For the adsorption of a gas on a solid surface following the Langmuir adsorption isotherm, the fraction of surface coverage theta is given by theta = (KP) / (1 + KP). At very high pressure, the rate of adsorption becomes independent of pressure. What is the order of the reaction with respect to the gas pressure in this limit?

A. Zero order — At high pressure, the surface is fully covered and the rate becomes independent of pressure, indicating zero order kinetics.

JEE Main · ChemistryHard

$For the adsorption of a gas on a solid surface following the Langmuir adsorption isotherm, the fraction of surface coverage is given by . At very high pressure, the rate of adsorption becomes independent of pressure. What is the order of the reaction with respect to the gas pressure in this limit?$

Show correct answer & step-by-step solution

Correct answer: A — $Zero order$

$The rate of adsorption is proportional to the fraction of surface coverage .$
$As P \to \infty, the expression θ = \frac{K P}{1 + K P} approaches \frac{K P}{K P} = 1 .$
$Since θ becomes constant at high pressure, the rate of reaction is independent of P .$
$A rate independent of concentration or pressure corresponds to zero order kinetics.$
$Hence the answer is (A).$