🔬 Langmuir Surface Area Calculator
Calculate Specific Surface Area from Adsorption Data
For researchers, chemists, and materials scientists
Langmuir Surface Area Calculator
⚡ Direct Calculation from Known Parameters
Langmuir Isotherm Theory
The Langmuir adsorption isotherm describes the equilibrium between gas molecules and a solid surface. It's based on the assumption that:
- Monolayer adsorption — Only one layer of molecules adsorbs on the surface
- Uniform surface — All adsorption sites are equivalent
- No lateral interaction — Adsorbed molecules don't interact with each other
- Definite sites — Fixed number of adsorption sites
Langmuir Equations & Formulas
Langmuir Isotherm Equation
Where V = volume adsorbed, Vm = monolayer capacity, K = Langmuir constant, P = pressure
Linearized Form
Plot P/V vs P: slope = 1/Vm, intercept = 1/(K·Vm)
Surface Area Calculation
Where NA = Avogadro's number, σ = molecular cross-sectional area, Vm,STP = 22,414 cm³/mol
Number of Molecules
Common Adsorbate Properties
| Adsorbate | Cross-section (σ) | Molar Volume | Common Use |
|---|---|---|---|
| Nitrogen (N₂) | 0.162 nm² | 34.7 cm³/mol (77K) | Standard BET analysis |
| Argon (Ar) | 0.138 nm² | 28.5 cm³/mol (87K) | Micropore analysis |
| Krypton (Kr) | 0.195 nm² | 32.2 cm³/mol (77K) | Low surface area samples |
| Xenon (Xe) | 0.218 nm² | 42.7 cm³/mol (165K) | Specialized applications |
| CO₂ | 0.125 nm² | — | Micropore characterization |
How to Calculate Langmuir Surface Area
- Collect adsorption data — Measure volume adsorbed vs pressure at constant temperature.
- Plot linearized form — Plot P/V vs P to get a straight line.
- Determine Vm from slope — Slope = 1/Vm, so Vm = 1/slope.
- Calculate K from intercept — Intercept = 1/(K·Vm), so K = 1/(intercept × Vm).
- Compute surface area — Use S = (Vm × NA × σ) / Vm,STP formula.
Scientific Resources
Frequently Asked Questions
The Langmuir isotherm is used to determine the surface area of porous materials from gas adsorption data. It's essential in catalysis research, materials characterization, pharmaceutical development, and carbon capture studies.
Langmuir assumes monolayer adsorption (one layer of molecules). BET (Brunauer-Emmett-Teller) extends this to multilayer adsorption. Langmuir is better for microporous materials and chemisorption; BET is standard for mesoporous materials and physisorption.
Monolayer capacity (Vm) is the volume of gas (at STP) required to cover the entire surface with exactly one layer of molecules. It's the key parameter for calculating surface area.
Nitrogen (N₂) at 77K is the standard because: it's chemically inert, readily available, has a well-defined cross-sectional area (0.162 nm²), and 77K (liquid N₂ temperature) is easily achieved.
The Langmuir constant (K) relates to the adsorption energy and equilibrium. Higher K means stronger adsorption. It's the ratio of adsorption to desorption rate constants.
For reliable Langmuir analysis, R² should be > 0.99. Values between 0.95-0.99 are acceptable but suggest some deviation. Below 0.95 indicates poor fit — consider other isotherm models.
Use a surface area analyzer (volumetric or gravimetric) at constant temperature. The instrument measures pressure changes as gas adsorbs onto the sample, generating the isotherm data.
The cross-sectional area (σ) is the area occupied by one adsorbed molecule on the surface. For N₂, it's 0.162 nm² (or 16.2 Ų). Different gases have different values based on their molecular size.
The Langmuir model can describe liquid-solid adsorption too, but the parameters and equations differ slightly. This calculator is designed for gas adsorption. For liquid systems, concentration replaces pressure.
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Last Updated: January 2026