Langmuir isotherm calculator explained
The Langmuir adsorption isotherm models how gas molecules occupy a solid surface. It states that the fractional coverage equals , where is the adsorption equilibrium constant and is the adsorbate partial pressure. This calculator evaluates {surface_fraction} and {surface_percent} as you adjust {eq_constant} and {partial_pressure}.
Use it to predict catalyst site utilization, fit adsorption data, or convert fractional coverage into an intuitive percent value for reports.
How the conversion works
For monolayer adsorption with identical sites:
Multiply by 100 to express percent coverage. If you know coverage and want , rearrange to . The calculator keeps both and percent coverage synchronized.
Units and conversions
| Quantity | Units | Notes |
|---|---|---|
| Pressure (e.g., atm) | Depends on temperature. | |
| atm, bar, Pa | Use a consistent unit with . | |
| fraction | Between 0 and 1. | |
| Surface percent | % | . |
Worked examples
- CO adsorption on Pt at 400 K
, .
Only 14% of the surface is covered, so the catalyst retains free sites.
- Low-pressure dosing during TPD experiments
, .
Coverage is 11%; doubling pressure would raise it to 20% according to the Langmuir model.
Tips and pitfalls
- Langmuir assumptions break down when adsorbate interactions exist or multiple site types are present; check residuals before trusting fitted .
- Keep temperature constant; follows van't Hoff behavior, so coverage changes with temperature even at fixed pressure.
- Convert liquid-phase concentrations to effective pressure (via Henry's law) before applying the gas-phase form.
- When , the surface is nearly saturated and increasing pressure yields diminishing returns.