Problem 33 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

A liquid is in equilibrium with its vapour at its boiling point. On the average, the molecules in the two phases have equal : (a) inter-molecular forces (b) potential energy (c) total energy (d) kinetic energy

Step-by-Step Solution

Answer

(d) kinetic energy

Step 1: Understanding the Problem

We need to determine which property among inter-molecular forces, potential energy, total energy, or kinetic energy is equal for molecules in the liquid and gas phase at the boiling point.

Step 2: Concept of Phase Equilibrium

At the boiling point, a liquid is in dynamic equilibrium with its vapour. This means the rate of evaporation equals the rate of condensation.

Step 3: Molecular Energy Considerations

Potential energy varies due to different intermolecular forces in liquid and gas phases. Total energy, including potential and kinetic energy, also varies. Intermolecular forces depend on phase and aren't directly equal between phases.

Step 4: Key to Equality: Kinetic Energy

When a liquid is in equilibrium with its vapour at the boiling point, the average kinetic energy of the molecules must be equal in both phases. This is because temperature, which is a measure of average kinetic energy, is the same for both liquid and vapour at equilibrium.

Key Concepts

Boiling Point

The boiling point of a liquid is a special temperature where it transitions from a liquid to a gas. At this point, the liquid is in a state of phase equilibrium with its vapor. This means that the amounts of liquid and vapor remain constant over time as long as the temperature is maintained. The molecules have enough energy to break free from the forces holding them in the liquid state.
At the boiling point, the phenomenon of phase change becomes continuous. It isn't just a simple transformation but rather an ongoing exchange.

• Boiling Point Conditions: Liquid molecules have enough energy to escape into the gas phase.
• Phase Equilibrium: The liquid and vapor phases coexist stably.

At this temperature, important to note, the pressure of the vapor equals the atmospheric pressure, allowing this transition to occur without any net change in the amount of liquid or vapor.

Kinetic Energy

Kinetic energy refers to the energy that molecules possess due to their motion. At the boiling point of a liquid, there's an essential equality in the kinetic energy of the molecules in both the liquid and vapor states. This is because, at this temperature, the energy from heat raises both phases to the same average molecular velocity.

Understanding Kinetic Energy at Boiling Point

Since temperature is a measure of average kinetic energy, at the boiling point, both the liquid and vapor phases share the same temperature and hence the same average kinetic energy.

• Equality of Kinetic Energy: Crucial for phase equilibrium.
• Temperature and Kinetic Energy: Direct relationship; as temperature increases, so does kinetic energy.

The equal average kinetic energy ensures that molecules in each phase are equally dynamic, allowing for a balanced exchange between phases, characteristic of equilibrium.

Dynamic Equilibrium

When a liquid is at its boiling point, it is in dynamic equilibrium with its vapor. Dynamic equilibrium is a condition where two opposing processes occur at equal rates.
In the context of phase changes, this means the rate of evaporation of liquid molecules into a gas equals the rate of condensation of gas molecules back into a liquid.

• Evaporation and Condensation: These processes occur simultaneously and at equal rates.
• Balance of Phases: Neither phase increases or decreases in amount.

This equilibrium is dynamic because molecules are in constant motion, changing between states, yet the overall quantities of liquid and vapor do not change. This balance is crucial for maintaining stable conditions at the boiling point.