Isotherms

Isotherm Equation

Uses and notes

Ref.

One-Parameter Isotherm

Henry’s

q e = K H E C e

Simplest adsorption isotherm

Two-Parameter Isotherm

Hill-Deboer

ln [ C e ( 1 θ ) θ ] θ 1 θ = ln k 1 k 2 θ R T Math_9#

o Defines the case where there is mobile adsorption and lateral interaction and K2 is the energetic constant of the interaction between adsorbed molecules (kJ∙mol−1)

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Fowler- Guggenheim

ln [ C e ( 1 θ ) θ ] = ln k F G + 2 w θ R T Math_11#

o Side contact between adsorbed molecules and the heat of adsorption (w) varies linearly with loading. If attractive, w = positive, repulsive w = negative and w = 0 no interaction between absorbate. But applicable only if θ < 0.6

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Langmuir

q e = q m k L C e 1 + k L C e

C e q e = 1 q m k L + C e q m

R L = 1 1 + k L C o

o Homogeneous binding sites (same affinities), alike sorption energies, and no interactions between adsorbed species. RL is separation aspect which decides whether the adsorption is un-favorable when its value is >1, linear (=1), favourable (0 < RL < 1), and irreversible (RL = 0)

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Freundlich

q e = k f c e 1 / n

log q e = log k F + 1 n log c e

o Heterogonous surfaces(varied affinities), 1/n (adsorption intensity) that specifies the energy and the heterogeneity of the adsorbent sites (1/n < 1= Langmuir, 1/n > 1cooperative adsorption and generally, n in b/n 2 - 10 indicates good favorability of sorption

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