In case of adsorption hysteresis, the desorption equilibrium pressure is
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- Always lower than that obtained during adsorption
- Always higher than that obtained during adsorption
- Same as that obtained during adsorption
- Can be either higher or lower than that obtained during adsorption
The Correct Option is A
Solution and Explanation
Adsorption hysteresis occurs when the adsorption and desorption isotherms of a gas on a solid surface do not follow the same path. An isotherm plots the amount of gas adsorbed (or desorbed) versus the equilibrium pressure at a constant temperature:
Adsorption isotherm: As pressure increases, more gas is adsorbed onto the surface.
Desorption isotherm: As pressure decreases, gas is released from the surface.
Hysteresis is typically observed in porous materials (e.g., mesoporous solids) where the pore structure affects the adsorption and desorption processes differently. It manifests as a loop in the isotherm, where the desorption curve lies above the adsorption curve in terms of the amount adsorbed at a given pressure. Step 2: Analyze the equilibrium pressure in hysteresis.
In adsorption hysteresis:
During adsorption, gas molecules fill the pores of the material as pressure increases. Capillary condensation may occur in mesopores, where gas condenses into a liquid-like phase at a pressure below the saturation pressure, following the Kelvin equation.
During desorption, the gas is released as pressure decreases. However, the liquid-like condensate in the pores evaporates at a lower pressure than it condensed due to the geometry of the pores (e.g., ink-bottle pores with narrow necks). This is because desorption often involves overcoming additional energy barriers, such as the formation of a meniscus in the pore neck, which delays evaporation. The equilibrium pressure refers to the pressure at which a given amount of gas is adsorbed or desorbed. In a hysteresis loop:
For a fixed amount of gas adsorbed (\( q \)), the pressure on the desorption curve (\( P_{\text{des}} \)) is lower than the pressure on the adsorption curve (\( P_{\text{ads}} \)).
This means that to desorb the same amount of gas that was adsorbed, a lower pressure is required during desorption compared to the pressure at which it was adsorbed.
Step 3: Evaluate the options.
(1) Always lower than that obtained during adsorption: Correct, as the desorption pressure is consistently lower than the adsorption pressure for the same amount of gas in a hysteresis loop. Correct.
(2) Always higher than that obtained during adsorption: Incorrect, as the desorption pressure is lower, not higher. Incorrect.
(3) Same as that obtained during adsorption: Incorrect, as hysteresis implies a difference between adsorption and desorption pressures. Incorrect.
(4) Can be either higher or lower than that obtained during adsorption: Incorrect, as hysteresis in adsorption consistently shows the desorption pressure to be lower. Incorrect. Step 4: Select the correct answer.
In case of adsorption hysteresis, the desorption equilibrium pressure is always lower than that obtained during adsorption, matching option (1).
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