Question

Which of the following can be most readily liquefied? (Given: value of ' \(a\) ' for \(\mathrm{NH}_{3}=4.17, \mathrm{CO}_{2}=3.59, \mathrm{SO}_{2}=6.71, \mathrm{Cl}_{2}=6.49\) ) (a) \(\mathrm{NH}_{3}\) (b) \(\mathrm{Cl}_{2}\) (c) \(\mathrm{SO}_{2}\) (d) \(\mathrm{CO}_{2}\)

Short answer

SO2 (\text{Sulfur dioxide}) can be most readily liquefied because it has the highest 'a' value of 6.71.

Step-by-step solution

Understanding the Problem

The exercise is asking which substance among NH3, Cl2, SO2, and CO2 can be most readily liquefied based on the given 'a' values. The 'a' value is a measure of the attractive forces between the particles in a gas and is part of the Van der Waals equation. The larger the 'a' value, the stronger the attractive forces, and the more readily a gas can be liquefied.

Comparing 'a' Values

You need to compare the given 'a' values for each substance. The substance with the highest 'a' value will have the strongest intermolecular forces and hence can be liquefied more readily than the others.

Identifying the Substance

Review the 'a' values for each substance: for NH3 it's 4.17, for Cl2 it's 6.49, for SO2 it's 6.71, and for CO2 it's 3.59. The substance with the highest 'a' value is SO2 (6.71), which means that among the given options, SO2 can be most readily liquefied.

Key concepts

Van der Waals Forces

When studying the liquefaction of gases, one crucial factor to consider is the Van der Waals forces. These are a type of intermolecular force named after Johannes Diderik van der Waals, who described these forces as part of his equation for real gases. Van der Waals forces include attractions between molecules, such as dipole-dipole interactions, London dispersion forces, and hydrogen bonds.

These forces vary in strength depending on the type of interaction and the molecules involved. For example, in gases where polar molecules are present, the dipole-dipole interactions can be significant, leading to higher Van der Waals forces. In nonpolar molecules, London dispersion forces dominate, which are weaker than other types of Van der Waals forces but still play a crucial role in bringing molecules closer together, enabling the gas to be liquefied under the right conditions.

In the context of the exercise, the 'a' value in the Van der Waals equation represents the strength of these attractive forces. A higher 'a' value indicates stronger Van der Waals forces, suggesting that the substance would have a higher tendency to liquefy. This is because the stronger the attractive forces among molecules, the more energy is required for them to remain in the gaseous state and vice versa.

Intermolecular Forces

Intermolecular forces are the forces of attraction and repulsion between molecules that influence the physical properties of substances, such as boiling and melting points, vapor pressure, and their ability to liquefy. Unlike bonds within molecules, intermolecular forces are weaker and do not involve the sharing or transfer of electrons. However, they are fundamental to the phase behavior of substances.

There are three primary types of intermolecular forces:

• Dipole-dipole forces: Occur between polar molecules, where there is an uneven distribution of electron density.
• London dispersion forces: Present in all molecules, they are due to temporary dipoles formed by random fluctuations in electron distribution and are stronger in larger, heavier atoms and molecules.
• Hydrogen bonds: A particularly strong type of dipole-dipole force that occurs when hydrogen is bound to highly electronegative atoms such as oxygen, nitrogen, or fluorine, leading to a significant polarity.

The relative strength of these intermolecular forces determines how easily a molecular substance can be converted from a gas into a liquid. In the exercise, the gas with the highest 'a' value, which is indicative of strong intermolecular forces, is the most readily liquefied gas due to the increased attractions between its molecules.

Critical Constants

Understanding critical constants is essential when discussing the liquefaction of gases. Critical constants include the critical temperature, critical pressure, and critical volume. These constants represent the conditions above which a substance cannot exist in the liquid state, regardless of the pressure applied.

The critical temperature is the highest temperature at which a gas can be liquefied by pressure alone. Above this temperature, the gas cannot condense into a liquid and becomes a supercritical fluid. The critical pressure is the minimum pressure required to liquefy a gas at its critical temperature. Finally, the critical volume is the volume of the substance at the critical temperature and pressure.

In practice, gases are liquefied by cooling and compressing them below their critical temperature and then applying pressure. As per the exercise, by knowing the 'a' value—which is linked to the strength of intermolecular forces—we can infer the relative ease with which a gas can be liquefied. Gases with larger 'a' values typically have higher critical pressures and lower critical temperatures, making them easier to liquefy under practical conditions.