Question

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

Short answer

The correct answer is (d) Forces operative between its molecules are negligible. This is due to the properties of an ideal gas, where there are no forces between the gas molecules, preventing it from liquifying.

Step-by-step solution

Understanding the properties of an ideal gas

An ideal gas is a theoretical gas composed of a set of randomly moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.

Evaluate each choice

(a) The critical temperature of an ideal gas is irrelevant to its ability to liquefy. An ideal gas cannot be liquefied, regardless of its temperature; hence option (a) is not the answer. \n\n(b) The size of the gas molecules in an ideal gas does not affect its capacity to become liquid, so option (b) is not correct. \n\n(c) Solidification before becoming a liquid does not apply to ideal gases, so option (c) is not correct.

Choose the correct answer

The correct answer is (d) forces operative between its molecules are negligible. The reason an ideal gas cannot be liquefied is that there are no forces of attraction or repulsion between the molecules of an ideal gas. Hence forces operative between its molecules are negligible. This lack of interaction and the high kinetic energy of the particles prevent the gas from liquefying.

Key concepts

Ideal Gas Law

The ideal gas law is a fundamental principle in thermodynamics that relates the pressure, volume, and temperature of a gas with the number of its molecules. The equation is given as \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the amount of substance in moles, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

Understanding the ideal gas law is crucial for comprehending why an ideal gas cannot be liquefied. The law is based on the assumption that gases consist of particles in constant, random motion, and that these particles do not exhibit any interactive forces between them, whether attractive or repulsive. This assumption works well for explaining and predicting the behavior of real gases at high temperatures and low pressures, where the interactions between molecules are minimal and the gases behave more ideally. However, when we consider the liquefaction of gases, intermolecular forces become significant, which is an aspect not accounted for by the ideal gas law.

Critical Temperature

The critical temperature of a substance is the highest temperature at which a gas can be turned into a liquid by applying pressure. Above this temperature, no amount of pressure is sufficient to liquefy the gas because the kinetic energy of the particles is too high for intermolecular forces to bring them together into a liquid state.

For an ideal gas, the concept of a critical temperature does not apply because the ideal gas law assumes no intermolecular forces. Real gases have a critical temperature because their particles do interact. By understanding that an ideal gas is a theoretical construct with assumptions that do not hold under conditions required for liquefaction, students can see why option (a) in the given exercise is incorrect. Nonetheless, recognizing what critical temperature represents for real gases reinforces the importance of intermolecular forces in the transition from a gaseous to a liquid phase.

Intermolecular Forces

Intermolecular forces are attractive or repulsive forces between the molecules of a substance that determine the physical properties of that substance, such as boiling point, melting point, and ability to liquefy. Examples of intermolecular forces include van der Waals forces, hydrogen bonding, and dipole-dipole interactions.

In the context of the provided exercise, the key to understanding why an ideal gas cannot be liquefied is recognizing that it is an abstract concept where these intermolecular forces are considered negligible. In reality, these forces become significantly stronger as a gas is cooled and compressed, leading to the condensation of the gas into a liquid form. Since an ideal gas assumes no such forces, no amount of cooling or compressing would result in liquefaction, making option (d) the correct answer. It's also insightful to illustrate how the presence of strong intermolecular forces in real gases enables processes like refrigeration and air conditioning, which are based on the principles of gas liquefaction and evaporation.