Problem 73 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The INCORRECT statement among the following, for this reaction, is (a) Decrease in the total pressure will result in formation of more moles of gaseous \(X\) (b) At the start of the reaction, dissociation of gaseous \(X_{2}\) takes place spontaneously (c) \(\beta_{\text {equilboium }}=0.7\) (d) \(K_{C}<1\)

Step-by-Step Solution

Answer

Statement (d) is incorrect as a high degree of dissociation (\(\beta = 0.7\)) conflicts with \(K_{C} < 1\).

Step 1: Analyze Each Statement

Review each statement provided in the question to determine if they are true or false based on chemical equilibrium principles.

Step 2: Apply Le Chatelier’s Principle to Statement (a)

According to Le Chatelier’s Principle, if the total pressure decreases, the system will shift towards the side with more moles of gas. Since the formation of more moles of gaseous \(X\) implies an increase in moles, statement (a) seems true on this basis.

Step 3: Evaluate Statement (b) on Spontaneity

The spontaneous dissociation of gaseous \(X_{2}\) implies that the reaction proceeds without the need for external energy input. If the reaction is at initial conditions and moves forward on its own, this is a correct statement.

Step 4: Check Equilibrium Degree for Statement (c)

The degree of dissociation, \(\beta_{\text{equilibrium}} = 0.7\), implies a high level of dissociation of \(X_{2}\). This high degree suggests that the product formation is significant but doesn’t directly indicate correctness or incorrectness.

Step 5: Evaluate Statement (d) With Equilibrium Constant

The equilibrium constant \(K_{C} < 1\) indicates that at equilibrium, reactants are favored over products. For a high degree of dissociation (\(\beta = 0.7\)), a low \(K_C\) would be unexpected, suggesting statement (d) is incorrect.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle helps us understand how a chemical system at equilibrium responds to changes in conditions. When a change is applied to a system, the equilibrium shifts to counteract the change and restore balance. In a gaseous system, like the reaction involving gaseous \(X_2\) dissociating into \(X\), this principle predicts the direction in which the reaction will shift if the total pressure is altered.
For instance, if you decrease the pressure of the system, Le Chatelier’s Principle states that the equilibrium will shift towards the side with more gas molecules. This is how the system tries to increase pressure by producing more moles of gas, supporting the idea presented in statement (a) of the exercise, that more moles of gaseous \(X\) will form when the pressure decreases. Understanding this principle is crucial for predicting how external changes affect chemical equilibria.

Reaction Spontaneity

A spontaneous reaction is one that occurs naturally, without outside intervention, typically because it leads to greater stability and lower energy. Initially, when the reaction starts, the dissociation of gaseous \(X_2\) to form \(X\) occurs spontaneously if the energy barrier is overcome naturally by the system's conditions.
This concept is crucial because it tells us about the initial tendency of the reaction under given conditions. In statement (b), the spontaneous dissociation of \(X_2\) suggests that the initial conditions favor the breaking down of \(X_2\) without the need for added energy. This conforms with the general understanding of spontaneous reactions in chemistry, which often depend on factors like energy changes and entropy.

Equilibrium Constant

The equilibrium constant \(K_C\) is a value that reflects the ratio of concentrations of products to reactants at equilibrium for a given reaction. When \(K_C < 1\), it implies that the reactants are favored at equilibrium, meaning the system contains more reactants than products.
This concept plays a pivotal role in understanding statement (d) from the exercise. While a high degree of dissociation suggests that a significant amount of product forms, a \(K_C\) less than 1 contradicts this, indicating more reactants than products are present at equilibrium. This contradiction suggests a reevaluation of statement (d), pointing to its inaccuracy given the provided conditions.

Degree of Dissociation

The degree of dissociation, often denoted by \(\beta\), indicates the fraction of the original compound that dissociates in a reaction. A \(\beta = 0.7\) means 70% of \(X_2\) dissociates into \(X\) molecules, reflecting a substantial shift towards product formation.
In chemical equilibria, understanding the degree of dissociation helps gauge how much a reaction progresses. It's crucial for judging the correctness of statement (c) in the exercise. A higher degree, like 0.7, typically suggests significant product formation. Yet, this indicator alone does not automatically validate the reaction's efficiency without considering other factors like the equilibrium constant. Thus, while high, \(\beta\) doesn’t directly explain why \(K_C < 1\) in this context, but it underscores the dissociation extent.