Non-linear equation



q e = K F C e 1 / n

KF (mg∙g−1)(L∙mg−1)1/n: Freundlich adsorption constant n (dimensionless): empirical parameter representing the energetic heterogeneity of surface

qe (mg∙g−1): equilibrium adsorbed quantity


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

qm (mg∙g−1): monolayer adsorption capacity

Ce (mg∙L−1): equilibrium concentration

KL (L∙mg−1): equilibium adsorption constant


q e = q s exp ( k a d [ R T ln ( 1 + 1 C e ) ] 2 )

qs: maximum adsorbed amount

R (8.314 J∙mol−1K−1): gas constant

T (K): temperature


q t = q e [ 1 exp ( k 1 t ) ]

qt (mg∙g−1): adsorbed quantity at time t

t (min): contact time

k1 (min−1): pseudo-fist order rate constant


q t = q e 2 k 2 t 1 + q e k 2 t

k2 (−1∙min−1): pseudo-fist order rate constant

Intraparticular diffusion

q t = k i p t 2 + C i

Kip (mg∙g−1∙min1/2): intraparticle diffusion rate constant

Ci: constant value depicting the boundary layer effect