Table 1.

Kinetic model parameters of phosphorus adsorption on alumina adsorbents.

	Parameter	SB-500	GA-1-500	GA-2-500
Pseudo-first-order $\frac{\mathrm{d}{q}_t}{\mathrm{d}t}=k_1\left(q_{\mathrm{e}}-q_t\right)$	qe,exp (mg·g−1)	48.9	99.6	82.3
	qe,cal (mg·g−1)	14.6	2.6	11.3
	k1 (10−2·min−1)	1.13	3.04	3.998
	R2	0.660	0.588	0.852
Pseudo-second-order $\frac{\mathrm{d}{q}_t}{\mathrm{d}t}=k_2{\left(q_{\mathrm{e}}-q_t\right)}^2$	qe,cal (mg·g−1)	49.0	99.7	82.6
	k2 (10−2·g·mg−1·min−1)	0.34	7.03	1.47
	R2	0.998	0.999	0.999

where t is the adsorption time (min); q_e and q_t are the amounts adsorbed at the equilibrium state and at given time t, respectively (mg·g⁻¹); k₁ (min⁻¹) and k₂ (g·mg⁻¹·min⁻¹) represents the rate constants of the pseudo-first-order and pseudo-second-order kinetic adsorption, respectively; q_e,exp and q_e,cal is the experimental and calculated values of q_e.