. 2023 Jun 16;30(34):82387–82405. doi: 10.1007/s11356-023-27688-6

Table 5.

Calculated parameters for four kinetic models, including pseudo-first-order (PFO), pseudo-second-order (PSO), Elovich, and Weber–Morris (WM)

Models	Parameter	Value
Models	Parameter	PRO	PMT
Pseudo-first order (PFO) $\frac{d q_{t}}{dt}$ = k₁(q_e−q_t)	K₁ (min⁻¹)	2.054	1.832
	q_e (mg/g)	75.29	74.07
	R²	0.4337	0.7188
Pseudo-second order (PSO) $\frac{d q_{t}}{dt}$ = k₂(q_e−q_t)²	K₂ (g.mg⁻¹.min⁻¹)	0.069	0.064
	q_e(mg/g)	76.95	75.68
	R²	0.7746	0.9628
Elovich model q_t = $\frac{1}{β} \times l n (1 + α β t)$	α	3.00 × 10¹⁰	1.67 × 10¹¹
	β	0.34	0.374
	R²	0.9855	0.8794
Weber − Morris model (WM) $q_{t} = K_{I} t^{0.5} + C$	K_I	1.420	1.177
	C	68.60	68.13
	R²	0.8542	0.6245

where K₂ is rate constant (g.mg⁻¹.min⁻¹) and 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