Online Langmuir Isotherm Calculator
Use this Online Langmuir Isotherm Calculator to work through the same calculation as the main calculator page with clear steps, examples, and result context.
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Run the calculator.
What This Online Langmuir Isotherm Calculator Helps You Do
This page gives the two outputs most people want from the Langmuir model: the fraction of the surface covered and the actual adsorbed amount when qmax is known. That keeps the tool useful both for conceptual adsorption work and for quick material-comparison calculations.
The interpretation text makes it clear whether the system is far from saturation or already close to monolayer coverage.
How to Calculate Online Langmuir Isotherm Calculator
- Choose the adsorption output: Use coverage mode for fractional surface coverage, or switch to adsorbed-amount mode if you also know the monolayer capacity qmax.
- Enter K and the gas-pressure term: The Langmuir model uses the product KP, so both adsorption strength and pressure influence the result.
- Compute surface occupancy: The calculator evaluates the Langmuir relation and reports either theta or q depending on the selected mode.
- Interpret the saturation level: As KP grows large, the surface approaches saturation and theta tends toward 1.
Online Langmuir Isotherm Calculator Formula
| Variable | Meaning | Unit |
|---|---|---|
| theta | Fraction of surface covered by adsorbate | 0 to 1 |
| K | Langmuir equilibrium constant | 1/pressure |
| P | Adsorbate pressure or concentration term | chosen pressure basis |
| q | Adsorbed amount | same basis as qmax |
| qmax | Maximum monolayer adsorption capacity | chosen adsorption unit |
Use the worked examples below to check how the formula behaves with real values. If the result looks unexpected, verify the unit assumptions and the meaning of each variable before interpreting the answer.
Worked Examples
- K: 2.0 1/bar
- P: 0.50 bar
Result: Surface coverage theta is 0.50.
A KP product of 1 means half the adsorption sites are occupied in the simple Langmuir model.
- K: 5.0 1/bar
- P: 2.0 bar
Result: Surface coverage theta is 0.91.
Large KP drives the surface close to full monolayer coverage.
- qmax: 1.80 mmol/g
- K: 3.0 1/bar
- P: 0.40 bar
Result: Adsorbed amount q is 0.98 mmol/g.
Only the covered fraction of the full monolayer capacity is realized at the chosen pressure.
- qmax: 2.50 mmol/g
- K: 1.2 1/bar
- P: 0.10 bar
Result: Adsorbed amount q is 0.27 mmol/g.
At low KP values, adsorption remains far from saturation.
How to Interpret Your Results
| Range | Meaning | Action |
|---|---|---|
| Theta below 0.2 | Low surface coverage. | The surface is mostly unoccupied under the stated conditions. |
| Theta from 0.2 to 0.8 | Partial monolayer coverage. | Adsorption is significant but not yet saturated. |
| Theta above 0.8 | Surface close to saturation. | Further increases in pressure will produce smaller gains in coverage. |
Frequently Asked Questions
References
Last reviewed: March 2026