Synthetic Sulfide Concentrate Dissolution Kinetics in HNO3 Media

The nature of tennantite (Cu12As4S13), chalcopyrite (CuFeS2) and sphalerite (ZnS) particles’ mixture dissolution in nitric acid (HNO3) media was investigated in this study. The effects of temperature (323–368 K), HNO3 (1–8 mol/L) and Fe3+ (0.009–0.036 mol/L) concentrations, reaction time (0–60 min) and pyrite (FeS2) additive (0.5/1–2/1; FeS2/sulf.conc.) on the conversion of the minerals were evaluated. It has been experimentally shown that the dissolution of the mixture under optimal conditions (>353 K; 6 mol/L HNO3; FeS2/synt. conc = 1/1) allows Cu12As4S13, CuFeS2 and ZnS conversion to exceed 90%. The shrinking core model (SCM) was applied for describing the kinetics of the conversion processes. The values of Ea were calculated as 28.8, 33.7 and 53.7 kJ/mol, respectively, for Cu12As4S13, CuFeS2 and ZnS. Orders of the reactions with respect to each reactant were calculated and the kinetic equations were derived to describe the dissolution rate of the minerals. It was found that the interaction between HNO3 solution and Cu12As4S13, CuFeS2 and ZnS under the conditions investigated in this are of a diffusion-controlled nature. Additionally, the roles of Fe(III) in the initial solution and FeS2 in the initial pulp as catalysts were studied. The results indicated that the increase in Fe3+ concentration significantly accelerates the dissolution of the mixture, while the addition of FeS2 forms a galvanic coupling between FeS2, and Cu12As4S13 and CuFeS2, which also accelerates the reaction rate. The results of the study are considered useful in developing a hydrometallurgical process for polymetallic sulfide raw materials treatment.


Introduction
Intensive exploitation of the primary raw materials in the non-ferrous metals industry resulted in the depletion of the rich deposits as a consequence of seeking alternative sources of raw materials. In view of the current trend in decreasing the metal content in the ore, smelters adapt to lower grade and technogenic raw materials [1]. One of the most specific raw material types are arsenic-containing ores and concentrates since their treatment is associated with additional environmental risks and technological complexity. Thus, along with the familiar minerals in copper industry such as chalcopyrite (CuFeS 2 ), covellite (CuS), chalcocite (Cu 2 S), bornite (Cu 5 FeS 4 ) and sphalerite (ZnS), sulfide ores occasionally contain minerals of the Fachlor group, such as tennantite (Cu 12 As 4 S 13 ) and tetrahedrite (Cu 12 Sb 4 S 13 ), which complicates the processing of the obtained ore/concentrates using typical approaches [2].

