Problem 98 - A Complete Resource Book in Chemistry for JEE Main

Question

For the reaction \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{~g}), \Delta \mathrm{H}=-93.6 \mathrm{~kJ} \mathrm{~mol}^{-1}\) the concentration of \(\mathrm{H}_{2}\) at equilibrium can be increased by (i) lowering the temperature (ii) increasing the volume of the system (iii) adding \(\mathrm{N}_{2}\) at constant volume (iv) adding \(\mathrm{H}_{2}\) at constant volume (a) (ii) and (iv) are correct (b) only (ii) is correct (c) (i), (ii) and (iii) are correct (d) (iii) and (iv) are correct

Step-by-Step Solution

Answer

(a) (ii) and (iv) are correct.

Step 1: Understanding the Chemical Reaction

In this reaction, nitrogen gas (\(\mathrm{N}_2\)) and hydrogen gas (\(\mathrm{H}_2\)) react to form ammonia (\(\mathrm{NH}_3\)), releasing energy as indicated by \(\Delta\mathrm{H} = -93.6\, \mathrm{kJ/mol}\). This negative \(\Delta H\) suggests the reaction is exothermic, favoring products at lower temperatures.

Step 2: Effect of Temperature on Equilibrium

Lowering the temperature shifts the equilibrium towards the right to produce more ammonia due to the exothermic nature of the reaction, decreasing \(\mathrm{H}_2\). Therefore, option (i) is not correct for increasing \(\mathrm{H}_2\).

Step 3: Effect of Volume on Equilibrium

Increasing the volume of the system lowers the pressure which, according to Le Chatelier's principle, will shift the equilibrium towards the side with more gas moles, which is the left side (reactants). This increases \(\mathrm{H}_2\) concentration, making option (ii) correct.

Step 4: Effect of Adding N_2 on Equilibrium

Adding \(\mathrm{N}_2\) shifts the equilibrium towards products to counteract the change, consuming \(\mathrm{H}_2\) and forming more \(\mathrm{NH}_3\). This decreases \(\mathrm{H}_2\) concentration, so option (iii) is incorrect for increasing \(\mathrm{H}_2\).

Step 5: Effect of Adding H_2 on Equilibrium

Adding \(\mathrm{H}_2\) would increase its concentration directly. While this might create a shift to restore equilibrium, the immediate effect is simply to increase \(\mathrm{H}_2\) concentration, making option (iv) correct.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemical equilibrium, which helps predict how a reaction will respond to changes in conditions. It states that if a dynamic equilibrium is disturbed by changing the conditions, the system adjusts itself to counteract the change and restore a new equilibrium. Understanding this principle helps chemists and students predict the direction in which a reaction will shift:

• Adding or removing reactants or products
• Changing the temperature
• Altering the pressure or volume

In the given reaction, increasing the volume causes the equilibrium to shift towards the side with more gaseous molecules (reactants) to balance the pressure change. This is the direct application of Le Chatelier's Principle, as altering the system's conditions forces the equilibrium to adjust itself.

Exothermic Reaction

An exothermic reaction is one that releases energy in the form of heat. In the chemical reaction \[ \mathrm{N}_2(g) + 3\mathrm{H}_2(g) \longrightarrow 2\mathrm{NH}_3(g), \] it is given that \[\Delta H = -93.6 \, \mathrm{kJ/mol}\].The negative sign indicates the reaction is exothermic, meaning it releases heat, favoring the products at lower temperatures. When you lower the temperature of an exothermic reaction, it shifts the equilibrium to the right to produce more heat, thus favoring product formation.However, if the goal is to increase the concentration of \(\mathrm{H}_2\), lowering the temperature would not achieve that. It would actually consume \(\mathrm{H}_2\), moving the reaction toward more product formation.

Volume Effect on Equilibrium

Changing the volume of a system affects the equilibrium position, especially for reactions involving gases. When you increase the volume of the system, the pressure decreases. According to Le Chatelier's Principle, the equilibrium will shift towards the side with more gaseous molecules to increase pressure.In the provided reaction: \[ \mathrm{N}_2(g) + 3\mathrm{H}_2(g) \longrightarrow 2\mathrm{NH}_3(g), \]there are four gas moles in the reactants and only two in the products. Thus, increasing the volume shifts the equilibrium towards the left side (the reactants) because there are more gas moles there.This shift increases the concentration of \(\mathrm{H}_2\), making options involving volume increase, such as option (ii), correct for boosting \(\mathrm{H}_2\) concentration.

Temperature Effect on Equilibrium

Temperature changes significantly impact chemical equilibrium, particularly in exothermic and endothermic reactions. For exothermic reactions, like the formation of ammonia from nitrogen and hydrogen, cooling the system favors the exothermic direction, effectively shifting equilibrium towards more product formation.However, if the target is to enhance the concentration of a reactant, like \(\mathrm{H}_2\), the temperature needs to be carefully considered. Increasing the temperature in exothermic reactions shifts equilibrium towards the reactants, reducing product formation.Conversely, lowering the temperature does the opposite by promoting product formation. It is vital to identify the desired outcome—whether increasing products or reactants—to determine the correct temperature adjustment.