CHE-31

Langmuir adsorption

qe = qmax b Ce /(1 + b Ce). Monolayer on uniform sites.

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AdsorptionLangmuir 1918

Governing equation

q_e=q_{\max}\dfrac{b C_e}{1+b C_e}

where

q_{\max}: Monolayer capacity (mmol/g)
b: Affinity b (L/mmol)
C_e: Fluid conc. (mmol/L)
q_e: Solid loading (mmol/g)
\theta: Coverage (—)

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-31 — Langmuir adsorption) is the form associated with Langmuir 1918. Working symbols: $q_{\max}$ , $b$ , $C_e$ $\rightarrow$ $q_e$ , $\theta$ . Langmuir balanced adsorption and desorption on a finite number of identical sites, giving a hyperbolic isotherm that saturates at qmax.

Purpose

Purpose: compute

q_e

\theta

from

q_{\max}

b

C_e

in Chemical engineering via

q_e=q_{\max}\dfrac{b C_e}{1+b C_e}

qe = qmax b Ce /(1 + b Ce). Monolayer on uniform sites. Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

q_{\max} = 2.500\,\mathrm{mmol/g}

b = 0.800\,\mathrm{L/mmol}

C_e = 1.200\,\mathrm{mmol/L}

, the governing relation

q_e=q_{\max}\dfrac{b C_e}{1+b C_e}

yields

q_e = 1.224\,\mathrm{mmol/g}

\theta = 0.490\,\mathrm{—}

. A surface of sites, a filling fraction θ. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Monolayer capacity q_{\max}2.5 mmol/gAffinity b b0.8 L/mmolFluid conc. C_e1.2 mmol/L

Outputs

Solid loading q_e1.224 mmol/g
Coverage \theta0.490 —

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Narration of this film

A surface of sites, a filling fraction θ.

Langmuir balanced adsorption and desorption on a finite number of identical sites, giving a hyperbolic isotherm that saturates at qmax.

Reading speed

Watch on YouTube