Langmuir Isotherm Calculator

Calculate surface coverage and adsorption based on Pressure/Concentration.

Adsorption Parameters

Langmuir Constant (K or b)

Pressure / Concentration (P or C)

Maximum Capacity (qm)

Results

Overview

The Langmuir isotherm describes monolayer adsorption on homogeneous surfaces. It assumes: (1) all adsorption sites are equivalent, (2) each site can hold only one molecule, (3) adsorbed molecules don't interact, and (4) adsorption is reversible. The model fits chemisorption better than physisorption and works well at low pressures/concentrations.

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Pro Tips

The formula for coverage (θ) is θ = KP / (1 + KP), where K is the Langmuir constant and P is pressure or concentration.
K represents the affinity between the gas and the surface; higher K means the surface fills up at lower pressures.
At very low pressures (KP ≪ 1), the coverage is directly proportional to pressure (θ ≈ KP).
At very high pressures (KP ≫ 1), the coverage approaches 100% (θ ≈ 1).
In heterogeneous catalysis, the reaction rate is often proportional to the surface coverage θ.
If you know the maximum capacity (qm), you can calculate the total amount adsorbed: q = qm × θ.

Fun Facts

"Irving Langmuir won the Nobel Prize in Chemistry in 1932 for his work on surface chemistry and this very model."
"The model assumes that all adsorption sites are equivalent and that there's no interaction between adjacent adsorbed molecules."
"Langmuir's work also led to the invention of the gas-filled incandescent light bulb."
"Activated carbon filters in water pitchers use principles of the Langmuir isotherm to trap organic pollutants."
"Hemoglobin's binding of oxygen is actually better described by the Hill equation, but the simplest form is equivalent to a Langmuir model."
"The model assumes 'monolayer' coverage—once every site is filled, no more molecules can be adsorbed, even if pressure increases infinitely."
"Many modern gas sensors (like those for CO or CH₄) rely on the changes in surface electrical properties defined by Langmuir adsorption."

Formula: θ = (K · P) / (1 + K · P)

Adsorption Isotherm Curve

Visualizing the relationship between partial pressure and surface site occupancy (θ).

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