Answer the question on the basis of passage given below:

Adsorption is a surface phenomenon which can be expressed by means of an emprical relationship known as Freundlich Adsorption isotherm. The relationship is given by

\(\frac{x}{m} = KP^{\frac{1}{n}}\left(n > 1\right)\)

\(x = \)Mass of the gas adsorbed

\(m = \)Mass of adsorbent

\(P = \)Pressure at which adsorption takes place

\(K\) and \(n\) are constant

On the basis of given data which one of the following gases shows maximum absorption on a definite amount of charcoal

\(SO_2\)

The correct answer is option 2. \(SO_2\).

Sulfur dioxide (\(SO_2\)) has a critical temperature of 630 K, which is higher than that of the other gases listed. A higher critical temperature indicates that \(SO_2\) is less easily liquefied compared to gases with lower critical temperatures.

When a gas is passed through charcoal, it gets adsorbed onto the surface of the charcoal due to intermolecular forces. The ease of adsorption depends on the nature of the gas molecules and the surface of the charcoal.

In the case of \(SO_2\), although it has a higher critical temperature than hydrogen, it still exhibits strong intermolecular forces, particularly due to its polar nature and the presence of sulfur-oxygen bonds. These intermolecular forces allow \(SO_2\) molecules to readily adsorb onto the surface of charcoal.

Therefore, \(SO_2\) is likely to show significant adsorption on a definite amount of charcoal, making it the correct answer.