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Langmuir Isotherm Calculator

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

100.0%
Surface Coverage
1.0000
Coverage Fraction (θ)
Saturation Region
Adsorption Regime
Plateau region
System Behavior
Maximum surface utilization
Surface Efficiency

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)

Keq = 0.00001 pa-1, P = 101325 pa

CO₂ on MOF

Carbon dioxide on metal-organic framework

Application: Carbon capture

Keq = 0.00005 pa-1, P = 100000 pa

H₂ on Pt Surface

Hydrogen on platinum catalyst

Application: Heterogeneous catalysis

Keq = 0.0001 pa-1, P = 101325 pa

Protein on Silica

Protein adsorption from solution

Application: Chromatography

Keq = 1000 m-1, P = 0.001 pa

Dye on Activated Carbon

Organic dye removal from water

Application: Water treatment

Keq = 500 m-1, P = 0.01 pa
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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

Monolayer Adsorption
Only one layer of molecules
Uniform Surface
Homogeneous adsorption sites
No Lateral Interactions
Molecules don't interact
Ideal Gas Behavior
Gas phase ideality

Other Isotherm Models

BET Isotherm
Multilayer adsorption
Freundlich Isotherm
Heterogeneous surfaces
Temkin Isotherm
Heat of adsorption varies
Dubinin-Radushkevich
Microporous materials

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.

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