Table 1 Kinetics model constants and determination coefficients and standard error of estimate for Pb(II) adsorption by bentonite and composite sorbents.

Models	Parameter	Bentonite	Nano-composite
Elovich q_t = (1/β) ln(α β) + (1/β) lnt	α (mg g⁻¹ min⁻¹)	1.15E+20	1.25E+90
	β (mg g⁻¹)	0.0010	0.0041
	R²	0.723	0.974
	SE	1081.751	8.198
First order ln (q_ο − q) = a − k_a t	K_d (min⁻¹)	− 0.0082	− 0.003
	a (µg g⁻¹)	8.193	4.847
	R²	0.794	0.955
	SE	2.365	0.163
Parabolic diffusion q = a + k_at^1/2	K_d (µg g⁻¹ min^−1/2)	109.21	3.5773
	a (μg g⁻¹)	40,501	49,865
	R²	0.450	0.923
	SE	1657	14.23
Power function q = k_a C_o t^1/m	K_a (min⁻¹)	36.98 × 10³	50.79 × 10³
	1/m	0.0233	0.0005
	R²	0.932	0.956
	SE	0.0012	0.0004

q or q_t = Pb adsorbed (mg kg⁻¹) at time t, q_o = Pb adsorbed (mg kg⁻¹) at equilibrium, k_a = apparent sorption rate coefficient, α = the initial adsorption rate (mg g⁻¹ min⁻¹), β = a constant related to the extent of surface coverage (mg g⁻¹), a = a constant; k_d = apparent diffusion rate coefficient, q = adsorbed Pb (mg kg⁻¹), C_ο = initial Pb concentration (mg L⁻¹), t = reaction time (min), k_a = sorption rate coefficient (min⁻¹), and 1/m = constant. R₂ = determination coefficient, SE standard error of estimate.

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