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) \(\mathrm{K}_{\mathrm{p}}\) does not changes significantly with pressure

Step-by-Step Solution

Answer

Option (d) is correct; \( K_p \) does not change significantly with pressure.

Step 1: Understand the Question

We need to analyze the effects of pressure on different aspects of equilibrium for the dissociation of ammonia. The task is to determine which statements about the system at equilibrium are true.

Step 2: Analyze the Reaction

For ammonia dissociation, the reaction is: \[ \text{NH}_3(g) \rightleftharpoons \text{NH}_2(g) + \text{H}(g) \]. This reaction shows that one molecule of ammonia decomposes into two molecules, indicating a change in the number of moles.

Step 3: Discuss the Effect of Pressure on Equilibrium

According to Le Chatelier’s principle, an increase in pressure will favor the side of the reaction with fewer gas molecules. Since decomposition increases the number of moles, increased pressure shifts the equilibrium to the side with fewer moles, which is the reactants' side.

Step 4: Evaluate Each Option

(a) Alpha does change with pressure due to change in position of equilibrium.(b) Concentration of \( \text{NH}_2 \) could change as equilibrium shifts.(c) The concentrations of hydrogen and nitrogen are equal due to stoichiometry.(d) \( K_p \), being a function of temperature, does not significantly change with pressure under ideal conditions.

Step 5: Select the Right Answer

Given the analysis, (d) is correct because \( K_p \), the equilibrium constant for pressure, is not affected by changes in pressure for a given temperature.

Key Concepts

Le Chatelier’s principle

Le Chatelier’s principle is a fundamental principle in chemistry that helps predict how a change in conditions can affect chemical equilibrium. It's like a balancing act for chemical reactions. When a stress or change is applied to a system at equilibrium, such as a change in concentration, temperature, or pressure, Le Chatelier’s principle states that the system will adjust itself to counteract the change and restore a new equilibrium.

For example, if we increase the pressure in a gaseous system, the equilibrium will shift to the side with fewer gas molecules. This is because fewer gas molecules exert less pressure. This principle is particularly useful when analyzing the dissociation of gases, such as ammonia, by understanding how the system responds to various stresses.

Le Chatelier’s principle helps chemists predict the direction of the shift in equilibrium but doesn't tell us the rate at which equilibrium will be reached. This insightful tool is crucial for understanding and manipulating chemical processes in real-world applications.

Dissociation of ammonia

The dissociation of ammonia is a chemical process where ammonia (H_3) breaks down into its constituent gases, nitrogen (H_2) and hydrogen (H). The reaction is represented as:

\[ \text{NH}_3(g) \rightleftharpoons \text{NH}_2(g) + \text{H}(g) \]

In this reaction, one molecule of ammonia decomposes into two separate molecules, resulting in an increase in the total number of gas molecules. Understanding this change is essential when analyzing effects on equilibrium.

In terms of stoichiometry, the balanced chemical equation shows that every ammonia molecule produces one nitrogen and one hydrogen molecule. Therefore, under equilibrium conditions, in a closed system, the moles of ammonia will decrease while those of nitrogen and hydrogen will increase until a new equilibrium is reached.

• Ammonia decomposes into one nitrogen and one hydrogen molecule.
• The process is balanced, meaning it follows the stoichiometric ratios needed to maintain equilibrium.

The degree of dissociation, denoted by \( \alpha \), helps determine how much of the ammonia has broken down at a given set of conditions.

Pressure effects on equilibrium

Pressure is a significant factor influencing chemical equilibria, especially in gaseous reactions like the dissociation of ammonia. According to the principle discussed above, increasing pressure will shift the equilibrium position to the side with fewer gas molecules. In the case of ammonia dissociation, this means shifting towards the reactant side, where fewer molecules exist, thus counteracting the pressure change.

But how exactly does pressure influence the equilibrium constant \( K_p \)? Interestingly, the equilibrium constant \( K_p \) for gaseous reactions is not affected by changes in pressure at a constant temperature. This is because \( K_p \) depends solely on temperature.

• Pressure changes cause shifts towards the side with fewer gas molecules.
• \( K_p \) remains constant since it is a temperature-dependent value.

Thus, while changing pressure can and will shift the equilibrium position, it does not alter \( K_p \) under constant temperature conditions, highlighting the importance of maintaining specific temperatures during pressure changes in equilibrium reactions.