Problem 3 - A Complete Resource Book in Chemistry for JEE Main

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) \(\mathrm{CO}_{2}, \mathrm{He}\)

Step-by-Step Solution

Answer

Pairs (b) NH3 > H2 and (c) NH3 > He have higher latter critical temperatures.

Step 1: Understanding Critical Temperature

The critical temperature of a gas is the maximum temperature at which it can be liquefied by pressure alone. A higher critical temperature means the gas will condense to liquid more easily.

Step 2: Checking Pair (a) (\mathrm{CO}_{2}, \mathrm{H}_{2}\)

Critical temperature of CO2 is approximately 31°C, and for H2, it is approximately -240°C. Since 31°C is higher than -240°C, the critical temperature of CO2 is higher than that of H2.

Step 3: Checking Pair (b) (\mathrm{H}_{2}, \mathrm{NH}_{3}\)

Critical temperature of H2 is approximately -240°C, while for NH3, it is about 132°C. Comparatively, 132°C is higher than -240°C, so NH3 has a higher critical temperature than H2.

Step 4: Checking Pair (c) (\mathrm{NH}_{3}, \mathrm{He}\)

Ammonia (NH3) has a critical temperature of about 132°C, while Helium (He) has a critical temperature of -268.9°C. Therefore, NH3 has a higher critical temperature than He.

Step 5: Checking Pair (d) (\mathrm{CO}_{2}, \mathrm{He}\)

The critical temperature of CO2 is approximately 31°C, while He has a critical temperature of -268.9°C. Therefore, CO2 has a higher critical temperature than He.

Step 6: Conclusion

In each pair, compare the critical temperatures. The latter gas has a higher critical temperature than the first in pairs (b) and (c).

Key Concepts

Liquefaction of Gases

Liquefaction of gases refers to the process of turning a gas into a liquid. This is achieved by applying pressure or reducing the temperature. The critical temperature of a gas plays a crucial role here. It is the highest temperature at which a gas can be turned into a liquid by applying pressure alone. Beyond this temperature, no amount of pressure will liquefy the gas. This is why gases with higher critical temperatures are generally easier to liquefy compared to those with lower critical temperatures.

• Gases below their critical temperature can be liquefied by pressure.
• Above the critical temperature, the gas can't turn into a liquid regardless of pressure.

Understanding the concept of critical temperature helps in designing processes that involve gas liquefaction, like in industrial applications and natural gas handling.

Gas Properties

Gases have unique properties that distinguish them from liquids and solids. These properties include compressibility, low density, and the ability to fill available space. One important property is the critical temperature, which influences how gases behave under pressure.
Gases with higher critical temperatures tend to be denser and have stronger intermolecular forces. For instance, ammonia (\(\mathrm{NH}_{3}\)) possesses a critical temperature of 132°C, indicating strong intermolecular forces, making it more practical for use in refrigeration than a gas like helium (\(\mathrm{He}\)) with a critical temperature of -268.9°C.

• Critical temperature affects how easily a gas turns to liquid.
• Gases with higher intermolecular forces have higher critical temperatures.

Comparative Analysis of Gases

Comparing gases through their critical temperatures provides insight into their physical properties and potential applications. For example, when comparing pairs like carbon dioxide (\(\mathrm{CO}_{2}\)) and hydrogen (\(\mathrm{H}_{2}\)), it's clear that CO2, with a critical temperature of 31°C, can be liquefied more easily than H2, which has a critical temperature of -240°C.
Such comparisons help in selecting gases for specific functions. Ammonia's higher critical temperature makes it useful for refrigeration, while helium, with its exceedingly low critical point, is ideal for applications requiring inert conditions at very low temperatures.

• Comparing critical temperatures aids in choosing gases for specific applications.
• Higher critical temperature generally means easier liquefaction and stronger intermolecular forces.