List these substances in order of increasing boiling point: $$ \mathrm{H}_{2} \mathrm{O}, \mathrm{Ne}, \mathrm{NH}_{3}, \mathrm{NaF}, \mathrm{SO}_{2} $$

Introducing the concept of intermolecular forces is essential to grasp why different substances have varying boiling points. Simply put, intermolecular forces are the attractive forces between neighboring molecules. The strength of these forces is a key factor in determining the phase of matter, melting points, boiling points, and solubilities.

When comparing substances, those with stronger intermolecular forces require more energy, in the form of heat, to overcome these attractions and transition into a gas phase - thus, they have higher boiling points. On the flip side, weaker intermolecular bonds lead to lower boiling points, as less energy is needed for the molecules to break free from each other and vaporize.

Among the strongest of intermolecular forces is hydrogen bonding. It's a special case that occurs when a hydrogen atom is covalently bonded to a highly electronegative atom like nitrogen, oxygen, or fluorine, and is attracted to another electronegative atom in a different molecule.

In the context of our substances, both water (\r\(H_2O\)) and ammonia (\(NH_3\)) exhibit hydrogen bonding. However, water's hydrogen bonding is stronger due to oxygen's higher electronegativity compared to nitrogen. This means more energy is required to boil water than ammonia, hence water has a higher boiling point.

Moving onto ionic bonding, this type of force is even more powerful than hydrogen bonding. Ionic bonds form between atoms that transfer electrons from one to another, resulting in positively charged cations and negatively charged anions. These ions then attract each other with a significant force.

In sodium fluoride (NaF), the sodium (\r\(Na^+\)) and fluoride (\r\(F^-\)) ions are held together by ionic bonds. This strong attraction requires a large amount of energy to break, giving NaF a higher boiling point than substances with hydrogen bonding or weaker forces. It's the ionic bonds that place NaF at the top of the boiling point list among the given substances.

Dipole-dipole interactions occur in polar molecules where there is an uneven distribution of electron density. This causes a permanent dipole with positive and negative ends, which attract the opposite ends of nearby molecules in a comparable manner.

Sulfur dioxide (\(SO_2\)) is a perfect example with a bent molecular geometry causing a polar structure, leading to dipole-dipole interactions. These are stronger than London dispersion forces but weaker than hydrogen bonding, placing \(SO_2\) above neon in terms of boiling point within our list of substances.

The weakest of the bunch are London dispersion forces, also known as van der Waals forces. These are temporary dipoles that occur when electrons within an atom or molecule are unevenly distributed, creating a temporary polarity. All molecules experience these forces, but they are the only type for nonpolar molecules such as neon (Ne).

Given that these forces are fleeting and weak, they require the least amount of energy to overcome, reflecting in the lowest boiling points for substances that depend solely on them, like Ne. It is thus the dispersion forces that put Ne at the lowest end of the boiling point spectrum.