Table 1.

Calculated parameters for kinetic models via linear and nonlinear regression.

C0 (mg/L)	qe(exp)	Pseudo-first-order				Pseudo-second-order				Intra-particle diffusion
		Linear regression
		$\mathbf{ln}\left({\mathit{q}}_{\mathit{e}}-{\mathit{q}}_{\mathit{t}}\right)=\mathbf{ln}{\mathit{q}}_{\mathit{e}}-{\mathit{k}}_1\mathit{t}$				$\frac{\mathit{t}}{{\mathit{q}}_{\mathit{t}}}=\frac{1}{{\mathit{k}}_2{\mathit{q}}_{\mathit{e}}^2}+\frac{\mathit{t}}{{\mathit{q}}_{\mathit{e}}}$				${\mathit{q}}_{\mathit{t}}={\mathit{k}}_{\mathit{p}}{\mathit{t}}^{\frac{1}{2}}+\mathit{C}$
		qe(cal)	k1	R2	Δq	qe(cal)	k2	R2	Δq	kp	C
1	1.99	0.61	0.003	0.66	3.85	2.01	0.029	1.00	0.90	0.030	0.875
5	6.34	1.85	0.004	0.55	3.27	5.85	1.476	0.998	1.03	0.067	3.541
10	10.44	4.64	0.002	0.76	3.22	10.46	0.004	1.00	0.48	0.150	4.312
		Nonlinear regression
1	1.99	1.97	0.029	0.98	0.34	2.08	0.020	0.981	0.17	-	-
5	6.34	5.87	0.067	0.99	0.06	6.16	0.016	0.992	0.15	-	-
10	10.44	9.59	0.048	0.91	0.25	10.13	0.007	0.984	0.20	-	-

Note: k₁ pseudo-first-order rate constant (min⁻¹); t time (min); q_e and q_t phosphate adsorbed per adsorbent mass at equilibrium and at time t (mg/g); k₂ pseudo-second-order rate constant (g/mg·min); k_p intraparticle diffusion constant (mg/g·min^1/2); C boundary layer thickness constant (mg/g).