Understanding Freundlich Adsorption Isotherm

The Freundlich adsorption isotherm describes how the amount of gas adsorbed by a unit mass of solid adsorbent relates to the pressure of the gas at a constant temperature. The general form of the isotherm is given by:

$\frac{x}{m}=k\cdot p^{1/n}$

where:

• $\frac{x}{m}$ is the amount of gas adsorbed per unit mass of adsorbent
• $p$ is the pressure of the gas
• $k$ and $n$ are constants that depend on the nature of the adsorbent and adsorbate, and the temperature ($n$ is always greater than 1)

Step-by-Step Analysis of the Options

Step 1: Analyze the general form

The correct mathematical representation is $\frac{x}{m}\propto p^{1/n}$. This is the direct proportionality stated by the Freundlich isotherm.

Step 2: Analyze the specific cases at different pressure ranges

The value of the exponent $1/n$ changes the relationship between adsorption and pressure.

• At low pressure, the exponent $1/n$ is approximately equal to 1. Therefore, adsorption is directly proportional to pressure: $\frac{x}{m}\propto p^1$.
• At high pressure, the exponent $1/n$ approaches 0. Therefore, adsorption becomes nearly independent of pressure: $\frac{x}{m}\propto p^0$ (and $p^0=1$).

Step 3: Draw the final conclusion

All three proportionalities are correct, but each one is valid for a specific range of pressure. They are not universally true for all pressures. The first option correctly states this.

Final Answer

The correct choice is: "All the above are correct for different ranges of pressure."

Related Formulae and Theory

Freundlich Adsorption Isotherm Formula:

$\frac{x}{m}=k\cdot p^{1/n}$

The logarithmic form of the equation is often used to determine the constants $k$ and $n$ from experimental data:

$\log \left(\frac{x}{m}\right)=\log k+\frac{1}{n}\log p$

A plot of $\log \left(\frac{x}{m}\right)$ vs. $\log p$ gives a straight line with a slope of $\frac{1}{n}$ and an intercept of $\log k$.

Related Topics

• Langmuir Adsorption Isotherm: Another model that assumes the formation of a monolayer of adsorbate on the surface of the adsorbent. It is based on different assumptions than the Freundlich isotherm.
• Physisorption vs. Chemisorption: Understanding the different types of adsorption (physical and chemical) is crucial, as different isotherms may apply.
• Factors Affecting Adsorption: The nature of the adsorbent and adsorbate, surface area, pressure, and temperature all influence the extent of adsorption.