## 3 Results and Discussion
### Corrosion Rate Estimation  
Once the quality of the estimation of the kinetic parameters of the corrosion process was assessed, the study focused on the quality of the predicted corrosion rate by comparison with the experimental results. The corrosion rate was calculated as defined in (8), while the experimental corrosion rate was obtained via mass loss tests and its empirical dependance on temperature and pH was defined as follows:  
\[\text{CR}(\text{pH,T})=10^{X_{1}(\text{T})}\text{pH}+\chi_{0}(\text{T}) \tag{21}\]  
Figure 8: Comparison between experimental and predicted anodic exchange current density exponential decay with respect to pH in acetic acid solutions at 20 \({}^{\circ}\)C (a), 40 \({}^{\circ}\)C (b), and 60 \({}^{\circ}\)C (c). Figure 7: Comparison between experimental and predicted anodic exchange current density exponential decay with respect to pH in valeric acid solutions at 20 \({}^{\circ}\)C (a), 40 \({}^{\circ}\)C (b), and 60 \({}^{\circ}\)C (c). The dependences of the experimental corrosion rates on temperature for valeric acid solutions and acetic acid solutions are illustrated in the box plot analyses in Figure 9a,b, respectively. Moreover, a statistical analysis of the experimental and predicted dependance of the corrosion rate on temperature, reporting the mean value (\(\mu\)), interquartile range (IQR), mean absolute error (MAE), and root mean squared error (RMSE) for both acids was performed and reported in Table 8.  
The experimental results showed a rising trend of the corrosion rate with temperature, as expected due to the acceleration in the kinetics of the corrosion reactions. The Tafel-Piontelli model fits the experimental data well for both valeric and acetic acids, as indicated by the RMSE and MAE values reported in Table 8. The average error values are consistent with those found in previous validation experiments, supporting the effectiveness of the Tafel-Piontelli model in estimating the uniform corrosion rate of metals in weak acids. The relation between the corrosion rate (CR) and pH was graphically represented by the regression lines of log\({}_{10}\)(CR) with respect to pH. The experimental and predicted trends for valeric acid solutions at 20, 40, and 60 \({}^{\circ}\)C are reported in Figure 10a, Figure 10b, and Figure 10c, respectively. The trends for acetic acid solutions at 20, 40, and 60 \({}^{\circ}\)C are reported in Figure 11a-c. The graphs suggest that the experimental corrosion rate has an exponential dependance from the acidity of the electrolyte, increasing with the decrease in pH. This experimental evidence is made clear by looking at the variation in the logarithm of the corrosion rate with the variation in pH, that represents the slope (\(\partial\text{log}_{10}(\text{CR})/\partial\text{pH}\)) of the experimental regression lines between the log\({}_{10}\) CR and pH. Figures 10 and 11 also report the trends of the predictions of the model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Acid**} & \multirow{2}{*}{**T [\({}^{\circ}\)C]**} & \multicolumn{3}{c}{**Experimental**} & \multicolumn{3}{c}{**T-P Model**} \\ \cline{3-8}  & & \(\mu_{\text{logCR}}\) & \(\text{IQR}_{\text{logCR}}\) & \(\mu_{\text{logCR}}\) & \(\text{IQR}_{\text{logCR}}\) & **MAE** & **RMSE** \\ \hline \multirow{3}{*}{Valeric (C\({}_{5}\)H\({}_{10}\)O\({}_{2}\))} & 20 & \(-\)0.20 & [\(-\)0.27, \(-\)0.13] & \(-\)0.07 & [\(-\)0.29, +0.16] & +0.18 & +0.21 \\ \cline{2-8}  & 40 & +0.33 & [+0.27, +0.42] & \(-\)0.01 & [\(-\)0.21, +0.20] & +0.40 & +0.45 \\ \cline{2-8}  & 60 & +0.65 & [+0.43, +0.87] & +0.15 & [+0.01, +0.29] & +0.50 & +0.53 \\ \cline{2-8}  & 20 & \(-\)0.10 & [\(-\)0.28, +0.19] & \(-\)0.11 & [\(-\)0.45, +0.22] & +0.10 & +0.13 \\ \cline{2-8}  & 40 & +0.24 & [\(-\)0.03, +0.58] & +0.07 & [\(-\)0.18, +0.32] & +0.18 & +0.21 \\ \cline{2-8}  & 60 & +0.87 & [+0.17, +1.38] & +0.22 & [\(-\)0.03, +0.47] & +0.65 & +0.82 \\ \hline \hline \end{tabular}
\end{table}