## 3 Results and Discussion  
### Determination of Ozone Rate Constants for the Selected Antibiotics  
Kinetics of both FF and OA ozonation indicate second-order reactions of the oxidant (ozone or bromine) and target compound, as shown in Equation (2) and (3). \[\text{Antibiotic}+\text{Ozone}\ \overset{\text{k}_{\text{i}}}{\rightarrow}\text{ Products} \tag{2}\]  
\[-\frac{\text{d}[\text{Antibiotic}]}{\text{dt}}=\text{k}_{\text{app}}[\text{ Ozone}]_{\text{t}}[\text{Antibiotic}]_{\text{t}}=\text{k}_{\text{obs}}[\text{Antibiotic}]_{\text{t}} \tag{3}\]  
where the terms \([\text{Antibiotic}]_{\text{t}}\), and \([\text{Ozone}]_{\text{t}}\) represent the total concentrations of the selected pharmaceuticals FF and OA, and ozone (i.e., sum of the concentrations of the different species present in the solution), respectively, and \(\text{k}_{\text{app}}\) is the apparent second-order rate constant. When \([\text{Ozone}]_{\text{t}}\) is in significant excess with respect to \([\text{Antibiotic}]_{\text{t}}\), a pseudo-first-order rate constant \(\text{k}_{\text{obs}}\) can  
Figure 1: Schematic diagram of the batch reactor for ozonation. be introduced, which is equal to \(\rm{k_{app}[Ozone]_{t}}\). The second part of Equation (3) can be integrated to yield Equation (4) as follows. \[\rm{ln}\frac{[Antibiotic]_{0}}{[Antibiotic]_{t}}=k_{obs}t=k_{app}[Ozone]_{t}t \tag{4}\]  
This rate constant typically shows a pH dependence that can be explained by the presence of several species of both the oxidant and antibiotics in the aqueous solution. To determine the species-specific rate constants of FF and OA with ozone, ozonation at various pH conditions ranging from pH 3 to 9, were carried out. The apparent rate constant at each pH value was determined for the pseudo first-order reaction, using the ozone exposure method. The target antibiotics assume only a single pKa value each in this study. The pKa values for FF and OA are 9 and 6.8, respectively. Considering the chemical characteristics of these antibiotics, the species of FF and OA can be expected to be either neutral or anionic (PhH, Ph\({}^{-}\)). Thus, two species can be formed as shown in Equations (5) and (6) below:  
\[\rm{PhH}\ \stackrel{{ K_{s1}}}{{\rightarrow}}\ Ph^{-}+\ H^{+} \tag{5}\]  
\[\rm{K_{a1}}=\frac{[Ph^{-}][H^{+}]}{[PhH]} \tag{6}\]  
The two species of antibiotics react with ozone according to Equations (7) and (8). \[\rm{PhH}+Ozone\stackrel{{ k_{1}}}{{\rightarrow}}\ Products \tag{7}\]  
\[\rm{Ph^{-}}+Ozone\stackrel{{ k_{2}}}{{\rightarrow}}\ Products \tag{8}\]  
Hence, the removal of antibiotics can be expressed by Equation (9) below. Considering the equilibrium of the dissociation reactions of FF and OA, the apparent second-order rate constant \(\rm{k_{app}}\) for FF and OA are given by Equation (10). \[-\frac{\rm{d[Ph]}}{\rm{dt}}=\rm{k_{1}[PhH][Ozone]}+\rm{k_{2}[Ph^{-}][Ozone]} \tag{9}\]  
\[\rm{k_{app}}=\frac{[H^{+}]\rm{k_{1}}+\rm{k_{2}}K_{a1}}{\rm{\left[H^{+}\right] +K_{a1}}} \tag{10}\]  
where, \(\rm{k_{1}}=\frac{Products}{[PhH][Ozone]}\), \(\rm{k_{2}}=\frac{Products}{[Ph^{-}][Ozone]}\), \(\rm{K_{a1}}=\frac{[Ph^{-}][H^{+}]}{[PhH]}\). The kinetic model represented by Equation (10) allows the determination of the intrinsic rate constants \(\rm{k_{1}}\) and \(\rm{k_{2}}\) for the elementary reactions of each pharmaceutical species with each oxidant species. Because the reaction of FF with ozone presented intermediate or slow reactions in the pre-test phase of FF removal by ozone, the measuring rate constant, \(\rm{k_{app}}\), for FF was determined under the pseudo first-order condition with FF in excess ([FF]t \(>>\) [O\({}_{3}\)]t). In general, rate constants for ozonation depend on the speciation of the antibiotic compounds. The ease with which ozone reacts with a molecule will be determined by the structural and chemical properties of the molecule. Being an oxidizing agent, ozone is highly electrophilic in nature. Therefore, it is attracted to antibiotic molecules with the highest electron density.