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Langmuir isotherm calculator

Solve fractional monolayer coverage, gas pressure or the adsorption constant under a single-site Langmuir model.

Calculator

Occupied-site coverage
50.0000%
Occupied-site fraction
0.500000
Equilibrium pressure
1
Langmuir constant (Pa^-1)
0.001000

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How this calculator works

Assume identical independent sites, one adsorbate per site and a single adsorbed layer at equilibrium. The adsorption constant depends on adsorbate, surface and temperature. Its reciprocal-pressure units must match pressure: this tool uses Pa^-1 and converts the pressure selector to Pa. Multilayer adsorption and interactions between neighbouring adsorbates require other models.

Formula

θ = KP/(1 + KP); P = θ/[K(1 - θ)].

Worked example

K = 0.001 Pa^-1 and P = 1000 Pa give θ = 0.5. At P = 3000 Pa, θ = 0.75.

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Frequently asked questions

Can coverage reach exactly 100%?

It approaches 100% as pressure grows without bound, so inverse calculations at 100% are rejected.

Is this suitable for liquid adsorption?

A concentration form exists, but its constant has reciprocal-concentration units. This page uses the pressure form.

Does K remain constant with temperature?

No. Use a value measured or modelled at the chosen temperature.

Sources

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