Langmuir Isotherm Calculator
Calculate surface coverage and adsorption isotherms using the Langmuir adsorption model
Calculate Langmuir Adsorption
Adsorption equilibrium constant
Gas partial pressure
Langmuir Isotherm Results
Langmuir Equation: θ = (Keq × P) / (1 + Keq × P)
Calculation: (1.000e+0 × 101325) / (1 + 1.000e+0 × 101325) = 1.0000
Analysis: Near-complete monolayer formation, minimal additional adsorption
Common Adsorption Systems
N₂ on Activated Carbon
Nitrogen adsorption at 77K
Application: Surface area measurement (BET)
CO₂ on MOF
Carbon dioxide on metal-organic framework
Application: Carbon capture
H₂ on Pt Surface
Hydrogen on platinum catalyst
Application: Heterogeneous catalysis
Protein on Silica
Protein adsorption from solution
Application: Chromatography
Dye on Activated Carbon
Organic dye removal from water
Application: Water treatment
Coverage Interpretation
θ < 0.1 (Low)
Henry's law region
Linear response to pressure
0.1 ≤ θ < 0.5
Intermediate coverage
Non-linear adsorption
0.5 ≤ θ < 0.9
High coverage
Approaching saturation
θ ≥ 0.9 (High)
Near saturation
Monolayer formation
Langmuir Model Assumptions
Other Isotherm Models
Understanding the Langmuir Isotherm
What is Adsorption?
Adsorption is the process by which molecules, atoms, or ions from a gas, liquid, or dissolved solid adhere to the surface of a solid or liquid (adsorbent). The Langmuir isotherm describes this process for monolayer adsorption on homogeneous surfaces.
Key Concepts
- •Adsorbate: The substance being adsorbed
- •Adsorbent: The surface or material doing the adsorbing
- •Surface Coverage (θ): Fraction of surface sites occupied
- •Equilibrium Constant: Measure of adsorption affinity
Langmuir Equation
θ = (Keq × P) / (1 + Keq × P)
- θ: Surface coverage fraction (0-1)
- Keq: Equilibrium adsorption constant
- P: Partial pressure (gas) or concentration (liquid)
Linearized Forms
P/θ = 1/Keq + P
1/θ = 1 + 1/(Keq × P)
Applications and Importance
Catalysis
Understanding reactant adsorption on catalyst surfaces for optimizing reaction conditions.
Environmental
Designing adsorbents for pollution control, water treatment, and air purification systems.
Material Science
Characterizing surface properties and predicting material behavior in various applications.