Question

The adsorption of a gas on a solid surface follows Freundlich adsorption isotherm. At \( T \)(K), the gas pressure is \( 2 \) atm. What is the value of \( \frac{x}{m} \)? (\( n = 2 \) and \( k \) = constant)

• A. \( \frac{x}{m} = 4k \)
• B. \( \frac{x}{m} = \frac{1.414}{k} \)
• C. \( \frac{x}{m} = \frac{k}{1.414} \)
• D. \( \frac{x}{m} = 1.414k \)

Hint:

The Freundlich isotherm follows \(\frac{x}{m} = k P^{1/n}\), allowing adsorption calculations at different pressures.

Answer 1

The Correct Option is D

Step 1: Freundlich Adsorption Isotherm The Freundlich adsorption isotherm is given by: \[ \frac{x}{m} = k P^{\frac{1}{n}} \] where: - \( P \) is the gas pressure, - \( k \) is a constant, - \( n = 2 \). Step 2: Substituting Values \[ \frac{x}{m} = k \times 2^{\frac{1}{2}} \] \[ \frac{x}{m} = k \times \sqrt{2} \] Approximating \( \sqrt{2} \approx 1.414 \): \[ \frac{x}{m} = 1.414k \] Conclusion Thus, the correct answer is: \[ 1.414k \]