Consider the adsorption isotherms given below and interpret the variation in the extent of adsorption (x/m) when: (i) Temperature increases at constant pressure. (ii) Pressure increases at constant temperature

Adsorption isotherms are essential for understanding how substances adhere to surfaces, and they can provide valuable insights into the behavior of adsorbates under varying conditions. Let's break down the effects of temperature and pressure on the extent of adsorption, denoted as \( x/m \), where \( x \) is the amount of adsorbate and \( m \) is the mass of the adsorbent.

Impact of Temperature Increase at Constant Pressure

When the temperature rises while keeping the pressure constant, the extent of adsorption typically decreases. This phenomenon can be explained through the principles of thermodynamics and molecular interactions.

• Kinetic Energy: As temperature increases, the kinetic energy of the molecules also rises. This means that the adsorbate molecules move faster and are more likely to overcome the attractive forces that hold them on the adsorbent's surface.
• Desorption Dominance: Higher temperatures can lead to increased desorption rates, where adsorbate molecules leave the surface of the adsorbent. This results in a net decrease in the amount of adsorbate that remains attached.
• Equilibrium Shift: According to Le Chatelier's principle, if the adsorption process is exothermic (releases heat), increasing the temperature will shift the equilibrium towards the reactants, thereby reducing adsorption.

For example, consider activated carbon adsorbing a gas at room temperature. If the temperature is raised significantly, the gas molecules may gain enough energy to escape from the carbon surface, leading to a lower \( x/m \) value.

Effect of Pressure Increase at Constant Temperature

In contrast, increasing the pressure while maintaining a constant temperature generally enhances the extent of adsorption. This can be understood through the behavior of gases and the principles of adsorption.

• Increased Collision Frequency: Higher pressure means that gas molecules are more densely packed, leading to more frequent collisions with the adsorbent surface. This increases the likelihood of adsorption occurring.
• Adsorption Sites Saturation: As pressure rises, more molecules are available to occupy the available adsorption sites on the surface. This can lead to a higher \( x/m \) value until the surface becomes saturated.
• Langmuir and Freundlich Isotherms: These models illustrate that at higher pressures, the adsorption isotherm typically shows an increase in \( x/m \) until it approaches a plateau, indicating saturation.

For instance, if we consider a gas being adsorbed onto a solid at a constant temperature, increasing the pressure will push more gas molecules onto the surface, thereby increasing the amount adsorbed until the surface reaches its capacity.

Summary of Effects

To summarize, the variation in the extent of adsorption \( x/m \) is influenced significantly by temperature and pressure. An increase in temperature at constant pressure tends to decrease adsorption due to increased kinetic energy and desorption rates. Conversely, an increase in pressure at constant temperature typically enhances adsorption by increasing the frequency of molecular collisions and allowing more molecules to occupy available sites on the adsorbent. Understanding these dynamics is crucial for applications in fields such as catalysis, environmental science, and material engineering.