# Binding of Arsenic by Common Functional Groups: An Experimental and Quantum-Mechanical Study
## 3 Results
### Predictive Relationships  
Taking into account all values, the formation constants can be modeled by using another approach that considers all the contributions of the functional groups of the ligands under examination (Additivity Factors Approach) [27; 28]. Thus, logK can be written as  
\[\log\text{K}=\sum\text{n}_{\text{x-donor}} \tag{3}\]  
where \(\text{n}_{\text{x-donor}}\) is representative of -S, -N, or -O donor groups.  
For a more accurate analysis of the data, together with the logK values, in Table 2, we report the number of thiol (\(\text{n}_{\text{SH}}\)), carboxylic (\(\text{n}_{\text{COOH}}\)), and amino (\(\text{n}_{\text{NH2}}\)) groups of the molecules and, for each species, the number of deprotonated carboxylic (\(\text{n}_{\text{COOH}}\)), thiol (\(\text{n}_{\text{S}}\)), and protonated amino (\(\text{n}_{\text{NH3+}}\)) groups available for the coordination. The latter were obtained considering that the stepwise formation equilibria are referred to the reaction As(OH)\({}_{3}\) + H\({}_{3}\)L and, therefore, considering the protonation degree and the form under which the molecules participate to the single reaction.  
Considering the data of Table 2 and the comments reported in the previous section, the contribution of each functional group can be represented by the following equation, which takes into account not only the total number of functional groups in the molecule (\(\text{n}_{\text{SH}}\), \(\text{n}_{\text{COOH}}\), and \(\text{n}_{\text{NH2}}\)), but also the number of functional groups available for coordination  
Figure 2: Distribution diagrams of (**a**) As(III)-_asp_ and (**b**) As(III)-_cys_ systems. Conditions: \(\text{C}_{\text{As}}=3\) mmol/L, \(\text{C}_{\text{L}}=6\) mmol/L, \(\text{I}=0.15\) mol/L (NaCl), \(\text{T}=298.15\) K.  
(n\({}_{\rm S-}\), n\({}_{\rm COO-}\), and n\({}_{\rm NH3+}\)) and, therefore, the charge with which the ligand participates to the stepwise formation reaction:  
\[\log\rm K=2.39(\pm 0.11)\ n_{\rm SH}+0.30(\pm 0.07)\ n_{\rm COOH}+0.64(\pm 0.08)\ n _{\rm NH2}+0.17(\pm 0.09)\ (n_{\rm S-}+n_{\rm COO-}+n_{\rm NH3+}) \tag{4}\]  
The equation confirms the experimental results from which it was observed, as expected, that the thiol group mostly contributes to the overall stability of the species. The contribution of the other functional groups is two orders of magnitude lower, but not negligible in the calculation of the stability of the species with polyfunctional ligands. Furthermore, Equation (4) shows that an approximate stability calculation can be performed simply by considering the type and the number of functional groups of the molecule (therefore independently of the pH and of the exact stoichiometry of the species) and, to a lesser extent, the form under which the functional group (protonated or deprotonated, depending on the pH) is present. On the other hand, considering the data in Table 2, we observed that, for the same molecule, no significant differences in stability between the different species were recorded.  
Figure 3 shows the stability constant values calculated by means of Equation (4) plotted as a function of the experimental ones. A fairly good agreement is recorded, being the correlation coefficient R\({}^{2}\) equal to 0.92 and the slope equal to 0.97\(\pm\)0.03. The mean deviation of the calculated logK value was \(\pm\)0.5, which is relatively high. It is worth emphasizing that Equation (4) allows only for a rough estimate of the stability of the species and that the experimental approach is always highly encouraged for an accurate determination.