Question

Select the graph that correctly describes the adsorption isotherms at two temperatures \( T_1 \) and \( T_2 \) (\( T_1>T_2 \)) for a gas : (x - mass of the gas adsorbed, m - mass of adsorbent, P - pressure) 

• A. A
• B. B
• C. C
• D. D

Hint:

Physisorption is always exothermic (\( \Delta H<0 \)). Therefore, low temperature and high pressure are the favorable conditions for the adsorption of gases on solids.

Answer 1

The Correct Option is A

The question asks us to identify the correct adsorption isotherm graph for a gas on a solid surface at two different temperatures, \( T_1 \) and \( T_2 \), where \( T_1 > T_2 \). 

Adsorption isotherms describe how the amount of gas adsorbed (x/m) on a solid adsorbent varies with pressure (P) at a constant temperature. According to the basic principles of adsorption:

• At lower temperatures (e.g., \( T_2 \)), adsorption is more pronounced because the kinetic energy of gas molecules is lower, allowing them to adhere more easily to the adsorbent surface.
• At higher temperatures (e.g., \( T_1 \)), adsorption decreases since the increased kinetic energy reduces the gas molecules' tendency to stick to the adsorbent.

The key principle here is that, for constant pressure, the amount adsorbed \( \frac{x}{m} \) is greater at lower temperatures. This is depicted in Option A:

• In Option A, for a given pressure, the curve at \( T_2 \) shows more adsorption compared to the curve at \( T_1 \).

This aligns with the observed behavior of adsorption isotherms:

• The isotherm at a lower temperature (\( T_2 \)) lies above that at a higher temperature (\( T_1 \)) for the same pressure range, indicating higher adsorption.

Therefore, the correct graph that represents the adsorption isotherms is Option A.