When does Langmuir fail?

Heterogeneous surfaces, lateral interactions, and multilayer adsorption break the identical-site monolayer assumptions. Freundlich or BET are then better qualitative models.

What is the BET constant c?

c ≈ exp((E₁ − E_L)/RT) compares first-layer adsorption energy to liquefaction energy. Large c gives a knee near monolayer completion before multilayer rise.

Adsorption Isotherms

Langmuir, Freundlich, and BET isotherms: surface coverage, monolayer capacity n_m, and multilayer rise near P₀.

About this model

Adsorption isotherms relate equilibrium adsorbed amount n to gas pressure P (or relative pressure P/P₀). Langmuir assumes a monolayer of identical sites and saturates at n_m. Freundlich is an empirical power law without a hard ceiling. BET extends Langmuir to multilayers and rises sharply as P approaches P₀. The simulator overlays the chosen curve with a pressure probe so students can compare coverage, affinity, and multilayer behavior.

Who it's for: Physical chemistry, surface science, catalysis, materials characterization (BET surface area), and chemical engineering.

Key terms

Langmuir isotherm
Freundlich isotherm
BET isotherm
Surface coverage
Monolayer capacity
Relative pressure

How it works

Compare Langmuir, Freundlich, and BET adsorption isotherms. Tune affinity and capacity, move the pressure probe, and see monolayer saturation versus multilayer rise near P₀.

Key equations

Langmuir: n = n_m K P / (1 + K P) · θ = K P / (1 + K P)

Freundlich: n = K_F P^{1/n}

BET: n/n_m = c x / ((1−x)(1+(c−1)x)) , x = P/P₀

Frequently asked questions

When does Langmuir fail?: Heterogeneous surfaces, lateral interactions, and multilayer adsorption break the identical-site monolayer assumptions. Freundlich or BET are then better qualitative models.
What is the BET constant c?: c ≈ exp((E₁ − E_L)/RT) compares first-layer adsorption energy to liquefaction energy. Large c gives a knee near monolayer completion before multilayer rise.

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