\mathrm{g})\). According to Le Chatelier's Principle:

• If you increase the concentration of \(\mathrm{X}\) or \(\mathrm{Y}\), the system will react by forming more \(\mathrm{X}_3 \mathrm{Y}\) to use up the excess.
• If the concentration of \(\mathrm{X}_3 \mathrm{Y}\) is increased, the reaction will shift towards the reactants, \(\mathrm{X}\) and \(\mathrm{Y}\).

The principle is like a guideline that allows us to predict the direction in which the reaction will shift to restore balance when disrupted.

Effects of Temperature on Equilibrium

Temperature is an interesting factor that can have a notable effect on chemical equilibria. It's all about understanding whether the reaction is exothermic (releases heat) or endothermic (absorbs heat).
If the reaction \(3 \mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g}) \leftrightarrows \mathrm{X}_3 \mathrm{Y}(\mathrm{g})\) is exothermic:

• Increasing the temperature will shift the equilibrium to the left, favoring the production of reactants \(\mathrm{X}\) and \(\mathrm{Y}\).

On the other hand, if it is endothermic:

• Increasing the temperature will cause the equilibrium to favor the formation of more products, pushing it to the right.

Therefore, knowing the heat exchange is crucial to predict the exact impact of temperature. Understand that raising the temperature tends to favor the direction that absorbs heat.

Effects of Pressure on Equilibrium

Pressure impacts reactions with gaseous reactants and products, particularly when there is a change in the number of gas molecules. For our reaction, \(3 \mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g}) \rightleftharpoons \mathrm{X}_3 \mathrm{Y}(\mathrm{g})\), the number of moles goes from 4 to 1.
Using Le Chatelier's Principle:

• Increasing pressure favors the side with fewer moles of gas. Thus, it will shift the equilibrium towards forming more \(\mathrm{X}_3 \mathrm{Y}\).
• Conversely, decreasing pressure will favor the side with more moles of gas, resulting in the formation of more reactants, \(3 \mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g})\).

In essence, pressure changes are a lot like squeezing a balloon, where increasing pressure tightens and directs the chemical system toward the side with fewer gas molecules.

Role of Catalysts in Reactions

Catalysts are like a fast-forward button for reactions. They speed up the rate at which equilibrium is reached but do not alter the position of equilibrium itself. This means catalysts can help systems reach equilibrium faster, but they won’t change the amount of each species at equilibrium.
For the reaction \(3 \mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g}) \rightleftharpoons \mathrm{X}_3 \mathrm{Y}(\mathrm{g})\):

• A catalyst will increase the rate at which \(\mathrm{X}_3 \mathrm{Y}\) is formed and decomposed but not its equilibrium concentration.

Thus, a catalyst is simply a facilitator. Think of it as a traffic officer at a busy intersection who allows cars to move more efficiently but does not change the direction or destination of the cars.