Problem 37 - A Complete Resource Book in Chemistry for JEE Main

Question

Pure ammonia is placed in a vessel at a temperature where its dissociation constant \((\alpha)\) is appreciable. At equilibrium (a) \(\alpha\) does not change with pressure (b) concentration of \(\mathrm{NH}_{2}\) does not change with pressure (c) concentration of hydrogen is less than that of nitrogen (d) \(\mathrm{K}\) does not changes significantly with pressure

Step-by-Step Solution

Answer

Correct statements are: (d) \(\mathrm{K}\) does not change significantly with pressure.

Step 1: Understanding the Reaction

Pure ammonia (NH_3) is placed at equilibrium with its dissociated form. The equilibrium involves dissociation into nitrogen and hydrogen gases. The chemical reaction can be written as:\[2\mathrm{NH}_3(g) \rightleftharpoons \mathrm{N}_2(g) + 3\mathrm{H}_2(g)\]The dissociation constant \(\alpha\) is a measure of the extent to which \(\mathrm{NH}_3\) dissociates into \(\mathrm{N}_2\) and \(\mathrm{H}_2\).

Step 2: Analyzing the Effects of Pressure on Dissociation

When the pressure in the system changes, Le Chatelier's Principle can be used to predict the direction of the reaction. According to the principle, an increase in pressure shifts the equilibrium towards the side with fewer moles of gas. Thus, increasing pressure will favor the reverse reaction (towards fewer moles of gas), which decreases \(\alpha\), implying that \(\alpha\) does change with pressure.

Step 3: Finding the Relation of NH2 Concentration with Pressure

The given reaction and species do not form any \(\mathrm{NH}_2\) molecules in the dissociation of \(\mathrm{NH}_3\), thus suggesting a potential typo in the problem. No \(\mathrm{NH}_2\) should form, so its concentration should not be affected by pressure changes as it remains at zero.

Step 4: Relation of Concentration of Hydrogen with Nitrogen

From the balanced equation:\[2\mathrm{NH}_3 \rightleftharpoons \mathrm{N}_2 + 3\mathrm{H}_2\]The formation of one molecule of \(\mathrm{N}_2\) leads to the formation of three molecules of \(\mathrm{H}_2\). Thus, the concentration of hydrogen will always be greater than that of nitrogen chemically.

Step 5: Examining Effect of Pressure on Equilibrium Constant

The equilibrium constant \(\mathrm{K}\) for a reaction depends only on temperature and not on pressure. Therefore, \(\mathrm{K}\) is not significantly affected by changes in pressure, which remains constant at a given temperature.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle helps us predict how chemical equilibria react to changes in conditions. When a change is applied to a system at equilibrium, the system adjusts in a way that counteracts that change and re-establishes equilibrium. If we apply this principle to a reaction involving gases, an increase in pressure will cause the system to shift toward the side with fewer gas molecules.

For the ammonia dissociation reaction, 2 moles of \(\mathrm{NH}_3\) dissociate into 1 mole of \(\mathrm{N}_2\) and 3 moles of \(\mathrm{H}_2\). Therefore, the forward reaction produces more moles than it consumes, and an increase in pressure will favor the reverse reaction where fewer gas molecules are present, thus decreasing dissociation constant \(\alpha\). Conversely, a decrease in pressure will favor more gas formation, shifting the equilibrium to the right.

Dissociation Constant

The dissociation constant \(\alpha\) is a key concept when analyzing the extent to which a compound breaks into its components. It essentially measures how much of the initial compound dissociates.

In the context of the ammonia dissociation reaction, \(\alpha\) indicates the fraction of ammonia that has dissociated into nitrogen and hydrogen gases. The value of \(\alpha\) can change depending on external conditions such as temperature and pressure, following Le Chatelier's Principle. However, under constant temperature and increased pressure, the tendency is for \(\alpha\) to decrease as the equilibrium favors the formation of \(\mathrm{NH}_3\) by moving towards the side with fewer total moles of gas.

Gas Laws

Gas laws are essential for understanding how gases behave under various conditions. They describe the relationships between pressure, volume, temperature, and the amount of gas.

When studying equilibrium reactions involving gases, knowing how pressure influences gas volumes can help us predict shifts in equilibrium. For ammonia dissociation, as pressure increases, we expect the system to respond by reducing the number of gas molecules to restore equilibrium, which adheres to Boyle's Law (pressure and volume are inversely related at constant temperature).

Being familiar with gas laws allows you to anticipate how changes in pressure and temperature can alter the position of the equilibrium in gas-phase reactions.

Ammonia Dissociation Reaction

The ammonia dissociation reaction involves \(\mathrm{NH}_3\) breaking down into \(\mathrm{N}_2\) and \(\mathrm{H}_2\). The balanced chemical equation is: 2\(\mathrm{NH}_3(g) \rightleftharpoons \mathrm{N}_2(g) + 3\mathrm{H}_2(g)\).

This reaction is an essential part of studying chemical equilibria involving gases. Pay attention to stoichiometry, as the coefficients tell us that two moles of ammonia dissociate to produce one mole of nitrogen and three moles of hydrogen. This nature of the reaction influences how changes in conditions affect equilibrium positions and concentrations of products and reactants.

Remember, in equilibrium systems like this one, the concentrations of different species (like \(\mathrm{H}_2\) compared to \(\mathrm{N}_2\)) relate directly to the stoichiometric coefficients in the balanced equation, ensuring more \(\mathrm{H}_2\) is formed than \(\mathrm{N}_2\). Understanding this relationship is crucial for interpreting results from chemical reactions at equilibrium.