Problem 61 - A Complete Resource Book in Chemistry for JEE Main

Question

The equilibrium constant of a reaction is 300 . If the volume of reaction flask is tripled, the equilibrium constant is (a) 300 (b) 600 (c) 900 (d) 100

Step-by-Step Solution

Answer

(a) 300

Step 1: Understand the Equilibrium Constant Concept

The equilibrium constant ( K ) of a chemical reaction is a measure of the relative concentrations of the products and reactants at equilibrium. It is determined by the reaction equation and remains constant for a given reaction at a specific temperature. Changing the volume of the reaction flask does not affect the equilibrium constant, as K is independent of changes in pressure or volume.

Step 2: Consider the Reaction's Dependency on Volume

For gaseous reactions, the concentration of reactants and products (and hence the partial pressures) depend on the volume of the container. However, the equilibrium constant K is not affected by changes in volume since it only depends on the reaction's inherent properties at a given temperature.

Step 3: Apply the Principle to the Given Problem

Since the equilibrium constant K is independent of volume, even if the volume of the reaction flask is tripled, the equilibrium constant remains unchanged. It is essential to note that volume changes may shift the position of equilibrium but not the equilibrium constant itself.

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K \), is pivotal in understanding chemical reactions at equilibrium. Essentially, \( K \) tells us how products and reactants compare in concentration when a reaction reaches equilibrium. Think of it as a way to predict how far a reaction will proceed. Importantly, \( K \) is fixed for a given reaction at a specific temperature.

The value of \( K \) is derived from the ratio of the concentration of the products to the concentration of the reactants, each raised to the power of their respective coefficients in the balanced chemical equation. This means \( K \) doesn't alter when we change variables like pressure or volume in the container. What's crucial is maintaining a consistent temperature, as \( K \) is sensitive to changes in this factor. Therefore, even when the volume of the reaction flask is tripled, \( K \) remains the same, being 300 in this scenario.

Reaction Volume

Reaction volume refers to the space in which the reactants and products of a reaction are contained. Volume changes can impact the concentrations and partial pressures of gases in a reaction mixture. This is due to their dependency on volume as defined by the equation \( \text{PV} = n\text{RT} \).

When the volume of a container is altered, while the concentrations of individual components may shift, the equilibrium constant \( K \) does not change. The system may adjust to the new conditions by shifting the equilibrium position to maintain balance, but \( K \), which is a measure of the chemical species' equilibrium concentrations at a given temperature, is constant.

• For example, increasing the volume decreases the concentration of reactants and products, potentially shifting the equilibrium towards the side with more moles of gas to counterbalance this change.
• However, the \( K \) value itself, representative of reaction quotient equilibrium, remains unaffected by these volume-induced shifts.

Le Chatelier's Principle

Le Chatelier's Principle is a helpful tool for predicting how a system at equilibrium will respond to external changes. Essentially, this principle states that if an external change is applied to a system at equilibrium, the system will adjust itself to partially counteract the effect of the change and re-establish equilibrium.

When volume is increased, for instance, the system will react by favoring the process that occupies more volume—often, this entails shifting towards the side with more gas molecules. This is how the system tries to reduce the impact of the increase in volume and restore equilibrium conditions.

• However, even while the equilibrium position shifts, the equilibrium constant \( K \) does not change. This is because \( K \) is dictated solely by temperature, not volume or pressure.
• Understanding this principle allows chemists to manipulate conditions to favor the formation of desired products, all while knowing that the \( K \) will remain a steadfast point of reference.