Effect of Potassium Salt Addition on Silver Precipitation During Hydrothermal Synthesis of Argentojarosites

Abstract

This paper presents the laboratory study results of the hydrothermal synthesis of compounds structurally related to the jarosite group, which is characterized by basic iron sulfate AFe₃(SO₄)₂(OH)₆ as the main structural component containing A⁺ cations such as K⁺, Ag⁺, and NH₄⁺. The synthesis process involves preparing the initial model solution using soluble salts of the studied metals, either jointly or individually. The resulting solution is then processed in a sealed vessel (autoclave) at a temperature exceeding 100 °C. This study was conducted within a temperature range of 105–200 °C, with experiment durations varying and a maximum dwell time of 300 min. The zero-time value was defined as the moment the autoclave reached the required temperature. It was observed that adding potassium salts to the solution during hydrothermal synthesis reduced the amount of silver precipitated as argentojarosite. An increase in process temperature from 105 °C to 200 °C resulted in a rise in silver precipitation, from 35% to 69%. The equilibrium constants of the reactions involved in the precipitation of specific jarosite group compounds were calculated, and the reaction order was determined.

1. Introduction

In recent years, processing raw copper–silver-bearing sulfide materials has gained increasing importance [1]. This is attributed to the depletion of reserves with high contents of valuable components and the need for energy-efficient methods of extraction. Consequently, low-grade materials rich in valuable metals like gold, silver, and copper, but also containing high levels of harmful impurities such as arsenic, are now being processed [2,3].

There are two primary methods for processing such materials: hydrometallurgical and pyrometallurgical techniques. Both methods involve extracting arsenic alongside valuable components [4].

Effective processing must ensure harmful impurities are converted into stable, non-toxic compounds [5,6], reducing environmental impact and avoiding penalties associated with stricter environmental regulations. For instance, in China, raw materials with arsenic content exceeding 0.5% are penalized for every 0.1% excess, significantly affecting economic viability [7,8].

Oxidative roasting followed by smelting, converting, anode casting, and electrolysis is a common method for processing copper–gold–silver sulfide ores [9,10]. Despite being well studied and extensively developed, this scheme is challenged by high levels of harmful impurities, particularly arsenic, which complicates technical operations, necessitating additional processing removal steps [11,12].

Alternatively, in addition to pyrometallurgical methods, hydrometallurgical hydrometallurgical methods like atmospheric leaching, pressure oxidation leaching (POX), and bioleaching can be employed for gold and silver recovery [13,14]. This study focuses on the POX process.

In the POX process, the sulfide components of the raw material are oxidized under high pressures and temperatures in specialized vessels operating above atmospheric pressure—autoclaves [15]. This method offers several significant advantages, including its versatility, applicability to a wide range of raw materials, rapid reaction rates, and high degree of sulfide oxidation. Additionally, the process facilitates the conversion of arsenic and sulfur into insoluble and stable compounds [16,17]. However, the POX process also has notable drawbacks, such as higher capital costs compared to other methods (e.g., oxidation roasting, bioleaching) and the need for equipment capable of withstanding high-pressure conditions.

Despite these challenges, POX has proven promising for processing the described type of raw materials. Autoclave oxidative leaching of sulfide raw materials not only enables the efficient extraction of valuable components, such as copper, gold, and silver, with separation into separate processing streams but also converts arsenic into its water-soluble form, which is subsequently precipitated as low-solubility, stable compounds like iron arsenate [18,19].

During this process, silver co-precipitates alongside arsenic and iron due to its high concentration in the feedstock, leading to the formation of argentojarosite. Argentojarosite, composed of iron and silver hydroxosulfates, forms through Reaction (1), while basic iron sulfates are generated via Reaction (2):

3Fe₂(SO₄)₃ + Ag₂SO₄ + 12H₂O ⇆ 2AgFe₃(SO₄)₂(OH)₆↓ + 6H₂SO₄

(1)

Fe₂(SO₄)₃ + 2H₂O ⇆ 2Fe(OH)SO₄↓ + H₂SO₄

(2)

Argentojarosite is virtually insoluble during the cyanide leaching (CIL) process, yet its solubility is critical for the effective extraction of gold and silver from the products of pressure oxidation. This insolubility results in economic losses and the dispersion of valuable components into production waste [20,21].

To mitigate the formation of argentojarosite, it is essential to understand the primary factors contributing to its formation.

