Question

Which from following represents the Freundlich’s empirical equation for adsorption of gas on solid (for \(n > 1\))?

• A. \(x = k p^{1/n}\)
• B. \(m = k p^n\)
• C. \( \frac{x}{m} = k p^n\)
• D. \( \frac{x}{m} = k p^{1/n}\)

Hint:

Freundlich’s equation is useful for describing adsorption on surfaces where adsorption sites are not uniform. The exponent \(1/n\) shows that adsorption decreases with increasing pressure.

Answer 1

The Correct Option is D

Step 1: Understanding Freundlich's equation.
Freundlich's adsorption isotherm describes how the amount of gas adsorbed on a solid varies with pressure. It is empirical and assumes that adsorption occurs on a heterogeneous surface. The Freundlich equation is given by:
\[ \frac{x}{m} = k p^{1/n} \]
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 the gas.

Step 2: Analyze the options.
- Option \((1)\): \(x = k p^{1/n}\) is incorrect because it does not match the correct form of Freundlich's equation.
- Option \((2)\): \(m = k p^n\) is incorrect because it does not have the correct structure.
- Option \((3)\): \( \frac{x}{m} = k p^n\) is incorrect as the exponent should be \(1/n\).
- Option \((4)\): \( \frac{x}{m} = k p^{1/n}\) matches the correct form of the Freundlich adsorption equation.

Step 3: Final Answer.
Thus, the correct answer is option \((4)\).