Question

In which of the following pairs, the critical temperature of latter gaseous species is higher than the first? (a) \(\mathrm{CO}_{2}, \mathrm{H}_{2}\) (b) \(\mathrm{H}_{2}, \mathrm{NH}_{3}\) (c) \(\mathrm{NH}_{3}, \mathrm{He}\) (d) \(\mathrm{CO}_{2}, \mathrm{He}\)

Short answer

Options (b) and (c).

Step-by-step solution

Understanding Critical Temperature

Critical temperature of a gas is the temperature above which it cannot be liquefied, regardless of the pressure applied. A higher critical temperature indicates stronger intermolecular forces and larger molecular size.

Analyzing Option (a)

First pair is \(CO_2\) and \(H_2\). For \(CO_2\), the critical temperature is 304.2 K. For \(H_2\), the critical temperature is 33 K. Thus, \(CO_2\) has a higher critical temperature than \(H_2\).

Analyzing Option (b)

Second pair is \(H_2\) and \(NH_3\). For \(H_2\), the critical temperature is 33 K and for \(NH_3\), it is 405.5 K. \(NH_3\) has a higher critical temperature than \(H_2\).

Analyzing Option (c)

Third pair is \(NH_3\) and \(He\). The critical temperature for \(NH_3\) is 405.5 K, while for \(He\), it is 5.2 K. Hence, \(NH_3\) has a higher critical temperature than \(He\).

Analyzing Option (d)

Last pair is \(CO_2\) and \(He\). For \(CO_2\), the critical temperature is 304.2 K and for \(He\), it is 5.2 K. \(CO_2\) has a higher critical temperature than \(He\).

Conclusion

From the analysis, in pairs (b) \((H_2, NH_3)\) and (c) \((NH_3, He)\), the latter species has a higher critical temperature than the first.

Key concepts

Intermolecular Forces

Intermolecular forces play a crucial role in determining the physical properties of substances, including their critical temperatures. These forces are the attractions between molecules that hold them together in a liquid or solid state. There are several types of intermolecular forces:

• London Dispersion Forces: These are the weakest intermolecular forces and arise from temporary fluctuations in electron density, which creates temporary dipoles.
• Dipole-Dipole Interactions: When molecules have permanent dipoles, they can attract each other more strongly than those without. These interactions occur between polar molecules.
• Hydrogen Bonds: A special type of dipole-dipole interaction, hydrogen bonds occur when a hydrogen atom is bonded to a highly electronegative atom like nitrogen, oxygen, or fluorine.

The strength of these forces affects how easily a substance can become a liquid. Stronger intermolecular forces mean a higher critical temperature, as more energy (in the form of heat) is required to overcome these forces and keep the substance in a gaseous state.

In the context of critical temperatures, gases with stronger intermolecular forces tend to have higher critical temperatures.

Molecular Size

The size of a molecule significantly influences its properties, including critical temperature. Larger molecules often have more electrons and a larger surface area, both of which enhance the strength of London dispersion forces. These are the forces that occur due to temporary shifts in electron density, leading to instantaneous dipoles.

Larger molecules have:

• Increased Surface Area: More surface area allows more contact points for attraction between molecules, increasing the chances of interactions.
• Greater Electron Cloud: This tends to make electron shifts more prominent and increases the intensity of London dispersion forces.

The relationship between molecular size and critical temperature is evident in heavier molecules tending to exhibit higher critical temperatures. More robust intermolecular forces due to size require greater energy to remain a gas, contributing to a higher critical temperature.

Gas Liquefaction

Gas liquefaction is the process of converting a gas into a liquid by cooling it below its critical temperature or increasing its pressure. This process relies heavily on understanding critical temperatures and intermolecular forces.

• Below the critical temperature, applying sufficient pressure can force molecules close enough to form a liquid, despite their natural tendency to disperse in a gas form.
• Strong intermolecular forces favor liquefaction, as they more readily pull molecules together, transitioning the gas to a liquid phase.

For effective liquefaction, understanding the properties of gases, such as critical temperatures and the nature of intermolecular forces at play, is crucial. Liquefaction is applied in various fields, including industrial gas processing and refrigeration, where gases are often required in a liquid state for storage or transportation.

Properties of Gases

Gases are characterized by several fundamental properties that influence their behavior and interactions. These properties are essential for understanding how gases behave under different conditions and why critical temperatures matter.

• Compressibility: Gases can be compressed easily since the molecules are far apart. This affects how they can be turned into a liquid at specific temperatures and pressures.
• Expansion: They expand to fill their container, which is an essential concept for gas liquefaction.
• Low Density: Gases have lower densities compared to liquids and solids, linked to the larger gaps between molecules.
• Independence of Molecules: Because gas molecules move freely, they rarely interact unless confined, which relates to the lack of significant intermolecular forces when not under pressure.

These properties underline why gases can change phases under specific conditions, and understanding these fundamentals helps in predicting and controlling their behavior, particularly concerning critical temperature and liquefaction.