ENV-29

Freundlich isotherm

qe = Kf Ce^{1/n}. Empirical adsorption on heterogeneous sites.

Reading speed

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: Equilibrium conc. (mg/L)
q_e: Solid loading (mg/g)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

q_e=K_f C_e^{1/n}

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

$C_e = 0.05$ $q_e = 2.05$

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}

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

$C_e = 0.05$ $q_e = 2.05$

Along the curve

④

Rate of change — amber

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

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

$C_e = 0.553$ $q_e^{\prime} = 6.115$

Along the curve

Lecture brief

Historical brief

Streeter–Phelps (1925) oxygen sag, settling theory and Guldberg–Waage kinetics made water and air quality a rate problem. The lab computes sag, overflow and a snapshot of reactor mass balance. This sheet (ENV-29 — Freundlich isotherm) is the form associated with Freundlich 1906. Working symbols: $K_f$ , $n$ , $C_e$ $\rightarrow$ $q_e$ . Freundlich's power law is the log-linear fit of batch adsorption data. 1/n < 1 is favourable.

Purpose

Purpose: compute

q_e

from

K_f

n

C_e

in Environmental via

q_e=K_f C_e^{1/n}

qe = Kf Ce^{1/n}. Empirical adsorption on heterogeneous sites. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

K_f = 8.000\,\mathrm{(mg/g)(L/mg)^1/n}

n = 2.200\,\mathrm{—}

C_e = 5.000\,\mathrm{mg/L}

, the governing relation

q_e=K_f C_e^{1/n}

yields

q_e = 16.627\,\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_f8 (mg/g)(L/mg)^{1/n}Freundlich n n2.2 —Equilibrium conc. C_e5 mg/L

Outputs

Solid loading q_e16.627 mg/g

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A carbon grain, a solute, a loading bar.

Freundlich's power law is the log-linear fit of batch adsorption data. 1/n < 1 is favourable.

Reading speed

Watch on YouTube