An article entitled “Synthesis of Jarosite, KFe₃(SO₄)₂(OH)₆” presents data on the stability regions of various compounds in the Fe-S-O system as a function of temperature and pH, in particular, the stability regions of jarosite and basic iron sulfate [22].

According to data in the literature, jarosite and basic iron sulfate are formed in acidic solutions (pH < 2) and at high temperatures (>140 °C) [23]. At lower temperatures and pH values, iron hydroxosulfate and the double salts of iron and silver hydroxosulfates are able to decompose. The release of iron sulfate into solution proceeds by reaction (3) [24].

2Fe(OH)SO₄ + H₂SO₄ ⇆ Fe₂(SO₄)₃ + 2H₂O

(3)

At pH values greater than 2, basic iron sulfates decompose to hematite at temperatures greater than 100 °C or to goethite at temperatures between 60 and 100 °C. Jarosite is destroyed at pH values greater than 2. In practice, this process requires strongly alkaline conditions and high temperatures [25].

The technology of gold–silver-bearing copper raw material processing is known, and it includes special operations that allow the destruction of the double salts of iron and silver.

The Hot Curing process is the agitation at low temperature (98 °C) of the slurry obtained after the POX process. The conversion of the basic iron sulfates into iron sulfates according to the reaction (3) [26,27].

The Lime Boil process is based on the reaction of the interaction between an alkaline solution (calcium hydroxide) and basic sulfates of iron and silver at a temperature of 95 °C (Equation (4)).

2AgFe₃(SO₄)₂(OH)_6s + 4Ca(OH)₂ + 7H₂O → Ag₂O + 6Fe(OH)₃ + 4CaSO₄·2H₂O↓

(4)

At Pueblo Viejo in the Dominican Republic, Hot Curing and Lime Boil operations are utilized in conjunction with pressure oxidation of feed and cyanide leaching of intermediate products. This process is utilized for the recovery of gold and silver [28,29].

It has been demonstrated by preceding studies that Hot Curing and Lime Boil operations exert a beneficial influence on the final silver recovery, effecting a severalfold increase. However, in the context of industry, these operations will require a substantial complication of the extant technological schemes of raw material processing.

The problem is not yet considered to be acute, and it is being addressed, particularly at the Dominican plant, through the implementation of ore conditioning operations and the utilization of pyrometallurgical processing for the concentrates. In the context of hydrometallurgical autoclave treatment of copper silver-bearing feedstock, comprising, for instance, 100 g/t silver and with a processing capacity of 100,000 tons of material per year, the formation of jarosite formation can potentially incur losses amounting to up to USD 11 million (price per ounce of silver as of 13 December 2024 is USD 31).

Following a thorough analysis of the experimental results, the authors advanced a solution to the problem of argentojarosite formation. This solution was based on the thermodynamic advantage of iron sulfate in the formation of other metals [30,31].

As demonstrated in the extant literature, the Gibbs energy value of the reactions involving the formation of basic iron sulfates of potassium and sodium is more negative than that of silver (

Table 1. Gibbs energies of jarosite group minerals (T = 298 K), adapted from Ref [32].

Mineral	Chemical Formula	Gibbs Energy Value Calculated from Reference Data, kJ/mol
Jarosite	KFe3(SO4)2(OH)6	−3314
Natrojarosite	NaFe3(SO4)2(OH)6	−3271
Ammoniojarosite	NH4Fe3(SO4)2(OH)6	−3095
Argentojarosite	AgFe3(SO4)2(OH)6	−2949
Hydroniumjarosite	(H3O)Fe3(SO4)2(OH)6	−3247

).

It can be posited that, in accordance with the prevailing thermodynamic data, the process of silver precipitation will be accompanied by the initial formation of sodium and potassium compounds from solution.

The authors selected potassium for investigation in terms of its role in the reduction of silver content within the crystal structure of jarosite during the precipitation of solid precipitates from solution. This decision was determined by the more negative value of the Gibbs energy of the formation of KFe₃(SO₄)₂(OH)₆ [33].

According to the literature data, hydroxonium ions (H₃O⁺) can be introduced into the structure of jarosite and argentojarosite. The article [34] presents data on the synthesis of various crystalline structures belonging to the group of jarosite. However, there is no information on the formation of these compounds under conditions in which pressure oxidation of sulfide ores and concentrates is carried out.

The raw materials that are subjected to this method of processing have complex chemical and phase compositions, which vary significantly between different deposits. This complicates the study of phase interactions [35].

