*3.8. Adsorption Kinetics*

The pseudo first-order rate equation is given as:

$$\log\left(\mathbf{q}\_{\text{e}} - \mathbf{q}\_{\text{t}}\right) = \log\mathbf{q}\_{\text{e}} - \frac{\mathbf{K}\_1}{2.303}\mathbf{t} \tag{3}$$

where, qe and qt are the adsorption capacity at equilibrium (mg g<sup>−</sup>1) and time t respectively and K1 is the pseudo first order kinetics rate constant.

The pseudo second-order rate equation is given as:

$$\frac{\text{t}}{\text{q}\_{\text{t}}} = \frac{1}{\text{K}\_{2}\text{ q}\_{\text{e}}^{2}} + \frac{\text{t}}{\text{q}\_{\text{e}}} \tag{4}$$

where K2 is the pseudo second-order kinetics rate constant.

The removal mechanism for Hg2<sup>+</sup> and Cr6<sup>+</sup> by GT-cl-poly(DMA) and GT-cl-poly(DMA)/RGO were solved by different kinetic models as given in Equations (3) and (4). The parameters (pseudo-first-order: R2, K1, qe) were calculated from Figure 7a,b (Table 4). The parameters (pseudo-second-order: K2, qe) and correlation coefficient (R2) were calculated from Figure 7c,d (Table 4). The higher R<sup>2</sup> values for the pseudo-second-order kinetic model supports Hg2<sup>+</sup> and Cr6<sup>+</sup> ions adsorption onto GT-cl-poly(DMA) hydrogel and GT-cl-poly(DMA)/RGO hydrogel composite through the pseudo-second-order kinetic model.

**Figure 7.** Pseudo first order for (**a**) Hg2<sup>+</sup> and (**b**) Cr6+, pseudo second order for (**c**) Hg2<sup>+</sup> and (**d**) Cr6<sup>+</sup>. (Experimental conditions for Hg2+: adsorbent dose—0.035 g, pH—5.5, metal ion concentration—20 ppm, rpm =200 and for Cr6<sup>+</sup>: adsorbent dose—0.045 g, pH—3.5, metal ion concentration—20 ppm, rpm =200).


