Question

Arrange the following compounds in order of increasing boiling point. (a) \(\mathrm{Ar}\) (b) \(\mathrm{He}\) (c) \(\mathrm{Ne}\) (d) \(\mathrm{Xe}\)

Short answer

Question: Arrange the following noble gases in order of increasing boiling point: Argon (Ar), Helium (He), Neon (Ne), and Xenon (Xe). Answer: Helium (He) < Neon (Ne) < Argon (Ar) < Xenon (Xe)

Step-by-step solution

Identify which forces are responsible for holding the noble gases together as liquids

London dispersion forces play a significant role in determining the boiling points of noble gases since these gases have no other bonding.

Compare the molar mass and atomic size of each noble gas

The molar mass and atomic size and of each noble gas are as follows: (a) Argon (Ar): Molar Mass = 39.95 g/mol, Atomic size = 71 pm (b) Helium (He): Molar Mass = 4.00 g/mol, Atomic size = 31 pm (c) Neon (Ne): Molar Mass = 20.18 g/mol, Atomic size = 38 pm (d) Xenon (Xe): Molar Mass = 131.29 g/mol, Atomic size = 108 pm

Relate the strength of the London dispersion forces to molar mass and atomic size

The strength of the London dispersion forces increases with increasing molar mass and size, bigger atoms are more polarizable and can create temporary dipoles easier; therefore, noble gases with larger molar mass and atomic size will generally have higher boiling points.

Arrange the noble gases in order of increasing boiling point

Based on the strength of the London dispersion forces, the boiling points of the noble gases will increase in the following order: Helium (He) < Neon (Ne) < Argon (Ar) < Xenon (Xe)

Key concepts

London Dispersion Forces

The notion of London dispersion forces can seem abstract at first, but it’s a fundamental concept when examining the boiling points of inert gases, like noble gases. Even though these gases do not form molecules and are monatomic, they can still exert forces on each other. This is where London dispersion forces come into play. Imagine if you had a group of people standing still but occasionally bumping into each other; these 'bumps' are somewhat analogous to London dispersion forces. They are weak intermolecular forces that arise due to the temporary shifts in electron density within an atom, causing a temporary dipole. These forces are present in all atoms and nonpolar molecules and become stronger as the atoms increase in size and molar mass. Why? Larger atoms have more electrons, leading to greater chances of uneven electron distribution and thus stronger temporary dipoles.

When atoms come close together, if one atom has a temporary dipole, it can induce a dipole in its neighbor, creating an attraction. Although very feeble compared to other types of intermolecular forces, London dispersion forces are significant in noble gases because they are the only type of intermolecular force between these solitary atoms.

Molar Mass

What could the weight of a mole of atoms possibly have to do with how they behave in terms of their boiling points? This is where the concept of molar mass becomes vital. Molar mass, commonly expressed in grams per mole (g/mol), measures the mass of 6.022 x 10²³ (Avogadro's number) atoms of an element. It's an average, accounting for the mix of isotopes found in nature. The heavier the molar mass of a noble gas, the more mass each atom has. More mass means more electrons, which in turn means a greater ability to form those temporary dipoles we talked about, enhancing the strength of London dispersion forces. Thus, as the molar mass increases, boiling points typically increase as well because more energy (heat) is required to overcome these stronger forces to transition from liquid to gas.

Atomic Size

Think of atomic size as the 'reach' an atom has. The larger the atom, the more area it covers, and the easier it is for its electrons to be distributed unevenly, forming temporary dipoles. This is known as polarizability. Bigger atoms, like a large balloon, are more 'deformable' compared to smaller ones. In noble gases, atomic size increases with the number of electron shells. As the atoms get larger, their electrons are further from the nucleus and are shielded by inner-shell electrons, making them more influenced by nearby atoms. Therefore, larger atoms are more polarizable and can more easily induce dipoles in each other, leading to stronger intermolecular attractions — and therefore higher boiling points.

Intermolecular Forces

Intermolecular forces are the glue that holds substances together, but not all 'glue' is made equal. Among intermolecular forces, you have dipole-dipole interactions in polar molecules, hydrogen bonds in molecules like water, and London dispersion forces, which all atoms and molecules exhibit to some extent. Due to their full valence shells, noble gases don't form permanent dipoles and hence only exhibit London dispersion forces. It’s fascinating to observe how these only forces at work can lead to distinct boiling points, as seen in the noble gases. The boiling point indicates the temperature at which a substance transitions from liquid to gas. This transition requires enough energy to overcome the intermolecular forces holding the atoms together in the liquid state.

The more potent the intermolecular forces, the more energy is necessary to break free from the liquid phase, leading to a higher boiling point. So, if a student wants to predict the boiling point order of noble gases based on intermolecular forces, they would look for indications of the strength of London dispersion forces— primarily molar mass and atomic size.