## 4 Conclusions  
The Tafel-Piontelli model was presented as a tool for the prediction of the corrosion rate of active metals, like carbon steel, exposed to acidic solutions. A comprehensive validation campaign was presented in the current work, encompassing electrochemical and mass loss tests in weakly acidic solutions prepared with valeric and acetic acids, varying the pH and temperature conditions. The electrochemical analysis included potentiodynamic polarization tests, aimed at the evaluation of the kinetic parameters of the corrosion process, namely the Tafel slopes and exchange current densities of the cathodic process of hydrogen evolution and the anodic process of iron dissolution. Each parameter was defined in the Tafel-Piontelli model via a mechanistic approach and assessed individually via a statistical analysis and comparison with the experimental results. The tests show that the Tafel slopes of the anodic and cathodic processes are basically independent from the electrolyte pH thus confirming the validity of the model description of the two parameters. The cathodic exchange current density, instead, shows an exponential decay with pH that is very well captured by the Tafel-Piontelli model across the entire experimental range considered. The experimental results of the anodic exchange current density show a dependance on temperature that is partially captured by the model. Overall, the comparison between the experimental data and the predicted parameters highlighted the capability of the Tafel-Piontelli model to describe the complex electrochemical interactions taking place at the interface between the electrolyte and the metal surface, and specifically the effect of pH and temperature on these parameters. Nonetheless, the results also suggested that there is room for further improvement and refinement of the model, specifically in the description of the effect of the environmental parameters on the anodic exchange current density. The comparison between the predicted corrosion rates and the experimental corrosion rates derived via weight loss tests allowed the evaluation of the general performance of the model. The experimental data indicate an increasing trend of the corrosion rate with temperature, which accelerates the kinetics of the corrosion process, and an exponential dependance on the acidity of the electrolyte. The Tafel-Piontelli model is able to account for these dependances on temperature and pH, providing good estimates of the corrosion rate across all the different acids, pH, and temperatures tested. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Acid**} & \multirow{2}{*}{**T [\({}^{\circ}\)C]**} & \multicolumn{3}{c}{**Experimental**} & \multicolumn{2}{c}{**T-P Model**} \\ \cline{3-6}  & & \(\Delta\)**logCR/\(\Delta\)pH** & \(\mathbf{CI_{\text{{alogCR/\Delta pH}}}}\) & \(\Delta\)**logCR/\(\Delta\)pH** & \(\mathbf{CI_{\text{{alogCR/\Delta pH}}}}\) \\ \hline \multirow{3}{*}{Valeric (C\({}_{5}\)H\({}_{10}\)O\({}_{2}\))} & 20 & \(-\)0.22 & \([-\)0.27, \(-\)0.17] & \(-\)0.66 & \([-\)0.80, \(-\)0.52] \\ \cline{2-6}  & 40 & \(-\)0.42 & \([-\)1.18, +0.34] & \(-\)0.81 & \([-\)1.05, \(-\)0.56] \\ \cline{2-6}  & 60 & \(-\)0.64 & \([-\)0.87, \(-\)0.41] & \(-\)0.35 & \([-\)0.42, \(-\)0.28] \\ \hline \multirow{3}{*}{Acetic (CH\({}_{3}\)COOH)} & 20 & \(-\)0.70 & \([-\)0.96, \(-\)0.43] & \(-\)0.71 & \([-\)0.77, \(-\)0.65] \\ \cline{2-6}  & 40 & \(-\)0.94 & \([-\)1.19, \(-\)0.69] & \(-\)0.69 & \([-\)0.72, \(-\)0.66] \\ \cline{1-1} \cline{2-6}  & 60 & \(-\)1.52 & \([-\)1.99, \(-\)1.05] & \(-\)0.54 & \([-\)0.68, \(-\)0.40] \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Statistical analysis of experimental and predicted dependence of corrosion rate (CR) on pH for valeric and acetic acids.