Question

For adsorption of a gas on a solid surface, the plot that represents Freundlich isotherm is 

• A. (A)
• B. (B)
• C. (C)
• D. (D)

Hint:

The Freundlich isotherm is an empirical equation used to describe the adsorption of gases on solids. The plot of \( \log x/m \) vs. \( \log P \) is characteristic of this isotherm.

Answer 1

The Correct Option is D

Freundlich adsorption isotherm:

The Freundlich equation is: $$\frac{x}{m} = k P^{1/n}$$

where:

• $x$ = mass of gas adsorbed
• $m$ = mass of adsorbent
• $P$ = pressure
• $k$ and $n$ are constants (n > 1)

Step 1: Taking logarithm: $$\log\left(\frac{x}{m}\right) = \log k + \frac{1}{n}\log P$$

This is a linear equation of the form: $$y = c + mx$$

where:

• $y = \log(x/m)$
• $x = \log P$
• slope = $1/n$ (positive, since n > 1)
• intercept = $\log k$

Step 2: Expected plot characteristics:

1. Plot of $\log(x/m)$ vs $\log P$ should be linear
2. Slope = $1/n$ is positive (since n > 1, we have 0 < 1/n < 1)
3. The line should be straight, not curved

Step 3: Analyzing the options:

(A): Shows curved (plateauing) relationship - represents Langmuir isotherm behavior, not Freundlich 

(B): Shows upward curving (accelerating) relationship - not linear 

(C): Shows negative slope - contradicts Freundlich equation 

(D): Shows straight line with positive slope - matches $\log(x/m) = \log k + \frac{1}{n}\log P$ 

Answer: (D) 

The Freundlich isotherm gives a straight line when plotting log(x/m) versus log P, with a positive slope equal to 1/n.