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  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)  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)