The accumulation of molecular species at the surface rather than in the bulk of a solid or liquid is termed as adsorption. There are two types of adsorption. In physisorption, attractive forces are mainly van der Waals while in chemical adsorption adsorbate is held with chemical bonds adsorbent. Adsorption increases with increase in pressure and decrease as temperature is increased.

Critical temperature of few gases are given \(SO_2\) (630K), \(CH_4\) (190 K), \(H_2\) (33K). What is the correct order of case of physi-adsorption of these gases?

\(SO_2 > CH_4 > H_2\)

The correct answer is (2) \(SO_2 > CH_4 > H_2\).

Physisorption, also known as physical adsorption or Van der Waals adsorption, occurs due to weak attractive forces between molecules or atoms. These forces are primarily Van der Waals forces (London dispersion forces and dipole-dipole interactions). The strength of Van der Waals forces depends on the polarizability and size of the molecules.

Now, let's break down the order you provided:

1. Sulfur Dioxide (\(SO_2\)): \(SO_2\) has a relatively high critical temperature of 630 K. This means that at lower temperatures, it is less likely to reach its critical temperature and exists in a gaseous state. With its larger, polarizable molecules, \(SO_2\) can exhibit stronger Van der Waals forces compared to smaller, non-polar molecules like hydrogen and methane. Therefore, it is less likely to undergo physisorption at low temperatures.

2. Methane (\(CH_4\)): Methane has a critical temperature of 190 K, which is lower than that of \(SO_2\) but higher than hydrogen. It falls in the middle in terms of critical temperature. Methane molecules are larger than hydrogen but smaller than \(SO_2\), and they are non-polar. While methane can exhibit Van der Waals forces, they are weaker than those in \(SO_2\). Therefore, it is less likely to undergo physisorption than \(SO_2\) but more likely than hydrogen.

3. Hydrogen (\(H_2\)): Hydrogen has the lowest critical temperature of 33 K among the three gases. Hydrogen molecules are small and non-polar, which results in weaker Van der Waals forces compared to \(SO_2\) and methane. Due to its low critical temperature and weaker intermolecular forces, hydrogen is the most likely to be adsorbed through physisorption at low temperatures.

In summary, the ease of physisorption at low temperatures is primarily determined by the strength of Van der Waals forces, which is influenced by molecular size, polarizability, and critical temperature. As a result, \(SO_2\) is the least likely to undergo physisorption at low temperatures due to its high critical temperature and stronger forces, while hydrogen is the most likely due to its low critical temperature and weaker forces. Methane falls in between these two gases in terms of physisorption tendencies.