Question

Which member in each pair has the stronger intermolecu- lar dispersion forces? (a) \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{CH}_{3} \mathrm{OH},\) (b) \(\mathrm{CBr}_{3} \mathrm{CBr}_{3}\) or (c) \(\mathrm{C}\left(\mathrm{CH}_{3}\right)_{4}\) or \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) \(\mathrm{CCl}_{3} \mathrm{CCl}_{3}\)

Short answer

The molecules with stronger intermolecular dispersion forces in each pair are: - Pair (a): \(\mathrm{CH}_{3} \mathrm{OH}\) - Pair (b): \(\mathrm{CBr}_{3} \mathrm{CBr}_{3}\) - Pair (c): \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\)

Step-by-step solution

Pair (a): \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{CH}_{3} \mathrm{OH}\)

Both \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CH}_{3} \mathrm{OH}\) are polar molecules with hydrogen bonding and dipole-dipole interactions. However, we need to compare their dispersion forces. \(\mathrm{H}_{2} \mathrm{O}\) has a smaller size and less polarizable electron cloud compared to \(\mathrm{CH}_{3} \mathrm{OH}\), which has an additional \(\mathrm{CH}_3\) (methyl) group. The presence of the one more methyl group in methanol makes its electron cloud more polarizable; therefore, the dispersion forces are stronger in \(\mathrm{CH}_{3} \mathrm{OH}\).

Pair (b): \(\mathrm{CBr}_{3} \mathrm{CBr}_{3}\) or \(\mathrm{CCl}_{3} \mathrm{CCl}_{3}\)

Comparing \(\mathrm{CBr}_{3} \mathrm{CBr}_{3}\) and \(\mathrm{CCl}_{3} \mathrm{CCl}_{3}\), we can see that both have a similar shape but have different halogens attached to the carbon atoms. Bromine atoms are larger and more polarizable than chlorine atoms, and therefore, the dispersion forces will be stronger in \(\mathrm{CBr}_{3} \mathrm{CBr}_{3}\).

Pair (c): \(\mathrm{C}\left(\mathrm{CH}_{3}\right)_{4}\) or \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\)

Both \(\mathrm{C}\left(\mathrm{CH}_{3}\right)_{4}\) (neopentane) and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) (pentane) are nonpolar hydrocarbons. Neopentane has a compact, spherical shape, while pentane has a linear, extended shape. The extended shape of pentane allows it to have a larger surface area in contact with neighboring molecules, which leads to stronger dispersion forces compared to the more spherical neopentane. So, the molecules with stronger intermolecular dispersion forces in each pair are: - Pair (a): \(\mathrm{CH}_{3} \mathrm{OH}\) - Pair (b): \(\mathrm{CBr}_{3} \mathrm{CBr}_{3}\) - Pair (c): \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\)

Key concepts

Dispersion Forces

Dispersion forces, also known as London dispersion forces, are a type of weak intermolecular force that occurs in all molecules, regardless of their polarity. These forces arise due to temporary fluctuations in the electron distribution within molecules, leading to a temporary dipole. When a temporary dipole forms, it can induce a dipole in a neighboring molecule, causing an attractive force between them. While these attractions are weak individually, they become significant with larger numbers of interactions.

Dispersion forces are size-dependent, meaning the larger a molecule or atom, the stronger the dispersion force. This is because larger molecules or atoms have greater numbers of electrons and a larger electron cloud that can fluctuate more readily. For instance, - extit{In the comparison between \\( ext{CBr}_3 ext{CBr}_3\) and \( ext{CCl}_3 ext{CCl}_3\), the larger bromine atoms provide stronger dispersion forces than the smaller chlorine atoms.}"},{

Polarizability

Polarizability describes the ease with which the electron cloud around an atom or a molecule can be distorted by an external electric field, leading to an induced dipole moment. A molecule that is easily polarizable will exhibit stronger dispersion forces because its electrons can be more readily rearranged to create temporary dipoles.

This factor heavily depends on the size of the molecule and the number of electrons present. Larger molecules or atoms with more electrons are typically more polarizable because they have a bigger and more diffuse electron cloud that can be influenced more easily.

For example:

• In pair (a), $ ext{CH}_3 ext{OH}$ shows stronger dispersion forces than $ ext{H}_{2} ext{O}$, attributed to its additional $ ext{CH}_3$ group, which increases its size and polarizability.
• In pair (b), the electron cloud of $ ext{CBr}_3 ext{CBr}_3$ is more extensive and can be polarized more easily than $ ext{CCl}_3 ext{CCl}_3$ due to the larger bromine atoms.

Molecular Structure

The molecular structure of a compound is a crucial factor in determining the strength of its intermolecular forces, especially dispersion forces. The shape and structure affect how much surface area is available for interaction between molecules.

A linear or extended shape in molecules often increases the surface area that can interact with neighboring molecules, leading to stronger dispersion forces. Conversely, spherical or compact shapes may lessen these forces because they reduce the contact area.

For instance:

• In pair (c), $ ext{CH}_3 ext{CH}_2 ext{CH}_2 ext{CH}_2 ext{CH}_3$ (pentane) has a more extended structure compared to the compact spherical structure of neopentane ($ ext{C}( ext{CH}_3)_4$). This greater surface area in pentane allows for stronger dispersion forces.

Understanding how molecular structure influences intermolecular forces helps explain why certain substances have different boiling and melting points and other physical properties.