3.2.3. Effect of the Concentration of [Na2S2O3]

The study of gold and silver extraction contained in a sedimentary ore, using the Na2S2O3-Air system, was done to establish the effect of the [Na2S2O3] concentration, temperature, and pH.

Figure 6A shows the leached fraction of Ag that was analyzed by the core model for diffusive control [41–43], which was [1 − 2/3XAg − (1 − XAg) <sup>2</sup>/3]. Straight lines were obtained, and their slopes represented the experimental rate constant (kexp). Thiosulfate concentration had no effect on the rate of reaction. Since all experiences were done at a high stirring rate, the oxygen input could be enough to maintain a stoichiometric excess during the progress of the reaction. This caused a limited effect on the leaching of silver with respect to thiosulfate concentration, getting a low order of the reaction, n = −0.61 (Figure 6B).

Figure 7A shows the leached fraction of Au, which was evaluated by the same core model for diffusive control [1 − 2/3XAu − (1 − XAu) <sup>2</sup>/3]. Similar to silver leaching, thiosulfate concentration did not affect the leaching reaction rate. In this case, the presence of pyrite and Ag2S could promote the generation of *S***<sup>0</sup>** (*s*)) and/or *<sup>S</sup>*+**<sup>2</sup>** (*s*) , which would be deposited on the gold surface, passivating its dissolution. This also provided a low order of reaction, n = −0.09 (Figure 7B).

**Figure 6.** Kinetic study of silver leaching; effect of the thiosulfate concentration: (**A**) *kexp* and (**B**) order of reaction n = −0.61.

**Figure 7.** Kinetic study of gold leaching; effect of the thiosulfate concentration: (**A**) *kexp* and (**B**) order of reaction n = −0.09.

#### 3.2.4. Effect of the Temperature

The effect of temperature for silver leaching in thiosulfate solutions is shown in Figure 8A,B. For low and high temperatures (298–328 K), the values were quite similar, giving low reaction rates. In conclusion, the influence of temperature was limited.

The activation energy was calculated by plotting the natural logarithm of *kexp* against the reciprocal of temperature. The slope (m= −(Ea/R)) of the linear curve represented the activation energy (Ea) divided by the negative value of the universal gas constant (Figure 8B). For silver leaching, the calculated energy of activation was of 3.15 kJ/mol, which was representative of a diffusive control [41–43]. This was also observed by the fitting obtained with the diffusive control model. The obtained order of reaction was low, and the curve type "S" had no induction period, then the process was not dependent on both thiosulfate and temperature, and the slow diffusion of products from the particle's surfaces to the deep of solution controlled the overall process.

For gold leaching, the effect of temperature according to the diffusive control model is shown in Figure 9A. The rate constants were quite similar in the range of temperature from 298 to 313 K (0.0011–0.0014), but he slight increase at higher temperatures (318 and 323 K) could indicate that the process was carried out by a combination of both chemical and diffusive control. Besides, the activation energy that is shown in Figure 9B was 36.44 kJ/mol, which, according to the literature, is representative of mixed control [41–43].

**Figure 8.** Kinetic study of silver leaching; effect of the temperature: (**A**) *kexp* and (**B**) energy of activation, Ea = 3.15 kJ/mol.

**Figure 9.** Kinetic study of gold leaching; effect of the temperature: (**A**) *kexp* and (**B**) energy of activation, Ea = 36.44 kJ/mol.

According to the obtained results, the kinetic expressions for silver (Equation (7)) and gold (Equation (8)) leaching in *S*2*O*−<sup>2</sup> <sup>3</sup> medium were:

For silver, diffusive control

$$\frac{r\_0^2}{V\_M} \left[ 1 - \frac{2}{3} \left| X\_{A\mathfrak{g}} - \left( 1 - \left| X\_{A\mathfrak{g}} \right)^{\frac{2}{3}} \right) \right. \right] = \ 2D\_\varepsilon \left[ \mathcal{S}\_2 O\_3^{-2} \right] \times t \tag{8}$$

For gold, when control could be by chemical reaction

$$\frac{r\_0^2}{V\_M} \left[ 1 - \left( 1 - X\_{A\mu} \right)^{\frac{1}{3}} \right] = 3.736 \,\text{x} \,\text{10}^3 \,\text{exp}^{\frac{-36.440}{RT}} \left[ S\_2 O\_3^{-2} \right]^{-0.09} \times \text{t} \tag{9}$$

