Question

Under the same conditions of temperature and density, which of the following gases would you expect to behave less ideally: \(\mathrm{CH}_{4}\) or \(\mathrm{SO}_{2}\) ? Explain.

Short answer

SO_2 behaves less ideally due to stronger intermolecular forces and greater polarizability.

Step-by-step solution

Understanding Ideal Gas Behavior

To determine which gas behaves less ideally, we need to consider the factors contributing to ideal gas behavior. Ideal gases are hypothetical gases that perfectly follow the ideal gas law ( PV=nRT ). Real gases deviate from this due to forces between molecules and the volume occupied by the gas molecules themselves.

Intermolecular Forces

Gases deviate from ideal behavior because of intermolecular forces. Stronger forces cause greater deviation. SO_2 is a polar molecule with significant dipole-dipole interactions, while CH_4 is nonpolar with weaker London dispersion forces. Hence, SO_2 has stronger intermolecular forces.

Molecular Shape and Polarizability

SO_2 has a bent shape, which increases dipole-dipole interaction, making it more polarizable than CH_4 , a tetrahedral molecule. This increased polarizability leads to stronger van der Waals forces, causing greater deviation from ideal behavior.

Effect of Molecular Size

The larger the molecule, the more the space it occupies, which also affects gas behavior. SO_2 is larger and thus occupies more volume compared to CH_4 , contributing to its greater deviation from ideal gas laws.

Conclusion

Considering all factors - intermolecular forces, molecular shape, polarizability, and size, SO_2 behaves less ideally than CH_4 under the same conditions.

Key concepts

Intermolecular Forces

Intermolecular forces are the forces that act between molecules. They are pivotal in determining the physical properties of substances like boiling point, melting point, and solubility. These forces include dipole-dipole interactions, London dispersion forces, and hydrogen bonds.

• **Dipole-Dipole Interactions**: Occur between polar molecules with permanent dipoles. For example, in \( \text{SO}_2 \), the presence of a bent molecular shape gives rise to a permanent dipole moment, leading to significant dipole-dipole attractions.
• **London Dispersion Forces**: Present in all molecules, they are the only forces in nonpolar molecules like \( \text{CH}_4 \). These are weaker compared to dipole-dipole forces because they result from temporary dipoles occurring due to momentary polarization.

Understanding these forces helps us predict deviations from ideal gas behavior in real gases.

Van der Waals Forces

Van der Waals forces are a type of weak chemical bond that arises from induced electrical interactions between atoms or molecules. These forces include both the attractive forces (such as London dispersion forces) and repulsive forces that arise when electron clouds of atoms come very close to each other.

• **Attractive Forces**: Such as those seen in \( \text{SO}_2 \), included in van der Waals forces are significant due to its polar nature. This makes \( \text{SO}_2 \) deviate more from ideality.
• **Repulsive Forces**: Occur at very short ranges and are responsible for molecules not collapsing into each other.

Overall, van der Waals forces are crucial in understanding why \( \text{SO}_2 \) behaves less ideally than \( \text{CH}_4 \), as stronger forces between molecules cause greater deviations from the ideal gas law.

Molecular Polarizability

Molecular polarizability refers to the tendency of a molecule's electron cloud to distort, which is influenced by the molecule's size and shape. A larger and more asymmetrical molecule like \( \text{SO}_2 \) is more polarizable compared to \( \text{CH}_4 \).

• **Increased Polarizability**: Enhances the temporary dipoles that give rise to London dispersion forces, particularly affecting nonpolar or less polar molecules.
• **Shape Influence**: \( \text{SO}_2 \)'s bent shape increases its polarizability, leading to stronger London dispersion forces in addition to the dipole-dipole interactions, making it behave less ideally.

Thus, the molecular polarizability of \( \text{SO}_2 \) significantly affects its behavior under the same conditions compared to \( \text{CH}_4 \).

Ideal Gas Law

The ideal gas law is a crucial equation that relates the pressure, volume, number of moles, and temperature of a gas. It is expressed as \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) the number of moles, \( R \) the gas constant, and \( T \) the temperature.
Although the ideal gas law provides a very useful approximation for the behavior of gases, real gases exhibit deviations. These deviations occur due to

• **Actual Volume**: Gases don’t have zero volume like the assumption in the ideal gas law; larger molecules, such as \( \text{SO}_2 \), occupy more volume.
• **Intermolecular Forces**: Real gases have intermolecular forces, which are not considered in the ideal gas law. Strong forces like those in \( \text{SO}_2 \) further lead to non-ideal behavior.

This law helps as a baseline to predict and understand the degree of non-ideality in gases such as \( \text{SO}_2 \) and \( \text{CH}_4 \).