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

The correct answer is (a) (ii) and (iv) are correct.

Step 1: Understand the Reaction

The given reaction is \(\mathrm{N}_2(\mathrm{~g}) + 3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{~g})\), which is exothermic as indicated by \(\Delta \mathrm{H} = -93.6 \mathrm{~kJ} \mathrm{~mol}^{-1}\). This means that the reaction releases heat while proceeds towards the formation of ammonia (\(\mathrm{NH}_3\)).

Step 2: Analyze Le Chatelier's Principle for Temperature

According to Le Chatelier's Principle, for an exothermic reaction, lowering the temperature favors the formation of more product (\(\mathrm{NH}_3\)), consuming \(\mathrm{H}_2\) and \(\mathrm{N}_2\), thus decreasing \([\mathrm{H}_2]\). Hence, option (i) will **not** increase the concentration of \(\mathrm{H}_2\).

Step 3: Analyze Le Chatelier's Principle for Volume

Increasing the volume of the system will decrease the pressure and shift the equilibrium towards the side with more gaseous moles. Here, the reactants side initially has 4 moles of gas (1 \(\mathrm{N}_2\) + 3 \(\mathrm{H}_2\)) compared to 2 moles of \(\mathrm{NH}_3\). Therefore, increasing the volume increases \([\mathrm{H}_2]\), making option (ii) correct.

Step 4: Impact of Adding \(\mathrm{N}_2\) at Constant Volume

Adding \(\mathrm{N}_2\) will increase the concentration of reactants, shifting the equilibrium towards the products (more \(\mathrm{NH}_3\) is formed), thus consuming \(\mathrm{H}_2\) and causing \([\mathrm{H}_2]\) to decrease. So, option (iii) is **not** correct.

Step 5: Impact of Adding \(\mathrm{H}_2\) at Constant Volume

Adding \(\mathrm{H}_2\) directly increases its concentration. At equilibrium, even with some \(\mathrm{H}_2\) being consumed to form \(\mathrm{NH}_3\), \([\mathrm{H}_2]\) will still be higher than before the addition. Thus, option (iv) is correct.

Key Concepts

Chemical Equilibrium

Chemical equilibrium occurs in a reversible chemical reaction when the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of the reactants and products remain constant. However, this does not mean the concentrations are equal, just stable. For chemical reactions like the synthesis of ammonia \[\mathrm{N}_2(\mathrm{g}) + 3 \mathrm{H}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{g}),\]the system reaches equilibrium under specific conditions of temperature and pressure.
Here, the reaction moves forward or backward depending on changes in the system, largely according to Le Chatelier's Principle. If the system at equilibrium experiences a change in concentration, temperature, or pressure, the equilibrium will shift to counteract the effect of the change and re-establish equilibrium.

Exothermic Reaction

Exothermic reactions are chemical processes that release heat into their surroundings. In the context of our reaction, as specified by \(\Delta \mathrm{H} = -93.6 \mathrm{~kJ} \mathrm{~mol}^{-1},\)which indicates the reaction is exothermic.
For exothermic reactions, heat can be considered as a product. Lowering the temperature, therefore, makes the reaction shift towards the product side (forming more ammonia, in this case). The system essentially tries to produce more heat to make up for the loss by increasing the concentration of products.
Key characteristics of exothermic reactions include:

• Heat is released.
• Energy is transferred to the surroundings.
• The surrounding environment typically gets warmer.

Understanding these can help predict how the equilibrium position might shift under various temperature changes.

Effect of Volume and Concentration Changes

Volume and concentration changes can significantly affect chemical equilibrium. For reactions involving gases, changes in volume are directly tied to pressure changes (according to Boyle's Law).
Increasing the volume of the system lowers the system's pressure. For the ammonia synthesis reaction, increasing the volume shifts the equilibrium towards the side with more gaseous moles to increase pressure again. Hence, it shifts toward the reactant side, increasing \([\mathrm{H}_2]\).
Similarly, adding more reactants directly increases their concentration, temporarily shifting the equilibrium position until a new balance is reached. In our case, adding \(\mathrm{H}_2\) alone ensures more ammonia is formed, but the overall concentration of \(\mathrm{H}_2\) at equilibrium will be higher than before the addition.
The key points to remember about volume and concentration effects include:

• Volume changes affect gaseous reactions by altering pressure.
• Adding more reactants or products will temporarily shift equilibrium away from what's added until a new equilibrium is established.

Thus, understanding these shifts can help predict reaction behavior under different conditions.