For gold, when control could be by diffusion of products through the product layer

$$\frac{r\_0}{V\_M} \left[ 1 - \frac{2}{3} \left( X\_{Au} - \left( 1 - X\_{Au} \right)^{\frac{2}{3}} \right) \right] = \ 2D\_\varepsilon \left[ S\_2 O\_3^{-2} \right] \times t \tag{10}$$

where *VM* <sup>=</sup>1.44×10−<sup>9</sup> m3·mol−<sup>1</sup> for silver, and *VM* <sup>=</sup>6.22×10−<sup>9</sup> m3·mol−<sup>1</sup> for gold, *<sup>R</sup>*=8.31 J·mol−1·K<sup>−</sup>1, *r*<sup>0</sup> in m, *De* is the diffusion coefficient through the product layer, T in Kelvin, [*S*2*O*<sup>3</sup> <sup>−</sup>2] is in mol·m−3, and *t* is in seconds.

#### 3.2.5. Effect of the pH

The effect of the pH for silver leaching is shown in Figure 10A,B. Figure 10A represents the treatment of results with the diffusive control model and the obtained experimental rates. The rates decreased with increasing the pH, which was faster at pH 7, having a poor effect at a higher pH. Figure 10B shows that the influence of pH over the overall reaction rate was significant, finding an order of reaction of n = 5.03.

**Figure 10.** Kinetic study of silver leaching; effect of the pH: (**A**) *kexp* and (**B**) order of reaction n = 5.03.

To conclude, for gold leaching, the pH effect is shown in Figure 11A,B. Unlike what happened with the leaching of silver, the experimental rate constants were similar for all the analyzed pH values. Consequently, a poor effect of this variable over the overall rate of the process was observed (Figure 11A). However, all experimental rate constants were low. This might be explained by the presence of small amounts of sulfur minerals since their formation is inevitable even in small quantities, promoting a partial degradation of thiosulfate. The deposition of this formed sulfur on the surface of the gold particles promoted the decrease in its dissolution rate. Finally, Figure 11B displays the effect of pH over the overall gold leaching reaction rate. The order of reaction was n = 0.94, concluding that the pH had no effect on gold leaching under the thiosulfate concentration and temperatures considered.

**Figure 11.** Kinetic study of gold leaching; effect of the pH: (**A**) *kexp* and (**B**) order of reaction n = 0.94.

#### **4. Discussion**

The mineral studied here presented significant amounts of Ag and Au, including light rare earths contents, which increased its commercial importance. However, this research aimed to analyze the leaching kinetics of gold and silver in thiosulfate solutions without adding Cu(II), which allowed verifying the ability of the leaching reagent according to the nature and composition of the ore. Although leaching using thiosulfate solutions is considered a viable alternative to cyanidation [16–18,39], nowadays, it is not used at a big scale due to the high reagent consumption and the difficulty in recovering metallic gold and silver [9]. Still, it works appropriately with metallic ores containing carbonaceous materials [35], like the ore here studied (having about a 2% C).

The use of thiosulfate as a leaching reagent needs more attention since some problems can arise, the reagent is unstable, and it can self-decomposed or reduced to *S*0, *S*−, and *S*−<sup>2</sup> <sup>3</sup> . These species may deposit on the surface of the metal, hindering its dissolution [25]. Additionally, the reaction is prolonged without the addition of Cu(II) and ammonia [44]. However, for this study, we decided to use sodium thiosulfate solely since the characteristics of mineral gave a chance to get promising results. Yen et al. [45] concluded that high concentrations of thiosulfate, high dissolved oxygen, and high temperatures increased the consumption of thiosulfate. Consequently, low metallic recoveries were obtained. In parallel, dilute concentrations of thiosulfate, low oxygen concentration, and low temperatures could reduce the rate of gold dissolution. However, the results of this study were encouraging, getting 80% of silver recovery using 500 mol·m<sup>3</sup> of sodium thiosulfate, pH 7, the temperature of 298 K, stirring rate of 500 s<sup>−</sup>1, and using air in low concentration (just by incorporation during mechanical stirring). In the case of gold, the maximum dissolution was of 20% using 130 mol·m3 of sodium thiosulfate, pH 9, the temperature of 298 K, stirring rate of 500 s−1, and using air in low concentration (just by incorporation during mechanical stirring). As known, the experimental conditions constantly change during leaching, and it could be difficult to control each of them with adequate precision. Similarly, the use of relatively low leaching reagent concentrations with limited oxygen supply is an easy method to avoid high thiosulfate consumption during the leaching process [9].

