A gas undergoes physical adsorption on a surface and follows the given Freundlich adsorption isotherm equation
$$\frac{x}{m} = kp^{0.5}$$
Adsorption of the gas increases with:

1. Effect of Pressure (p)

From the given equation, x/m is directly proportional to p^0.5 (or the square root of pressure):

• As pressure (p) increases, the value of p^0.5 increases.
• Consequently, the extent of adsorption (x/m) increases.
• Therefore, adsorption increases with an increase in p.

2. Effect of Temperature (T)

The problem explicitly mentions that the gas undergoes physical adsorption (physisorption).

• Physical adsorption is an exothermic process (releases heat).
• According to Le Chatelier's principle, an increase in temperature shifts the equilibrium in the backward direction, favoring desorption.
• Therefore, the extent of physical adsorption (x/m) decreases as temperature increases, and it increases with a decrease in T.