## 3 Results and Discussion
### Adsorption Experiments of Pb(II)/Cd(II) with O-MWCNT\({}_{S}\)
#### 3.2.3 Initial Concentration  
Understanding the relations between the concentration of the metal ion in an aqueous solution and the quantity adsorbed by the adsorbent at equilibrium is crucial for comprehending the adsorption mechanism. The impact of the starting concentration of Pb(II)/Cd(II) on the adsorbability of O-MWCNT\({}_{\rm S}\) was examined, as depicted in Figure 5a. The removal rate of Pb(II)/Cd(II) using O-MWCNT\({}_{\rm S}\) decreased significantly when the starting concentrations increased. The removal rate decreased from 76.34% to 55.59% in the case of Pb(II) and from 29.83% to 16.68% in the case of Cd(II). Typically, the removal of both ions decreased with increasing initial concentration, which is attributed to the limited amount of adsorption sites for the adsorbent during the adsorption process [37]. The findings of this study suggest that Pb(II) undergoes easier adsorption onto O-MWCNT\({}_{\rm S}\) in comparison to Cd(II). Due to the inverse relationship between the hydrated ionic radius and the hydration energy, a reduction in the hydrated ionic radius corresponds to an increase in hydration energy. Consequently, the removal efficiency of metal ions increases with a decrease in hydrated ionic radius. The results of this experiment demonstrated that the hydration ion radius of Pb(II) is comparatively greater, resulting in a significantly higher removal rate. The role of hydration energy is higher than that of hydration ion radius. The results of the competitive tests are shown in Figure 5b. After adsorption equilibration was reached, the removal of Pb(II) was about 60.46%, while that of the other metal ion, Cd(II), was 9.70%. When the removal rate is compared to individual adsorption, a slight decrease in quantity is observed. This observation may indicate an antagonistic effect in the sorption of Pb(II) and Cd(II) on the surface of O-MWCNT\({}_{\rm S}\). Figure 4: The changes in lnk with 1/T for the reaction of O-MWCNT\({}_{\rm S}\) with Pb(II)/Cd(II). (**a**) Pb; (**b**) Cd. Figure 5: (**a**) Effect of initial concentration on Cd(II) and Pb(II) adsorption in a single system. (**b**) Adsorption experiments with Pb(II)-Cd(II) = 1:1. The results of fitting the Langmuir and the Freundlich isothermal curves to the experimental data at 298 K are displayed in Figure 6, and the parameters of the models are indicated in Table 2. Table 2 demonstrates that the Langmuir isothermal models could better describe the adsorption of both ions, according to an R\({}^{2}\) of 0.99 with Pb(II) and 0.91 with Cd(II). This outcome suggests that chemical adsorption was the major reaction [38; 39]. The linear Langmuir model yielded the highest absorption capabilities: 5.73 mg.g\({}^{-1}\) with Pb(II) and 3.34 mg.g\({}^{-1}\) with Cd(II). The sorption isotherm results for the competing systems are consistent with the single system. The linear Langmuir model fitted the highest uptake capacity of 7.11 mg:g\({}^{-1}\) in the case of Pb(II), and 0.78 mg:g\({}^{-1}\) in the case of Cd(II). It can be concluded that it is easier to absorb Pb(II) than Cd(II) on the O-MWCNTs' surface, and this result is in mutual agreement with the activation energy calculations. Table 3 lists the fitting parameters associated with quasi-primary and quasi-secondary kinetics for the experimental study. All the R\({}^{2}\) values of the quasi-primary kinetics and quasi-secondary kinetics are greater than 0.80. That is to say, both models can better describe the data. A more precise depiction of the adsorption process of metal ions Pb(II)/Cd(II) is offered by both the quasi-primary and quasi-secondary kinetic models [40; 41; 42; 43]. Upon