An experimental study was carried out in order to prove the preferential formation of basic potassium sulfates in the presence of silver salts. This study concerned the precipitation of jarosite from salt solutions, and the variables that were investigated included different values of the temperature and duration of the process.

2. Materials and Methods

The present study investigated phase interactions in the K-Ag-Fe-SO₄ system at three different temperatures: 120, 160, and 200 °C.

In the course of this study, three series of experiments were conducted on the deposition under autoclave conditions of jarosite KFe₃(SO₄)₂(OH)₆, argentojarosite AgFe₃(SO₄)₂(OH)₆, and potassium–silver-bearing jarosite KAgFe₃(SO₄)₂(OH)₆.

A series of analytical procedures were conducted in the laboratory, including mineralogical analysis and quantitative chemical analysis, employing physicochemical methods.

The determination of iron and silver concentrations in both the initial and final solutions was achieved through the utilization of atomic absorption spectroscopy (AAS), a method that employs a SpektrAA 220 spectrometer (Varian Australia Pty Ltd., Mulgrave, Victoria, Australia). The determination of potassium and sulfur concentrations was achieved through the utilization of inductively coupled plasma atomic emission spectrometry (ICP-AES) on a Thermo iCAP 6300 radial spectrometer (Thermo Fisher Scientific, Waltham, MA, USA). The mineral composition was analyzed using powder X-ray diffraction analysis (XRDA). Powder preparations were imaged on a Miniflex 2 diffractometer (Rigaku Corporation, Tokyo, Japan) using a cobalt anode. Mineral phases were identified using the PDXL2 program using X-ray PDF mineral databases. The total mineral composition of the samples was quantitatively analyzed using the Topas 5 program and the Rietveld method.

The hydrothermal synthesis was conducted within a titanium laboratory autoclave that was manufactured by “Parr” (Parr Instrument Company, Moline, IL, USA) and had a volume of 1 dm³. The initial solution was prepared using distilled water with the addition of the appropriate reagents:

• Iron (III) sulfate (Fe₂(SO₄)₃·9H₂O), over 98 wt%;
• Potassium sulfate (K₂SO₄), over 98 wt%;
• Silver nitrate (AgNO₃), over 99 wt%.

The deposition process was conducted in a nitrogen atmosphere, with temperatures ranging from 105 to 200 °C. Under these conditions, the process was simulating the formation of jarosite during the autoclave oxidation of sulfide gold-bearing raw materials (

Table A1. Experimental conditions.

Option	Value
Temperature	105 °C, 120 °C, 160 °C, 200 °C
The speed of mixing	600 rpm 1
Nitrogen partial pressure	0.2 MPa
Time	0–300 min 2
Operating medium	sulfuric acid

¹ Here, 600 rpm was chosen on the basis of previously conducted studies to exclude diffusion limitations on the formation of jarosite. ² After reaching the operating temperature.

).

For each series of experiments, model solutions were prepared containing components, with the initial concentrations of these components listed in

Table 2. Chemical composition of solutions for hydrothermal synthesis.

Series No.	Element Content in the Initial Solution, g/L
	K	Ag	Fe	S	SO42−	pH
1	4.50	0.00	19.40	19.30	57.90	1.26
2	0.00	6.18	19.40	16.71	50.05	1.26
3	4.50	6.18	19.40	19.30	57.90	1.26

.

The choice of concentrations of sulfate ions and iron (III) is based on their correspondence to their content in the solutions obtained at the plant during pressure oxidation of silver–copper concentrates.

According to the literature data [23] and conducted studies (Figure S3 of the Supplementary Materials), when there is a deficiency of metal cations capable of precipitation in the crystal lattice of jarosite, the formation of a precipitate of trivalent iron oxide (hematite) occurs. Therefore, the concentrations of potassium and silver cations were chosen so that the excess of iron and sulfate anions did not lead to their complete precipitation.

Following the hydrothermal synthesis, the resultant suspension was subjected to a process of sedimentation, thereby effecting a separation into liquid and solid phases. Thereafter, the solid residue was thoroughly washed with distilled water and subsequently dried, and its mass was fixed. Phase analysis was then conducted.

3. Results and Discussion

3.1. Laboratory Tests on Hydrothermal Synthesis of Jarosites

In the first series of experiments, we studied the precipitation of jarosite at given concentrations of initial substances (Table 2). The results of experiments conducted at temperatures of 105, 120, 160, and 200 °C showed that the amount of jarosite formed increases with increasing temperature (Figure 1).

