The Langmuir isotherm expresses the amount adsorbed q as a function of partial pressure P. Which form represents the Langmuir expression?

• A. q = q_max P / (1 + P)
• B. q = q_max (1 - e^{-bP})
• C. q = q_max b P / (1 + b P)
• D. q = q_max b P^2 / (1 + b P)

Answer: (C)

Langmuir describes adsorption on a finite number of identical sites with no interactions between adsorbates, leading to an equilibrium between adsorption and desorption. At equilibrium, the fraction of surface sites covered, θ, is set by adsorption proportional to pressure and available sites, and desorption proportional to coverage. Solving gives θ = (K P)/(1 + K P), where K is an equilibrium constant. The amount adsorbed is q = q_max θ, so q = q_max (K P)/(1 + K P). This is typically written with a constant b: q = q_max b P / (1 + b P). This form saturates at q_max as pressure grows large, and at low pressures it behaves linearly as q ≈ q_max b P.

The other forms do not match this equilibrium structure. An exponential form corresponds to a different mechanism and does not arise from the Langmuir monolayer assumptions. A squared-P term in the numerator would cause q to grow without bound at high pressure, which contradicts the finite capacity q_max of a Langmuir monolayer. The standard form explicitly includes the adsorption constant b to ensure the correct dimensionless argument and proper saturation behavior.