## 3 Results and Discussion
### Adsorption Isotherms
Table 5 shows the thermodynamic parameters for the adsorption of As(III) and As(V) at 4, 22 and 45 \({}^{\circ}\)C. In addition, Figure 8 shows the thermodynamic plots for the binding of both As(III) and As(V) to the ZnO nanomaterials. The Gibbs free energy of the process was determined using the equation below based on the distribution coefficient:  
\[\Delta G=-RTlnK_{d} \tag{3}\]  
where \(\Delta G\) is the change in Gibbs free energy, \(R\) is the gas constant (8.314 J mol\({}^{-1}\) K\({}^{-1}\)), T is the temperature in Kelvin, and \(K_{d}\) is the distribution coefficients. The Gibbs free energy in an equilibrium process can be related to the equilibrium constant for a reaction or the distribution constant, as shown above. The relationship between ln \(K_{d}\) can be substituted in the Gibbs free energy equation and be related to \(\Delta H\) and \(\Delta S\), as shown in the equation below:  
\[lnk_{d}=\frac{\Delta S}{R}-\frac{\Delta H}{RT} \tag{4}\]  
where \(k_{d}\) is the distribution coefficient, \(\Delta S\) is the change in entropy, \(\Delta H\) is the change in enthalpy, \(T\) is the temperature in Kelvin, and \(R\) is the gas constant (8.314 J mol\({}^{-1}\) K\({}^{-1}\)). The values of enthalpy and entropy changes were calculated from the slope and the intercept of the plot of \(ln\)\(K_{d}\) versus \(1/T\). Figure 8A shows the thermodynamic plot for the binding of As(III) to the ZnO, and Figure 8B shows the thermodynamic plot for the binding of As(V) to ZnO. The calculated thermodynamic data are shown in Table 5; the enthalpy change for As(III) and As(V) sorption was determined to be \(-63.44\) kJ mol\({}^{-1}\) and \(-47.29\) kJ/mol kJ mol\({}^{-1}\), respectively. From the enthalpy data both the As(III) and As(V) bind to the ZnO through an exothermic reaction, as dictated by the negative sign. The higher observed enthalpy for the binding of As(III) may be due to the oxidation of the As(III) in conjunction with the chemisorption process. The oxidation of the As(III) was indicated in the Raman data, a chemical process may have increased the enthalpy of the reaction. The Gibbs free energy for the sorption process for both As(III) and As(V) was observed to be spontaneous at low and medium temperatures and became nonspontaneous at the highest temperature, \(45\)\({}^{\circ}\)C, as can be seen in Table 5. The increase in \(\Delta G\) with increasing temperature indicates the binding reaction becomes less favorable for both As(III) and As(V), indicating the binding is occurring through an exothermic reaction. Exothermic binding for As(III) and As(V) has been observed for different materials, including Fe\({}_{2}\)S\({}_{8}\), ZnO, CeO\({}_{2}\), CuO nanomaterials, and As(V) binding to red mud [40, 51, 73, 74, 75, 76]. These results suggest that As(III) and As(V) adsorption onto ZnO nanoparticles is an exothermic process and proceeds through chemisorption. As(V) \(\Delta H\) is around \(-40\) kJ/mol and indicates chemisorption may be the binding mechanism. However, the As(III) enthalpy was very high at \(-63.4\) kJ/mol, which is well above the accepted 40 k/mol, the maximum energy value for physisorption. It has been shown in the literature that chemisorption occurs at enthalpies between 40 and 200 kJ/mol [77, 78, 79]. The higher enthalpy for As(III) binding may also be a reflection of the reaction occurring between As(III) and ZnO, causing the oxidation of the As(III), as is indicated by the binding shown in the Raman data. The Raman results for both, the As(III) and As(V) binding to the ZnO after reaction, are shown in Figure 6 and show that only As(V) is present. The absolute values of enthalpy of binding for both As(III) and As(V) are comparable to values reported in the literature on other nanomaterials. For example, [PERSON] et al. determined that the binding of As(III) and As(V) had binding enthalpies of 43.5 and 7 kJ mol\({}^{-1}\), respectively [40]. [PERSON] et al. showed that As(III)showed an enthalpy of binding of 120 kJ mol\({}^{-1}\) to copper(II) oxide nanoparticles [51]. [PERSON] et al.