Table 3 Linear form of PFO, PSO, and intraparticle diffusion kinetic models.

PFO

\(\:\text{log}\left({\text{q}}_{\text{e}}-{\text{q}}_{\text{t}}\right)=\text{l}\text{o}\text{g}{\text{q}}_{\text{e}}\frac{{\text{K}}_{1}.\text{t}}{2.303}\:\:\:\:\)

q_t (mg/g) = Adsorption capacity at time (t)

q_e (mg/g) = Adsorption capacity at equilibrium

k₁(min⁻¹) = The PFO rate constant

PSO

\(\:\frac{\text{t}}{{\text{q}}_{\text{t}}}=\frac{1}{{\text{K}}_{2}{\text{q}}_{\text{e}}^{2}}+\frac{1}{{\text{q}}_{\text{e}}\left(\text{t}\right)}\:\:\:\:\:\:\:\:\)

K₂ (mg/g. min) = The rate constant of the PSO

Intraparticle diffusion

\(\:{\text{q}}_{\text{t}}={\text{K}}_{\text{d}\text{i}\text{f}}{\text{t}}^{\frac{1}{2}}+\text{C}\:\:\:\:\:\:\:\:\:\:\:\)

C (mg/g) = A constant of the model