Problem 84 - A Complete Resource Book in Chemistry for JEE Main

Question

The volume of gases \(\mathrm{H}_{2}, \mathrm{CH}_{4}, \mathrm{CO}_{2}\) and \(\mathrm{NH}_{3}\) adsorbed by \(1 \mathrm{~g}\) of charcoal at \(288 \mathrm{~K}\) are in the order of (a) \(\mathrm{CO}_{2}>\mathrm{NH}_{3}>\mathrm{H}_{2}>\mathrm{CH}_{4}\) (b) \(\mathrm{NH}_{3}>\mathrm{CO}_{2}>\mathrm{CH}_{4}>\mathrm{H}_{2}\) (c) \(\mathrm{CO}_{2}>\mathrm{NH}_{3}>\mathrm{H}_{2}>\mathrm{CH}_{4}\) (d) \(\mathrm{CH}_{4}>\mathrm{CO}_{2}>\mathrm{NH}_{3}>\mathrm{H}_{2}\)

Step-by-Step Solution

Answer

(b) NH_{3} > CO_{2} > CH_{4} > H_{2}.

Step 1: Understanding Adsorption

Adsorption is a process where gas molecules adhere to the surface of a solid material, like charcoal. The volume of gas adsorbed is related to the intermolecular forces between the gas molecules and the surface.

Step 2: Factors Influencing Adsorption

The key factors influencing adsorption include the polarity and size of the gas molecules. Typically, more polar and larger molecules are adsorbed more strongly due to higher interaction with the surface.

Step 3: Analyzing Molecular Properties

1. **Ammonia (NH_{3})**: Highly polar and small. 2. **Carbon dioxide (CO_{2})**: Slightly polar with larger size than NH_{3}. 3. **Methane (CH_{4})**: Non-polar and small molecule. 4. **Hydrogen (H_{2})**: Non-polar and very small molecule.

Step 4: Rank Order Based on Adsorption

Based on the properties, the order of increasing adsorption generally is: Non-polar small < Non-polar large < Slightly polar larger < Highly polar small. Thus, the order is NH_{3} > CO_{2} > CH_{4} > H_{2}.

Step 5: Comparing to Choices

Compare the order from the previous step with the provided options. The correct answer should be NH_{3} > CO_{2} > CH_{4} > H_{2}, which matches option **(b)**.

Key Concepts

Intermolecular Forces

Intermolecular forces are the forces that occur between molecules, affecting how these molecules interact with each other and with surfaces. These forces play a crucial role in adsorption, where gas molecules adhere to surfaces such as charcoal. There are several types of intermolecular forces, including:

• **Van der Waals Forces:** These are the weakest forces and occur due to the temporary dipoles in molecules.
• **Dipole-Dipole Interactions:** These occur between polar molecules where the positive part of one molecule attracts the negative part of another.
• **Hydrogen Bonds:** A special type of dipole-dipole interaction that occurs when hydrogen is bonded to a highly electronegative atom like nitrogen, oxygen, or fluorine.

For gas adsorption on surfaces like charcoal, the strength of these interactions determines how much gas will be adsorbed. Gases that exhibit strong intermolecular interactions with the surface tend to be adsorbed more efficiently.

Polarity

Polarity refers to the distribution of electrical charge over the atoms joined by the bond. In polar molecules, electrons are distributed unevenly, causing one end of the molecule to have a slight negative charge and the other end a slight positive charge.
This partial charge difference enables polar molecules to interact more strongly with surfaces and with each other, enhancing adsorption. For instance:

• **Ammonia (NH₃):** Is highly polar. This allows it to interact strongly with other molecules and surfaces, enhancing its adsorption on charcoal.
• **Carbon Dioxide (CO₂):** While generally considered non-polar due to its linear shape, it can exhibit some polar characteristics near other molecules, allowing moderate adsorption.
• **Methane (CH₄) and Hydrogen (H₂):** Both are non-polar, resulting in weaker interactions with charcoal, thus less adsorption.

Understanding molecular polarity provides key insights into the order and extent to which different gases will be adsorbed.

Molecular Size

The size of a molecule influences how easily it can be adsorbed onto a surface like charcoal. Generally, larger molecules have a greater surface area available for interaction with the adsorbent.
This can enhance their ability to adhere to a surface. However, it's important to note that size alone does not dictate adsorption; it works in conjunction with other factors like polarity. For the gases considered:

• **Carbon Dioxide (CO₂):** Despite being slightly polar, its larger size compared to smaller non-polar gases like hydrogen (H₂) enhances its interaction with charcoal.
• **Methane (CH₄):** Small and non-polar, thus has weak adsorption.
• **Ammonia (NH₃):** Though smaller, its high polarity ensures strong adsorption.

Thus, while larger size can generally mean stronger adsorption characteristics, when it aligns with suitable polarity and intermolecular forces.

Gas Adsorption on Charcoal

Gas adsorption on charcoal involves the adherence of gas molecules to the surface area of charcoal. Charcoal, due to its porous structure, offers a high surface area for adsorption, making it effective for trapping gases.
Factors affecting how gases adhere to charcoal include:

• **Surface Area:** Charcoal has a large surface area due to its porous nature, providing ample space for gases to adhere.
• **Intermolecular Forces and Polarity:** As discussed earlier, gases with stronger intermolecular attractions are more readily adsorbed. Charcoal, being largely carbon-based, can interact well with molecules exhibiting van der Waals forces and dipoles.
• **Adsorption Mechanics:** In adsorption, gas molecules stick to the surface of the charcoal rather than penetrating it, making good intermolecular interactions crucial.

Overall, properties such as molecular size and polarity, along with the inherent nature of the charcoal, govern the extent and effectiveness of gas adsorption.