Kinetic adsorption models based on reaction kinetics^a.

Models	Equation in batch system	Half time of adsorption	Eq. number
PFO		t 0.5 = ln 2/k1	(6)
PSO		t 0.5 = 1/k2qe	(7)
BSf (n,a)			(8)
Weibull n = 1		t 0.5 = τ1,a(ln 2)1/a	(9)
Hill n = 2		t 0.5 = τ2,a	(10)
PFOf			(11)
PSOf			(12)

^aWhere q_e and q_t represent the uptake at equilibrium and at time t (mg g⁻¹), t is the contact time in the batch system. k₁ (min⁻¹), k_1f (min^−(1−h)) and k₂ (g mg⁻¹ min⁻¹), k_2f (g mg⁻¹ min^−(1−h)) are the rate sorption constants of the PFO and PSO canonical and fractal models, respectively. τ_n,α, τ_1,α, and τ_2,α (min) are the characteristic times of the process for the BSf, Weibull and Hill models, respectively, α is the fractional time index, h is the fractal exponent, and n is the rate order.