Problem 5 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Given gas critical temperature/ \(\mathrm{K}\) for\(\mathrm{H}_{2} \mathrm{CH}_{4} \mathrm{CO}_{2} \quad \mathrm{SO}_{2}\) is \(\begin{array}{llll}33 & 190 & 304 & 630\end{array}\) On the basis of data given above, predict which of the following gases shows least adsorption on a definite amount of charcoal?(a) \(\mathrm{SO}_{2}\) (b) \(\mathrm{CH}_{4}\) (c) \(\mathrm{CO}_{2}\) (d) \(\mathrm{H}_{2}\)

Step-by-Step Solution

Answer

\( \mathrm{H}_2 \) shows least adsorption.

Step 1: Understanding Critical Temperature

Critical temperature is the temperature above which a gas cannot be liquefied by pressure alone. It is directly proportional to the ease with which gas molecules can be liquefied and hence adsorbed.

Step 2: Analyzing Adsorption Characteristics

Adsorption of gases on a solid surface usually increases with a higher critical temperature. This is because gases with higher critical temperatures are closer to liquefaction and have stronger intermolecular forces, making them more easily adsorbed.

Step 3: Evaluating Given Data

The given critical temperatures for the gases are as follows: \( \mathrm{H}_2 = 33 \, \mathrm{K}\), \( \mathrm{CH}_4 = 190 \, \mathrm{K}\), \( \mathrm{CO}_2 = 304 \, \mathrm{K}\), \( \mathrm{SO}_2 = 630 \, \mathrm{K}\).

Step 4: Determining Least Adsorbed Gas

Since gases with lower critical temperatures show less adsorption, the gas with the lowest critical temperature, \( \mathrm{H}_2 \) at \( 33 \, \mathrm{K} \), will be the least adsorbed on charcoal.

Key Concepts

Gas Adsorption

Adsorption is a process where gas molecules adhere to the surface of solids, such as charcoal. This phenomenon is quite different from absorption, where the gas would enter the solid or liquid. The extent to which a gas is adsorbed depends on several factors:

• **Nature of the gas**: Gases with higher polarity or those that can easily be liquefied tend to be adsorbed more.
• **Surface area of the adsorbent**: Larger surface areas provide more opportunities for gas molecules to adhere.
• **Pressure and temperature**: Generally, increasing pressure enhances adsorption, while increasing temperature reduces it as gas molecules have more kinetic energy to escape. However, these effects are complex and contingent upon specific conditions of both the gas and the solid.

The critical temperature of a gas plays a significant role in its adsorption characteristics. Gases closer to their critical temperature are easier to liquefy and hence more readily adsorbed.

Liquefaction of Gases

Liquefaction refers to the process of converting a gas to its liquid state. It occurs when a gas is cooled below its critical temperature, or when sufficient pressure is applied below this temperature. The critical temperature is crucial in this process. It is the highest temperature at which a gas can be liquefied, no matter how much pressure is applied. Beyond this temperature, the kinetic energy of gas molecules is too high for liquefaction to occur by pressure alone. Understanding critical temperature helps predict gas behavior in various processes:

• **Storage and Transport**: Gases must be stored below their critical temperature to remain liquefied.
• **Industry Applications**: Processes that rely on gas liquefaction utilize critical temperature data for optimal conditions.

Gases with higher critical temperatures are generally easier to handle as liquids because less pressure and lower temperatures are needed to keep them in liquid form.

Intermolecular Forces

Intermolecular forces are the attractive forces that act between molecules. They are vital in determining the physical properties of substances, such as boiling and melting points. These forces include:

• **Van der Waals forces**: These are weak forces that arise from temporary charge imbalances at the atomic level, often increasing with larger molecular size and mass.
• **Dipole-dipole interactions**: Occur between molecules with permanent dipoles, such as in polar molecules.
• **Hydrogen bonding**: A strong type of dipole interaction, particularly in molecules containing N, O, or F bonded to hydrogen.

In the context of gas adsorption and liquefaction, intermolecular forces play a decisive role. Stronger forces generally mean higher critical temperatures, making it easier for the gas to liquefy and adsorb on surfaces like charcoal.

Charcoal Adsorption

Charcoal is a form of carbon that is particularly effective at adsorbing gases. Its porous structure provides a vast surface area that maximizes the contact between the gas molecules and the charcoal. The efficiency of charcoal as an adsorbent relates to:

• **Surface Area**: The highly porous nature means more surface is available for gases to adhere.
• **Affinity for gases**: Charcoal has a strong ability to attract and hold gas molecules closer, especially those with polar characteristics or significant intermolecular forces.

When analyzing which gas is adsorbed least on charcoal, it's not just the critical temperature that matters, but also how these gases interact with the surface of charcoal due to their respective intermolecular forces. Hydrogen ( H_2 ), for example, shows the least adsorption due to its low critical temperature and weaker intermolecular forces compared to gases like SO_2 or CO_2 .