## 3 Results and Discussion
### Phenomena Related to Shifts in Chemical Equilibria during Electrodialysis of Multivalent Ions
#### 3.1.1 Chronopotentiometric Features
Accordingly, a shift in chemical equilibrium inside the membrane at high levels of concentration polarization may cause a decrease in pH (increase in pOH corresponding with a shift towards the right side in Figure 3a) and an increase of pSO\({}_{4}\) (shift towards the right side in Figure 3b) inside the membrane phase. Consequently, the dissociation of CrSO\({}_{4}\)\({}^{+}\) is favored:  
\[\text{CrSO}_{4}\text{${}^{+}$}\rightarrow\text{Cr}^{3+}+\text{SO}_{4}\text{${} ^{2-}$} \tag{1}\]  
The Cr\({}^{3+}\) ions originated through Reaction (1) would initially compensate the membrane fixed charges and then permeate towards the concentrate compartment. The SO\({}_{4}\)\({}^{2-}\) ions, on the contrary, migrate back to the DBL attracted by the anode. The generation of new current carriers via dissociation of CrSO\({}_{4}\)\({}^{+}\) would therefore explain the stabilization of U\({}_{\text{m}}\) between the first and the second inflexion points detected in the chronopotentiometric curves. The subsequent exhaustion of Reaction (1) inside the membrane and the intensified depletion in the DBL give rise to the second inflection point in U\({}_{\text{m}}\). Since the Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) electrolyte system is similar to the Cr\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) one, a homologous response was expected. On the contrary, the decrease in membrane resistance at increasing current densities obtained for Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) solutions can be associated with the generation of more ions (Fe\({}^{3+}\)) at polarization levels that are significantly below the i\({}_{\text{lim}}\), before the ultimate ion depletion at the membrane surface takes place. This difference leads to the reduction of U\({}_{\text{m}}\) registered in the chronopotentiograms without a subsequent registration of a second inflexion point. The more differentiated stages of concentration polarization in the case of Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) solutions can be more clearly understood from the current-voltage curves explained in the next subsection. Figure 3: Equilibrium diagrams for 2.5 \(\times\) 10\({}^{-3}\) M Cr\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) solutions: (**a**) Speciation diagram as a function of pOH, (**b**) speciation diagram as a function of pSO\({}_{4}\). Finally, the formation of precipitates observed with NiSO\({}_{4}\) solutions can also be tracked with the help of solubility diagrams. Figure 4 shows the solubility plot for 10\({}^{-2}\) M NiSO\({}_{4}\) solutions. The dot in the plot represents the initial equilibrium conditions, corresponding to a pH value of 5.58. As current densities above the i\({}_{\text{lim}}\) are applied to the system, the transport of H\({}^{+}\) through the membrane is enhanced because of the lack of Ni\({}^{2+}\) ions next to the depleting membrane surface. Consequently, the pH in the depleting DBL increases until the formation of precipitates starts to occur (pH of 7.6) and the concentration of soluble species of Ni(II) drops abruptly. A similar phenomenon occurred with Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) solutions at overlimiting currents. The Ni(OH)\({}_{2}\) and Fe(OH)\({}_{3}\) precipitates formed at the membrane surface are shown in Figure 4b.