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

$q_e=K_F{C}_e^{\frac{1}{n_F}}$

$\ln q_e=\ln K_F+\frac{1}{n_F}\ln C_e$

$\ln q_e=f\left(\ln C_e\right)$

Temkin

$\frac{q_e}{q_m}=\theta =\frac{RT}{\Delta Q}\ln \left(A_T{C}_e\right)$

$q_e=B\cdot \ln A_T+B\cdot \ln C_e$

$q_e=f\left(\ln C_e\right)$

Dubinin-Radushkevich

$\frac{q_e}{q_{mDR}}=\exp \left(-\beta {\epsilon }^2\right)$

$\ln q_e=\ln q_{mDR}-\beta {\epsilon }^2$

$\ln q_e=f\left({\epsilon }^2\right)$

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

$K_{FG}{C}_e=\frac{\theta }{1-\theta }\exp \left(\frac{2\theta W}{RT}\right)$

$\ln \left[\frac{C_e\left(q_m-q_e\right)}{q_e}\right]=-\ln K_{FG}+\frac{2W}{RT}\frac{q_e}{q_m}$

$\ln \left[\frac{C_e\left(q_m-q_e\right)}{q_e}\right]=f\left(\frac{q_e}{q_m}\right)$