## 3 Results and Discussion
### Adsorption Mechanism  
In order to gain further insight into the nature of the inhibitor adsorption on the bronze surface, the polarization data obtained from the two corrosive solutions were used. The surface coverage, \(\theta\), was calculated as a function of the NAC concentration, based on the following equation:  
\[\theta=\frac{\eta_{\rm pol}}{100} \tag{6}\]  
Several widely studied adsorption isotherms, such as Langmuir, Temkin, Frumkin, and Freundlich were applied to the experimental data, according to the following equations [77]:  
\[\rm{Langmuir\ isotherm:\ \frac{c_{Inh}}{\theta}=\frac{1}{K}+c_{Inh}} \tag{7}\]  
\[\rm{Temkin\ isotherm:\ \exp^{(-2a\theta)}=Kc_{Inh}} \tag{8}\]  
\[\rm{Frumkin\ isotherm:\ \ln}\bigg{[}\frac{\theta}{(1-\theta)}c_{Inh} \bigg{]}=\rm{InK}+2\alpha\theta \tag{9}\]  
\[\rm{Freundlich\ isotherm:\ \log\theta=\log K+\frac{1}{n}\log c_{Inh}} \tag{10}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**NAC** & \(\bf{E_{corr}}\) & \(\bf{i_{corr}}\) & \(\bf{i\beta_{c}}\) & \(\bf{\beta_{a}}\) & \(\bf{\eta_{pol}}\) \\
**(mM)** & **(mV vs. ESC)** & **(\(\bf{\mu A\ cm^{-2}}\))** & **(mV dec\({}^{-1}\))** & **(mV dec\({}^{-1}\))** & **(\%)** \\  & & & & & \\  
where \(c_{\rm{Inh}}\) is the concentration of NAC, K is the adsorption equilibrium constant, and a is the molecular interaction parameter. Figure 5 shows the fitting plots of the four isotherm models used to study the adsorption of NAC-containing drug on the bronze surface in the tested electrolytes. The correlation coefficient (R\({}^{2}\)) values were used to select the isotherm that best fitted the experimental data. Figure 5: Langmuir (**a**,**a**), Temkin (**b**,**b**), Frumkin (**c**,**c**), and Freundlich (**d**,**d**) adsorption isotherms of NAC-containing drug on the bronze surface exposed to 35% NaCl (**a**–**d**) and 0.2 g L\({}^{-1}\) Na\({}_{2}\)SO\({}_{4}\) + 0.2 g L\({}^{-1}\) NaHCO\({}_{3}\) + 0.2 g L\({}^{-1}\) NaNO\({}_{3}\), pH = 3.4 (**a**–**d**) solutions, at 298 K.  
The results in Figure 5 reveal that the Langmuir model is the most suitable to describe the adsorption of NAC on bronze in both corrosive environments [78]. It is known that the Langmuir isotherm approach assumes that the inhibitor is adsorbed in the form of a monolayer on a fixed number of equivalent adsorption sites (one molecule occupies a single surface site), and the adjacent adsorbed molecules do not interact with each other on a homogenous solid surface [34]. However, in real experimental conditions, the functional groups grafted on the adsorbed organic molecules could interact through common repulsive or attractive forces, and these might explain the small deviations from unity in the slopes of the Langmuir plots shown in Table 4.  
The standard free energy of adsorption \(\Delta G_{\text{ads}}^{0}\) was calculated from the adsorption equilibrium constant, K, according to Equation (11), and the results are presented in Table 4[79]. \[K=\frac{1}{55.5}\text{exp}\left(\frac{-\Delta G_{\text{ads}}^{0}}{\text{RT}}\right) \tag{11}\]  
As shown in Table 4, the calculated values of \(\Delta G_{\text{ads}}^{0}\) for NAC adsorption laid in the range from \(-20\) to \(-40\) kJ mol\({}^{-1}\) in both corrosive environments, suggesting that it acts by mixed adsorption on bronze, including physical and chemical processes. The large negative values of \(\Delta G_{\text{ads}}^{0}\) also show the spontaneity of the adsorption process on the bronze surface. As we previously mentioned, the inhibition behavior of NAC on bronze corrosion primarily arises from its adsorption on the metal surface. This process is pH-dependent and controlled by the ionization states of NAC's functional groups [63; 80]. It is known [61] that the pKa values of NAC are 3.14 for the carboxyl group and 9.27 for the thiol group. In the simulated acid rain of a pH = 3.4, NAC existed mainly in a protonated form.