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 \(0^{\circ} \mathrm{C}\)

Short answer

An ideal gas cannot be liquefied because forces between its molecules are negligible (option b).

Step-by-step solution

Understanding Critical Temperature

The critical temperature of a gas is the temperature above which it can't be liquefied by pressure alone. If the critical temperature is above ambient temperature, the gas can be liquefied by applying sufficient pressure. Therefore, a key factor in liquefying a gas is its critical temperature.

Analyzing Ideal Gas Behavior

An ideal gas is a hypothetical gas whose molecules do not interact. This means there are no attractive forces that would normally facilitate the transition to a liquid. The behavior of an ideal gas is described by the Ideal Gas Law, and it assumes the gas molecules do not exert any intermolecular forces.

Evaluating Molecular Forces

In reality, gases can be liquefied due to intermolecular forces like Van der Waals forces. An ideal gas, by definition, assumes negligible intermolecular forces, implying no attraction between molecules that facilitate liquefaction.

Examining Given Options

Among the given options, liquefaction relies on the presence of intermolecular forces. Since the ideal gas assumes negligible intermolecular forces, it aligns with option (b). Other options like solidifying first, molecular size, and always having a high critical temperature do not consistently account for the fundamental assumptions of the ideal gas model.

Conclusion

The inability of an ideal gas to be liquefied stems from the key assumption of negligible intermolecular forces. Thus, an ideal gas cannot be liquefied because the forces operative between its molecules are negligible, which is option (b).

Key concepts

Critical Temperature

The critical temperature of a gas is a fundamental concept in understanding the behavior of gases and their ability to transition into liquids. It is defined as the highest temperature at which a gas can be converted to a liquid, simply by applying pressure. Beyond this temperature, no amount of pressure will cause the gas to liquefy.

For example, if a gas has a critical temperature of 31°C, applying pressure at 30°C could liquefy the gas, but at 32°C, it remains a gas regardless of the pressure applied. This concept is especially crucial for distinguishing between real gases and the theoretical ideal gas.

• Ideal gases are assumed to have critical temperatures that cannot be practically reached for liquefaction.
• The critical temperature is different for each type of gas and relates to the strength of intermolecular forces.

Understanding critical temperature helps explain why some gases can be liquefied under normal conditions, while others cannot be readily compressed into a liquid.

When practical applications like industrial gas liquefaction occur, the critical temperature guides engineers to choose the right conditions for operation.

Intermolecular Forces

Intermolecular forces are the attractions between molecules that influence the behavior of gases, liquids, and solids. These forces are essential when considering the liquefaction of gases. In ideal gases, the assumption is that these intermolecular forces are negligible.

This lack of attractive forces between molecules in an ideal gas means that they move independently of each other, expanding to fill any container they're in. As a result, ideal gases cannot transition to a liquid state since there are no attractions to hold the molecules together.

• In reality, gases show attractive forces such as Van der Waals forces, which help them evolve to liquids under sufficiently low temperatures and high pressures.
• These forces arise due to dipole-dipole attractions, hydrogen bonds, or dispersion forces, depending on the gas molecules.

However, in theoretical scenarios involving ideal gases, these forces are completely disregarded, making liquefaction an impossibility.

Understanding the role of intermolecular forces aids in differentiating ideal gases from real gases, as real gases exhibit behaviors impacted by these attractions.

Liquefaction of Gases

Liquefaction of gases is the process where gases transition into a liquid state, often through cooling or applying pressure. This process is fundamental in various industrial and scientific applications, allowing gases to be stored and transported more efficiently.

For a gas to be liquefied, it must be below its critical temperature and subjected to sufficient pressure. However, in the case of an ideal gas, liquefaction is deemed impossible because the key assumption is the absence of intermolecular forces.

• In reality, gases are composed of molecules that do interact, leading to possibilities for liquefaction through natural attractive forces.
• These interactions enable the gas particles to come closer together, forming a liquid when temperature and pressure conditions are right.

The liquefaction process demonstrates significant challenges when dealing with ideal gases due to these theoretical considerations.

Awareness of gas liquefaction furthers understanding of both chemical properties and practical applications, offering insights into the design of cooling systems and the storage of gases in liquid form.