Problem 70 - A Complete Resource Book in Chemistry for JEE Main

Question

The vapour pressure of water at \(300 \mathrm{~K}\) in a closed container is \(0.4 \mathrm{~atm}\). If the volume of the container is doubled, its vapour pressure at \(300 \mathrm{~K}\) will be (a) \(0.8 \mathrm{~atm}\) (b) \(0.2 \mathrm{~atm}\) (c) \(0.4 \mathrm{~atm}\) (d) \(0.6 \mathrm{~atm}\)

Step-by-Step Solution

Answer

The vapour pressure will remain 0.4 atm (option c).

Step 1: Understanding Vapour Pressure

Vapour pressure is an intrinsic property of a liquid at a given temperature. It is the pressure exerted by the vapor when in thermodynamic equilibrium with its liquid at a given temperature in a closed system.

Step 2: Relate with Constant Temperature

At constant temperature, the vapour pressure of a pure liquid depends only on the temperature and not on the volume of the container. This is because the volume does not affect the equilibrium between liquid and its vapour.

Step 3: Conclude Based on Concept

Since the temperature remains 300 K, doubling the volume of the container does not change the vapour pressure of water. Thus, the vapour pressure will remain at 0.4 atm because vapour pressure depends only on temperature.

Key Concepts

Thermodynamic Equilibrium

When a liquid is in a sealed container, it has a special state known as thermodynamic equilibrium. In this state, the rate at which molecules evaporate from the liquid into the vapor phase is equal to the rate at which they return from the vapor back into the liquid. This means that over time, the concentration of molecules in both states remains unchanged. It's like a peaceful dance, where molecules keep moving between the liquid and the vapor, but their numbers on each side stay balanced.

This balance is crucial because it defines the vapor pressure of the liquid at a specific temperature. When the system is undisturbed, thermodynamic equilibrium allows the liquid and vapor to coexist harmoniously, without any sudden changes in pressure or phase.

Intrinsic Property of Liquids

An intrinsic property is a characteristic of a substance that remains constant regardless of the amount or shape of the sample. For liquids, vapour pressure is one such intrinsic property. This means that for a given liquid at a specific temperature, its vapor pressure will always be the same, no matter how much of the liquid is present or the size of its container.

This is why even if you take a small amount of water or fill a large container with it, if both are at the same temperature, their vapor pressures will be identical. This intrinsic nature makes vapor pressure a powerful tool for chemists and physicists when studying the properties of liquids across different circumstances.

• Vapour pressure is consistent at a given temperature.
• Does not depend on the amount of liquid.
• Remains unchanged even if the container size changes.

Temperature Dependence of Vapour Pressure

Vapour pressure of a liquid is directly tied to its temperature. As temperature increases, so does the kinetic energy of its molecules. This movement allows more molecules to escape into the vapor phase, thereby increasing the vapor pressure. Conversely, if the temperature drops, the kinetic energy decreases and fewer molecules can escape, reducing the vapour pressure.

This relationship can be summarized as:\[ \text{higher temperature} \rightarrow \text{higher vapour pressure}\]Temperature acts like a dial that controls how much vapor forms over a liquid, which is why keeping temperature constant is key when studying equilibrium properties like vapor pressure. A change in container volume or the amount of liquid does not influence the vapour pressure at a constant temperature.