Problem 46 - A Complete Resource Book in Chemistry for JEE Main

Question

An ideal gas cannot be liquefied because (a) it solidifies before becoming a liquid (b) forces operative between its molecules are neglgible (c) its molecules are relatively smaller in size (d) its critical temperature is always above \(0^{\circ} \mathrm{C}\)

Step-by-Step Solution

Answer

(b) forces operative between its molecules are negligible.

Step 1: Understanding Ideal Gas Behavior

Ideal gases follow the ideal gas law, where intermolecular forces are negligible, and particles occupy no volume compared to the space they move in. This behavior affects how they transition phases.

Step 2: Analyzing Phase Changes in Gases

For a gas to transition to a liquid, intermolecular forces must become significant to bring molecules together. In real substances, this happens below critical temperature, which is different for each material.

Step 3: Connecting Ideal Gas Assumptions to Phase Transition

Since ideal gases assume no intermolecular forces, they fail to condense into liquids under any condition, making them unable to liquefy due to the assumption of negligible forces between molecules.

Step 4: Evaluating Given Options

Option (b) states that forces operative between its molecules are negligible. This aligns with ideal gas theory, explaining why an ideal gas cannot liquefy. Other options incorrectly address phase solidification, molecular size, and critical temperature in real gases.

Key Concepts

Intermolecular Forces

In the realm of chemistry, intermolecular forces play a vital role in determining the behavior and properties of substances. These forces are the attractions between molecules that arise due to electric charges within the molecules themselves. In the case of ideal gases, these forces are considered to be negligible, which means they are too weak to have any substantial effect on gas behavior.
In real gases, intermolecular forces determine how easily a gas can change into another phase, like a liquid. For transition from gas to liquid, sufficient attractive forces must exist between the molecules to pull them closer together. The absence of these forces in ideal gases explains why they don't liquefy.

• Ideal gases assume no intermolecular forces.
• Intermolecular forces are necessary for phase transitions.
• Negligible forces result in no condensation of gases.

Phase Transitions

Phase transitions involve the change of substances from one state to another, such as from gas to liquid. This process occurs when the energy interactions and intermolecular forces between molecules change.
For gases to liquefy, intermolecular forces need to become significant to allow molecules to come close enough to form a liquid. In real gases, this means overcoming the energy that keeps the molecules apart.
Critical temperature is a concept associated with phase transitions. It is the highest temperature at which a substance can exist as a liquid. Above this temperature, no amount of pressure will cause the gas to condense into a liquid. Ideal gases, by their very approximation, don't follow typical phase change behaviors because they assume no intermolecular forces.

• Phase transition requires significant molecular interactions.
• Critical temperature influences phase change ability.
• Ideal gases deviate from typical phase transitions.

Ideal Gas Law

The ideal gas law provides a simple equation, \(PV = nRT\), that relates the pressure (P), volume (V), and temperature (T) of a gas with the number of moles (n) and the ideal gas constant (R). This law assumes ideal conditions, where gas particles do not interact with each other and occupy no volume.
The behavior predicted by the ideal gas law is often used as a reference to understand the deviations observed in real gases under various conditions. Because the law neglects intermolecular forces and the physical volume of the particles, it does not accurately predict the behavior of gases at very high pressures or low temperatures where phase transitions are more likely.
Understanding the ideal gas law allows one to grasp why ideal gases are unable to undergo phase changes like real gases, reinforcing the concept that negligible forces don't facilitate condensation.

• Ideal gas law assumes no particle interaction.
• This law aids in understanding real gas behavior deviations.
• Critical for conceptualizing non-condensing ideal gases.