Problem 19 - Chemistry: The Central Science

Question

Which member of the following pairs has the larger London dispersion forces: (a) \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{H}_{2} \mathrm{~S},(\mathrm{~b}) \mathrm{CO}_{2}\) or \(\mathrm{CO},(\mathrm{c}) \mathrm{SiH}_{4}\) or \(\mathrm{GeH}_{4} ?\)

Step-by-Step Solution

Answer

(a) \(\mathrm{H}_{2}\mathrm{S}\) has stronger London dispersion forces than \(\mathrm{H}_{2}\mathrm{O}\), (b) \(\mathrm{CO}_{2}\) has stronger London dispersion forces than \(\mathrm{CO}\), (c) \(\mathrm{GeH}_{4}\) has stronger London dispersion forces than \(\mathrm{SiH}_{4}\).

Step 1: (a) Comparing \(\mathrm{H}_{2}\mathrm{O}\) and \(\mathrm{H}_{2}\mathrm{S}\)

First, we need to compare the sizes of \(\mathrm{H}_{2}\mathrm{O}\) and \(\mathrm{H}_{2}\mathrm{S}\) molecules. Oxygen has an atomic number of 8, while sulfur has an atomic number of 16. Since sulfur has more electrons and is larger than oxygen, \(\mathrm{H}_{2}\mathrm{S}\) is expected to have stronger London dispersion forces than \(\mathrm{H}_{2}\mathrm{O}\).

Step 2: (b) Comparing \(\mathrm{CO}_{2}\) and \(\mathrm{CO}\)

Next, let's compare the sizes of \(\mathrm{CO}_{2}\) and \(\mathrm{CO}\) molecules. The \(\mathrm{CO}_{2}\) molecule has one carbon atom and two oxygen atoms, while the \(\mathrm{CO}\) molecule has one carbon and one oxygen atom. As a result, \(\mathrm{CO}_{2}\) has a higher number of electrons and a larger molecular size than \(\mathrm{CO}\). Therefore, \(\mathrm{CO}_{2}\) has stronger London dispersion forces than \(\mathrm{CO}\).

Step 3: (c) Comparing \(\mathrm{SiH}_{4}\) and \(\mathrm{GeH}_{4}\)

Finally, consider the sizes of \(\mathrm{SiH}_{4}\) and \(\mathrm{GeH}_{4}\) molecules. Silicon has an atomic number of 14, while germanium has an atomic number of 32. Since germanium has more electrons and is larger than silicon, \(\mathrm{GeH}_{4}\) is expected to have stronger London dispersion forces than \(\mathrm{SiH}_{4}\). In conclusion, (a) \(\mathrm{H}_{2}\mathrm{S}\) has stronger London dispersion forces than \(\mathrm{H}_{2}\mathrm{O}\), (b) \(\mathrm{CO}_{2}\) has stronger London dispersion forces than \(\mathrm{CO}\), (c) \(\mathrm{GeH}_{4}\) has stronger London dispersion forces than \(\mathrm{SiH}_{4}\).

Key Concepts

Understanding Intermolecular Forces

When studying molecules and how they interact, a fundamental concept is the understanding of intermolecular forces. These are the forces that exist between molecules and influence key properties such as boiling and melting points, solubility, and viscosity. One type of these forces are the London dispersion forces, named after the physicist Fritz London. These are weak forces that arise from temporary dipoles created when the electrons within an atom or molecule create an instantaneous imbalance of charge.

Even though London dispersion forces are the weakest type of van der Waals forces, they are critically important for non-polar molecules and atoms. All atoms and molecules with electrons (which is essentially all of them) exhibit these dispersion forces, although their strength varies depending on the structure and size of the molecule.

Molecular Size and Electron Count Influence

The strength of the London dispersion forces in a molecule is significantly influenced by the molecular size and the electron count. To understand this influence, consider that larger molecules have more electrons. This increase in electrons leads to a greater likelihood of temporary dipoles occurring within the molecule, intensifying the London dispersion forces.

In context, when comparing different molecules, as in our textbook exercise, these two factors become the deciding elements. For instance, H_{2}S has a larger atomic size and more electrons than H_{2}O, due to sulfur having a higher atomic number than oxygen. These characteristics lead to stronger London dispersion forces in H_{2}S. Similarly, other comparisons made between molecules can be explained by this logic.

Comparing Molecule Properties

The comparison of molecular properties is a valuable exercise in understanding chemical behavior. London dispersion forces have a direct correlation with how molecules interact, which can determine the behavior of substances in different states of matter. When comparing the properties of molecules, remember that a higher number of electrons and a larger molecular size usually result in stronger dispersion forces, thus affecting the overall intermolecular attractions.

Using the textbook exercise, we've seen this comparison in action. Bigger molecules like GeH_{4}, compared to SiH_{4}, experience stronger dispersion forces because germanium has a larger atomic number than silicon. These comparative analyses can help students predict the physical properties and reactivity of different substances based on their dispersion forces.