Question

If you compare the solubilities of the noble gases in water, you find that solubility increases from smallest atomic weight to largest, Ar \(<\mathrm{Kr}<\mathrm{Xe} .\) Which of the following statements is the best explanation? [ Section 13.3\(]\) (a) The heavier the gas, the more it sinks to the bottom of the water and leaves room for more gas molecules at the top of the water. (b) The heavier the gas, the more dispersion forces it has, and therefore the more attractive interactions it has with water molecules. (c) The heavier the gas, the more likely it is to hydrogen-bond with water. (d) The heavier the gas, the more likely it is to make a saturated solution in water.

Short answer

The best explanation for the observed trend in solubility of noble gases in water is statement (b): The heavier the gas, the more dispersion forces it has, and therefore the more attractive interactions it has with water molecules.

Step-by-step solution

Statement (a)

(a) The heavier the gas, the more it sinks to the bottom of the water and leaves room for more gas molecules at the top of the water. This statement suggests that the solubility depends on the physical location of gas molecules. However, solubility is mainly determined by the molecular interactions between the solute and solvent, not the physical location of the molecules within the mixture. Thus, this statement does not explain the observed trend in solubility.

Statement (b)

(b) The heavier the gas, the more dispersion forces it has, and therefore the more attractive interactions it has with water molecules. This statement correctly associates the larger atomic weight of noble gases with an increase in dispersion forces, which are a type of van der Waals forces. Dispersion forces increase with the size and polarizability of the molecules, making the larger noble gases more likely to form favorable attractive interactions with water molecules. This seems like a good explanation for the observed trend in solubility.

Statement (c)

(c) The heavier the gas, the more likely it is to hydrogen-bond with water. This statement is incorrect because noble gases do not form hydrogen bonds with water. Hydrogen bonds occur between highly electronegative atoms (O, N, or F) covalently bonded to hydrogen, and another highly electronegative atom (O, N, or F). Since noble gases are nonpolar and do not form covalent bonds, they cannot engage in hydrogen bonding with water.

Statement (d)

(d) The heavier the gas, the more likely it is to make a saturated solution in water. This statement is ambiguous and does not provide a clear explanation for the observed trend. The term "saturated solution" refers to a solution where no more solute can dissolve in the solvent at a given temperature and pressure. Although solubility increases with atomic weight, the statement does not explain the underlying reason why heavier noble gases are more soluble in water.

Conclusion

Comparing the given statements, statement (b) provides the best explanation for the observed trend in noble gas solubility within water, as it correctly links larger atomic weight to an increase in dispersion forces, resulting in more favorable attractive interactions with water molecules.

Key concepts

Dispersion Forces

When exploring the solubility of noble gases in water, a key factor to consider is the role of dispersion forces. Often the least understood among the molecular interactions, dispersion forces are weak, temporary attractive forces that occur between the electrons of one molecule and the nucleus of another. These momentarily dipole-induced forces enhance solubility by promoting intermolecular attractions.

Understanding Dispersion Forces

Dispersion forces emerge because electrons are in constant motion. When they temporarily arrange asymmetrically in a molecule, a fleeting dipole is formed. This temporary dipole can then induce a dipole in neighboring molecules, leading to an attraction between them. This phenomenon is more pronounced in larger atoms such as xenon (Xe) since they have more electrons that can become unevenly distributed.

In the context of noble gases, heavier gases boast more electrons, and thus a greater tendency to form temporary dipoles and induce them in nearby water molecules, enhancing their solubility over their lighter counterparts.

Molecular Interactions

The solubility of a substance in a solvent is largely determined by the extent of molecular interactions between the two. These interactions can be thought of as the 'social bonds' at the microscopic level that bring about the dissolution of one substance into another.

Examining Molecular Interactions

Molecular interactions in solutions involve a variety of forces, including ion-dipole, hydrogen bonding, and van der Waals forces. In the case of noble gases, ion-dipole and hydrogen bonding are off the table, as these gases are neutral and nonpolar. Hence, their solubility relies on weaker interactions like dispersion forces.

Despite their weakness compared to other types of interactions, dispersion forces are crucial for noble gases. They facilitate the 'conversation' between the water molecules and gas atoms, allowing for the establishment of a solution. This shows that even the most gentle forces can yield significant outcomes—like higher solubility for heavier noble gases in water.

Van der Waals Forces

Van der Waals forces encompass a group of intermolecular attractions, including dispersion forces, dipole-dipole interactions, and dipole-induced dipole forces. These forces are named after the Dutch scientist Johannes Diderik van der Waals, who described how molecules attract one another even without the presence of a full-fledged bond.

The Spectrum of van der Waals forces

Van der Waals forces are ubiquitous and vary in strength. They ensure that molecules with varying polarities can still find a way to stick together in a solution. Larger noble gases have stronger van der Waals forces due to their increased polarizability—the ease with which their electron cloud can be distorted to form a temporary dipole.

As students, understanding van der Waals forces provides insight into why a substance like xenon, with a larger electron cloud, is more soluble in water compared to a smaller noble gas such as argon. It's the subtlety of these forces that governs how gases dissolve in liquids, and appreciating their role is vital in mastering concepts related to solubility.