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. 2025 Jan 23;11(3):e42162. doi: 10.1016/j.heliyon.2025.e42162

Table 2.

Kinetic parameters of Cr (VI) adsorption on AC obtained from SCB.

Model	Non-Linear Model			Cr (VI)
Pseudo First Order (PFO)	$q_{t} = q_{e} (1 - e^{- k 1 ∙ t})$		q₁ (mg g⁻¹)	10.45
			K₁ (min⁻¹)	0.187
			R₁²	0.5621
Pseudo Second Order (PSO)	$q_{t} = \frac{q_{2}^{2} k_{2} t}{q_{e} k_{2} t + 1}$		q₂ (mg g⁻¹)	11.12
			K₂ (g mg⁻¹•min⁻¹)	0.02
			R₂²	0.7013
Elovich	$q = (\frac{1}{β}) Ln (1 + α β t)$		α (mg g⁻¹)	5.76
			β (g mg⁻¹•min⁻¹)	0.55
			R_E²	0.8832
Weber and Morris	$q = k_{i n} t^{0.5} + C$	Region I	K_in,1 (mg g⁻¹ min^−1/2)	0.24
			C (mg g⁻¹)	5.33
			R²	0.9362
		Region II	K_in,2 (mg g⁻¹ min^−1/2)	1.14
			C (mg g⁻¹)	–
			R²	0.9996
		Region III	K_in,3 (mg g⁻¹ min^−1/2)	0.05
			C (mg g⁻¹)	12.17
			R²	0.9219