Question

The ease of liquefaction of noble gases increases 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) \(\mathrm{He}>\mathrm{Ne}>\mathrm{Ar}>\mathrm{Kr}>\mathrm{Xe}\)

Short answer

The correct order is (d) bfHe>bfNe>bfAr>bfKr>bfXe.

Step-by-step solution

Understanding Liquefaction of Noble Gases

The ease of liquefaction of gases is influenced by the intermolecular forces between the atoms or molecules. For noble gases, these forces are dominantly van der Waals forces (London dispersion forces), which depend on the size of the atom. Larger atoms have stronger dispersion forces.

Identifying the Order of Atomic Sizes

List the noble gases in order of increasing atomic size: Helium (bfHf), Neon (bfNe), Argon (bfAr), Krypton (bfKr), and Xenon (bfXe). Therefore, Xe > Kr > Ar > Ne > He in terms of atomic size.

Relating Size to Ease of Liquefaction

Since larger atoms have stronger van der Waals forces, and thus, can be more easily liquefied, the ease of liquefaction follows the order of increasing atomic size for noble gases: Xe > Kr > Ar > Ne > He.

Matching with Given Options

From the options, find the one that matches the order Xe > Kr > Ar > Ne > He. Compare each option to find a match with the theoretical order derived.

Key concepts

van der Waals forces

Van der Waals forces are weak interactions that act between atoms and molecules, playing a crucial role in the behavior of noble gases. These forces arise from temporary dipoles that occur when the electrons orbiting an atom create slight positives and negatives. These temporary dipoles then induce similar dipoles in neighboring atoms, causing an attraction between them.
This intermolecular force is generally weak because it is not dependent on permanent charges or dipoles, unlike ionic or covalent bonds. However, they are significant for noble gases, which lack other types of intermolecular forces.
Van der Waals forces are important because they influence the physical state and properties like boiling and melting points. Stronger van der Waals forces mean that more energy is required to overcome these attractions and change the state from gas to liquid.

London dispersion forces

A subset of van der Waals forces, London dispersion forces specifically refer to the attractive forces that occur due to instantaneous dipoles in nonpolar molecules, including noble gases.
Even though noble gases are composed of single atoms and are nonpolar, the movement of electrons around an atom leads to temporary electron clouds that are denser on one side, creating an instantaneous dipole. Neighboring atoms experience this asymmetry, resulting in induced dipoles and mutual attraction.
The strength of these forces depends upon the number of electrons, which scales with atomic size. The more electrons an atom has, the more likely it is to have strong London dispersion forces. Therefore, larger noble gas atoms like xenon have stronger dispersion forces than smaller ones like helium.

atomic size of noble gases

The atomic size of noble gases is an essential factor influencing their behavior, especially when considering their ease of liquefaction. As one moves down the noble gas group in the periodic table, the atomic size increases.
This increase in size is due to added electron shells, which place the outermost electrons further from the nucleus. As a result, larger noble gases have a greater radius.
The order of atomic size from smallest to largest among the noble gases is: Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), and Xenon (Xe).

• Helium and Neon are very small, thus having weaker dispersion forces.
• Argon is larger than Neon and Helium, possessing stronger forces.
• Krypton and Xenon, being larger, have especially strong dispersion forces, leading to easier liquefaction.

Understanding this helps explain why the ease of liquefaction increases with the atomic size.