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

Question

For the reaction \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}), \Delta \mathrm{H}=-93.6 \mathrm{~kJ} \mathrm{~mol}^{-1}\) 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 Le Chatelier's Principle

The reaction is exothermic (\(\Delta \mathrm{H}=-93.6 \, \mathrm{kJ} \, \mathrm{mol}^{-1}\)). According to Le Chatelier's Principle, a decrease in temperature will shift the equilibrium towards the exothermic side (right to \(\mathrm{NH}_3\) formation), decreasing \(\mathrm{H}_2\). Hence, lowering the temperature will not increase \(\mathrm{H}_2\) concentration.

Step 2: Effect of Volume Increase on Equilibrium

Increasing the volume of the system decreases the pressure, which shifts the equilibrium towards the side with more moles of gas. The left side of the equation, \(\mathrm{N}_2+3 \mathrm{H}_2\), has 4 moles (more than 2 moles of \(\mathrm{NH}_3\)), so increasing volume favors the left side, increasing \(\mathrm{H}_2\) concentration.

Step 3: Adding More \(\mathrm{N}_2\)

Adding \(\mathrm{N}_2\) at constant volume will shift the equilibrium towards the right to form more \(\mathrm{NH}_3\), reducing \(\mathrm{H}_2\) concentration.

Step 4: Adding More \(\mathrm{H}_2\)

Adding \(\mathrm{H}_2\) at constant volume increases its concentration directly and may shift the equilibrium towards the right side temporarily, but since \(\mathrm{H}_2\) is being added directly, its concentration increases.

Step 5: Evaluating the Options

Based on the analysis, options (ii) and (iv) increase \(\mathrm{H}_2\) concentration. Therefore, option (a) is correct.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a handy tool for predicting the direction of an equilibrium shift in response to changes in conditions. If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change. This principle helps us understand how a reaction will respond to changes in temperature, pressure, volume, and concentration. For example, in an exothermic reaction like our reaction of nitrogen and hydrogen forming ammonia, a decrease in temperature favors the formation of ammonia, as the system tries to generate more heat by favoring the exothermic direction. However, this also means the concentration of reactants like hydrogen decreases when the system shifts to produce more products.

Effect of Volume on Equilibrium

The effect of volume changes on equilibrium is closely tied to the concept of pressure in a system involving gas. According to Le Chatelier's Principle, if the volume of a gaseous system is increased, the equilibrium will shift to the side with more gas molecules to counteract the decrease in pressure. In our specific reaction:

• The left side (reactants: nitrogen and hydrogen) contains 4 moles of gas (1 mole of nitrogen + 3 moles of hydrogen).
• The right side (product: ammonia) contains 2 moles of gas (2 moles of ammonia).

Therefore, increasing the volume of the reaction vessel decreases the overall pressure and causes the equilibrium to shift towards the side with more moles, which in this case is the reactants' side. This shift results in an increased concentration of hydrogen gas. This is why option (ii) is correct in the exercise.

Exothermic Reactions

Exothermic reactions release heat energy as the reaction proceeds. In the context of equilibrium, the heat released can be considered as a product. Therefore, for exothermic reactions, increasing the temperature adds more heat, and according to Le Chatelier's Principle, the system will favor the direction that absorbs this excess heat, which is the endothermic direction (opposite to the heat release).

• Exothermic reactions typically become more favorable at lower temperatures, which is why cooling the system often shifts the equilibrium towards the products.
• However, for our specific reaction of nitrogen and hydrogen forming ammonia, decreasing the temperature increases the formation of ammonia and thus lowers the concentration of hydrogen.

Thus, to increase the concentration of hydrogen, we must avoid temperature decreases. This explains why option (i) in the exercise does not lead to an increase in hydrogen concentration.