Table 7.

The kinetics study results corresponding to the data shown in Fig. 10

Model	Type and model equation	Parameter	Time (min)
			0–10	10–30
PFO	Linear ln(qe − qt) = ln(qe) − k1t	K1 (min−1)	0.011	0.002
		qe (mg/g)	36.60	34.17
		R2	0.963	0.838
	Nonlinear $\frac{d{q}_t}{\mathit{dt}}$= k1(qe−qt)	K1 (min−1)	3.207	0.369
		qe (mg/g)	45.90	47.80
		R2	0.589	0.937
PSO	Linear $\frac{t}{\mathit{qe}}=\frac{1}{k_2{q}_e^2}+\frac{1}{q_e}$t	K2 (g.mg−1.min−1)	0.075
		qe (mg/g)	48.31
		R2	1.000
	Nonlinear $\frac{d{q}_t}{\mathit{dt}}$= k2(qe−qt)2	K2 (g.mg−1.min−1)	0.3565	0.049
		qe (mg/g)	46.54	48.67
		R2	0.908	0.976
Elovich	Linear $q_t=\frac{1}{\beta }ln\left(\mathit{\alpha \beta }\right)+\frac{1}{\beta }ln\left(t\right)$	α	3.7 × 1015
		β	0.812
		R2	0.983
	Nonlinear qt= $\frac{1}{\beta }\times ln\left(1+\mathit{\alpha \beta t}\right)$	α	6.9 × 1017	4.9 × 1016
		β	0.930	0.867
		R2	0.909	0.925
WM	Linear qt = KIt0.5 + C	KI	1.127	0.311
		C	43.17	46.27
		R2	0.967	0.993
	Nonlinear qt = KIt0.5 + C	KI	1.127	0.535
		C	43.17	45.17
		R2	0.967	0.883

where q_t is adsorbed quantity at time t; while α and β are initial sorption concentration rate (mg.g⁻¹.min⁻¹) and desorption constant (g/mg), K_I is intraparticle diffusion rate constant (mg.g⁻¹.min^−0.5), and C is boundary thickness effect