## 3 Results and Discussion
### Determination of Bromine Rate Constants for the Selected Antibiotics  
The second-order rate constant of FF for reaction with bromine was determined using the pseudo first-order method, in the bromine-excess condition. The concentration of bromine was 3 mM for pH 3 to 6, and 5 mM for pH 7 to 9 with the pH adjusted using a 0.2 M phosphate buffer. The rate constant of  
Figure 2: pH dependence of the apparent rate constants for the ozonation of (**a**) florfenicol (FF) and (**b**) oxolinic acid (OA). Symbols: experimental values; dotted line: calculated values of the apparent rate constant; solid line: speciation of florfenicol ([Ozone]\({}_{0}\) = 20 \(\upmu\)M, [FF]\({}_{0}\) = 200 \(\upmu\)M, [OA]\({}_{0}\) = 1 \(\upmu\)M, [t\(-\)BuOH]\({}_{0}\) = 10 mM, pH 3–9, Temp. = 20 \({}^{\circ}\)C). FF for reaction with bromine was similar for different concentrations of bromine at the same pH value (Table 2). The species-specific rate constants for reaction of FF or OA with bromine were determined at various pH ranges. The apparent rate constants were determined based on Equations (11)-(16) with K\({}_{\text{HOB}}\) = 10\({}^{-8.8}\), K\({}_{\text{FF}}\) = 10\({}^{-9}\), and K\({}_{\text{OA}}\) = 10\({}^{-6.8}\). \[\text{PhH}+\text{HOBr}\xrightarrow{\text{k}_{1}}\text{ Products} \tag{11}\]  
\[\text{Ph}^{-}+\text{HOBr}\xrightarrow{\text{k}_{2}}\text{ Products} \tag{12}\]  
\[\text{PhH}+\text{OBr}^{-}\xrightarrow{\text{k}_{3}}\text{ Products} \tag{13}\]  
\[\text{Ph}^{-}+\text{OBr}^{-}\xrightarrow{\text{k}_{4}}\text{ Products} \tag{14}\]  
\[\text{HOBr}\xleftrightarrow{\text{K}_{\text{HOB}^{-}}}\text{OBr}^{-}+\text{H}^ {+} \tag{15}\]  
\[\text{PhH}\xrightarrow{\text{K}_{\text{J}}}\text{Ph}^{-}+\text{H}^{+} \tag{16}\]  
The removal of FF and OA through bromination reactions corresponding to rate constants k\({}_{1}\), k\({}_{2}\), k\({}_{3}\), and k\({}_{4}\), can be expressed by Equation (17). \[-\frac{\text{d}[\text{Ph}]}{\text{dt}}=\text{k}_{1}[\text{PhH}][\text{HOBr}]+ \text{k}_{2}[\text{Ph}^{-}][\text{HOBr}]+\text{k}_{3}[\text{PhH}][\text{OBr}^{ -}]+\text{k}_{4}[\text{Ph}^{-}][\text{OBr}^{-}] \tag{17}\]  
From Equations (11)-(16), the apparent second-order rate constant k\({}_{\text{app}}\) for FF and OA, considering the equilibrium of the dissociation reactions of FF and OA, is derived, as given by Equation (18):  
\[\text{k}_{\text{app}}=\frac{\text{k}_{1}\big{[}\text{H}^{+}\big{]}2+\text{k}_{ 2}\text{K}_{\text{a}1}\big{[}\text{H}^{+}\big{]}+\text{k}_{3}\text{K}_{\text{ HOB}}\big{[}\text{H}^{+}\big{]}+\text{k}_{3}\text{k}_{4}\text{K}_{\text{a}1}}{ \big{\{}\big{[}\text{H}^{+}\big{]}+\text{K}_{\text{a}1}\big{\}}\big{\{[}\text{H }^{+}\big{]}+\text{K}_{\text{a}1}\big{\}}\big{\{[}\text{H}^{+}\big{]}+\text{K}_ {\text{a}1}\big{\}}\big{\{}\big{[}\text{H}^{+}\big{]}+\text{K}_{\text{HOB}} \big{\}}} \tag{18}\]  
where, k\({}_{1}\) = \(\frac{\text{Products}}{[\text{PhH}][\text{HOB}]^{\prime}}\), k\({}_{2}\) = \(\frac{\text{Products}}{[\text{Ph}][\text{HOB}]^{\prime}}\), k\({}_{3}\) = \(\frac{\text{Products}}{[\text{PhH}][\text{OBr}^{-}]}\), k\({}_{4}\) = \(\frac{\text{Products}}{[\text{Ph}^{-}][\text{OBr}^{-}]}\), K\({}_{\text{HOB}r}\) = \(\frac{[\text{OBr}^{-}][\text{H}^{+}]}{[\text{HOBr}]}\), and K\({}_{\text{a}1}\) = \(\frac{[\text{Ph}^{-}][\text{H}^{+}]}{[\text{PHH}]}\). The species-specific rate constants were determined by a nonlinear least-squares regression of the experimental value of the apparent rate constant at each pH for the bromination process. The experimental and calculated values for the apparent rate constants for different values of pH in the range 3-10, for the bromination of FF are shown in Figure 3a. The symbols represent the experimental values while the dotted line represents the calculated values of the apparent rate constant; the solid line represents the speciation of FF and bromine. The experimental values and calculated values matched well.