Experimental Procedure
The dissolution of the synthetic concentrate in HNO3 solution was conducted in a 500 mL round-bottom borosilicate glass reaction vessel (Lenz Laborglas GmbH & Co. KG, Wertheim, Germany) with a thermostatic jacket, which was thermostated using a Huber KISS-205B circulator (Huber Kältemaschinenbau AG, Offenburg, Germany). The reactor is equipped with an IKA EUROSTAR 20 digital overhead stirrer (IKA ® -Werke GmbH & Co. KG, Staufen, Germany).
The values of the change in the Gibbs energy were calculated using the HSC Chemistry Software v. 9.9 (Metso Outotec Finland Oy, Tampere, Finland).
To examine the synthetic concentrate dissolution in HNO3 solution, a 5 g synthetic concentrate sample (particle size +20-40 µm) was added into the 200 mL of 1-8 mol/L HNO3 solution when the temperature inside the leaching vessel reached the desired temperature (323-368 K). When applicable, an additive of FeS2 was added to the initial pulp with different mass ratios of FeS2 to synthetic concentrate sample: 0.5/1, 1/1, 1.5/1, 2/1. The latter was equal to 2.5, 5, 7.5 and 10 g of FeS2 additive, respectively. During the experimental runs, samples were withdrawn from the reaction vessel at regular time intervals (1, 1.5, 2, 5, 15, 30, 45 and 60 min) using an automatic dispenser Sartorius Proline (Mine-beaIntecAachen GmbH & Co. KG, Aachen, Germany) and filtered using a 45 µm syringe filter. The final pulp after the experiments was filtered using a Buchner funnel with filter paper. The solid residue (cake) was washed with distilled water, dried in an oven at a temperature of 274 K at least for 1 h, weighed, and analyzed further for the residue characterization. The solution samples received during the experiments as well as solutions after filtration of the final pulp were subjected to volume measuring and analysis for Cu, Fe, As and Zn. The received data was used in calculating the fraction reacted (X) and the conversion (E, %) of the minerals with the following equations:  To examine the synthetic concentrate dissolution in HNO 3 solution, a 5 g synthetic concentrate sample (particle size +20-40 µm) was added into the 200 mL of 1-8 mol/L HNO 3 solution when the temperature inside the leaching vessel reached the desired temperature (323-368 K). When applicable, an additive of FeS 2 was added to the initial pulp with different mass ratios of FeS 2 to synthetic concentrate sample: 0.5/1, 1/1, 1.5/1, 2/1. The latter was equal to 2.5, 5, 7.5 and 10 g of FeS 2 additive, respectively. During the experimental runs, samples were withdrawn from the reaction vessel at regular time intervals (1, 1.5, 2, 5, 15, 30, 45 and 60 min) using an automatic dispenser Sartorius Proline (Mine-beaIntecAachen GmbH & Co. KG, Aachen, Germany) and filtered using a 45 µm syringe filter. The final pulp after the experiments was filtered using a Buchner funnel with filter paper. The solid residue (cake) was washed with distilled water, dried in an oven at a temperature of 274 K at least for 1 h, weighed, and analyzed further for the residue characterization. The solution samples received during the experiments as well as solutions after filtration of the final pulp were subjected to volume measuring and analysis for Cu, Fe, As and Zn. The received data was used in calculating the fraction reacted (X) and the conversion (E, %) of the minerals with the following equations: where m s and m i are the mass of As, Cu and Zn in solution after the treatment and the mass of As, Cu, Zn in the initial synthetic concentrate, respectively.

Effect of Temperature
Temperature range under investigation in this study was taken as 323-368 K, since previously published works [45] show a low conversion of sulfide minerals at ambient temperature. Thus, the chosen temperature range is of primary interest for the atmospheric leaching processes investigation.
Increasing the temperature seemed to have a significant effect on the conversion of Cu 12 As 4 S 13 (Figure 2a), CuFeS 2 ( Figure 2b) and ZnS (Figure 2c). To illustrate, at 323 K for 60 min, only 65% of Cu 12 As 4 S 13 , 45% of CuFeS 2 and 53% of ZnS were reacted, while at 368 K conversion increased to 96, 75 and 98%, respectively for Cu 12 As 4 S 13 , CuFeS 2 and ZnS.

Effect of Temperature
Temperature range under investigation in this study was taken as 323-368 K, since previously published works [45] show a low conversion of sulfide minerals at ambient temperature. Thus, the chosen temperature range is of primary interest for the atmospheric leaching processes investigation.
Increasing the temperature seemed to have a significant effect on the conversion of Cu12As4S13 (Figure 2a), CuFeS2 ( Figure 2b) and ZnS (Figure 2c). To illustrate, at 323 K for 60 min, only 65% of Cu12As4S13, 45% of CuFeS2 and 53% of ZnS were reacted, while at 368 K conversion increased to 96, 75 and 98%, respectively for Cu12As4S13, CuFeS2 and ZnS.
(a) According to the conversion profiles, the progress of the reaction was observed to slow down with time. Additionally, the presence of a clear inflection line in curves allowed us to suggest an internal diffusion mechanism of the interactions. The possible internal diffusion  Figure 3 illustrates the effect of increasing the initial concentration of HNO 3 ranging from 1 to 8 mol/L on the conversion of Cu 12 As 4 S 13 , CuFeS 2 and ZnS. The increase in HNO 3 concentration seemed to also improve the rate and extent of the sulfides conversion. Over the reaction period, the conversion of Cu 12  According to the conversion profiles, the progress of the reaction was observed to slow down with time. Additionally, the presence of a clear inflection line in curves allowed us to suggest an internal diffusion mechanism of the interactions. The possible internal diffusion may cause elemental sulfur formation during the processing of the synthetic concentrate by the following reactions:

