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GATE 2023 CY – Question 56

Physical Chemistry · Surfaces and Interfaces: Physisorption and chemisorption. Langmuir, Freundlich and Brunauer-Emmett-Teller (BET) isotherms. Surface catalysis: Langmuir-Hinshelwood mechanism. Surface tension, viscosity, Self- assembly/ physical chemistry of colloids, micelles and macromolecules. · 2 marks · Multiple select

For nondissociative gas adsorption on a solid, the Freundlich isotherm is $\theta=kp^{1/n}$, where θ is coverage, p pressure, and k,n empirical constants. The source gives BET as $p/(p^*-p)=\theta/c+\theta(c-1)(p/p^*)$, with empirical constants $p^*,c$ and $p<p^*$. Which statements are correct?

  1. At low coverage Langmuir reduces to Freundlich with $n=1$
  2. At high coverage Langmuir reduces to Freundlich with $n=\infty$
  3. At very low pressure $p\ll p^*$ BET reduces to Langmuir
  4. At very high pressure $p\to p^*$ BET reduces to Langmuir

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Show answer and explanation

Correct answer: (A) At low coverage Langmuir reduces to Freundlich with $n=1$; (B) At high coverage Langmuir reduces to Freundlich with $n=\infty$; (C) At very low pressure $p\ll p^*$ BET reduces to Langmuir

Explanation

Langmuir θ=Kp/(1+Kp) becomes Kp at low coverage, matching Freundlich n=1. At saturation θ→1, corresponding to pressure exponent 1/n→0 or n→∞. BET at very low pressure neglects multilayers and has the corresponding monolayer/linear limit, so C is accepted. Near p*, BET diverges rather than saturates; D false. **Select A, B, C**.