## 3 Results and Discussion  
### Parameters Estimation  
As reported in Section 2.2, the main electrochemical parameters of the corrosion process are the Tafel slopes (\(\mathrm{b_{H_{2}}}\) and \(\mathrm{b_{Fe}}\)) and exchange current densities (\(\mathrm{i_{0,H_{2}}}\) and \(\mathrm{i_{0,Fe}}\)) of the hydrogen evolution and iron dissolution reactions. These parameters were evaluated for the different experimental conditions tested via potentiodynamic polarization tests and their empirical dependance on temperature and pH is described as follows:  
\[\mathrm{b_{H_{2}}(T)}=10^{\mathrm{g_{0}(T)}}; \tag{17}\]  
\[\mathrm{b_{Fe}(T)}=10^{\mathrm{\gamma_{0}(T)}}; \tag{18}\]  
\[\mathrm{i_{0,H_{2}}(pH,T)}=10^{\mathrm{\alpha_{1}(T)pH+\mathrm{\alpha_{0}(T)}}}; \tag{19}\]  
\[\mathrm{i_{0,Fe}\left(pH,T\right)}=10^{\mathrm{\
u_{1}(T)pH+\mathrm{\
u_{0}(T) }}}. \tag{20}\]  
Each kinetic parameter was assessed individually via a statistical analysis comprising the estimation of the mean value \(\mathrm{\mu}\), the theoretical value predicted by the model, the interquartile range (IQR), the mean absolute error (MAE), and the root mean squared error (RMSE). The cathodic Tafel slope (\(\mathrm{b_{H_{2}}}\)) in the case of valeric acid (\(\mathrm{C_{5}H_{10}O_{2}}\)) shows minimal variations around its theoretical value at 20 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, and 60 \({}^{\circ}\)C, as reported in Table 4. Specifically, there is a very close correspondence between the experimental and theoretical values at lower temperatures, while the MAE and RMSE slightly increase at higher temperatures. Similar results were obtained in the case of acetic acid (\(\mathrm{CH_{3}COOH}\)). Figure 3 reports the dependance of the cathodic Tafel slope on pH and temperature. As displayed in Figure 3c for valeric acid and Figure 3d for acetic acid, the experimental data show an overall slight increase in the cathodic Tafel slope with temperature. On the contrary, pH does not particularly affect the cathodic Tafel slope, as can be seen from the horizontal trends of \(\text{b}_{\text{H}_{2}}\) with respect to pH in both Figure 3a for valeric acid and Figure 3b for acetic acid. This behavior aligns well with the theoretical description of the parameter provided by the Tafel-Piontelli model. The anodic Tafel slope (\(\text{b}_{\text{Fe}}\)) was evaluated for valeric and acetic acids at 20, 40, and 60 \({}^{\circ}\)C, as reported in Figure 4, with some fluctuations from the predicted values with temperature. The data variations, quantiles, and error metrics (MAE and RMSE) are reported in Table 5, which shows a slight decrease in the error metrics with the increase in temperature across the two acids. The experimental values show the basically null impact of pH on the anodic Tafel slope, confirming the validity of the theoretical description of the parameter reported in (18). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Acid**} & \multicolumn{1}{c}{**T**} & \multirow{2}{*}{**Theoretical \(\text{b}_{\text{H}_{2}}\)**} & \multirow{2}{*}{\(\text{\boldmath$\mu$}_{\text{b}_{\text{H}_{2}}}\)} & \multirow{2}{*}{**IQR\({}_{\text{b}_{\text{H}_{2}}}\)**} & \multirow{2}{*}{**MAE**} & \multirow{2}{*}{**RMSE**} \\  & [\({}^{\circ}\)C] & & & & & \\ \hline Valeric & 20 & \(-0.116\) & \(-0.116\) & \([-0.117\), \(-0.113]\) & \(+0.002\) & \(+0.003\) \\ (\(\text{C}_{5}\text{H}_{10}\text{O}_{2}\)) & 40 & \(-0.124\) & \(-0.123\) & \([-0.120\), \(-0.115]\) & \(+0.014\) & \(+0.018\) \\  & 60 & \(-0.132\) & \(-0.115\) & \([-0.116\), \(-0.113]\) & \(+0.018\) & \(+0.018\) \\ \hline Acetic & 20 & \(-0.116\) & \(-0.117\) & \([-0.117\), \(-0.116]\) & \(+0.001\) & \(+0.001\) \\ (\(\text{CH}_{3}\text{COOH}\)) & 40 & \(-0.124\) & \(-0.116\) & \([-0.117\), \(-0.114]\) & \(+0.008\) & \(+0.009\) \\  & 60 & \(-0.132\) & \(-0.117\) & \([-0.116\), \(-0.115]\) & \(+0.015\) & \(+0.016\) \\ \hline \hline \end{tabular}
\end{table}