*3.1. Theoretical Background for the Dissolution of Metals*

To better understand the processes that occur in the case of WPCB disassembly, through the dissolution of metals with Fe3+ in the presence of Cl−, the standard apparent potentials (*E*') were calculated for the potentially active reactions (PAR) based on the standard normal potentials (*E*0) and the thermodynamic equilibrium constants for the formation of complexes [37–39]. In order to calculate the *E*, it is necessary to identify the chemical species present in the solution, with respect to the equilibriums in which they are involved. In the case of copper, the species involved in the process were considered on the basis of the Pourbaix diagram for the copper–chlorine–water system at 25 ◦C at a total Cl− concentration of 1.5 M [40].

In the case of the other metals, the species involved in the chemical process have been identified from the literature based on their stability in the reaction environment [37,38,41,42]. The *E*' values (Table 3) were obtained (Equation (1)) based on the Nernst equation applied for redox reactions, which involves the complexation of the oxidized form of the redox couple [21].

$$E' = E^0 - \frac{0.059}{n} \log \mathcal{K}\_{f\_{\rm av}} \tag{1}$$

where *<sup>E</sup>*<sup>0</sup> is the standard normal potential, *<sup>n</sup>* is the number of electrons changed, and *Kfox* is the thermodynamic equilibrium constant for the formation of complexes with the oxidized form of the redox couple.


**Table 3.** *E*' values for the involved potential active reaction.

As was expected, the standard apparent potential decreases when the complexing agent employs the oxidized form, and the potential shift will be greater as the stability of the complexes is higher. Therefore, *E'* differs the most from *E*<sup>0</sup> in the case of Au, Ag, and Cu(I), for which the thermodynamic equilibrium constants for the formation of chloro-complexes are the highest. In the case of the other metals, where the complexation equilibrium is less shifted to the formation of chloro-complexes, the redox potential varies insignificantly under the experimental conditions. Additionally, from the E' values calculated for the PAR, it can be seen that Fe3+ is an efficient oxidant in the dissolution of metals, with the exception of gold.

It is also important to note that the dissolution processes lead to chloride complexes of Cu, Sn, Pb, Fe, in which the metals may have different oxidation forms. As a result, the *E'* values (Table 4) for these redox couples, in which both forms are involved in complexation processes, was calculated by the following equation:

$$E' = E^0 + \frac{0.059}{n} \log \frac{K\_{f\_{ox}}}{K\_{f\_{red}}}.\tag{2}$$


**Table 4.** *E'* values for PAR that involve the complexation of both forms of the redox couple.

As can be seen from Table 4, the existence of significant differences between the E' values of these redox couples implies a state of un-equilibrium in these working conditions. The evolution of the system towards equilibrium determines the change in the concentration of the electroactive species, especially in the case of metals that may have different oxidation forms. The most important redox reactions leading to the installation of redox equilibrium are those in which Fe3+ oxidizes Cu+ to Cu2+ and Sn2+ to Sn4+. From the strong positive value of E' for the couple PbCl2<sup>−</sup> <sup>6</sup> /PbCl2<sup>−</sup> <sup>4</sup> , it is concluded that Pb is more stable in the reduced form PbCl2<sup>−</sup> <sup>4</sup> .

Therefore, from the oxidation reaction of Pb by Fe3+, only Pb2+ is formed without its subsequent oxidation to Pb4+. The above conclusions are in agreement with the values of redox equilibrium constants (Kr) for the dissolution reactions of the metals from the WPCBs samples, calculated on the basis of Equation (4) using the E' values from Tables 3 and 4.

For a redox reaction in the general form:

$$\mathbf{m}\,\mathrm{ox}\_1 + \,\mathrm{p}\,\mathrm{red}\_2 \rightleftharpoons \mathbf{m}\,\mathrm{red}\_1 + \,\mathrm{p}\,\mathrm{ox}\_2\tag{3}$$

The equilibrium constant is defined as follows [32]:

$$\mathbf{K\_{r}} = 10^{\frac{\text{mp}(\text{E}'\_{1} - \text{E}'\_{2})}{0.099}} \tag{4}$$

where mp—number of electrons transferred between the redox couples.

The Kr values increase (the equilibrium will be shifted to the right) with the number of electrons transferred between the redox couples and greater the difference between the values of *E'* for the two systems. The values of the redox equilibrium constants, calculated according to Equation (4), are presented in Table 5.

**Table 5.** The values of redox equilibrium constants calculated for the leaching reactions.


From the values of redox equilibrium constants, Table 5, it is observed that, for all metals except gold, redox reactions are strongly displaced towards their dissolution with the formation of chloro-complexes. Based on the redox equilibrium constant values from Table 5, it can be assumed that the dissolution rate of metals will have following order: Zn > Sn > Fe > Ni > Pb > Cu > Ag. Tin is located after Zn, although from the E' value from Table 3, Sn should be between Pb and Cu. This can be explained by the fact that the redox equilibrium constant depends both on the potential difference between the redox couples and on the number of electrons transferred. Considering that Sn changes 4e− while the other metals change only 2e−, the redox equilibrium constant is much higher (1.42 × <sup>10</sup>49), which is assumed to promote its dissolution.
