Parameters

Isotherms

Non-Linear Forms

Equation Number

References

Two

Langmuir

$Q_e=\frac{Q_m{K}_L{C}_e}{1+K_L{C}_e}$

(13)

[27]

and $R_L=\frac{1}{1+K_L{C}_0}$

(14)

Freundlich

$Q_e=K_f{C}_e^{1/n}$

(15)

[28]

Temkin

$Q_e=\frac{RT}{\Delta Q}\ln \left(A{C}_e\right)$

(16)

[29]

Dubinin-Radushkevich

$Q_e=Q_m\exp \left(-\beta {\epsilon }^2\right)$ Math_21#

(17)

[30]

Elovich

$\frac{Q_e}{Q_m}=K_E{C}_e\exp \left(-\frac{Q_e}{Q_m}\right)$

(18)

[31]

Jovanovic

$Q_e=Q_m\left(1-{\text{e}}^{-K_J{C}_e}\right)$

(19)

[32]

Kiselev

$K_{1k}{C}_e=\frac{{\theta }_k}{\left(1-{\theta }_k\right)\left(1+K_n{\theta }_k\right)}$

${\theta }_k=Q_e/Q_m$

(20)

[3]

Halsey

$Q_e=\exp \left(\frac{\ln K_H-\ln C_e}{n_H}\right)$

(21)

[3]

Three

Redlich-Peterson

$Q_e=\frac{K_{RP}{C}_e}{1+A_{RP}{C}_e^g}$

(22)

[3]

Hill

$Q_e=\frac{Q_{SH}{C}_e^{nH}}{K_D+C_e^{nH}}$

(23)

[33]

Radke-Prausnitz

$Q_e=\frac{Q_{mRP}{K}_{RP}{C}_e}{{\left(1+K_{RP}{C}_e\right)}^{mRP}}$

(24)

[3]

Langmuir-Freundlich

$Q_e=\frac{Q_{mLF}{\left(K_{LF}{C}_e\right)}^{M_{LF}}}{1+{\left(K_{LF}{C}_e\right)}^{M_{LF}}}$

(25)

[33]

Toth

$Q_e=\frac{Q_m{K}_T{C}_e}{{\left[1+{\left(K_T{C}_e\right)}^n\right]}^{1/n}}$

(26)

[33]

Jossens

$C_e=\frac{Q_e}{H}\exp \left(F{Q}_e^p\right)$

(27)

[3]

Fritz-Schlunder III

$Q_e=\frac{Q_{mFS}{K}_{FS}{C}_e}{1+Q_{mFS}{C}_e^{mFS}}$

(28)

[9]

Four

Fritz-Schlunder IV

$Q_e=\frac{A{C}_e^{\alpha }}{1+B{C}_e^{\beta }}$ With α and β ≤ 1

(29)

[3] [34]

Baudu

$Q_e=\frac{Q_{mo}{b}_o{C}_e^{\left(1+x+y\right)}}{1+b_o{C}_e^{\left(1+x\right)}}$

with $\left(1+x+y\right)$ and $\left(1+x\right)<1$

(30)

[3] [34]

Five

Fritz-Schlunder V

$Q_e=\frac{Q_{mFS}{K}_1{C}_e^{m_1}}{1+K_2{C}_e^{m_2}}$

with m₁ and m₂ ≤ 1

(31)

[3] [33]