Some authors [28,38] reported interesting results for the silver leaching with thiosulfate solutions, concluding that the diffusion of oxygen controls the process through the product layer. The order of the reaction was similar to that found here, which was n = −0.61 for thiosulfate concentrations 200–500 mol·m−3. Other cases displayed values like n = 0.074 for thiosulfate concentrations 100–500 mol·m−3, for silver leaching contained in mining burrows [38], n = 0.41 for thiosulfate concentration 25–200 mol·m−<sup>3</sup> [28], and n = 0 for thiosulfate concentration 200–600 mol·m−3, for leaching of metallic silver [28]. Thiosulfate concentration does not affect the reaction rate for silver leaching that contrast works with different mineralogies [9]. For this reason, more in-depth researches are needed to disclose the behavior of thiosulfate solutions over silver leaching, according to the nature of the minerals and species involved.

For gold leaching, the literature reports that the thiosulfate concentration, joint with some contents of Cu(II) and ammonia, have a detrimental effect on the gold dissolution by the presence of minerals, such as pyrite and other sulfurs [25]. This promotes a self-decomposition of the thiosulfate and, as a consequence, higher consumption of this reactant. In this study, it was found that the thiosulfate concentration had no effect on the reaction rate getting reaction order of n = −0.09 (quite similar to that obtained for silver leaching). The latter means that the absence of important amounts of sulfur minerals might avoid the formation of *S*<sup>0</sup> and *S*<sup>−</sup>2, which deposit on the gold surface, reducing the dissolution.

According to the evaluation of the effect of the temperature on the rate of silver leaching, the activation energy found here was Ea = 3.15 kJ/mol. This corresponded to a diffusive control, and it validated the model used for the treatment of data [41–43]. In this case, the overall reaction was controlled by oxygen diffusion through the product layer because the chemical reaction of the complexation of Ag is too fast. The above result was consistent with that obtained during the silver leaching contained in a mining waste [38], (even with the absence of Cu(II) where the apparent energy of activation was of Ea = 1.91 kJ/mol.

When evaluating the effect of temperature during the gold leaching, it was found that the apparent energy of activation was Ea = 36.44 kJ/mol. According to previous studies, this corresponded to a mixed control [41–43]. At low temperatures, the experimental rates were low (0.0011–0.0014 s<sup>−</sup>1), and diffusive control was dominant since thiosulfate was more stable. Then, at higher temperatures, the instability of thiosulfate could lead to its decomposition, generating *S*<sup>0</sup> and *S*2<sup>−</sup> that might deposit on the gold surface [9]. This avoided a fast chemical reaction, being this step that controlled the process.

Finally, due to the concentration of *S*2*O*−<sup>2</sup> 3 could be affected by the pH (below 4 and above 12), where thiosulfate degradation or decomposition occurred, with the consequent formation of elemental sulfur (especially below a pH 4) [28,38]. Consequently, this work was executed between the valid range pH, where the thiosulfate could be more stable and was not pH-dependent. For the leaching of silver, the order of reaction was n = 5.03, indicating an apparent effect of this variable but only at pH 7. At this condition, the rate of reaction was higher than at pH 8–10. For gold dissolution, the order of reaction was n = 0.94, indicating that the pH did not alter the reaction rate, which indicated the stability of the reactant. This was because of the operational conditions used in this work and the absence of minerals like pyrite that could promote thiosulfate decomposition.

**Author Contributions:** The conceptualization was done by E.S.-R., J.H.-Á., and E.C.-S.; the methodology was executed by E.R.-C., E.S.-R., and V.R.-L.; validation was done by E.S.-R.; data curation, E.S.-R.; writing—original draft preparation, E.S.-R., E.R.-C., and J.H.-Á.; writing—review and editing, E.S.-R. and R.I.J.; supervision, E.S.-R. and V.R.-L.; funding acquisition, N.T. and R.I.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** Authors want to thank the CONACyT of the Mexican Government for its support given through the Ph.D. scholarship to the student Edmundo R. C. (CVU 430931). Thanks also go to the Autonomous University of the State of Hidalgo, Mexico, especially to the Academic Group of Advanced Materials from the AACTyM-ICBI; University of Antofagasta, Chile; Polytechnic University of Cartagena, Spain, and Northern Catholic University, Chile.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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