## 3 Results and Discussion
### Phenomena Related to Shifts in Chemical Equilibria during Electrodialysis of Multivalent Ions
#### 3.1.2 Current-Voltage Curves  
Different phenomena related to shifts in the electrolyte speciation at different levels of polarization can also be examined from the current-voltage curves. These curves provide information about the resistance of the membrane system under quasi-steady state conditions and can serve to clearly distinguish between different operational regimes of electrodialysis. Figure 5a shows different current-voltage curves obtained for a strong electrolyte solution (Na\({}_{2}\)SO\({}_{4}\)) and for weak electrolytes (Cr\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) and Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\)). To facilitate a better comparison of the curves obtained with the different electrolytes, the current densities are normalized by the i\({}_{\text{lim}}\) value corresponding to each system. The curves registered for Na\({}_{2}\)SO\({}_{4}\) correspond with the typical shape obtained with strong electrolytes, where three clearly distinguishable regions are identified. At low membrane voltages, the system displays \"quasi-ohmic\" behavior, where a proportional linear relationship correlates current density with membrane voltage drop. As concentration polarization is intensified, for the same increase in current density, larger increases in U\({}_{\text{m}}\) are registered as compared to those obtained at lower current densities. The depletion of ions at the membrane surface entails a diffusional limitation of ion transport through the DBL, which leads to a tilted plateau region at current densities around the i\({}_{\text{lim}}\). When a certain threshold of U\({}_{\text{m}}\) is reached, the plateau region evolves into the third characteristic region. At these intense electric fields, additional mass transfer mechanisms become important, thus giving rise to a further increase in current density. These mechanisms are mostly related to the dissociation of strong polarized water molecules at the membrane/depleting DBL interface or to the formation of electroconvective vortices, as it will be explained below. Figure 4: (**a**) Precipitation diagram of 10\({}^{-2}\) M NiSO\({}_{4}\) solutions. The dot represents the initial pH under equilibrium conditions. (**b**) Pictures of the membrane surface facing the diluate compartment after the formation of precipitates of Ni(II) and Fe(III). In the case of Cr\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) solutions, an atypical current-voltage curve having two plateau regions was obtained. Such behavior coincides with the registration of two transition times in the chronopotentiograms obtained at significantly high current densities (in this case, at current densities in between the two \(\mathrm{i_{lim}}\) values determined). The Cowan-Brown plots obtained at different concentrations of Cr\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) solutions are shown in Figure 5b [19]. These plots are based on representing the specific electrical resistance of the system against the inverse of the current density, so that the transition between different regions of a current-voltage curve can be clearly identified. At low values of current density (right side of the plots), the resistance remains practically constant. As the first plateau emerges, the resistance increases notably. However, before reaching the second plateau and the overlimiting region, a region of currents where the system resistance decreases with the inverse of current can be clearly identified in the plots. This phenomenon occurs for different salt concentrations, although it is more marked for the more diluted ones. Finally, the polarization curve for Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) presented in Figure 5a also showcases an atypical shape, where two principal regions were obtained: the quasi-ohmic part predominating at low voltage drops and a very flat plateau emerging after surpassing \(\mathrm{i_{lim}}\) and not being continued by a further rise of current (overlimiting region). In this case, the formation of precipitates takes place at the anodic side of the membrane, as it happened with the NiSO\({}_{4}\) solutions.