CHM-15

Langmuir isotherm

θ = K p / (1 + K p). Monolayer coverage vs pressure.

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SurfacesLangmuir 1918

Governing equation

\theta=\dfrac{Kp}{1+Kp}

where

K: Langmuir K (1/kPa)
p: Pressure (kPa)
\theta: Coverage (—)

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-15 — Langmuir isotherm) is the form associated with Langmuir 1918. Working symbols: $K$ , $p$ $\rightarrow$ $\theta$ . Adsorption sites equivalent and independent. Half coverage at p = 1/K.

Purpose

Purpose: compute

\theta

from

K

p

in Physical chemistry via

\theta=\dfrac{Kp}{1+Kp}

θ = K p / (1 + K p). Monolayer coverage vs pressure. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

K = 0.500\,\mathrm{1/kPa}

p = 2.000\,\mathrm{kPa}

, the governing relation

\theta=\dfrac{Kp}{1+Kp}

yields

\theta = 0.5000\,\mathrm{—}

. Single-site Langmuir, no lateral interactions. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Langmuir K K0.5 1/kPaPressure p2 kPa

Outputs

Coverage \theta0.5000 —

Reading speed

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Narration of this film

Single-site Langmuir, no lateral interactions.

Adsorption sites equivalent and independent. Half coverage at p = 1/K.

Reading speed

Watch on YouTube