## 3 Results  
Potentionetry and spectrophotometry were used to determine the acidic constants of quercetin, luteolin and l-ascorbic acid--generically H\({}_{n}\)L. To acquire accurate results, the physical integrity of the molecules and the stability at different pH values in which the study was carried out must be taken into consideration during the whole experiment. So the systems were kept under an inert atmosphere and prevented from being exposed to light radiation. The general equilibria reported in Equations (3) and (4) fully explain the potentiometric data, treated by numerical and graphical methods:  
\[\mathrm{H}_{n}\mathrm{L}+\mathrm{H}_{3}\mathrm{O}^{+}\rightleftarrows\mathrm{ H}_{n+1}\mathrm{L}^{+}+\mathrm{H}_{2}\mathrm{O}\qquad\quad\log K^{\star}\left(\pm 3 \sigma\right) \tag{3}\]  
\[\mathrm{H}_{n}\mathrm{L}+\mathrm{H}_{2}\mathrm{O}\rightleftarrows\mathrm{H}_{ n-m}\mathrm{L}^{m-}+m\;\mathrm{H}^{+}\qquad\quad\log K_{nm}\left(\pm 3 \sigma\right) \tag{4}\]  
These correspond to the protonation of the carbonyl moiety, according to [31], and to the proteolysis of the -OH groups, respectively. The data used to determine the acidic constants, according to Equations (3) and (4), were obtained by conducting two titrations for each compound. The interpretation of the potentiometric experimental points, in terms of species and equilibrium constants, was carried out with the least-squares computer program Superquad [32] to get the minimum of the function reported by Equation (5):  
\[U=\sum(E_{l}\mathrm{obs}-E_{l}\mathrm{cal})^{2} \tag{5}\]  
The results are reported in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\log K^{\star}\) & \(\log K_{\mathrm{a1}}\) & \(\log K_{\mathrm{a2}}\) & \(\log K_{\mathrm{a3}}\) & \(\log K_{\mathrm{a4}}\) & \(\log K_{\mathrm{a5}}\) \\ \hline \multirow{4}{*}{**Quercetin**} & \multirow{2}{*}{2.00 \(\pm\) 0.06} & \multicolumn{4}{c}{\(-\)8.29 \(\pm\) 0.03} & \multicolumn{4}{c}{\(-\)8.61 \(\pm\) 0.01} & \(-\)9.5 \(\pm\) 0.1 & \(-\)9.7 \(\pm\) 0.3 & \(-\)10.4 \(\pm\) 0.3 \\  & & \multicolumn{4}{c}{\(\phantom{\mathrm{\mathbf{Hyperquad}}}\)} & \multicolumn{4}{c}{\(\phantom{\mathrm{\mathbf{Hyperquad}}}\)} \\  & / & \multicolumn{4}{c}{\(-\)8.5 \(\pm\) 0.6} & \(-\)9.0 \(\pm\) 0.3 & \(-\)9.5 \(\pm\) 0.6 & \(-\)10.0 \(\pm\) 0.3 & \(-\)10.5 \(\pm\) 0.9 \\ \hline \multirow{4}{*}{**Luteolin**} & \multirow{2}{*}{2.3 \(\pm\) 0.1} & \multicolumn{4}{c}{\(-\)8.29 \(\pm\) 0.03} & \multicolumn{4}{c}{\(\phantom{\mathrm{\mathbf{Hyperquad}}}\)} & \multirow{2}{*}{\(\phantom{\mathrm{\mathbf{Hyperquad}}}\)} \\  & & & & & & \\ \cline{1-1}  & / & \multicolumn{4}{c}{\(-\)8.1 \(\pm\) 0.3} & \(-\)8.80 \(\pm\) 0.05 & \(-\)9.6 \(\pm\) 0.6 & \(-\)9.8 \(\pm\) 0.6 \\ \hline \multirow{4}{*}{**L-ascorbic Acid**} & \multirow{2}{*}{1.2 \(\pm\) 0.1} & \multirow{2}{*}{-} & \multicolumn{4}{c}{\(\phantom{\mathrm{\mathbf{Hyperquad}}}\)} & \multirow{2}{*}{\(\phantom{\mathrm{\mathbf{Hyperquad}}}\)} \\  & & & & & & \\ \cline{1-1}  & & & & & & \\ \cline{1-1}  & & \multicolumn{4}{c}{\(-\)3.75 \(\pm\) 0.06} & \(-\)10.6 \(\pm\) 0.1 \\ \hline \end{tabular}
\end{table} 
Table 1: Survey of the log \(K^{\star}\) and log \(K_{m}\) values, according to general equilibria 3 and 4, by numerical methods. The uncertainties represent 3 \(\sigma\). The graphical evaluation was carried out by analyzing the trend of experimental points, depicted as \(Z_{\mathrm{H}}\) and obtained at different \(C_{\mathrm{L}}\) values, with respect to the pH. \(Z_{\mathrm{H}}\) represents the mean number of protons released for ligand [33], and it is equal to \(([\mathrm{H}^{+}]-C_{\mathrm{A}}+C_{\mathrm{B}}+K_{\mathrm{w}}/[\mathrm{H}^{+ }])/C_{\mathrm{L}}\). The values for the ion product of water, in our experimental condition (i.e., 37 \({}^{\circ}\)C and 0.16 M NaCl), was taken from [34]. The results are reported in Figure 11a-c, for quercetin, luteolin and L-ascorbic acid, respectively. For different \(C_{\mathrm{L}}\) values, the experimental points overlap, within the limit of experimental error.