Advanced Topic 322 of 1102 States of Matter & Solutions
Langmuir Isotherm
A model of monolayer adsorption on a fixed number of equivalent surface sites.
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In-depth explanation of Langmuir Isotherm
The Langmuir isotherm is a theoretical model describing monolayer adsorption on a surface with a fixed number of identical adsorption sites. Each site holds at most one molecule, and adsorbed molecules do not interact with their neighbours. The fractional coverage is given by θ = KP/(1 + KP), where K is the adsorption equilibrium constant. At low pressure the coverage is approximately proportional to pressure, while at high pressure the surface becomes saturated and the coverage approaches one. The model is the basis for understanding surface reaction kinetics in heterogeneous catalysis.
Going deeper: Langmuir Isotherm
Key ideas: Linear form: P/(x/m) = 1/(K a) + P/a, where a is the monolayer capacity, so a plot of P/(x/m) against P gives slope 1/a. Equivalent: 1/theta = 1 + 1/(KP). At low P, theta is about KP; at high P, theta tends to 1. For dissociative adsorption, theta = sqrt(KP) / (1 + sqrt(KP)).
Common mistakes and connections: Students apply Langmuir to multilayer adsorption, which is the BET model. Another mistake is assuming K is independent of temperature; K decreases with T for exothermic adsorption. Assumptions include a uniform surface and no interactions. Links to Freundlich, BET surface area, surface catalysis and Langmuir-Hinshelwood kinetics.
Visualization of Langmuir Isotherm
Langmuir isotherm: monolayer coverage rises with pressure then plateaus at theta = 1 when every site is occupied. The interactive lesson shows this as a live animation or chart.
Worked example and use case
Carbon monoxide adsorbing on a platinum surface follows the Langmuir isotherm, with coverage approaching saturation at high pressure.
Frequently asked questions about Langmuir Isotherm
What is Langmuir Isotherm?
A model of monolayer adsorption on a fixed number of equivalent surface sites.
Is Langmuir Isotherm a beginner, intermediate or advanced topic?
Langmuir Isotherm is a advanced topic in States of Matter & Solutions. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Langmuir Isotherm?
Study these earlier topics in States of Matter & Solutions first: Gels and Sols, Adsorption, Freundlich Isotherm.
What comes after Langmuir Isotherm?
The next topics in States of Matter & Solutions are Coagulation and Hardy-Schulze Rule.
Can I practise Langmuir Isotherm with quizzes?
Yes. The interactive lesson includes a self-check question on Langmuir Isotherm, and the States of Matter & Solutions quiz draws on every topic in this area.
Where Langmuir Isotherm fits in States of Matter & Solutions
Langmuir Isotherm is topic 103 of 109 in States of Matter & Solutions.