## 3 Results and Discussion
### Reasons for Selecting the Fe\({}^{3+}\)/Fe\({}^{2+}\) Couple  
#### 3.3.1 The Advantages of the Fe\({}^{3+}\)/Fe\({}^{2+}\) Couple  
This couple is already used to reduce H\({}_{2}\)S to sulfur in the industry. Only the ligand changes. In the literature, EDTA (ethylenediaminetetraacetic acid) [21], NTA (nitrilotriacetic acid) [22; 23; 24], and HEDTA (hydroxyethyl ethylenediaminetriacetic acid) [23; 24] have been typically used as ligand. Here, we used EDA. \(Fe^{3+}/Fe^{2+}\) has an equilibrium potential greater than that of S/H\({}_{2}\)S if one considers the free ions, and therefore it can oxidize H\({}_{2}\)S to S. The equilibrium potential is the potential at which the oxidation and reduction reaction take place at the same rate. This potential is calculated using the Nernst equation [25]:  
If one considers the noncomplexed species: \(E_{eq}=E^{*}\left(Fe^{3+}/Fe^{2+}\right)=0.77\;\text{V/SHE}\).  
If one considers the potential between \(\left[Fe(EDA)_{3}^{3+}\right]\) and \(\left[Fe(EDA)_{3}^{2+}\right]\):  
\[E_{eq}=E^{{}^{\circ}}\left(Fe^{3+}/Fe^{2+}\right)+0.06\log\left(\frac{\beta_{2} }{\beta_{3}}\right) \tag{16}\]  
\[\beta_{3}=\frac{\left[Fe(EDA)_{3}^{3+}\right]}{[Fe^{3+}][EDA]^{3}} \tag{17}\]  
\[\beta_{2}=\frac{\left[Fe(EDA)_{3}^{2+}\right]}{[Fe^{2+}][EDA]^{3}} \tag{18}\]  
\(\beta_{2}\approx 10^{10}\) and \(\beta_{3}=10^{35}\)[19]. The latter value is only a gross estimate by [PERSON] [19] and worth checking. With those values, \(E_{eq}=-0.73\)V/SHE.  
The equilibrium potential between S/H\({}_{2}\)S is  
\[E_{eq}=E^{{}^{\circ}}(S/H_{2}S)-0.06\ pH-0.06\ \log(Ctot) \tag{19}\]  
\(E^{{}^{\circ}}(S/H_{2}S)=0.14\)V/SHE ; \(pH=12\); \(C_{tot}\) is the total concentration of absorbed H\({}_{2}\)S. If one takes C\({}_{tot}=10^{-1}\) molL\({}^{-1}\), one obtains \(E_{eq}=-0.52\)V/SHE.  
The pH = 12 of the solution was obtained as follows:  
The amine solution consists of H\({}_{2}\)S and EDA. Ethylenediamine (EDA) has two pKas: pK\({}_{\text{a1}}\) = 9.7; pK\({}_{\text{a2}}\) = 7. The amine is a weak base, and thus the pH of the solution can be calculated from pH = \(\frac{1}{2}\) (pK\({}_{\text{A}}\) + pKe + logC\({}_{\text{am}}\)) = 12. Table 1 shows the composition of the solution.  
With the value \(\beta_{3}=10^{35}\), the Fe\({}^{3+}\) ions are not able to oxidize H\({}_{2}\)S because \(E_{eq}(\left[Fe(EDA)_{3}^{3+}\right]/\left[Fe(EDA)_{3}^{2+}\right])\ \leq E_{eq}(S/H_{2}S)\) (see Equation (14)). It should be stressed that the value \(\beta_{3}=10^{35}\) is only an estimate [19]. The reaction is possible if log(\(\beta_{3})\ -\ \log(\beta_{2})\leq 21.7\), which is only a difference of 25 with respect to the estimate of 35. Hence, it is necessary to measure \(\beta_{3}\) to confirm that the reaction is not possible.  
The Fe\({}^{3+}\) ion has a great affinity with amine functions. It has an overall formation constant with EDA of \(\sim\)10\({}^{35}\), so it will be able to regenerate the amine. The equilibrium constant for EDA-CO\({}_{2}\) is \(\sim\)10\({}^{5}\), so the inequality between \(\beta\) and K\({}_{\text{CO2}}\) is largely satisfied. Another advantage of iron is that it is inexpensive and nontoxic.