Effect of Fe(III) Concentration
The effect of Fe (III) concentration ranging from 0.009 to 0.036 mol/L on the conversion of Cu 12 As 4 S 13 , CuFeS 2 and ZnS was investigated. The results in Figure 4 show a moderate increase in the reaction rate by increasing the Fe (III) concentration. After 60 min of reaction at 0.009 mol/L Fe (III), 79, 65 and 91% of Cu 12 As 4 S 13 (Figure 4a), CuFeS 2 ( Figure 4b) and ZnS (Figure 4c), respectively, were converted, compared with 90, 96 and 98% conversions, respectively at 0.036 mol/L. The interaction of main minerals in synthetic concentrate with Fe(III) are supposed to proceed according to the following reactions: The significant effect of HNO3 concentration on the reaction rate and conversion extent may also indicate that the reactions are controlled by diffusion through the product layer, where the increasing HNO3 concentration in the initial solution leads to acceleration of S° to SO4 2− transformation and as consequence, the predominant course of reactions by Equations (3), (5) and (7).

Effect of FeS2 Additive
Four different mass ratios of FeS2 to synthetic concentrate (0.5/1, 1/1, 1.5/1, 2/1, which is equal to 2.5, 5, 7.5 and 10 g of FeS2 adding) were used in the experiments to examine the effect of galvanic coupling. The results are shown in Figure 5.

Effect of FeS 2 Additive
Four different mass ratios of FeS 2 to synthetic concentrate (0.5/1, 1/1, 1.5/1, 2/1, which is equal to 2.5, 5, 7.5 and 10 g of FeS 2 adding) were used in the experiments to examine the effect of galvanic coupling. The results are shown in Figure 5.
version [35]. The obtained results indicate that the oxidation of Cu12As4S13 and CuFeS2 (Equations (4) and (6)) may proceed with the formation of S°, which passivates the surface of the minerals. At the same time, FeS2 may act as an alternative catalytic surface for these minerals. The latter provides the reduction of HNO3 on FeS2 surface and decomposition of other sulfide minerals [45].
In the experiments with 0.5/1 mass ratio, the conversion of Cu12As4S13 (Figure 5a), CuFeS2 ( Figure 5b) and ZnS (Figure 5c) appeared to be limited to 64, 58 and 89%, respectively. Usage of the higher mass ratio (2/1) resulting the conversion of the minerals to be increased up to 83, 83 and 98%, respectively for Cu12As4S13, CuFeS2 and ZnS.  Figure 6 shows the SEM images (Figure 6a,b) and EDX-mapping of the residue (Figure 6c-f) after leaching the synthetic concentrate in HNO3 solution. EDX-mapping images confirm the formation of S° layer on the surface of unreacted synthetic concentrate particles. Thus, the dark layer over the muted points of Fe ( Figure 6c) and Cu (Figure 6d) as well as bright green points on the image of joint EDX-mapping (Figure 6f) over all other components allow us to confirm the S° presence. Thus, the mentioned conditions suggest proceeding interactions by Equations (4) and (6).

Characteristics of the Received Cakes
The S° content in the residue was observed to be 56% and the conversion of sulfide sulfur to S° appeared to be about 38%. Under these conditions, the conversion of Cu12As4S13, CuFeS2, and ZnS was 59, 60 and 84%, respectively. As expected, increasing the mass of additive resulted in moderately improved conversion [35]. The obtained results indicate that the oxidation of Cu 12 As 4 S 13 and CuFeS 2 (Equations (4) and (6)) may proceed with the formation of S • , which passivates the surface of the minerals. At the same time, FeS 2 may act as an alternative catalytic surface for these minerals. The latter provides the reduction of HNO 3 on FeS 2 surface and decomposition of other sulfide minerals [45].
In the experiments with 0.5/1 mass ratio, the conversion of Cu 12 As 4 S 13 (Figure 5a), CuFeS 2 ( Figure 5b) and ZnS (Figure 5c) appeared to be limited to 64, 58 and 89%, respectively. Usage of the higher mass ratio (2/1) resulting the conversion of the minerals to be increased up to 83, 83 and 98%, respectively for Cu 12 As 4 S 13 , CuFeS 2 and ZnS.

