## 3 Results and Discussion
### Reasons for Selecting the Fe\({}^{3+}\)/Fe\({}^{2+}\) Couple
#### 3.3.2 The Disadvantages of the Fe\({}^{3+}\)/Fe\({}^{2+}\) Couple  
At low pH, iron is no longer soluble in water. The products of the solubility of Fe\({}^{3+}\) and Fe\({}^{2+}\) are Fe(OH)\({}_{3}\) and Fe(OH)\({}_{2}\), respectively, with corresponding pKs3 = 37.2 and pKs2 = 15.1, respectively. If one calculates the pH corresponding to the precipitation limit for the two salts with a total iron concentration of 1 molL\({}^{-1}\), one obtains for the Fe(OH)\({}_{3}\) salt:  
\[K_{s3}=\left[Fe^{3+}\right]\left[HO^{-}\right]^{3}\]  
\[pH=pKe-\frac{1}{3}pK_{s3}-\frac{1}{3}\log\left[Fe^{3+}\right]=1.6\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **M\({}_{\text{w}}\) (gmol\({}^{-1}\))** & \(\rho\) (gL\({}^{-1}\)) \(\dot{\Delta}\) 25 \({}^{\circ}\)C & **w (\%)** & **X (\%)** & **C (molL\({}^{-1}\))** \\ \hline H\({}_{2}\)O & 18 & 1000 & 70 & 89 & 37.6 \\ \hline EDA & 60 & 900 & 30 & 11 & 4.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Composition of the solution. And for the Fe(OH)\({}_{2}\) salt:  
\[K_{s2}=\left[Fe^{2+}\right]\left[HO^{-}\right]^{2}\]  
\[pH=pKe-\frac{1}{2}pK_{s2}-\frac{1}{2}\log\left[Fe^{2+}\right]=6.5\]  
If one takes into account the stabilization of the ions by the ethylenediamine complexes, the pH corresponding to the precipitation limit will increase slightly. If the iron ions and the ethylenediamine are present in stoichiometric proportions, one has \(\left[Fe(EDA)_{3}^{3+}\right]\approx 1\ molL^{-1}\) and \(\left[Fe^{3+}\right]\approx\left[EDA\right]\approx 1.8\ 10^{-9}\). The pH of the precipitation limit is pH = 4.5. With the same hypotheses, one obtains for Fe(+II): \(\left[Fe(EDA)_{3}^{2+}\right]\approx 1\ molL^{-1}\) and \(\left[Fe^{2+}\right]\approx\left[EDA\right]\approx 3.2\ 10^{-3}\) and a precipitation limit of pH = 7.9. Therefore, even with the complexation of the Fe\({}^{2+}\) or Fe\({}^{3+}\) ions with the amine, the pH at which precipitation occurs remains lower than the pH of the solution. There exist many options to further increase the solubility of the Fe\({}^{3+}\) and Fe\({}^{2+}\) ions in the solution. The pH of the solution can be lowered. One could consider going down to 10, but if the pH is lower than the pKa of the amine (pKa of EDA is 9.96), then the predominant species will no longer be EDA but EDAH\({}^{+}\), which will significantly reduce the absorption of the acid gases. The temperature could be increased, but this has a limited impact on the solubility, as illustrated in Table 2.  
A second ligand can be added to complex the residual iron ions. To be beneficial, this ligand must have similar or even better complexing constants than ethylenediamine. Finally, the amine/iron proportions can be changed so that iron becomes the limiting reagent of the complexation reaction. To change the concentration of free iron ions, it suffices that the amine is slightly in excess. In the following example with amine in excess of 0.1 molL\({}^{-1}\), we managed to drastically increase the precipitation pH to 10.6 for Fe\({}^{3+}\) and to 10 for Fe\({}^{2+}\):  
\[\epsilon 3=\frac{\left[Fe(EDA)_{3}^{3+}\right]_{equilibrium}}{\beta_{3}\cdot \left[EDA\right]_{equilibrium}^{3}}=1.10^{-27}\rightarrow\ pH=10.6\]  
\[\epsilon 2=\frac{\left[Fe(EDA)_{3}^{2+}\right]_{equilibrium}}{\beta_{2}\cdot \left[EDA\right]_{equilibrium}^{3}}=1.10^{-7}\rightarrow\ pH=10\]  
The extent of the reaction is calculated in Table 3 for Fe\({}^{3+}\) complexation: \begin{table}
\begin{tabular}{c c c} \hline  & **pKs (298 K)** & **pKs (323 K)** \\ \hline Fe(OH)\({}_{2}\) & 15.4 & 14.8 \\ \hline Fe(OH)\({}_{3}\) & 38.2 & 36.8 \\ \hline \end{tabular}
\end{table} 
Table 2: Temperature dependence of the water solubility of Fe\({}^{2+}\) and Fe\({}^{3+}\) ions. \begin{table}
\begin{tabular}{c c c c} \hline  & **Fe\({}^{3+}\) +** & **3 EDA =** & **Fe(EDA)\({}_{3}\)\({}^{3+}\)** \\ \hline Initial & 1 & 3.1 & 0 \\ \hline Final & \(1-\mathrm{x}\) & \(3.1-3\mathrm{x}\) & \(\mathrm{x}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Extent of the reaction for Fe\({}^{3+}\) complexation.