In Langmuir's model of adsorption of a gas on a solid surface

Langmuir proposed a kinetic model for the adsorption of gases on solid surfaces. The fundamental assumptions of his model are:

1. The solid surface possesses a fixed number of identical sites. 2. Each site can hold, at most, one gas molecule (monolayer adsorption). 3. Adsorption and desorption are dynamic processes that occur with definite rate constants. 4. A gas molecule first collides with the surface; the rate of such collisions (or flux) is proportional to the gas pressure $$P$$.

Let $$\theta$$ be the fraction of surface sites already covered. Then:

• Rate of adsorption $$= k_\text{ads}\,P\,(1-\theta)$$, because it depends both on the collision rate (∝$$P$$) and on the fraction of vacant sites $$(1-\theta)$$. • Rate of desorption $$= k_\text{des}\,\theta$$, because only the sites that are occupied can release molecules.

Using steady-state (rate of adsorption = rate of desorption) leads to the familiar Langmuir isotherm $$\theta = \frac{KP}{1+KP}$$, where $$K = k_\text{ads}/k_\text{des}$$.

Now examine each statement:

Option A: “The rate of dissociation (desorption) of adsorbed molecules from the surface does not depend on the surface covered.” This contradicts assumption 3 above; desorption rate $$\propto\theta$$, so it definitely depends on how much surface is already covered. Hence A is incorrect.

Option B: “The adsorption at a single site on the surface may involve multiple molecules at the same time.” Langmuir assumes monolayer adsorption—only one molecule per site. Therefore B is incorrect.

Option C: “The mass of gas striking a given area of surface is proportional to the pressure of the gas.” The kinetic theory of gases shows that the number of molecules colliding with a unit area per second is directly proportional to the gas pressure. This is exactly Langmuir’s first kinetic assumption. Hence C is correct.

Option D: “The mass of gas striking a given area of surface is independent of the pressure of the gas.” This is the reverse of Langmuir’s assumption and is therefore false.

Thus, the only statement consistent with Langmuir’s adsorption model is:

Option C which is: the mass of gas striking a given area of surface is proportional to the pressure of the gas.