Given,
Gas : H2, CH4, CO2, SO2
Critical temp./K : 33, 190, 304, 630
On the basis of data given above

Q: Why do we only look at critical temperature and not pressure?

Critical temperature is a direct indicator of the strength of intermolecular forces (van der Waals forces) in a gas. Stronger forces naturally lead to a higher tendency to be adsorbed, making $T_c$ the perfect comparative metric.

Q: What exactly is the 'a' in the critical temperature formula?

The term 'a' is the van der Waals constant that measures the magnitude of attractive forces between gas molecules. A larger 'a' means molecules attract each other more strongly.

Q: Would the order change if we used a different adsorbent instead of charcoal?

No, the relative order of adsorption for these gases would remain the same on any given solid surface, because the order depends purely on the intrinsic properties (intermolecular forces) of the gases themselves.

Q: Is this physical or chemical adsorption?

This is physical adsorption (physisorption). It relies on weak van der Waals forces between the gas and the solid, which is exactly why gases with stronger intermolecular forces are adsorbed more.

Q: Can a gas be adsorbed above its critical temperature?

Yes, physical adsorption can still occur above the critical temperature, but the extent of adsorption is generally much lower because the gas cannot be liquefied and the kinetic energy of the molecules is very high.

Question

Given,
$\begin{array}{lcccc} 	ext{Gas :} & H_2 & CH_4 & CO_2 & SO_2 \ 	ext{Critical temp./K} & 33 & 190 & 304 & 630 \end{array}$
On the basis of data given above, predict which of the following gases shows least adsorption on a definite amount of charcoal?

Options:

(A) $CH_4$

(B) $SO_2$

(C) $CO_2$

(D) $H_2$

Sigma Percentile · Accepted Answer

### The Secret Link Between Critical Temperature and Adsorption

Imagine you are designing a gas mask for a hazardous environment. You need a material that can trap toxic gases effectively while letting breathable air pass through. This is where activated charcoal comes into play, acting as a microscopic sponge. But how do we know which gases will stick to the charcoal and which will slip right past? The answer lies in a fascinating property called the **Critical Temperature**.

In this problem, we are given four gases: Hydrogen ($H_2$), Methane ($CH_4$), Carbon Dioxide ($CO_2$), and Sulfur Dioxide ($SO_2$), along with their respective critical temperatures. Our mission is to determine which of these gases will show the **least** adsorption on a definite amount of charcoal.

### The Phenomenon of Physisorption

Before we dive into the numbers, let's understand the mechanism. When gas molecules accumulate on the surface of a solid (like charcoal), the process is called **adsorption**. Specifically, we are dealing with physical adsorption, or **physisorption**.

Unlike chemical adsorption, which involves strong chemical bonds, physisorption relies entirely on weak **van der Waals forces**. Think of these forces as a gentle, invisible glue. The stronger this invisible glue, the more tightly the gas molecules will cling to the charcoal surface.

### The Magic of Critical Temperature ($T_c$)

So, how do we measure the strength of this "invisible glue" for different gases? This is where the critical temperature ($T_c$) becomes our ultimate tool.

The critical temperature is the temperature above which a gas cannot be liquefied, no matter how much pressure you apply. Mathematically, it is defined by the equation:

$$T_c = \frac{8a}{27Rb}$$

Here, the term **$a$** is the van der Waals constant that represents the magnitude of intermolecular forces of attraction. Notice the direct relationship: a higher value of $a$ (stronger intermolecular forces) results in a higher critical temperature ($T_c$).

Because physisorption also depends on these exact same van der Waals forces, we arrive at a golden rule of surface chemistry:

**The extent of physical adsorption of a gas is directly proportional to its critical temperature.**

### Analyzing the Contenders

Armed with this powerful principle, let's look at the data provided in the question:

*   $SO_2$: $630 	ext{ K}$
*   $CO_2$: $304 	ext{ K}$
*   $CH_4$: $190 	ext{ K}$
*   $H_2$: $33 	ext{ K}$

If we were looking for the gas that is adsorbed the *most*, we would pick Sulfur Dioxide ($SO_2$), because its high critical temperature ($630 	ext{ K}$) indicates very strong intermolecular forces. It is easily liquefiable and will stick to the charcoal aggressively.

However, the question asks for the gas that shows the **least** adsorption. We need the gas with the weakest intermolecular forces, which corresponds to the lowest critical temperature.

### The Final Verdict

Scanning our list, Hydrogen ($H_2$) stands out with an incredibly low critical temperature of just $33 	ext{ K}$. Because its molecules exert very little attractive force on one another, they also exert very little attractive force on the charcoal surface. They are highly energetic and prefer to stay in the gaseous phase rather than settling down on the solid.

Therefore, Hydrogen will be adsorbed to the least extent. The correct option is **(d)**.

Animated Solution for Chemistry - Surface Chemistry: Given, $Gas : Critical temp./K H_{2} 33 C H_{4} 190 C O_{2} 304 S O_{2} 630$ On the basis of data given above, predict which of the following gases shows least adsorption on a definite amount of charcoal?

Select Answer:

Visualized Solution

\text{Given Data}

\text{Adsorption Principle}

\text{Intermolecular Forces}

\text{Comparing } T_c

\text{Conclusion}

\text{Food for Thought}

The Sigma Insight: Adsorption

The Secret Link Between Critical Temperature and Adsorption

The Phenomenon of Physisorption

The Magic of Critical Temperature ( $T_{c}$ )

Analyzing the Contenders

The Final Verdict

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