Characterization of Residues
Characteristics of the Received Cakes Figure 6 shows the SEM images (Figure 6a,b) and EDX-mapping of the residue (Figure 6c In contrast to the experiment without the FeS2 additive ( Figure 6), the results with the additive (FeS2/synt. conc = 1/1) showed a lesser S° content.
The Fe and Cu points indicated in one component EDX-mapping images (Figure 7c and Figure 7d, respectively) became brighter. According to Figure 7a,b, the residue has a heterogeneous surface resembling conglomerates, while the experiment without FeS2 additive shows a more homogeneous structure due to the covering of the particles by S°. The green zones in Figure 7f correspond to the distribution of S°, while the mixture of red and blue zones are copper minerals (Cu12As4S13 and CuFeS2) and FeS2.
Therefore, S° covers the surface of the synthetic concentrate in lesser extent, which confirms by the SEM-EDX residue investigation as well as the chemical composition of the residue-sulfide sulfur to S° transformation decreased to 23%, while the S° content in the solid residue decreased to 14%. Under these conditions of dissolution, the conversion of Cu12As4S13, CuFeS2 and ZnS was 87, 91 and 98%, respectively. The S • content in the residue was observed to be 56% and the conversion of sulfide sulfur to S • appeared to be about 38%. Under these conditions, the conversion of Cu 12 As 4 S 13 , CuFeS 2 , and ZnS was 59, 60 and 84%, respectively.
In contrast to the experiment without the FeS 2 additive (Figure 6), the results with the additive (FeS 2 /synt. conc = 1/1) showed a lesser S • content.
The Fe and Cu points indicated in one component EDX-mapping images (Figure 7c,d, respectively) became brighter. According to Figure 7a,b, the residue has a heterogeneous surface resembling conglomerates, while the experiment without FeS 2 additive shows a more homogeneous structure due to the covering of the particles by S • . The green zones in Figure 7f correspond to the distribution of S • , while the mixture of red and blue zones are copper minerals (Cu 12 As 4 S 13 and CuFeS 2 ) and FeS 2 .
Therefore, S • covers the surface of the synthetic concentrate in lesser extent, which confirms by the SEM-EDX residue investigation as well as the chemical composition of the residue-sulfide sulfur to S • transformation decreased to 23%, while the S • content in the solid residue decreased to 14%. Under these conditions of dissolution, the conversion of Cu 12 As 4 S 13 , CuFeS 2 and ZnS was 87, 91 and 98%, respectively. Figure 8 shows the XRD patterns of the solid residues after the dissolution of synthetic concentrate in HNO 3 solution. The obtained data additionally confirms that the presence of FeS 2 allows to limit the formation of S • . green zones in Figure 7f correspond to the distribution of S°, while the mixture of red and blue zones are copper minerals (Cu12As4S13 and CuFeS2) and FeS2. Therefore, S° covers the surface of the synthetic concentrate in lesser extent, which confirms by the SEM-EDX residue investigation as well as the chemical composition of the residue-sulfide sulfur to S° transformation decreased to 23%, while the S° content in the solid residue decreased to 14%. Under these conditions of dissolution, the conversion of Cu12As4S13, CuFeS2 and ZnS was 87, 91 and 98%, respectively.  Figure 8 shows the XRD patterns of the solid residues after the dissolution of synthetic concentrate in HNO3 solution. The obtained data additionally confirms that the presence of FeS2 allows to limit the formation of S°. SEM images (Figure 9) of the material after dissolution for 15 min (bend point in Figure 5 for Cu12As4S13 and CuFeS2) coupled with EDX analysis (Table 2) suggest that most of the S° was formed towards the end of this period and the subsequent dissolution of the material occurs at its coating by S°.
Therefore, it is appropriate to conclude that the diffusion in the system is the result  Figure 8 shows the XRD patterns of the solid residues after the dissolution of synthetic concentrate in HNO3 solution. The obtained data additionally confirms that the presence of FeS2 allows to limit the formation of S°. SEM images (Figure 9) of the material after dissolution for 15 min (bend point in Figure 5 for Cu12As4S13 and CuFeS2) coupled with EDX analysis (Table 2) suggest that most of the S° was formed towards the end of this period and the subsequent dissolution of the material occurs at its coating by S°.
Therefore, it is appropriate to conclude that the diffusion in the system is the result of S° formation during the first 10-20 min of the experiment. After that, the dissolution process shifts to diffusion control. SEM images (Figure 9) of the material after dissolution for 15 min (bend point in Figure 5 for Cu 12 As 4 S 13 and CuFeS 2 ) coupled with EDX analysis (Table 2) suggest that most of the S • was formed towards the end of this period and the subsequent dissolution of the material occurs at its coating by S • . Materials 2022, 15, x FOR PEER REVIEW 10 of 16

