Table 4.

Sorption isotherms and their non-linear and linear forms with corresponding plots.

Isotherm	Non linear	Linear	Parameters	Plot
Freundlich	$q_e=K_F{C}_e^{1/n}$	$log\left(q_e\right)=log{K}_F+\frac{1}{n}log\left(C_e\right)$	KF (mg g−1): sorption capacity 1/n: intensity of sorption Ce (mg L−1): equilibrium concentration qe (mgg−1): sorption capacity	$\mathit{log}\left(q_e\right)$ vs $log\left(C_e\right)$
Langmuir	$q_e=\frac{Q_{\mathit{max}}{K}_L{C}_e}{1+K_L{C}_e}$	$\frac{C_e}{q_e}=\frac{1}{Q_{\mathit{max}}{K}_L}+\frac{C_e}{Q_{\mathit{max}}}$ $R_L=\frac{1}{1+K_L{C}_o}$	Qmax (mg g−1): maximum monolayer sorption capacity KL (L mg−1): constant related with sorption energy RL: separation factor Co (mg L−1): Initial concentration	$\frac{C_e}{q_e}$ vs $C_e$
Temkin	$q_e=\left(\frac{\mathit{RT}}{b_T}\right)ln{K}_T{C}_e$	$q_e=RTln{K}_T+\frac{\mathit{RT}}{b_T}ln{C}_e$	bT (J mol−1): constant related with heat of sorption KT (L g−1): Temkin isotherm constant	$q_e$ vs $ln{C}_e$
D-R	$q_e=q_{d}exp\left(-,\beta ,{\epsilon }^2\right)$	${\mathit{lnq}}_e=ln{q}_d-\beta {\epsilon }^2$ $\epsilon =RTln\left[1,+,\frac{1}{C_e}\right]$ $E=\frac{1}{\sqrt{2\beta }}$	β (mol2/kJ2): constant related with free energy qd (mg g−1): maximum sorption capacity ε: Polanyi potential R (Jmol−1 K−1): gas constant T (K): temperature E (kJ mol−1): mean sorption energy	$ln{q}_e$ vs ${\epsilon }^2$