Chemistry
Langmuir Isotherm Calculator
Work out how much of a surface is covered by adsorbed gas at a given pressure.
Your inputs
Change any value to update the result instantly.
Surface coverage θ
0.8333
Coverage as a percentage
83.333 %
Fraction of sites still free
0.1667
Pressure for half coverage
2 kPa
Reading
More than half the sites are occupied
Langmuir assumes one adsorbed layer, identical independent sites and no interaction between adsorbed molecules. Real surfaces with multilayers need the BET model instead.
What this calculator does
Calculates the fraction of a surface covered by adsorbate at a given pressure.
What your result means
Coverage runs from bare surface at zero to a complete single layer as pressure rises.
Surface coverage (%) against pressure (kPa)
| Period | Input / invested | Calculated value |
|---|---|---|
| 0 | 0 | 0 |
| 2 | 2 | 50 |
| 4 | 4 | 66.667 |
| 6 | 6 | 75 |
| 8 | 8 | 80 |
| 10 | 10 | 83.333 |
| 12 | 12 | 85.714 |
| 14 | 14 | 87.5 |
| 16 | 16 | 88.889 |
| 18 | 18 | 90 |
| 20 | 20 | 90.909 |
Formula and working
θ = K·P / (1 + K·P)
- 1
Collect the inputs
Adsorption constant K = 0.5 1/kPa; Adsorbate pressure P = 10 kPa
- 2
Apply the formula
θ = K·P / (1 + K·P)
- 3
Result
Surface coverage θ = 0.8333
Frequently asked questions
Symbols and assumptions
- θ
- Fractional coverage
- K
- Adsorption equilibrium constant
- P
- Adsorbate pressure
- • One adsorbed layer only, with identical independent sites.
- • No interaction between adsorbed molecules.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • Multilayer adsorption needs the BET model instead.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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