Kinetics Analysis
As it was shown, the conversion of sulfides is significantly affected by temperature, HNO3 concentration and the presence of FeS2 in the system; that could mean possible control of the reactions by both chemical reaction and diffusion. To determine the limiting stage of the processes, the most commonly used kinetic equations of SCM describing liquid-solid reactions [46] were used to fit into the experimental data (Table 3). According to the results present in Figures 2-5, the higher conversion degree during the initial period of reaction was observed for ZnS, therefore, kinetic analysis of the mineral was carried out in the period from 0 to 2 min, while for Cu12As4S13 and CuFeS2, from 0 to 60 min. Table 3. Typical SCM kinetic equations applied for systems with spherical particles.

№
Limiting Stage Formula 1 Diffusion through the product layer (sp) Surface chemical reaction (sp) 1 − (1 − X) 1/3 As shown in Figure 10, the SCM equation typically applied for diffusion kinetic system (Table 4, Equation (1)) can be used to describe the conversion processes with high values of the determination coefficient (R 2 ).  Therefore, it is appropriate to conclude that the diffusion in the system is the result of S • formation during the first 10-20 min of the experiment. After that, the dissolution process shifts to diffusion control.

Kinetics Analysis
As it was shown, the conversion of sulfides is significantly affected by temperature, HNO 3 concentration and the presence of FeS 2 in the system; that could mean possible control of the reactions by both chemical reaction and diffusion. To determine the limiting stage of the processes, the most commonly used kinetic equations of SCM describing liquid-solid reactions [46] were used to fit into the experimental data (Table 3). According to the results present in Figures 2-5, the higher conversion degree during the initial period of reaction was observed for ZnS, therefore, kinetic analysis of the mineral was carried out in the period from 0 to 2 min, while for Cu 12 As 4 S 13 and CuFeS 2 , from 0 to 60 min.
Surface chemical reaction (sp) 1 − (1 − X) 1/3 As shown in Figure 10, the SCM equation typically applied for diffusion kinetic system (Table 4, Equation (1)) can be used to describe the conversion processes with high values of the determination coefficient (R 2 ).  The activation energy values (Ea) were calculated using the Arrhenius law ( Figure  11). Thus, Ea was determined as 28.8 kJ/mol for Cu12As4S13 and 33.7 kJ/mol for CuFeS2, values that are typical for inner-diffusion processes [46]. The activation energy values for ZnS treatment were determined as 53.7 kJ/mol, which is more typical for kinetically controlled processes. However, according to the literature [47][48][49][50][51][52], a high Ea value is not always allowed to make the final decision on the process nature.  The activation energy values (E a ) were calculated using the Arrhenius law ( Figure 11). Thus, E a was determined as 28.8 kJ/mol for Cu 12 As 4 S 13 and 33.7 kJ/mol for CuFeS 2 , values that are typical for inner-diffusion processes [46]. The activation energy values for ZnS treatment were determined as 53.7 kJ/mol, which is more typical for kinetically controlled processes. However, according to the literature [47][48][49][50][51][52], a high E a value is not always allowed to make the final decision on the process nature. The reaction order with respect to HNO3 concentration, Fe (III) ions concentration and amount of FeS2 additive were calculated using the graphical method ( Table 4). The fractional order of reaction with respect to Fe (III) ions concentration and amount of FeS2 additive at Cu12As4S13, CuFeS2 and ZnS treatment suggests that the nature of the processes is diffusion controlled. At the same time, the reaction order with respect to HNO3 concentration at Cu12As4S13, CuFeS2 and ZnS treatment is more typical for chemical reaction control. The latter could be a result of aggressive impact on the S° layer that allows it to overcome the effect of passivation.

