Table 3.

Fitted kinetic parameters of pseudo-first-order, pseudo-second-order, Elovich, and intra-particle diffusion models for adsorption of Cr(III) ions onto the Cr(III)-IIM at concentration 5 mg/L, pH 6, temperature 40 °C, and adsorbent dose (one membrane) 0.140 g.

Model	Parameters	Values
Pseudo-first-order model	k1 (1/h)	0.07529
	qe,calc * (mg/g)	0.4496
	R 2	0.9694
Pseudo-second-order model	k2 (g/(mg∙h))	0.07234
	qe,calc * (mg/g)	0.6974
	R 2	0.9626
Elovich equation	α (mg/(g∙h))	0.09449
	β (g/mg)	8.1739
	R 2	0.9331
Intra-particle diffusion model Region 1	ki (mg/(g∙h0.5)	0.1034
	Ci (mg/g)	−0.09989
	R 2	0.9558
Intra-particle diffusion model Region 2	ki (mg/(g∙h0.5)	0.03459
	Ci (mg/g)	0.1892
	R 2	0.8710

* q_e,_exp = 0.3521 mg/g.