GATE 2022 CY – Question 24

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. · 1 mark · Multiple choice

A gas at pressure P adsorbs nondissociatively on a solid according to Langmuir. For fixed fractional coverage at fixed temperature, which relation between K and P is correct? $K=k_a/k_b$, where $k_a,k_b$ are adsorption and desorption rate constants.

$K\propto P^{-1/2}$
$K\propto P$
$K\propto P^{-1}$
$K\propto P^{1/2}$

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Correct answer: (C) $K\propto P^{-1}$

Explanation

Rearranging θ=KP/(1+KP) gives KP=θ/(1−θ). Holding θ fixed therefore gives the formal relation **K∝P⁻¹, C**. At a fixed temperature for one unchanged adsorbent, K itself is a constant, so coverage also fixes P; this is an algebraic constraint rather than a claim that pressure changes K.