Table 7.

General and linearized equation of Langmuir, Freundlich, Temkin and Dubinin-Radushkevich isotherms, beside their parameters for the adsorption of SARA on RPNS.

Isotherm	Equations (Generalized/ Linearized Forms)	Parameters	Value
Langmuir	$q_e=\frac{q_m K_L C_e}{1-K_L C_e}$ $\frac{C_e}{q_e}=\frac{1}{q_m K_L}+\frac{C_e}{q_m}$	$q_m$ (mg/g)	49.75
		$K_L$ (L·mole−1)	0.0314
		R2	0.975
Freundlich	$q_e=K_F{C}_e^{\frac{1}{n}}$ $\log \left(q_e\right)=\log \left(K_F\right)+\left(\frac{1}{n}\right)\log \left(C_e\right)$	$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.$	0.651
		$K_F$ (mole/g) (L/mole)1/n	2.509
		R2	0.9785
Temkin	$q_e=\frac{RT}{b_T} \ln \left(A_T C_e\right)$ $q_e=\frac{RT}{b_T}\ln \left(A_T\right)+\frac{RT}{b_T}\ln \left(C_e\right)$	$b_T$ (J/mole)	250.0	45.54
		$A_T$ (L/mole)	0.389	0.025
		R2	0.964	0.984
DR	$\ln (q_e)=\ln \left(q_m\right)-\beta {ϵ}^2$	$\beta$	1.7 × 10−8	1.98 × 10−9
	$ϵ=RT\left(1+\frac{1}{C_e}\right)$	$E$ (kJ/mole)	5.423	15.891
		$q_m$ (mg/g)	48.04	6.23
	$E=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2\beta }$}\right.$	R2	0.984