Name

Form

Meaning of Parameter

Reference

Pseudo-nth-order model

n = 1, $\frac{d{q}_t}{dt}=k_1\left(q_e-q_t\right)$

(Pseudo-first-order model)

n = 2, $\frac{d{q}_t}{dt}=k_2{\left(q_e-q_t\right)}^2$

(Pseudo-second-order model)

n take other values, $\frac{d{q}_t}{dt}=k_n{\left(q_e-q_t\right)}^n$

$k_1$ : pseudo-first-order rate constant (h⁻¹)

$k_2$ : pseudo-second-order rate constant (g·mg⁻¹·h⁻¹)

$k_n$ : pseudo-nth-order rate constant (gⁿ⁻¹·mg¹⁻ⁿ·h⁻¹)

t: adsorption time (h)

$q_t$ : adsorption capacity at time t (mg·L⁻¹)

$q_e$ : equilibrium adsorption capacity (mg·L⁻¹)

n: number of active sites occupied by adsorbed ions/molecules

[70]

Mixed-order model

$\frac{d{q}_t}{dt}={k^{\prime }}_1\left(q_e-q\right)+{k^{\prime }}_2{\left(q_e-q\right)}^2$

${k^{\prime }}_1$ : pseudo-first-order rate constant of mixed-order model (h⁻¹)

${k^{\prime }}_2$ : pseudo-second-order rate constant of mixed-order model (g·mg⁻¹·h⁻¹)

[71]

Elovich equation

$\frac{d{q}_t}{dt}=\alpha e^{-\beta q_t}$

$\alpha$ : initial desorption rate constant (mg·g⁻¹·h⁻¹)

$\beta$ : desorption rate constant (g·mg⁻¹)

[72]