Kinetics model

Equation

Linear form

Curve

Pseudo-first order

$\text{d}{q}_t/\text{d}t=k_1\left(q_e-q_t\right)$

$\ln \left(q_e-q_t\right)=\ln q_e-k_{1}t$

$\ln \left(q_e-q_t\right)=f\left(t\right)$

Pseudo-second order

$\frac{\text{d}{q}_t}{\text{d}t}=k_2{\left(q_e-q_t\right)}^2$

$\frac{t}{q_t}=\frac{1}{k_2{q}_e^2}+\frac{t}{q_e}$

$t/q_t=f\left(t\right)$

intraparticle diffusion

-

$q_t=k_{di}{t}^{0,5}+C$

$q_t=f\left(t^{0,5}\right)$

Model of Boyd

$F=1-\left[\left(\frac{6}{{\pi }^2}\right)\exp \left(-B_t\right)\right]$

$B_t=-0.4977-\ln \left(1-F\right)$

$B_t=f\left(t\right)$

Model of Elovich

-

$q_t=\frac{1}{\beta }\ln \left(\alpha \cdot \beta \right)+\frac{1}{\beta }\ln t$

$q_t=f\left(\ln t\right)$