. 2026 Feb 4;16:7316. doi: 10.1038/s41598-026-36097-x

Table 5.

Kinetic model parameters for MG adsorption.

Model	Plot	Parameters	Values
First-order-kinetic	ln (q _e − q _t ) vs. t	k₁ (min⁻¹)	0.424
		q_{e (calc)} (mg g⁻¹)	184.0
		R²	0.869
Pseudo-second-order-kinetic	t/q_t vs. t	k₂ (min⁻¹)	0.005
		q_{e (calc)} (mg g⁻¹)	78.61
		R²	0.997
		h (mg g⁻¹ min⁻¹)	31.82
Intraparticle diffusion	q_t vs. t^1/2	K_diff (mg g⁻¹ min^−1/2)	10.08
		C (mg g⁻¹)	28.24
		R²	0.946
Elovich	q_t vs. ln t	β (g mg⁻¹)	115.2
		α (mg g⁻¹ min⁻¹)	0.072
		R²	0.973
Experimental data		q_{e (exp)} (mg g⁻¹)	69.19