Given below are two statement : one is labelled as Assertion (A) and the other is labelled as Reason

Q: Why does a higher critical temperature mean more adsorption?

A higher critical temperature indicates stronger intermolecular forces between the gas molecules. Stronger forces mean the gas is closer to the liquid state (more easily liquefiable), making it easier for the molecules to stick to the adsorbent surface.

Q: What kind of forces are present in $SO_2$ and $H_2$?

$SO_2$ is a polar molecule with a bent shape, so it experiences strong dipole-dipole interactions. $H_2$ is a non-polar diatomic molecule, so it only experiences weak London dispersion forces.

Q: Does the type of adsorbent matter here?

While the adsorbent (activated charcoal) provides the surface, the comparison is between the two gases. The relative order of adsorption for different gases remains the same on any given physical adsorbent, driven by the gases' critical temperatures.

Q: Is this physical or chemical adsorption?

This is physical adsorption (physisorption), which relies on weak van der Waals forces between the gas and the solid surface. That's why the intermolecular forces of the gas itself play such a huge role.

Q: Can we predict the exact amount of gas adsorbed just from the critical temperature?

Not the exact amount, as that depends on pressure, temperature, and the specific surface area of the adsorbent. However, we can confidently predict the *relative* extent of adsorption between different gases.

Question

Given below are two statement : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) $	ext{SO}_2(g)$ is adsorbed to a large extent than $	ext{H}_2(g)$ on activated charcoal.
Reason (R) $	ext{SO}_2(g)$ has a higher critical temperature than $	ext{H}_2(g)$.
In the light of the above statements, choose the most appropriate answer from the options given below.

Options:

(A) Both A and R are correct but R is not the correct explanation of A

(B) Both A and R are correct and R is the correct explanation of A.

(C) A is not correct but R is correct.

(D) A is correct but R is not correct.

Sigma Percentile · Accepted Answer

### Analyzing the Setup

Imagine you are observing a microscopic battle for real estate. We have a solid surface of activated charcoal acting as the host, and two different gases, sulfur dioxide ($SO_2$) and hydrogen ($H_2$), trying to stick or adsorb onto it.

This phenomenon is known as physical adsorption or physisorption. In physisorption, the gas molecules are held to the solid surface by weak van der Waals forces. The question asks us to compare the extent to which these two gases are adsorbed and to evaluate the reasoning behind it.

### The Master Concept: Critical Temperature

To understand which gas wins the battle for the charcoal surface, we need to look closely at the molecules themselves. Sulfur dioxide ($SO_2$) is a polar molecule with a bent geometry. Because of this polarity, it experiences relatively strong dipole-dipole interactions between its molecules.

On the other hand, hydrogen ($H_2$) is a perfectly symmetrical, non-polar diatomic molecule. The only intermolecular forces it can muster are very weak London dispersion forces.

This brings us to a crucial thermodynamic property: **Critical Temperature ($T_c$)**. The critical temperature of a gas is a direct reflection of the strength of its intermolecular forces. The stronger the forces pulling the molecules together, the higher the critical temperature. Since $SO_2$ has much stronger intermolecular forces than $H_2$, it naturally follows that $T_c(SO_2) > T_c(H_2)$.

### Connecting to Adsorption

So, what does a higher critical temperature mean for adsorption?

A higher critical temperature means that the gas is more easily liquefiable. It is already "closer" to being a liquid at room temperature compared to a gas with a low critical temperature. Because the molecules of an easily liquefiable gas already have a strong tendency to stick together, they also have a much stronger tendency to stick to the surface of an adsorbent.

Therefore, because $SO_2$ has a higher critical temperature, it is more easily liquefiable, which directly leads to a **greater extent of adsorption** on the charcoal surface compared to $H_2$.

### Final Conclusion

Let's evaluate our given statements.

**Assertion (A)** states that $SO_2(g)$ is adsorbed to a larger extent than $H_2(g)$ on activated charcoal. Based on our analysis, this is absolutely correct.

**Reason (R)** states that $SO_2(g)$ has a higher critical temperature than $H_2(g)$. This is also a factual statement.

Furthermore, the higher critical temperature is the exact physical reason *why* $SO_2$ is adsorbed more. Therefore, both Assertion and Reason are correct, and the Reason is the perfect, scientifically sound explanation for the Assertion.

Select Answer:

Visualized Solution

$S O_{2}$ vs $H_{2}$ Adsorption

Intermolecular Forces

Critical Temperature ( $T_{c}$ )

Extent of Adsorption

Conclusion

The Way Forward

The Sigma Insight: Adsorption

Analyzing the Setup

The Master Concept

Connecting to Adsorption

Final Conclusion

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