Equation
Plot
Langmuir model
Ce
q e
¼
1
q 0 b þ
Ce
q 0
C e (mg/L): equilibrium conc. of adsorbate
q e (mg/g): amount of adsorbate adsorbed onto
biosorbent at equilibrium.
q 0 (mg/g): adsorption capacity of adsorbent for adsorbate.
b (L/mg): Langmuir isotherm constant
Freundlich model
ln q e
ð Þ ¼ ln K f
À Á þ
1
n ln C e
ð Þ
K f (mg
1-(1/n) L
1/n g
À1
): Freundlich isotherm constant
n: Freundlich exponent
Redlich–Peterson (R-P) model
ln K RP
Ce
q e
À 1
¼ ln a RP
ð Þþg ln C e
ð Þ
K RP (g/L): Redlich–Peterson isotherm constant
a RP (L/mg): Redlich–Peterson constant
g: Redlich–Peterson exponent (values between 0 and
1)
Dubinin–Radushkevich (DR) model
ln(q e ) ¼ ln (X m ) À βε
2
ε ¼ RT ln 1 þ
1
Ce
E ¼
1
À2β
1
2
X m (mg/g): maximum adsorption capacity
β (KJ
2 mol
2
): activity constant
ε: Polyani potential
E (KJ/mol): mean free energy of adsorption
(continued)
254
K. J. Samuel P N et al.