Table 1.

Linear and non-linear isotherm equation

Isotherm	Non-Linear equation	Linear equation
Langmuir-1		$\frac{{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{q}}_{\mathrm{e}}}=\frac{{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{q}}_{\mathrm{m}}}+\frac{1}{{\mathrm{bq}}_{\mathrm{e}}}$
Langmuir-2	${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{q}}_{\mathrm{m}}{\mathrm{bC}}_{\mathrm{e}}}{1+{\mathrm{bC}}_{\mathrm{e}}}$	$\frac{1}{{\mathrm{q}}_{\mathrm{e}}}=\left(\frac{1}{{\mathrm{bq}}_{\mathrm{m}}}\right)\frac{1}{{\mathrm{C}}_{\mathrm{e}}}+\frac{1}{{\mathrm{q}}_{\mathrm{m}}}$
Langmuir-3		${\mathrm{q}}_{\mathrm{e}}={\mathrm{q}}_{\mathrm{m}}-\left(\frac{1}{\mathrm{b}}\right)\frac{{\mathrm{q}}_{\mathrm{e}}}{{\mathrm{C}}_{\mathrm{e}}}$
Langmuir-4		$\frac{{\mathrm{q}}_{\mathrm{e}}}{{\mathrm{C}}_{\mathrm{e}}}={\mathrm{bq}}_{\mathrm{m}}-{\mathrm{bq}}_{\mathrm{e}}$
Freundlich	${\mathrm{q}}_{\mathrm{e}}={\mathrm{K}}_{\mathrm{F}}{\mathrm{C}}_{\mathrm{e}}^{1/\mathrm{n}}$	$log\left({\mathrm{q}}_{\mathrm{e}}\right)=log\left({\mathrm{K}}_{\mathrm{F}}\right)+\frac{1}{\mathrm{n}}log\left({\mathrm{C}}_{\mathrm{e}}\right)$
Redlich-Peterson	${\mathit{q}}_{\mathit{e}}=\frac{{\mathit{K}}_{\mathit{Rp}}{\mathit{C}}_{\mathit{e}}}{\left[1+{\mathit{\alpha }}_{\mathit{RP}}{\left({\mathit{C}}_{\mathit{e}}\right)}^{\mathit{\beta }}\right]}$	$ln\left(\frac{{\mathrm{K}}_{\mathrm{RP}}}{{\mathrm{q}}_{\mathrm{e}}}-1\right)=\mathrm{\beta ln}\left({\mathrm{C}}_{\mathrm{e}}\right)+ln\left({\mathrm{\alpha }}_{\mathrm{RP}}\right)$