Non-linear equation

Parameters

Freundlich

$q_e=K_F{C}_e^{1/n}$

K_F (mg∙g⁻¹)(L∙mg⁻¹)^1/n: Freundlich adsorption constant n (dimensionless): empirical parameter representing the energetic heterogeneity of surface

q_e (mg∙g⁻¹): equilibrium adsorbed quantity

Langmuir

$q_e=\frac{q_m{K}_L{C}_e}{1+K_L{C}_e}$

q_m (mg∙g⁻¹): monolayer adsorption capacity

C_e (mg∙L⁻¹): equilibrium concentration

K_L (L∙mg⁻¹): equilibium adsorption constant

Dubinin-Radushkevich

$q_e=q_s\exp \left(-k_{ad}{\left[RT\ln \left(1+\frac{1}{C_e}\right)\right]}^2\right)$

q_s: maximum adsorbed amount

R (8.314 J∙mol⁻¹K⁻¹): gas constant

T (K): temperature

Pseudo-first-order

$q_t=q_e\left[1-\exp \left(-k_{1}t\right)\right]$

q_t (mg∙g⁻¹): adsorbed quantity at time t

t (min): contact time

k₁ (min⁻¹): pseudo-fist order rate constant

Pseudo-second-order

$q_t=\frac{q_e^2{k}_{2}t}{1+q_e{k}_{2}t}$

k₂ (g.mg⁻¹∙min⁻¹): pseudo-fist order rate constant

Intraparticular diffusion

$q_t=k_{ip}{t}^2+C_i$

K_ip (mg∙g⁻¹∙min^1/2): intraparticle diffusion rate constant

C_i: constant value depicting the boundary layer effect