Arrange the following compounds in order of increasing solubility in water: \(\mathrm{O}_{2}, \mathrm{LiCl}, \mathrm{Br}_{2},\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\)

Understanding the polarity of compounds is essential when studying solubility. A molecule is polar if it has a separation of charge, meaning one part of the molecule has a slight positive charge and another part has a slight negative charge. This usually happens due to differences in electronegativity between the atoms that are bonded together. For instance, water is a polar molecule because oxygen is more electronegative than hydrogen, creating a dipole moment.

Now, why does polarity affect solubility? In a mixture, polar molecules will preferentially interact with other polar substances, including solvents like water. This is because they can form favorable electrostatic interactions, which help them dissolve. Nonpolar molecules like \(O_2\) and \(Br_2\), on the other hand, do not have this kind of charge separation and tend to aggregate together, limiting their solubility in a polar solvent such as water.

The 'like dissolves like' principle is a simple rule that helps predict solubility behavior: polar solvents tend to dissolve polar or ionic substances, and nonpolar solvents tend to dissolve nonpolar substances. This principle stems from the fact that similar types of intermolecular forces exist between molecules of the solvent and the solute. In our example, methanol \(CH_3OH\) is polar and therefore dissolves readily in water, also polar, due to favorable intermolecular interactions.

The principle explains why nonpolar gases like \(O_2\) and \(Br_2\) have low solubility in water. Without significant intermolecular forces to break up the lattice of the solid or interactions in the gas, these substances do not integrate well with the structure of water.

The distinction between ionic and molecular compounds is also crucial when it comes to solubility in water. Ionic compounds, like \(LiCl\), consist of positively and negatively charged ions held together by strong electrostatic forces in a crystal lattice. When introduced to water, the polar water molecules surround and stabilize the ions, breaking apart the lattice and leading to high solubility.

Molecular compounds can be polar, like methanol, or nonpolar, like \(O_2\) and \(Br_2\). Polar molecular compounds tend to be more soluble in water than nonpolar ones because they can form favorable intermolecular interactions with water. Methanol, which can form hydrogen bonds with water, provides a good example of a soluble polar molecule.

Hydrogen bonding plays a pivotal role in the solubility of compounds in water. It's a special type of dipole-dipole attraction that occurs between a hydrogen atom bonded to a highly electronegative atom (usually nitrogen, oxygen, or fluorine) and another electronegative atom with a lone pair of electrons. Methanol has a hydroxyl (-OH) group that can engage in hydrogen bonding with water molecules, significantly increasing its solubility.

In addition, the ability of a substance to form hydrogen bonds with water increases the dissolution process. This explains why methanol, capable of acting both as a hydrogen bond donor (owing to its hydrogen) and acceptor (owing to its oxygen), is highly soluble in water, whereas nonpolar substances, which cannot form hydrogen bonds, exhibit much less solubility in water.