Question

An ideal gas cannot be liquefied because (1) Its critical temperature is always above \(0^{\circ} \mathrm{C}\) (2) Its molecules are relatively smaller in size (3) It solidifies before becoming liquid (4) Forces operative between the molecules are negligible

Short answer

An ideal gas cannot be liquefied because the forces operative between the molecules are negligible.

Step-by-step solution

- Understand the question

Determine why an ideal gas cannot be liquefied by eliminating incorrect options and identifying the correct reason.

- Analyze each option

Evaluate each option to see if it provides a valid reason: (1) Check if critical temperature relates to the inability to liquefy. (2) Consider if molecule size affects the gas's behavior. (3) Examine if solidification before liquefaction makes sense. (4) Assess if negligible intermolecular forces prevent liquefaction.

- Evaluate Option (1)

An ideal gas's critical temperature does not necessarily relate to its inability to liquefy. Hence, Option (1) is incorrect.

- Evaluate Option (2)

The size of the molecules in an ideal gas is not a factor when considering liquefaction. Therefore, Option (2) is also incorrect.

- Evaluate Option (3)

Solidification before becoming a liquid is not a property associated with ideal gases. Thus, Option (3) is incorrect.

- Evaluate Option (4)

Ideal gases are defined by having negligible intermolecular forces. These negligible forces mean the molecules do not attract each other strongly enough to condense into a liquid state, making Option (4) correct.

- Conclusion

Based on the evaluation, the correct reason why an ideal gas cannot be liquefied is that the forces operative between the molecules are negligible.

Key concepts

critical temperature

To begin understanding why an ideal gas cannot be liquefied, we must look at the concept of critical temperature. The critical temperature is the highest temperature at which a gas can be liquefied by pressure alone. For real gases, this temperature plays a crucial role. However, for an ideal gas, critical temperature is not applicable in determining its liquefaction. This is because ideal gases are hypothetical and assume no intermolecular forces. Therefore, the critical temperature does not influence their behavior in terms of condensation into a liquid state.

molecular size

Molecular size can influence how particles interact in real gases, but it is of less importance in the context of ideal gases. Ideal gases are defined by their non-interacting particles with negligible size. This assumption helps simplify equations and models for gases. The Liquefaction of a gas depends more on the forces between molecules rather than their actual size. Since ideal gases are assumed to have zero intermolecular forces, their molecules do not attract each other to form a liquid, regardless of size.

solidification

When we talk about phases of matter, solidification refers to the process of a liquid becoming a solid. This process requires temperature to drop below the freezing point. However, for an ideal gas, the matter of solidification before becoming a liquid doesn't make sense. Ideal gases assume a theoretical model where gas molecules are free-moving and do not attract each other. There exists no pathway for these gases to solidify into a crystalline arrangement or form liquids due to the lack of intermolecular attraction.

intermolecular forces

Intermolecular forces are attractive forces between molecules. They are crucial in forming liquids and solids from gases. For real gases, as these forces become stronger, the gas molecules can condense into liquids below a certain temperature and pressure. However, ideal gases are assumed to have no intermolecular forces. This assumption means there is no attraction between the molecules, which prevents them from coming together to form a liquid or a solid. Therefore, it is the negligible intermolecular forces in ideal gases that explain their inability to liquefy.