Insight into the Influence of the Integrated Chitosan on the Adsorption Properties of Chitosan/Al-MCM-41 Composite for As (V) Metal Ions: Characterization and Advanced Equilibrium Studies

Table 1

The theoretically obtained mathematical parameters of the evaluated kinetic models, classic isotherm models, and advanced isotherm models.

Materials	Models	Parameters	Values
Kinetic models
Al-MCM	Pseudo-first-order	K1 (1/min)	0.0046
		Qe(Cal) (mg/g)	69.8
		R^2	0.96
		X^2	1.122
	Pseudo-second-order	K2 (1/min)	4.1 × 10^−5
		Qe(Cal) (mg/g)	92.4
		R^2	0.94
		X^2	1.69
CH/Al-MCM	Pseudo-first-order	K1 (1/min)	0.0047
		Qe(Cal) (mg/g)	106
		R^2	0.97
		X^2	1.003
	Pseudo-second-order	K1 (mg/min)	2.83 × 10^–5
		Qe(Cal) (mg/g)	140.3
		R^2	0.95
		X^2	1.74
			293 K	303 K	313 K
Parameters of the classic isotherm models
		Qmax (mg/g)	125.4	90.7	82.8
Al-MCM	Langmuir model
		B (L/mg)	0.0054	0.00188	0.0011
		R^2	0.95	0.93	0.93
		X^2	0.98	1.65	1.43
	Freundlich model	1/n	0.56	0.80	0.89
		kF (mg/g)	4.64	0.83	0.41
		R^2	0.88	0.90	0.91
		X^2	2.22	2.4	2.02
	D-R model	β (mol^2/kJ^2)	0.0236	0.021	0.0177
		Qm (mg/g)	113	83.5	72
		R^2	0.97	0.96	0.96
		X^2	0.57	0.84	0.85
		E (kJ/mol)	4.6	4.87	5.3
CH/Al-MCM	Langmuir model	Qmax (mg/g)	202.6	183.2	102.5
		B (L/mg)	0.0069	0.004	0.0035
		R^2	0.95	0.90	0.91
		X^2	1.47	2.7	1.82
	Freundlich model	1/n	0.5	0.64	0.66
		kF (mg/g)	7.41	2.87	1.77
		R^2	0.86	0.84	0.85
		X^2	3.4	4.37	2.92
	D-R model	β (mol^2/kJ^2)	0.063	0.048	0.025
		Qm (mg/g)	169.2	113.5	82
		R^2	0.97	0.99	0.99
		X^2	0.68	0.15	0.19
		E (kJ/mol)	2.8	3.2	4.4
Steric and energetic parameters of the advanced isotherm model
Al-MCM		R^2	0.998	0.996	0.997
		N	2.02	2.25	2.31
		Nm (mg/g)	61.53	40.43	33.54
		QSat (mg/g)	124	91.2	77.8
		C1/2 (mg/L)	84.88	116.03	129.03
		ΔE (kJ/mol)	−16.03	−15.78	−16.03
CH/Al-MCM		R^2	0.996	0.994	0.997
		N	2.01	2.66	2.54
		Nm (mg/g)	88.86	46.69	38.3
		QSat (mg/g)	178.6	124.2	98.5
		C1/2 (mg/L)	74.15	83.7	89.58
		ΔE (kJ/mol)	−16.36	−16.6	−16.98