OR PEER REVIEW
As a result, the research data were generalized and the general kinetic equations were established separately for Cu12As4S13, CuFeS2 and ZnS treatment, which consider the influence of temperature, concentration of reagents and duration of the experiments. As it shown in Figure 12, the relationship between the equations 1 − 3(1 − X) 2/3 + 2·(1 − X) and CHNO3·CFe(III)·CFeS2·exp[-Ea/(R·T)]·τ·10 3 for all experimental data was established, and the data points were evenly distributed along straight lines with a high R 2 . The reaction order with respect to HNO 3 concentration, Fe (III) ions concentration and amount of FeS 2 additive were calculated using the graphical method ( Table 4). The fractional order of reaction with respect to Fe (III) ions concentration and amount of FeS 2 additive at Cu 12 As 4 S 13 , CuFeS 2 and ZnS treatment suggests that the nature of the processes is diffusion controlled. At the same time, the reaction order with respect to HNO 3 concentration at Cu 12 As 4 S 13 , CuFeS 2 and ZnS treatment is more typical for chemical reaction control. The latter could be a result of aggressive impact on the S • layer that allows it to overcome the effect of passivation.
As a result, the research data were generalized and the general kinetic equations were established separately for Cu 12 As 4 S 13 , CuFeS 2 and ZnS treatment, which consider the influence of temperature, concentration of reagents and duration of the experiments. As it shown in Figure 12, the relationship between the equations 1 -3(1 -X) 2/3 + 2·(1 -X) and C HNO3 ·C Fe(III) ·C FeS2 ·exp[-E a /(R·T)]·τ·10 3 for all experimental data was established, and the data points were evenly distributed along straight lines with a high R 2 .
The kinetic equations for treatment of Cu 12 As 4 S 13 , CuFeS 2 and ZnS can be written as follows (11)-(13), respectively: Thus, the processes of sulfide minerals dissolution under investigated conditions are limited by internal diffusion [53]. The assessment was based on the obtained E a values, orders of the reactions with respect to the reactants, SCM equations fitting and SEM-EDS investigation of the samples. Pyrite was proved as an effective catalytic surface for the reduction of nitrate ions and iron (III) with empirical order less than 1.
trol. The latter could be a result of aggressive impact on the S° layer that allows it to over-come the effect of passivation.
As a result, the research data were generalized and the general kinetic equations were established separately for Cu12As4S13, CuFeS2 and ZnS treatment, which consider the influence of temperature, concentration of reagents and duration of the experiments. As it shown in Figure 12, the relationship between the equations 1 − 3(1 − X) 2/3 + 2·(1 − X) and CHNO3·CFe(III)·CFeS2·exp[-Ea/(R·T)]·τ·10 3 for all experimental data was established, and the data points were evenly distributed along straight lines with a high R 2 .

Conclusions
The current work was undertaken to deepen the understanding of the nature of the dissolution process for sulfides Cu 12 As 4 S 13 , CuFeS 2 and ZnS in HNO 3 media with application FeS 2 and Fe (III) ions as catalysts.
It was observed that HNO 3 concentration and temperature have the most significant influence on the conversion degree of Cu 12 As 4 S 13 , CuFeS 2 and ZnS. The values of E a were calculated as 28.8, 33.7 and 53.7 kJ/mol, respectively for Cu 12 As 4 S 13 , CuFeS 2 and ZnS.
SEM-EDS scanning of the solid residues showed a presence of S • layer covering the surface of the minerals. The latter combined with E a values and orders of the reactions with respect to the reactants obtained as well as SCM equations fitting allowed us to propose that the dissolution processes are of a diffusion nature.
It was additionally demonstrated that the presence of FeS 2 in the system accelerates the conversion process due to galvanic coupling between minerals.
The results obtained can be used in predicting hydrometallurgical processes for sulfide materials such as copper-arsenic ores and concentrates treatment in HNO 3 media.
Further detailed kinetic studies on the dissolution of sulfide minerals in HNO 3 media such as Cu 3 AsS 4 , Cu 12 Sb 4 S 13 , Sb 2 S 3 , Cu 5 FeS 4 are of great interest. Furthermore, the complex processing of the low-grade sulfide raw materials in HNO 3 media is associated with the extraction of arsenic into the solution, which necessitates the following neutralization of nitrous gases as well as the arsenic utilization in the form of environmentally friendly compounds. These studies are of high relevance in terms of creating industrial hydrometallurgical technology.