Problem 62 - General Chemistry

Question

The heats of vaporization of liquid \(\mathrm{O}_{2}\), liquid \(\mathrm{Ne}\), and liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), are \(6.8 \mathrm{~kJ} / \mathrm{mol}, 1.8 \mathrm{~kJ} / \mathrm{mol}\), and \(34.5 \mathrm{~kJ} / \mathrm{mol}\), respectively. Are the relative values as you would expect? Explain.

Step-by-Step Solution

Answer

Yes, the values align with expectations based on intermolecular forces and boiling points.

Step 1: Understand Heat of Vaporization

The heat of vaporization is the amount of energy required to convert a liquid into a gas at its boiling point. It indicates how much energy is needed to overcome intermolecular forces that hold molecules in the liquid state.

Step 2: List Given Heats of Vaporization

We are given the heats of vaporization for three substances: liquid oxygen (\(\mathrm{O}_2\)) is \(6.8 \mathrm{~kJ} / \mathrm{mol}\), liquid neon (\(\mathrm{Ne}\)) is \(1.8 \mathrm{~kJ} / \mathrm{mol}\), and liquid methanol (\(\mathrm{CH}_3\mathrm{OH}\)) is \(34.5 \mathrm{~kJ} / \mathrm{mol}\).

Step 3: Compare Intermolecular Forces

Neon is a noble gas with weak van der Waals forces, thus having the lowest heat of vaporization. Oxygen (\(\mathrm{O}_2\)) is also small with weak London dispersion forces, hence a low, but higher than neon, vaporization heat. Methanol (\(\mathrm{CH}_3\mathrm{OH}\)) can form hydrogen bonds, the strongest intermolecular forces here, resulting in the highest heat of vaporization.

Step 4: Analyze the Expected Order

Based on the strength of intermolecular forces, we expect neon, with the weakest forces, to have the lowest heat of vaporization, followed by oxygen with moderate forces, and methanol with strong hydrogen bonding forces to have the highest heat of vaporization.

Step 5: Conclusion

The values—\(1.8 \mathrm{~kJ}/\mathrm{mol}\) for \(\mathrm{Ne}\), \(6.8 \mathrm{~kJ}/\mathrm{mol}\) for \(\mathrm{O}_2\), and \(34.5 \mathrm{~kJ}/\mathrm{mol}\) for \(\mathrm{CH}_3\mathrm{OH}\)—align with expectations based on their intermolecular forces, confirming reasoning.

Key Concepts

Intermolecular Forces

Intermolecular forces are the forces that hold molecules together in liquids and solids. They play a crucial role in determining the physical properties of a substance, such as boiling and melting points. For instance, when we say that methanol has a high heat of vaporization compared to oxygen and neon, it's because of the strong intermolecular forces present in methanol.
These forces can be of different types, including hydrogen bonding, dipole-dipole interactions, and van der Waals forces. Each of these forces has a different strength and effect on the physical properties of the molecules they act upon.

• Hydrogen bonding: A particularly strong form of dipole-dipole interaction, occurring in molecules with an electronegative atom such as fluorine, oxygen, or nitrogen, bonded to hydrogen.
• Van der Waals forces: Weaker than hydrogen bonds, these are due to temporary fluctuations in electron density in a molecule, causing temporary dipoles.

Understanding the strength and type of intermolecular forces can help predict the heat of vaporization as it indicates how much energy is required to overcome these forces and transition from liquid to gas.

Hydrogen Bonding

Hydrogen bonding occurs when a hydrogen atom is covalently bonded to a very electronegative atom, like oxygen, nitrogen, or fluorine. This interaction is relatively strong compared to other types of intermolecular forces due to the significant electronegativity difference between hydrogen and these atoms.
Methanol (\(\mathrm{CH}_3\mathrm{OH}\)) is a perfect example of a compound where hydrogen bonding is prominent. The hydroxyl group (\(\mathrm{-OH}\)) in methanol can form hydrogen bonds with other methanol molecules. This bonding requires significant energy to break, which is why methanol exhibits a high heat of vaporization compared to non-polar gases like oxygen and neon.

• Hydrogen bonding leads to higher boiling points.
• It increases the heat of vaporization, meaning more energy is required to vaporize the substance.

Therefore, methanol's heat of vaporization is much higher because of the energy needed to overcome these strong intermolecular forces.

Van der Waals Forces

Van der Waals forces are weak forces that arise due to temporary dipoles in molecules and atoms. They include London dispersion forces and are generally weaker than hydrogen bonds and even regular dipole-dipole interactions. Despite being weak, they are still significant in influencing the heat of vaporization for substances where stronger forces are absent.
In the context of liquids such as oxygen (\(\mathrm{O_2}\)) and neon (\(\mathrm{Ne}\)), these forces play a crucial role. Both \(\mathrm{O_2}\) and \(\mathrm{Ne}\) primarily experience London dispersion forces, a type of van der Waals force, due to their nonpolar nature.

• London dispersion forces arise from temporary shifts in electron density that create momentary dipoles.
• Such forces affect smaller, nonpolar molecules and explain their relatively low boiling points and heat of vaporization.

With these weak forces, less energy is required to move molecules from the liquid to the gaseous state, which explains the low heat of vaporization seen in substances like neon and oxygen compared to hydrogen-bonded liquids like methanol.