Problem 20 - Introductory Chemistry Atoms First

Question

Water vapor liquefies when cooled below \(100^{\circ} \mathrm{C}\). Gaseous nitrogen liquefies when cooled below \(-196^{\circ} \mathrm{C}\). What does this information tell you about the relative strengths of the intermolecular forces for these molecules?

Step-by-Step Solution

Answer

The given information indicates that the intermolecular forces in water vapor are stronger than those in gaseous nitrogen, as water vapor has a higher liquefaction temperature (\(100^{\circ} \mathrm{C}\)) compared to gaseous nitrogen (\(-196^{\circ} \mathrm{C}\)).

Step 1: Identify the given information

The liquefaction temperatures for water vapor and gaseous nitrogen are given as \(100^{\circ} \mathrm{C}\) and \(-196^{\circ} \mathrm{C}\) respectively.

Step 2: Compare the liquefaction temperatures

Water vapor liquefies at \(100^{\circ} \mathrm{C}\), which is higher than the liquefaction temperature of gaseous nitrogen, \(-196^{\circ} \mathrm{C}\).

Step 3: Relate the liquefaction temperatures to intermolecular forces

Since water vapor has a higher liquefaction temperature than gaseous nitrogen, it means that the intermolecular forces in water vapor are stronger than those in gaseous nitrogen.

Step 4: State the conclusion

The given information tells us that the intermolecular forces in water vapor are stronger than those in gaseous nitrogen, as indicated by the higher liquefaction temperature of water vapor compared to gaseous nitrogen.

Key Concepts

Liquefaction Temperature

The liquefaction temperature of a substance is the temperature at which it changes from a gas to a liquid. When gaseous molecules are cooled to this point, their kinetic energy decreases, allowing intermolecular attractions to pull them closer together, resulting in liquefaction.
Water vapor, for instance, has a liquefaction temperature of 100°C. This means at 100°C and normal atmospheric pressure, water vapor condenses into liquid.
Understanding liquefaction temperatures helps us infer the strength of intermolecular forces between molecules. Stronger forces usually lead to higher liquefaction temperatures because more energy (in the form of heat) is needed to separate the molecules.
The fact that water liquefies at a much higher temperature compared to nitrogen gives insight into how formidable these forces are, especially when compared to substances like gaseous nitrogen.

Water Vapor

Water vapor is the gaseous state of water, a key component of the Earth's atmosphere. It forms when water evaporates or boils.
As a powerful greenhouse gas, water vapor plays a critical role in regulating Earth's temperature. It is involved in weather processes like precipitation, cloud formation, and humidity.

• Unlike many gases, water vapor has relatively strong hydrogen bonds, contributing to its high liquefaction temperature.
• When we consider how water vapor changes back to liquid, its higher liquefaction temperature tells us there are significant intermolecular forces at play.

These bonds must be overcome before water vapor can shift to a liquid state, explaining why water maintains its gaseous state at high temperatures compared to other substances like nitrogen.

Gaseous Nitrogen

Gaseous nitrogen is the most abundant gas in the Earth's atmosphere, accounting for about 78% by volume. This diatomic molecule, made of two nitrogen atoms (N₂), plays a crucial role in life through the nitrogen cycle.
Nitrogen's liquefaction temperature is notably low at -196°C, highlighting the presence of weaker intermolecular forces compared to water vapor.

• The forces between nitrogen molecules are primarily weak van der Waals (or dispersion) forces.
• Because nitrogen liquefies at such a low temperature, we infer that these dispersive forces are much weaker than the hydrogen bonds found in water.

This characteristic helps industries in processes such as refrigeration and gas storage, where nitrogen's low liquefaction temperature is advantageous for cooling applications.