CHE-30

Freundlich adsorption

qe = Kf Ce^{1/n}. Heterogeneous-site isotherm used in adsorbers.

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AdsorptionFreundlich 1906

Governing equation

q_e=K_f C_e^{1/n}

$C_e \in \left[0.05, 80\right]$

where

K_f: Freundlich Kf ((mg/g)(L/mg)^{1/n})
n: Freundlich n (—)
C_e: Fluid conc. (mg/L)
q_e: Solid loading (mg/g)

The figure, part by part

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①

Governing law — red

q_e=K_f C_e^{1/n}

$C_e \in \left[0.05, 80\right]$

$C_e = 0.05$ $q_e = 3.444$

Along the curve

②

Domain of the variable — blue

C_e_{\min} = 0.05,\quad C_e_{\max} = 80

$C_e \in \left[0.05, 80\right]$

$C_e = 0.05$ $C_e = 0.05$

Along the curve

③

Response curve — green

q_e=K_f C_e^{1/n}

$C_e \in \left[0.05, 80\right]$

$C_e = 0.05$ $q_e = 3.444$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}q_e}{\mathrm{d}C_e}

$C_e \in \left[0.05, 80\right]$

$C_e = 0.553$ $q_e^{\prime} = 8.78$

Along the curve

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-30 — Freundlich adsorption) is the form associated with Freundlich 1906. Working symbols: $K_f$ , $n$ , $C_e$ $\rightarrow$ $q_e$ . A log–log fit of loading versus residual concentration. 1/n < 1 is favourable for packed-bed adsorption.

Purpose

Purpose: compute

q_e

from

K_f

n

C_e

in Chemical engineering via

q_e=K_f C_e^{1/n}

qe = Kf Ce^{1/n}. Heterogeneous-site isotherm used in adsorbers. 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

K_f = 12.000\,\mathrm{(mg/g)(L/mg)^1/n}

n = 2.400\,\mathrm{—}

C_e = 8.000\,\mathrm{mg/L}

, the governing relation

q_e=K_f C_e^{1/n}

yields

q_e = 28.541\,\mathrm{mg/g}

. A carbon grain, a solute, a loading bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Freundlich Kf K_f12 (mg/g)(L/mg)^{1/n}Freundlich n n2.4 —Fluid conc. C_e8 mg/L

Outputs

Solid loading q_e28.541 mg/g

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Narration of this film

A carbon grain, a solute, a loading bar.

A log–log fit of loading versus residual concentration. 1/n < 1 is favourable for packed-bed adsorption.

Reading speed

Watch on YouTube