Problem 6 - A Complete Resource Book in Chemistry for JEE Main

Question

An ideal gas, obeying kinetic theory of gases cannot be liquefied, because (a) its critical temperature is above \(0^{\circ} \mathrm{C}\) (b) its molecules are relatively small in size (c) it solidifies before becoming a liquid (d) forces acting between its molecules are negli-gible.

Step-by-Step Solution

Answer

The correct answer is (d): forces between molecules are negligible.

Step 1: Identifying Gas Properties

An ideal gas follows the assumptions of the kinetic theory of gases, where it is assumed that the intermolecular forces between gas molecules are negligible, and the volume of the molecules themselves is very small compared to the volume of the gas.

Step 2: Understanding Liquefaction Concept

Liquefaction of a gas involves cooling it down and applying pressure to bring the molecules close enough so that intermolecular forces can become significant and lead to a phase transition from gas to liquid.

Step 3: Analyzing Each Option

Review each option given: (a) The temperature being above or below zero doesn't directly relate to the difficulty in liquefying an ideal gas. (b) The size of molecules doesn't prevent liquefaction if forces can bring them together. (c) A gas needs to become liquid before solidifying, unless it sublimates. (d) The lack of significant forces between molecules means the gas won't condense into a liquid without those forces.

Step 4: Drawing Conclusion from Options

The distinguishing characteristic of an ideal gas, in this context, is the negligible intermolecular forces. Without such forces, the gas molecules cannot be made to stick together, preventing the gas from forming a liquid.

Key Concepts

Ideal Gas

The concept of an ideal gas is fundamental in the study of gases. It is a hypothetical gas that perfectly fits the assumptions of the kinetic theory of gases. Here's what makes an ideal gas special:

• Molecules are point particles: The molecules in an ideal gas are considered to have no volume, meaning they occupy no space individually.
• No Intermolecular Forces: There are no attractive or repulsive forces between molecules in an ideal gas.
• Elastic Collisions: The collisions between gas molecules and with the walls of the container are perfectly elastic, meaning no energy is lost in collisions.
• Random Motion: Molecules are in constant, random motion, moving in straight lines until they collide with something.

These assumptions simplify calculations and help in understanding the behavior of gases under various conditions. However, they are most accurate under low pressure and high temperature scenarios, where real gases behave similarly to ideal gases.

Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion between neighboring molecules. In real gases, these forces always play a crucial role, affecting their behavior significantly. There are several types of intermolecular forces, including:

• Van der Waals Forces: These are weak forces that arise due to temporary dipoles in molecules.
• Hydrogen Bonding: This is a stronger force that occurs between hydrogen and electronegative atoms like oxygen or nitrogen.
• Dipole-Dipole Interactions: These occur between polar molecules, where there is a permanent dipole moment due to the difference in electronegativity.

In the context of an ideal gas, the assumption is that intermolecular forces are negligible. This means the molecules do not "sense" each other, which is why ideal gases do not naturally liquefy.

Liquefaction

Liquefaction is the process of converting a gas into a liquid. This is typically achieved by cooling the gas or applying pressure, or both. Here's how it works:

• Cooling: Lowering the temperature of a gas slows down the molecules, decreasing their kinetic energy and allowing intermolecular forces to bring them closer together.
• Applying Pressure: Increasing pressure pushes molecules closer, allowing intermolecular forces to take effect and initiate a phase transition.

Real gases can be liquefied because they have intermolecular forces that can bind molecules together when conditions allow. Ideal gases cannot be liquefied under typical conditions because there are no intermolecular forces to condense them into liquids.

Phase Transition

A phase transition refers to the change of a substance from one state of matter to another, such as from a gas to a liquid. These transitions are driven by changes in temperature and pressure and the influence of intermolecular forces.

• Temperature Changes: Lowering temperature can lead to phase transitions like gas to liquid (condensation) or liquid to solid (freezing).
• Pressure Changes: Increasing pressure can also induce phase transitions, especially in gases.

For ideal gases, a phase transition is not straightforward because there are no intermolecular forces to facilitate the change from a gas to a liquid. Thus, phase transitions in ideal gases are theoretical constructs rather than physical realities.