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

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

Step 1: Understanding the Critical Temperature

The critical temperature ( c T_c ) of a gas is the highest temperature at which a gas can be liquefied by pressure alone. Above this temperature, the kinetic energy of the gas molecules is too high for the intermolecular forces to bring them into a liquid state.

Step 2: Analyzing Ideal Gas Properties

An ideal gas is a theoretical construct where it is assumed that there are negligible intermolecular forces between the molecules. This means that no amount of pressure can bring the molecules close enough to form a liquid.

Step 3: Evaluating Impossible Conditions

Considering the provided conditions, particularly option (d), where the critical temperature is above 0 ^ c C, this does not apply to the ideal gas as it would suggest a temperature dependency contrary to its negligible intermolecular forces. Ideal gases do not depend on temperature like real gases.

Step 4: Examining Molecular Forces

Option (b) states that the intermolecular forces are negligible. This aligns perfectly with the concept of an ideal gas, which is idealized by the fact there are no forces bringing the molecules together into a liquid.

Key Concepts

Critical Temperature

The concept of critical temperature is central to understanding why real gases can be liquefied while ideal gases cannot. Critical temperature is defined as the maximum temperature at which a gas can be converted into a liquid by applying pressure. Below this temperature, increasing pressure can cause gas molecules to slow down and get closer together, allowing intermolecular attractions to eventually condense the gas into a liquid.
For a real gas, the critical temperature is finite. However, for an ideal gas, this critical temperature doesn't hold the same significance. This is because ideal gases are theoretical constructs, characterized by having no intermolecular forces. An ideal gas assumes that these attractions are so weak or nonexistent that no pressure can push the molecules close enough to transform into a liquid state. As a result, the concept of a critical temperature is not applicable like it is for real gases.

Intermolecular Forces

Intermolecular forces are crucial when discussing the liquefaction of gases. These are the forces of attraction or repulsion which act between neighboring particles: molecules, atoms, or ions. Types of intermolecular forces include:

• Van der Waals forces: Weak and short-range forces.
• Dipole-dipole interactions: Occur between molecules that have permanent dipole moments.
• London dispersion forces: Present in all molecules, particularly important in nonpolar covalent molecules.

In an ideal gas, it is assumed that intermolecular forces are negligible. This simplification helps in studying gases' behavior without the complicating factors of these interactions. Therefore, these gases do not exhibit the ability to liquefy, as by definition, there are no forces to draw the molecules into a closer, more condensed phase.

Gas Liquefaction

Gas liquefaction is the process of converting a gas into a liquid. This typically involves reducing the temperature and/or increasing the pressure to bring the molecules closer together. By doing this, the intermolecular forces become significant enough to transition the gas to a liquid state.
For real gases, liquefaction can be achieved by manipulating critical temperature and pressure, given that real gases do have intermolecular attractions. However, in the case of an ideal gas, since the intermolecular forces are considered negligible, liquefaction is practically impossible. It's this theoretical absence of molecular attraction that challenges the notion of applying concepts like liquefaction to ideal gases.
In summary, gas liquefaction relies heavily on the presence of intermolecular forces, and since an ideal gas lacks these forces, it cannot be liquefied through any practical means.