Problem 13 - Chemistry The Science in Context

Question

In each of the following pairs of molecules, which one experiences the stronger dispersion forces? (a) \(\mathrm{CCl}_{4}\) or \(\mathrm{CF}_{4};\) (b) \(\mathrm{CH}_{4}\) or \(\mathrm{C}_{3} \mathrm{H}_{8}\)

Step-by-Step Solution

Answer

Question: Compare the strength of dispersion forces between (a) CCl4 and CF4, and (b) CH4 and C3H8. Answer: (a) CCl4 will have stronger dispersion forces compared to CF4 due to its larger molecular size and more electrons. (b) C3H8 will have stronger dispersion forces compared to CH4 because it has a more complex structure and more electrons.

Step 1: (a) Comparing CCl4 and CF4

First, we need to determine how many electrons there are in each molecule. For \(\mathrm{CCl}_{4}\) and \(\mathrm{CF}_{4}\), both molecules have a tetrahedral structure with carbon in the center. In \(\mathrm{CCl}_{4}\), there are 32 electrons: 4 for the central carbon and 28 from the four chlorine atoms (each has 7 electrons). In \(\mathrm{CF}_{4}\), there are 20 electrons: 4 from the carbon and 16 from the four fluorine atoms (each has 4 electrons). As \(\mathrm{CCl}_{4}\) has more electrons and a larger molecular size, it would experience stronger dispersion forces.

Step 2: (b) Comparing CH4 and C3H8

Comparing \(\mathrm{CH}_{4}\) and \(\mathrm{C}_{3}\mathrm{H}_{8}\), we need to first determine the number of electrons in each molecule and analyze their structures. In \(\mathrm{CH}_{4}\), there are 10 electrons: 4 from the carbon atom and 6 from the four hydrogen atoms (each has 1 electron). The molecule has a tetrahedral structure. In \(\mathrm{C}_{3}\mathrm{H}_{8}\), there are 26 electrons: 12 from the three carbon atoms and 14 from the eight hydrogen atoms (each has 1 electron). The molecule has a more complex structure compared to \(\mathrm{CH}_{4}\). As \(\mathrm{C}_{3}\mathrm{H}_{8}\) has more electrons and a more complex structure, it would experience stronger dispersion forces.

Key Concepts

Electrons

Electrons play a crucial role in determining how molecules behave, especially in the context of dispersion forces. So, what are dispersion forces? These are weak intermolecular forces that occur due to temporary fluctuations in electron density within molecules. When electrons shift randomly, they can create temporary poles in a molecule, which allow it to attract nearby molecules, albeit briefly. This effect is heightened when more electrons are involved because a larger electron cloud increases the likelihood of temporary charge imbalances.

For example, when comparing two molecules like

• \( \text{CCl}_4 \) with 32 electrons, \( \text{CF}_4 \), which contains fewer electrons,
• \( \text{CH}_4 \) with 10 electrons, \( \text{C}_3\text{H}_8 \) with 26,

the one with more electrons usually shows higher dispersion forces. More electrons provide more opportunities for creating temporary dipoles, thereby intensifying the dispersion force between molecules.

Molecular Structure

The shape or structure of a molecule can significantly influence its chemical properties, including its dispersion forces. Molecules like \( \text{CCl}_4 \)and \(\text{CF}_4\) are examples of tetrahedral configurations.

• The central atom is carbon, and four atoms are equally spaced around it, creating a symmetrical, balanced shape.

This symmetry often affects the polarity of the molecule, potentially evening out any temporary dipoles.

On the other hand,

• \( \text{C}_3\text{H}_8 \) features a more elongated and linear chain-like structure increased molecular complexity.

More complex structures typically permit greater surface area contact with neighboring molecules, enhancing dispersion forces. This happens because interactions are stronger when there's more molecular surface area to interact.

Understanding molecular structure helps in predicting not just dispersion forces but other interaction mechanisms among molecules.

Molecular Size

The size of a molecule is a critical factor affecting its intermolecular forces, such as dispersion forces. Larger molecules tend to have broader electron clouds, leading to more extensive temporary dipoles.

Comparing \(\text{CCl}_4\) with \(\text{CF}_4\), it is evident due to the larger atomic size of chlorine compared to fluorine.

• This results in a bigger overall molecular size for \( \text{CCl}_4 \), promoting stronger dispersion forces.

Similarly, in \(\text{C}_3\text{H}_8\), having three carbons and a more intricate structure, the molecule is considerably larger than \(\text{CH}_4\).

• The increased size causes \( \text{C}_3\text{H}_8 \) to experience enhanced dispersion forces.

Larger molecules have greater potential for overlapping interactions with other molecules; hence, they tend to stick together more strongly. This increased molecular "stickiness" is why larger molecules, in general, have higher boiling points and melting points, as separating them requires a great deal more energy.