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)
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Physisorption is always exothermic (\( \Delta H<0 \)). Therefore, low temperature and high pressure are the favorable conditions for the adsorption of gases on solids.
Step 1: Understanding the Concept:
Adsorption of gases on solids (physisorption) is an exothermic process. According to Le Chatelier's principle, an increase in temperature shifts the equilibrium in the direction that absorbs heat (desorption). Step 2: Detailed Explanation:
1. Effect of Temperature: At a given pressure, the amount of gas adsorbed (\( x/m \)) decreases with an increase in temperature.
2. Analyzing the Condition: We are given \( T_1>T_2 \). This means \( T_2 \) is the lower temperature and \( T_1 \) is the higher temperature.
3. Graph behavior: For any specific pressure \( P \), the extent of adsorption at the lower temperature (\( T_2 \)) must be higher than at the higher temperature (\( T_1 \)).
4. Visualizing: On a plot of \( x/m \) vs \( P \), the curve for the lower temperature (\( T_2 \)) will always lie above the curve for the higher temperature (\( T_1 \)). Step 3: Final Answer:
Graph (A) correctly shows the \( T_2 \) isotherm positioned above the \( T_1 \) isotherm for all values of \( P \).
