## 3 Results and Discussion
### The Effect of Relative Humidity on the Degradation Rate  
To corroborate the results obtained from the experimental tests, the Langmuir-Hinshelwood-bimolecular model was used [36]. In this model, the water-VOC system is assimilated into a binary system. The degradation kinetics can be expressed as follows:  
\[\mathrm{r_{A}}=\mathrm{k_{A}}\cdot\mathrm{F_{A}}\cdot\mathrm{F_{W}} \tag{12}\]  
\[F_{A}=\frac{K_{A}\cdot C_{A}}{(1+K_{A}\cdot C_{A}+K_{w}\cdot C_{w})} \tag{13}\]  
\[F_{w}=\frac{K^{\prime}_{w}\cdot C_{w}}{(1+K^{\prime}_{A}\cdot C_{A}+K^{\prime} _{w}\cdot C_{w})} \tag{14}\]  
\[r_{A}=k_{A}\cdot\frac{K_{A}\cdot C_{A}}{(1+K_{A}\cdot C_{A}+K_{w}\cdot C_{w})} \cdot\frac{K^{\prime}_{w}\cdot C_{w}}{(1+K^{\prime}_{A}\cdot C_{A}+K^{\prime} _{w}\cdot C_{w})} \tag{15}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**VOCs** & **k (mM/m\({}^{3}\cdot\)s)** & **K (m\({}^{3}\)/mM)** & **R\({}^{2}\) (\%)** \\ \hline CB & 0.92 & 8.4 & 99 \\ CN & 0.10 & 9.1 & 99 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: k and K values for CB and CN for model TM. The constants \(k_{A}\) and \(K_{A}\) are obtained by considering the mass transfer in the previous study, with a relative humidity value of 5% (dry air). \(C_{w}\) is the water vapor concentration, \(K_{w}\) is the Langmuir adsorption constant of the water, and \(K^{\prime}{}_{A}\) and \(K^{\prime}{}_{w}\) are the competitive adsorption constant of the pollutant and water. Table 4 displays values for the Langmuir-Hinshelwood model parameters for the Volatile Organic Compounds (VOCs) types, including reaction rate constants and adsorption constants. Relative humidity (RH) modeling confirmed that H\({}_{2}\)O molecules greatly influence the kinetics of VOC conversion in the photocatalytic process. The pace of the simulated and experimental speeds was identical. [PERSON] and his group [PERSON] and his group [PERSON] and his group [PERSON] (1986) showed that the photocatalytic removal rate of cyclohexane increases with the amount of water vapor. However, above a certain threshold, there is a detrimental effect on the degradation rate. Refs. [PERSON] and his group (1986); [PERSON] and [PERSON] (1986); [PERSON] (1986) have confirmed this assertion. Figure 4a,b present the influence of water molecules on treating VOCs during heterogeneous photocatalysis. The DR increased from 5 to 55% RH, while it decreased beyond 55% RH. The experimental and simulated speeds varied based on the flow and concentration conditions. When compared to CN, a higher CB degradation was observed under this study's humidity conditions. It is well known that the influence of humidity on the degradation of VOCs depends on the nature of the pollutant, especially its hydrophilic character and the concentration of the injected VOCs. Moreover, TiO\({}_{2}\) has a polar surface, which favors the adoption of water molecules on the catalyst's surface. Even though, there is a small amount of competition with the pollutants on the active's sites, at a low water content, this compaction is accompanied by another photocatalytic reaction (the oxidation of water by photocatalysis), which forms OH\({}^{\circ}\) radicals [40]. Therefore, the water molecules in the vapor phase must be consumed over the catalyst surface to promote radical generation. The increase in humidity, thus, facilitates the reactions between the VOC molecules and the radicals formed through the strong OH* production from H\({}_{2}\)O at the interface, as shown in the following reactions:  
\[ \begin{split}\text{H}_{2}\text{O}+\text{e}^{-}\rightarrow\text{H} ^{+}+\text{OH}^{+}+\text{e}^{-}\\ \text{H}_{2}\text{O}+\text{h}^{+}\rightarrow\text{OH}^{+}+\text{H} ^{+}\end{split}