Isotherm model Equation Linear form Curve Langmuir ${q}_{e}=\frac{{q}_{m}{K}_{L}{C}_{e}}{1+{K}_{L}{C}_{e}}$ $\frac{1}{{q}_{e}}=\frac{1}{{q}_{m}{K}_{L}}\cdot \frac{1}{{C}_{e}}+\frac{1}{{q}_{m}}$ $\frac{1}{{q}_{e}}=f\left(\frac{1}{{C}_{e}}\right)$ Freundlich ${q}_{e}={K}_{F}{C}_{e}^{\frac{1}{{n}_{F}}}$ $\mathrm{ln}{q}_{e}=\mathrm{ln}{K}_{F}+\frac{1}{{n}_{F}}\mathrm{ln}{C}_{e}$ $\mathrm{ln}{q}_{e}=f\left(\mathrm{ln}{C}_{e}\right)$ Temkin $\frac{{q}_{e}}{{q}_{m}}=\theta =\frac{RT}{\Delta Q}\mathrm{ln}\left({A}_{T}{C}_{e}\right)$ ${q}_{e}=B\cdot \mathrm{ln}{A}_{T}+B\cdot \mathrm{ln}{C}_{e}$ ${q}_{e}=f\left(\mathrm{ln}{C}_{e}\right)$ Dubinin-Radushkevich $\frac{{q}_{e}}{{q}_{mDR}}=\mathrm{exp}\left(-\beta {\epsilon }^{2}\right)$ $\mathrm{ln}{q}_{e}=\mathrm{ln}{q}_{mDR}-\beta {\epsilon }^{2}$ $\mathrm{ln}{q}_{e}=f\left({\epsilon }^{2}\right)$ Kiselev ${K}_{1}{C}_{e}=\frac{\theta }{\left(1-\theta \right)\left(1+{K}_{n}\theta \right)}$ $\frac{{q}_{m}}{\left({q}_{m}-{q}_{e}\right){C}_{e}}=\frac{{K}_{1}{q}_{m}}{{q}_{e}}+{K}_{1}{K}_{n}$ $\frac{{q}_{m}}{\left({q}_{m}-{q}_{e}\right){C}_{e}}=f\left(\frac{{q}_{m}}{{q}_{e}}\right)$ Fowler-Guggenheim ${K}_{FG}{C}_{e}=\frac{\theta }{1-\theta }\mathrm{exp}\left(\frac{2\theta W}{RT}\right)$ $\mathrm{ln}\left[\frac{{C}_{e}\left({q}_{m}-{q}_{e}\right)}{{q}_{e}}\right]=-\mathrm{ln}{K}_{FG}+\frac{2W}{RT}\frac{{q}_{e}}{{q}_{m}}$ $\mathrm{ln}\left[\frac{{C}_{e}\left({q}_{m}-{q}_{e}\right)}{{q}_{e}}\right]=f\left(\frac{{q}_{e}}{{q}_{m}}\right)$