Problem 31 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

(a) Explain how the fact that gases such as nitrogen or carbon dioxide can be liquefied by applying high pressures shows that the ideal gas equation can only be an approximation. (b) Why is a lower pressure needed to liquefy \(\mathrm{CO}_{2}\) than for \(\mathrm{N}_{2}\) ? (Section 8.6)

Step-by-Step Solution

Answer

The liquefaction of gases shows deviations from ideal behavior due to intermolecular forces. \\ \\ \(\text{CO}_2\) liquefies at lower pressures than \(\text{N}_2\) because it has stronger intermolecular forces.

Step 1: Understanding Gas Liquefaction

Gas liquefaction occurs when a gas is converted into a liquid by applying pressure while maintaining a low temperature. This happens because, under high pressure, gas molecules are forced closer together, allowing intermolecular forces to take effect and form a liquid.

Step 2: Limitations of the Ideal Gas Equation

The ideal gas equation, given by \( PV = nRT \), assumes that gas particles do not attract or repel one another and occupy no volume. When gases liquefy, it indicates that intermolecular forces are present, and the volume of gas molecules is non-negligible, revealing that the ideal gas law only approximates real gas behavior.

Step 3: Comparing Required Pressures for CO2 and N2 Liquefaction

\( ext{CO}_2\) can be liquefied at a lower pressure than \( ext{N}_2\) because \( ext{CO}_2\) has stronger intermolecular attractions (e.g., van der Waals forces) than \( ext{N}_2\). This is due to \( ext{CO}_2\) being a polar molecule, while \( ext{N}_2\) is nonpolar and has weaker dispersion forces.

Key Concepts

Ideal Gas Equation

The Ideal Gas Equation is a fundamental formula used in chemistry and physics to model the behavior of gases. Represented as \( PV = nRT \), it relates the pressure \( P \), volume \( V \), and temperature \( T \) of a gas to its amount in moles \( n \), with \( R \) being the ideal gas constant.While providing a strong foundation for understanding gas behaviors, this equation also comes with certain assumptions:

• The gas consists of a large number of small particles moving in random directions.
• There are no attractive or repulsive forces between the molecules.
• The volume of the molecules themselves is negligible compared to the volume occupied by the gas.

In reality, however, these assumptions do not always hold, especially under conditions of high pressure or low temperature where gas molecules are more likely to interact with each other.

Intermolecular Forces

Intermolecular Forces are the forces that act between molecules, affecting their physical properties such as boiling and melting points, solubility, and gas liquefaction.When gases are exposed to high pressure, their molecules are forced closer together. In this state, intermolecular forces such as van der Waals forces as well as dipole-dipole interactions in polar molecules like carbon dioxide come into play. These forces which tend to be weaker than chemical bonds, drive the condensation of gases, binding them into a liquid state.Understanding intermolecular forces helps explain why gases like \( \text{CO}_2 \) can be liquefied more easily than others, such as \( \text{N}_2 \). \( \text{CO}_2 \) has polar characteristics, leading to stronger intermolecular attractions compared to the nonpolar nature of \( \text{N}_2 \).