## 3 Results and Discussion  
### Extractions Experiments and Chemical Equilibrium Calcualitons  
The time-transient evolution of the dissolved metal (Co\({}^{2+}\) and Li\({}^{+}\)) from the solid matrix and of the solution pH are presented in Figure 2. The solid dissolution trend was approximately linear in the first few hours of the experiment, slowing down asymptotically as the particles were dissolved. It could be concluded that the kinetics of particle dissolution was moderately slow, reaching a plateau  
Figure 1: Experimental set-up scheme. after approximately 3 days. Regarding the pH evolution, a slight increase from pH = 1 to pH = 1.4 was observed, which could be associated with the consumption of protons during the extraction process. A non-equimolar proportion between Li\({}^{+}\) and Co\({}^{2+}\) was also observed; that is, the concentration of Li\({}^{+}\) in the equilibrium was approximately twice as high as the concentration of Co\({}^{2+}\). With the aim of evaluating the equilibrium system, the software PHREQC [26] was used to simulate the extraction experiments. The database \"phreeqc.dat\" adapted with the specific chemical system presented in Table 1 was used to simulate the chemical system. Equilibrium data for the solid phases were adapted from those reported in [25] while the Cl\({}^{-}\)/HCl/HClO equilibria was from [27]. According to Equation (1), Co\({}^{3+}\), within the LiCoO\({}_{2}\) particles, is reduced into soluble Co\({}^{2+}\). Using HCl solution, and according to Equations (9) and (10), the reducing agent could be expected to be the chloride ions. However, the experimental results indicated that the reducing agent was water and not the chloride ions. The chemical equilibrium simulations carried out corroborated that the oxidation of water, Equation (11), was thermodynamically favored in acid media. This was also consistent with the fact that other acids, such as HNO\({}_{3}\) and H\({}_{2}\)SO\({}_{4}\), were also used in the literature achieving similar results, rather than HCl [25]. Regarding the dissolution percentage of LiCoO\({}_{2}\), equilibrium simulations predicted the total dissolution of the LiCoO\({}_{2}\) particles and the complete re-precipitation of dissolved Co\({}^{2+}\) as Co\({}_{3}\)O\({}_{4}\) (s), together with the production of an aqueous phase rich in LiCl. However, in practice, the precipitation of Co\({}_{3}\)O\({}_{4}\) (s) from dissolved Co\({}^{2+}\) needs a precursor to take place [28]. This would explain the presence of Co\({}^{2+}\) in the dissolution at the end of the experiments. Instead, the formation of Co\({}_{3}\)O\({}_{4}\) is more likely to happen through the decomposition of Li\({}_{0.5}\)CoO\({}_{2}\) as follows:  
\[\mathrm{Li}_{0.5}\mathrm{CoO}_{2}(s)\rightleftarrows\frac{1}{2}\mathrm{LiCoO }_{2}(s)+\frac{1}{6}\mathrm{Co}_{3}\mathrm{O}_{4}(s)+\frac{1}{6}\mathrm{O}_{ 2}(g) \tag{20}\]  
Furthermore, the plateau observed in the experimental data could be associated with kinetic mechanisms where Co\({}_{3}\)O\({}_{4}\) (s) forms in the outer part of the LiCoO\({}_{2}\) (s) particles, acting as a passivating layer that stops the leaching process [29; 30]. This behavior would explain why higher acid concentrations and the use of stronger reducing agents, such as H\({}_{2}\)O\({}_{2}\), produce higher extraction yields through the elimination of that passive Co\({}_{3}\)O\({}_{4}\) (s) outer layer. Figure 2: Time-transient values for the percentage of extracted metal with respect to the amount in the initial solid. For a better understanding of the chemical processes involved, the solid surface properties of the solid matrix before and after experiments were studied by XPS analysis. Figure 3 presents the results of the XPS analysis of the LiCoO\({}_{2}\) (s) particles, showing the binding energy of the particles (a) before the extraction and (b) 6 days after the extraction.