Problem 91 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following reactions, the concentration of product is higher than the concentration of reactant at equilibrium? = equilibrium constant) (a) \(\mathrm{A} \rightleftharpoons \mathrm{B} ; \mathrm{K}=0.001\) (b) \(\mathrm{M} \rightleftharpoons \mathrm{N} ; \mathrm{K}=10\) (c) \(\mathrm{X} \rightleftharpoons \mathrm{Y} ; \mathrm{K}=0.005\) (d) \(\mathrm{R}=\mathrm{P} ; \mathrm{K}=0.01\)

Step-by-Step Solution

Answer

The reaction \( \mathrm{M} \rightleftharpoons \mathrm{N} \) with \( K = 10 \) has a higher product concentration at equilibrium.

Step 1: Understand Equilibrium Constant

The equilibrium constant \( K \) indicates the ratio of concentrations of products to reactants at equilibrium. A \( K \) greater than 1 suggests that the concentration of products is higher than the concentration of reactants.

Step 2: Evaluate Given Options

Compare the equilibrium constants for each reaction: - (a) \( K = 0.001 \) - (b) \( K = 10 \) - (c) \( K = 0.005 \) - (d) \( K = 0.01 \).Only option (b) has \( K > 1 \).

Step 3: Identify the Right Reaction

Since option (b) has an equilibrium constant \( K = 10 \), which is greater than 1, the concentration of products \( \mathrm{N} \) is higher than the concentration of reactants \( \mathrm{M} \) at equilibrium.

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K \), is a vital concept in understanding chemical equilibrium. It describes the ratio between the concentrations of products and reactants when a reaction has reached equilibrium. The equilibrium constant is expressed as:\[K = \frac{[Products]}{[Reactants]}\]Where the square brackets \( [] \) represent the concentration of the species at equilibrium. A few points to remember about the equilibrium constant:

• If \( K > 1 \), this indicates that at equilibrium, the concentration of products is higher than that of reactants. The reaction favors the formation of products.
• If \( K < 1 \), the reactants are favored, meaning their concentration is higher than that of the products at equilibrium.
• \( K \) is specific to a particular reaction at a set temperature; changes in temperature can affect the value of \( K \).

In our example, for reaction (b) with \( K = 10 \), the larger \( K \) value signifies a high concentration of products relative to reactants at equilibrium.

Reaction Quotient

The reaction quotient, \( Q \), is a measure similar to the equilibrium constant but calculated at any point other than equilibrium. The formula is the same:\[Q = \frac{[Products]}{[Reactants]}\]However, \( Q \) is evaluated with the current concentrations or pressures of the reactants and products, rather than those at equilibrium. Understanding \( Q \) in relation to \( K \):

• If \( Q = K \), the system is already at equilibrium.
• If \( Q < K \), the system will shift towards the products to create more equilibrium, indicating that the reaction will proceed forward.
• If \( Q > K \), the system will shift toward the reactants, indicating that the reaction will proceed in reverse, as there are too many products.

Knowing the relationship between \( Q \) and \( K \) helps predict the direction in which a reaction mixture will shift to reach equilibrium.

Le Chatelier's Principle

Le Chatelier's Principle is an essential tool in predicting the behavior of a reaction when external conditions change. This principle states that if a change is applied to a system at equilibrium, the system will adjust to minimize that change and restore a new equilibrium. Factors that affect equilibrium according to Le Chatelier's Principle:

• Concentration Changes: Adding more reactants will shift the equilibrium towards the products, while adding more products will shift it towards the reactants.
• Temperature Changes: Increasing temperature will favor the endothermic direction of a reaction, while lowering it favors the exothermic direction. The specific effects depend on whether the reaction is endothermic or exothermic.
• Pressure Changes (for gases): Increasing pressure by decreasing volume will shift the equilibrium towards the side with fewer gas moles, and vice versa.

Le Chatelier's Principle helps us understand how reactions can be manipulated, which is particularly important in industrial chemical processes where control over reaction conditions can lead to increased yield or efficiency.