Question

Which member in each pair has the larger dispersion forces: (a) \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{H}_{2} \mathrm{~S},(\mathbf{b}) \mathrm{CO}_{2}\) or \(\mathrm{CO}, \mathrm{C}\) (c) \(\mathrm{SiH}_{4}\) or \(\mathrm{GeH}_{4} ?\)

Short answer

In each pair, the members with the larger dispersion forces are (a) H₂S, due to its larger size and greater polarizability, (b) CO₂, because of its higher electron count and increased polarizability, and (c) GeH₄, as it has more electrons leading to stronger charge fluctuations and dispersion forces.

Step-by-step solution

Pair (a): H₂O and H₂S

Let us first analyze the properties of H₂O and H₂S. H₂S is a larger molecule with more electrons, making it more polarizable compared to H₂O. As a result, H₂S will be more prone to charge fluctuations that induce dispersion forces. Therefore, H₂S has larger dispersion forces than H₂O.

Pair (b): CO₂ and CO

Now, let's compare CO₂ and CO. CO has 10 electrons, while CO₂ has 22 electrons. Though CO₂ is a linear and non-polar molecule, it has a higher electron count than CO, making it more polarizable. The increased electron count results in stronger charge fluctuations and subsequently larger dispersion forces. Therefore, CO₂ has larger dispersion forces than CO.

Pair (c): SiH₄ and GeH₄

Finally, let us analyze and compare SiH₄ and GeH₄. SiH₄ has 20 electrons, while GeH₄ has 32 electrons. Both SiH₄ and GeH₄ have similar structures, but GeH₄ contains more electrons due to germanium's higher atomic number. The increased electron count leads to larger charge fluctuations and, as a result, stronger dispersion forces. Therefore, GeH₄ has larger dispersion forces than SiH₄. In summary, the members with the larger dispersion forces in each pair are (a) H₂S, (b) CO₂, and (c) GeH₄.

Key concepts

Polarizability

Polarizability is a key factor when discussing dispersion forces within molecules. It refers to the ability of a molecule to become polarized — which means that electrons within the molecule can be distorted by an external electric field, leading to temporary dipoles. These dipoles then affect how molecules interact with each other.

- **High Polarizability**: More easily allows for the creation of temporary dipoles, resulting in stronger dispersion forces. - **Factors Affecting Polarizability**: Larger molecules with more electrons are generally more polarizable, as the outer electrons are further away from the nucleus and are less tightly held, making them easier to distort.

In the exercise, we see that H₂S, CO₂, and GeH₄ have more electrons or a larger atomic structure compared to their counterparts, making them more polarizable. As polarizability increases, so do the dispersion forces.

Molecular Size

The size of a molecule significantly influences its dispersion forces. Generally, the larger the molecule, the greater the dispersion forces it can experience. This is because larger molecules have more electron cloud volume, increasing the possibility of induced dipole interactions.

- **Larger Molecules**: Have increased surface area for interactions, allowing for stronger force generation between molecules. - **Example in Exercise**: H₂S is larger than H₂O, CO₂ is larger than CO, and GeH₄ is larger than SiH₄, meaning they can exert stronger dispersion forces due to their greater size.

Understanding molecular size helps explain why larger molecules usually lead to stronger dispersion forces, helping to predict interactions between non-polar molecules.

Electron Count

Electron count plays a crucial role in determining the strength of dispersion forces. Molecules with a higher number of electrons can experience greater charge fluctuations, resulting in stronger temporary dipoles and thus stronger dispersion forces.

- **Higher Electron Counts**: Lead to larger and more frequent oscillations in electron density, enhancing the temporary polarity of molecules. - **Specific Pair Analyses**: - **CO₂ vs. CO**: CO₂ has more electrons than CO, creating larger induced dipoles despite CO₂ being non-polar. - **GeH₄ vs. SiH₄**: GeH₄'s greater number of electrons compared to SiH₄ supports more significant charge fluctuations. - **H₂S vs. H₂O**: H₂S boasts more electrons, leading to stronger dispersion forces.

A comprehensive understanding of electron count helps predict which molecules will exhibit stronger dispersion forces, critical for understanding molecular interactions in chemistry.