## 3 Results and Discussion
### Adsorption Kinetics  
Initial testing examined the duration of the various adsorbents to reach an equilibrium state, where removal of dyes becomes static or near-static (non-changing). Methylene blue  
Figure 2: X-ray diffraction (XRD) of (**a**) GAC, (**b**) GO and (**c**) NaY; (**d**) FT-IR analysis of NaY, GAC and GO. was removed rapidly by both GAC and GO, although GO outperformed the GAC with equilibrium at approximately 5 days versus 31 days for GAC (Figure 3). Meanwhile, the NaY selected for this research demonstrated poor removal and slow equilibrium times for both MB and RhB (Figure 3a,b). RhB removal was also poor under initial testing conditions with GAC and GO, with GO achieving higher removal at a slightly faster time to equilibrium compared to GAC. These initial experiments were intended to determine initial times of experiments for adsorption experiments, which are intended to be conducted once solutions reach an equilibrium timepoint, which was used for further adsorption experiments. However, it is clear in the initial testing, the GO outperformed GAC and NaY with both faster and higher removals for both MB and RhB. Kinetic models were fitted to the removal data to determine best kinetic fits. Overall data fitting indicated a better fit for the pseudo-second-order compared to the other models (Tables 1 and 2). The pseudo-second-order kinetic model was well fitted to the experimental data for removal of MB with GO (Figure 4) This model indicated a higher value of the coefficient of determination R\({}^{2}\) = 0.986 compared to pseudo-first-order, Elovich, and intraparticle models (Figure 4a). Moreover, the predicted maximum adsorption capacity with this model of q\({}_{\text{m}}\) = 303.0 mg/g was very close to the experimental adsorption capacity of q\({}_{\text{e}}\) = 285.1 mg/g (Table 1). This close agreement of the pseudo-second-order model for the removal of MB using GAC and NaY is consistent with previous studies that have reported similar findings for the adsorption of MB with GO, GAC, and zeolite [9; 19]. The pseudo-second-order kinetic model was also well fitted with experimental data for the adsorption of RhB with GAC, GO, and NaY (Figure 4b). The same observation was reported in previous studies [16; 25]; Table 2. Fitting of the pseudo-first-order kinetic model to the data is provided in the Supplementary Data. The intraparticle diffusion model indicated the adsorption diffusion mechanism involves three stages that were determined based on the diffusion plot. The first stage of the adsorption process has the highest number of empty sites available on the surface of the adsorbent for external adsorption, which makes this stage the fastest [1]. The diffusion plot was linearized from the origin to identify this first stage for the adsorption of RhB and MB with adsorbents (Figures S1 and S2). Comparing the constant rate of adsorption of MB with GO, a higher value for the first stage K\({}_{\text{1d}}\) = 28.97 (mg/(g.min\({}^{1/2}\))) is observed, which drops to K\({}_{\text{2d}}\) = 7.7 (mg/(g.min\({}^{1/2}\))) in other stages due to internal adsorption (Tables 1 and 2). Figure 3: Removal of (**a**) MB and (**b**) RhB concentrations with GAC, GO, and NaY to equilibrium levels (4 mg/L contaminant concentration with 5 mg of adsorbent at 100 rpm).