Problem 102 - A Complete Resource Book in Chemistry for JEE Main

Question

The ease of liquefaction of noble gases increase in the order (a) \(\mathrm{Ar}>\mathrm{Kr}>\mathrm{Xe}>\mathrm{Ne}>\mathrm{He}\) (b) \(\mathrm{Xe}>\mathrm{Kr}>\mathrm{Ne}>\mathrm{Ar}>\mathrm{He}\) (c) \(\mathrm{Kr}>\mathrm{Xe}>\mathrm{He}>\mathrm{Ne}>\mathrm{Ar}\) (d) \(\mathrm{He}>\mathrm{Ne}>\mathrm{Ar}>\mathrm{Kr}>\mathrm{Xe}\)

Step-by-Step Solution

Answer

The correct order is option (d): \( \mathrm{He} > \mathrm{Ne} > \mathrm{Ar} > \mathrm{Kr} > \mathrm{Xe} \).

Step 1: Understanding Liquefaction

Liquefaction of gases refers to the process of condensing a gas into a liquid. The ease with which a gas can be liquefied is largely dependent on the intermolecular forces present between the gas molecules. Noble gases are non-polar and experience weak van der Waals forces; hence, their ability to be liquefied increases with their molecular size (and polarizability). Larger atoms have stronger van der Waals forces.

Step 2: Comparing Noble Gases and Molecular Size

The noble gases in question (He, Ne, Ar, Kr, Xe) each have different atomic sizes. Helium (He) is the smallest, followed by Neon (Ne), Argon (Ar), Krypton (Kr), and Xenon (Xe), which is the largest. Larger noble gas atoms have more electrons and thus exhibit stronger van der Waals forces that make them easier to liquefy.

Step 3: Arranging Noble Gases by Liquefaction Ease

Considering the molecular size and the strength of the van der Waals forces, the ease of liquefaction for these gases increases as the size of the atom increases. Therefore, the order from most easily liquefied to least easily liquefied is: \( \mathrm{Xe} > \mathrm{Kr} > \mathrm{Ar} > \mathrm{Ne} > \mathrm{He} \).

Step 4: Identifying the Correct Choice

Compare the order identified in Step 3 with the provided options. The order matching \( \mathrm{Xe} > \mathrm{Kr} > \mathrm{Ar} > \mathrm{Ne} > \mathrm{He} \) is given in option (d): \( \mathrm{He} > \mathrm{Ne} > \mathrm{Ar} > \mathrm{Kr} > \mathrm{Xe} \), but flipped comparing least easily to most easily liquefied.

Key Concepts

van der Waals forces

Van der Waals forces are weak intermolecular interactions that occur between atoms and non-polar molecules, such as noble gases. Although these forces are relatively weak compared to other types of bonding, they play a crucial role in the liquefaction of gases. In noble gases, van der Waals forces originate from temporary dipoles induced in the atoms. When an electron cloud around a noble gas nucleus momentarily shifts, it creates a temporary positive and negative pole, allowing attraction between nearby similar atoms.

This slight attraction is enough to hold atoms together in the liquid state under low temperatures and higher pressures.

• Van der Waals forces increase with atomic size because larger atoms have more electrons, which enhances polarizability.
• Stronger van der Waals forces make it easier for a gas to liquefy.

The understanding of van der Waals forces is essential to explain why larger noble gases like xenon and krypton liquefy more readily compared to smaller ones like helium and neon.

atomic size

Atomic size refers to the volume occupied by an atom's electrons and nucleus. As you move down the noble gases group in the periodic table, the atomic size increases. Helium is the smallest noble gas, while xenon is the largest. This increase in atomic size has a direct impact on the physical properties of these gases, including their ease of liquefaction.

Larger atomic sizes mean:

• Increased distance over which electron interactions can occur.
• More extensive electron clouds that enhance the ability to polarize.
• A larger polarizable electron cloud leads to stronger van der Waals forces.

These factors in combination make larger atoms like xenon and krypton have higher boiling points and be easier to liquefy compared to smaller atoms like helium.

noble gases

Noble gases are a group of chemical elements with similar properties that are found in Group 18 of the periodic table. They include helium (He), neon (Ne), argon (Ar), krypton (Kr), and xenon (Xe). Known for their lack of reactivity, noble gases have complete outer electron shells, making them extremely stable. This stability contributes to their non-polar nature.

Despite being chemically inert, noble gases can be liquefied under certain conditions through the application of high pressure and low temperature. The ease of liquefaction varies among noble gases and is influenced by their atomic size and the corresponding van der Waals forces.

• Larger noble gases like xenon are more prone to liquefaction due to stronger van der Waals forces.
• Helium, being the smallest, exhibits very weak forces and thus requires very low temperatures to liquefy.

Understanding these characteristics helps in predicting and explaining their physical behaviors, including how they transition from gaseous to liquid states.