## 3 Results and Discussion
### Kinetic Analysis  
MO uptake versus the time at 293, 303, and 313 K was investigated for MO concentration of 40 ppm. Figure 9 shows that the adsorption capacity was very low at 303, and 313 K with less than 2% MO removal in 6 h. On the other hand, 12% removal after 6 h with an uptake capacity of 9 mg/g, and about 22% removal after 24 h (not shown in the graph) corresponding to 17 mg/g was achieved when operating at 293 K. This indicates an exothermic nature of MO adsorption on FeNP. The relatively slow MO uptake at 293 K is mainly because of the FeNP agglomeration. Therefore, the availability and the easily accessible adsorption sites were very limited. After a time of stirring the FeNP in the acidic solution of MO (pH = 4), the nanoparticles started to be separated under the peptization effect of the acidic medium as the surface will gain a positive charge. Accordingly, particles will repel each other, preventing agglomeration and increasing the available adsorption sites and that is why adsorption capacity did not stabilize during adsorption time. This was visually evidenced from the conversion of coarse FeNP agglomerated particles into colloidal solution with very small particle size as shown in  
Figure 8: Effect of MO initial concentration on adsorption capacity (q).  
Figure 10, which shows the change of solution color during the adsorption process from orange to black because of black FeNP dispersion.  
Figure 11 displays the intraparticle model, specifically: q (mg/g) vs. t\({}^{1/2}\). It is obvious from the figure that the adsorption of MO happens in multi-stages. The rate of adsorption in each stage depends on the diffusion of MO from the bulk solution to the FeNP surface. At the beginning, the FeNP were aggregated due to a known nanoparticles phenomenon, which is a challenging in the applications of these materials as it leads to a huge loss of active surface area. Aggregation occurs directly as particles are created as a result of the direct mutual attraction between particles via van der Waals forces, chemical bonding, or magnetic properties in FeNP [28]. Approaches for avoiding aggregation includes modifying the surface with a charge to separate particles by electrostatic repulsions or particle coating with capping agents. Figure 11 clearly indicates the importance surface charge in the control of the aggregation of nanoparticles and accordingly on its adsorption capacity.  
Figure 10: FeNP in MO solution after stirring at for: 5 min (**a**); 30 min (**b**); 60 min (**c**); and 120 min (**d**).  
Figure 9: Effect of time on MO removal efficiency (R%) at different temperatures.  
The slope of qt vs. t\({}^{1/2}\) plot change significantly because of the occupation of easily accessible adsorption sites on the external FeNP surface. At this stage, particles started to gain a positive charge since it is placed in a medium with pH \(<\) pH\({}_{2c}\), and thus, started to be separated from each other, once again the adsorption rate increase as the new surface area has been created by peptization effect of the acidic medium. Accordingly, more MO can be adsorbed. As stirring in acidic medium continue for a longer time, more peptization occurs and more active adsorption sites become available for adsorption, this may explain not reaching equilibrium even after 24 h of stirring.