Table 6.

General and linarized equation of Langmuir, Freudlich, Temkin, Dubinin Radushkevich, and Hasley isothems, beside their parameters for adsorption of Cu(II) on BDP.

Isotherm	Equations (generalized/linearized forms)	Curve segments
		Parameters	(I)	(II)	(III)
Langmuir	$q_e=\frac{q_m{K}_L{C}_e}{1-K_L{C}_e}$	qm(mg/g)	4.036	–	−0.885
		KL(L.mole−1)	83.3 × 103	–	−1.4 × 103
	$\frac{C_e}{q_e}=\frac{1}{q_m{K}_L}+\frac{C_e}{q_m}$	ΔGad(kJ.mole−1)	−28.07	–	+17.89
		R2	0.913	–	0.997
Freundlich	$q_e=K_F{C}_e^{\frac{1}{n}}$	1/n	–	–	2.488
			–	–	141.3
	$log(q_e)=log(K_F)+\left(\frac{1}{n}\right)log(C_e)$	$K_F(mole/g){(L/mole)}^{1/n}$
		R2	–	–	0.992
Temkin	$q_e=\frac{RT}{b_T}ln(A_T{C}_e)$	bT(J/mole)	20.41	−21.05	0.77
		AT (L/mole)	7.4 × 1012	2.7 × 103	8.4 × 105
	$q_e=\frac{RT}{b_T}ln(A_T)+\frac{RT}{b_T}ln(C_e)$	R2	0.404	0.0.326	0.919
DR	$ln(q_e)=\ln \left(q_m\right)-\beta {ϵ}^2$	β	1.37 × 10−8	1.52 × 10−9	3.63 × 10−8
	$ϵ=RT(1+\frac{1}{C_e})$	E(kJ/mole)	6.04I	18.17II	3.71IV
		qs(mg.g)	7.83 × 103	1.15 × 10−4	1.12 × 103
	$E=\frac{1}{\sqrt{2\beta }}$	R2	0.388	0.629	0.949

I, II, and IV refers to the energy of segments (I, II, and IV) of DR isotherm, respectively. While the data for segment (III)β, E, q_s, and R²are 3.06 × 10⁻⁹,−12.77, 1.79 × 10⁻⁶, and 0.216, respectively.