## 3 Results and Discussion
### LANGMLIR Isotherm, Activation and Adsorption Parameters  
Using the slopes and intercepts of linearly fitted Equations (3) and (4) (Figures 3 and 4), we deduced \(E_{a}\), \(\Delta S_{a}\)\({}^{0}\), and \(\Delta H_{a}\)\({}^{0}\) (Table 3). \begin{table}
\begin{tabular}{c c c c c} \hline  & **Concentration (g/L)** & **W (mg\(\cdot\)cm\({}^{-2}\).h\({}^{-1}\))** & **C\({}_{\text{R}}\) (mm/year)** & **EI \%** \\ \hline Blank & - & 0.7436 & 8.3 & - \\ \hline  & 0.06 & 0.3061 & 3.42 & 59.75 \\  & 0.12 & 0.2619 & 2.92 & 65.83 \\ AO & 0.25 & 0.1758 & 1.96 & 76.19 \\  & 0.5 & 0.1443 & 1.61 & 81.42 \\  & 1 & 0.11 & 1.23 & 85.36 \\  & 2 & 0.0951 & 1.06 & 87.18 \\ \hline  & 0.06 & 0.2878 & 3.21 & 61.22 \\  & 0.12 & 0.2583 & 2.88 & 65.09 \\ HERA & 0.25 & 0.2104 & 2.35 & 72.37 \\  & 0.5 & 0.177 & 1.98 & 76.28 \\  & 1 & 0.138 & 1.54 & 81.42 \\  & 2 & 0.1167 & 1.3 & 84.64 \\ \hline \end{tabular}
\end{table} 
Table 2: AO and HERA concentration effect on mild steel corrosion rate and corrosion inhibition efficiency. Figure 2: AO and HERA concentration effect on mild steel corrosion rate and corrosion inhibition efficiency. Figure 4: The alternative Arrhenius equation plots for steel in 1 M HCl in the absence and the presence of AO and HERA. Figure 3: Arrhenius plots for mild steel in 1 M HCl in the absence and the presence of AO and HERA. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \(E_{a}\) & \(\Delta H_{a}{}^{0}\) & \(\Delta S_{a}{}^{0}\) & & \\  & **(KJ\(\cdot\)mol\({}^{-1}\))** & **(KJ\(\cdot\)mol\({}^{-1}\))** & **(J\(\cdot\)mol\({}^{-1}\).K\({}^{-1}\))** & **\(K_{als}\)** & **\(\Delta G_{a}{}^{0}\)** \\  & **(KJ\(\cdot\)mol\({}^{-1}\))** \\ \hline Blank & 31.031 & 28.350 & \(-\)152.415 & – & – \\ \hline AO at 2 g/L & 67.407 & 64.726 & \(-\)50.682 & \(21.8867\times 10^{4}\) & \(-\)31.4871 \\ \hline HERA at 2 g/L & 61.343 & 58.662 & \(-\)68.586 & \(19.9641\times 10^{4}\) & \(-\)31.2516 \\ \hline \end{tabular}
\end{table} 
Table 3: Activation parameters in the presence and absence of AO and HERA. High \(\Delta{H_{a}}^{0}\) values reflect the lowering of the corrosion reaction's energy barrier, i.e., the corrosion reaction is less aggressive when \(\Delta{H_{a}}^{0}\) has higher values. The \(\Delta{H_{a}}^{0}\) results show that, at 2 g/L, AO is more efficient against mild steel corrosion. In addition, the positive values of \(\Delta{H_{a}}^{0}\) reflect the endothermic aspect of the mild steel's slow dissolution process in the inhibited mediums [35]. Negative values of \(\Delta{S_{a}}^{0}\) indicate that the inhibitors are more and more attached to the mild steel surface, which decreases the medium disorder. Furthermore, the inhibited medium \(\Delta{S_{a}}^{0}\) values are more positive than the blank. This behavior might be justified by water molecules' desorption during the inhibitor's adsorption [36]. The Langmuir isotherms plotted for AO and HERA (Figure 5) showed an R\({}^{2}\) close to the unit (0.9999 for AO and 0.9995 which reflects that the two tested inhibitors' adsorption obeys the Langmuir isotherm. Slopes, intercepts, and \(K_{ads}\) are calculated using Equation (4). the positive values of \(K_{ads}\) (21.8867 \(\times\) 10\({}^{4}\) g/L and 19.9641 \(\times\) 10\({}^{4}\) g/L, respectively, for AO and HERA at 2 g/L) suggest that AO and HERA adsorption on the mild steal surface is possible [37]. The values of \(\Delta{G_{a}}^{0}\) reflect the strong interaction between AO and HERA molecules and the mild steel surface. This interaction leads to the establishment of a chemical barrier between H\({}_{3}\)O\({}^{+}\)(aq) and Cl\({}^{-}\)(aq) ions and the mild steel surface [33]. On the other hand, researchers are more and more convinced that the calculation of \(\Delta{G_{a}}^{0}\) values is meaningless since the Langmuir isotherm is based on the adsorption of identical species (with a precisely defined molecular weight) on a homogenous flat surface [38; 39].