Table 3 Isotherm mathematical model equations used for adsorption data analysis

Langmuir

${\mathit{q}}_{\begin{array}{l}\mathit{e}\end{array}}=\frac{\left({\mathit{q}}_{\begin{array}{l}max\end{array}}{\mathit{K}}_{\begin{array}{l}\mathit{L}\end{array}}{\mathit{C}}_{\begin{array}{l}\mathit{e}\end{array}}\right)}{\left(1+{\mathit{K}}_{\begin{array}{l}\mathit{L}\end{array}}{\mathit{C}}_{\begin{array}{l}\mathit{e}\end{array}}\right)}·$

$\frac{1}{{\mathit{q}}_{\begin{array}{l}\mathit{e}\end{array}}}=\left(\frac{1}{{\mathit{K}}_{\begin{array}{l}\mathit{L}\end{array}}{\mathit{q}}_{\begin{array}{l}max\end{array}}}\right)\frac{1}{{\mathit{C}}_{\begin{array}{l}\mathit{e}\end{array}}}+\frac{1}{{\mathit{q}}_{\begin{array}{l}max\end{array}}}·$

$\frac{1}{{\mathit{q}}_{\begin{array}{l}\mathit{e}\end{array}}}\mathit{vs}.\frac{1}{{\mathit{C}}_{\begin{array}{l}\mathit{e}\end{array}}}$

Freundlich

${\mathit{q}}_{\begin{array}{l}\mathit{e}\end{array}}={\mathit{K}}_{\begin{array}{l}\mathit{F}\end{array}}{\mathit{C}}_{\begin{array}{l}\mathit{e}\end{array}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathit{n}$}\right.}·$

$1\mathrm{n}{\mathit{q}}_{\begin{array}{l}\mathit{e}\end{array}}=1\mathrm{n}{\mathit{K}}_{\begin{array}{l}\mathit{F}\end{array}}+\left(\frac{1}{\mathit{n}}\right)1\mathrm{n}{\mathit{C}}_{\begin{array}{l}\mathit{e}\end{array}}·$

$1\mathrm{n}{\mathit{q}}_{\begin{array}{l}\mathit{e}\end{array}}\mathit{vs}.1\mathrm{n}{\mathit{C}}_{\begin{array}{l}\mathit{e}\end{array}}$

Temkin

     -

${\mathit{q}}_{\begin{array}{l}\mathit{e}\end{array}}=\left(\frac{\mathit{RT}}{{\mathit{b}}_{\begin{array}{l}\mathit{T}\end{array}}}\right)1\mathrm{n}{\mathit{K}}_{\begin{array}{l}\mathit{T}\end{array}}+\left(\frac{\mathit{RT}}{\mathit{bT}}\right)1\mathrm{n}{\mathit{C}}_{\begin{array}{l}\mathit{e}\end{array}}·$

${\mathit{q}}_{\begin{array}{l}\mathit{e}\end{array}}\mathit{vs}.1\mathrm{n}{\mathit{C}}_{\mathit{e}}·$