The dependence of the concentration of potassium, iron, and sulfur in the process of hydrothermal synthesis on time at 120 °C is presented in Figure 2.

Notwithstanding the observation that, upon attaining a contact time of 120 min, the concentrations of components within the system remain almost unchanged, the time required to reach equilibrium within the studied system is not less than 300 min, as established through experimental means. In accordance with extant literature, under hydrothermal synthesis conditions, hydroniumjarosite is formed simultaneously with jarosite, which in turn affects the content of elements in the solid product and the final solution.

In the second series of experiments, the process of argentojarosite precipitation was investigated, with the temperature and duration of the process being selected in a manner analogous to that employed in the experiments on the deposition of potassium jarosite. The resulting experimental dependences are presented in Figure 3 and Figure 4.

The equilibrium time for argentojarosite precipitation is less than the time for potassium jarosite formation and is a minimum of 140 min. However, this time is insufficient for the precipitation of iron. The equilibrium time for the formation of basic iron sulfate is a minimum of 300 min.

The experimental results of the synthesis of argentojarosite with these initial concentrations of components showed that at process temperatures of 160 and 200 °C, complete precipitation of silver from the model solution occurred. In the absence of silver in the solution, the reaction of hematite formation was initiated (Equation (5)):

Fe₂(SO₄)₃ + 3H₂O ⇆ Fe₂O₃↓ + 3H₂SO₄

(5)

The validity of this process is substantiated by the results of the mineralogical analysis of the solid precipitate obtained (Figure S3 of the Supplementary Materials).

In the third series of experiments, the joint precipitation of potassium and silver jarosite was studied. The temperature and duration of the process were selected in a manner analogous to that employed in the preceding experiments. The experimental dependences are shown in Figure 5 and Figure 6.

The process of co-precipitation of potassium and silver jarosite is similar to the processes of individual jarosite precipitation. However, when the process time reaches 120 min, there is almost no change in the amount of synthesized solid phase in terms of potassium and silver content. The amount of iron in the final solution decreases slightly.

The result obtained indicates an increase in the synthesis rate of potassium–silver double jarosite in comparison with the precipitation rate of jarosite or argentojarosite. Furthermore, it has been demonstrated that iron continues to accumulate in the structure of the crystalline compound between 120 and 300 min. Consequently, the equilibrium of the solid precipitation process of K-Ag-H3O jarosite is established in a time period of at least 300 min.

As the process temperature increases from 105 to 200 °C, the amount of solid precipitate formed increases. At the same time, with increasing temperature of the process, silver is more actively transferred to jarosite than potassium, as evidenced by a more rapid decrease in the concentration of silver compared to the concentration of potassium. It is worth noting that the iron content in the solution decreases to a lower value compared to the previous series of experiments. It is important to note that complete precipitation of iron from the solution is not observed.

The molar ratio of potassium to silver in the initial solution was determined through experimentation and found to be 2:1. It was established that utilizing this ratio of components at a temperature of 120 °C results in a 53% reduction in the amount of silver precipitated in jarosite compared to a process conducted in the absence of potassium. The elemental concentrations in the final hydrothermal synthesis solutions are presented in

Table A2. Chemical composition of final solutions after hydrothermal synthesis.

Exp.	Temperature	Time	Element Content in the Final Solution, g/L
№	°C	min	K	Ag	Fe	S	pH
1	105	120	1.91	-	8.02	14.70	0.87
2	120	0	3.80	-	18.14	19.70	1.24
3	120	10	3.18	-	15.10	17.80	1.09
4	120	20	2.41	-	10.50	15.70	0.96
5	120	30	1.97	-	8.33	14.70	0.87
6	120	40	1.79	-	7.10	14.30	0.85
7	120	50	1.65	-	6.66	14.20	0.83
8	120	60	1.56	-	5.82	13.90	0.78
9	120	120	1.08	-	4.00	13.00	0.73
10	120	180	0.90	-	3.09	12.93	0.73
11	120	300	0.77	-	2.65	12.90	0.72
12	160	120	0.45	-	0.83	12.60	0.69
13	200	120	0.28	-	0.74	12.30	0.67
14	105	120	-	1.24	10.50	13.19	0.86
15	120	0	-	4.84	18.00	15.81	1.23
16	120	10	-	2.96	14.50	14.44	1.07
17	120	20	-	1.77	11.40	13.58	0.97
18	120	30	-	1.35	10.50	13.27	0.89
19	120	40	-	1.23	10.70	13.18	0.88
20	120	50	-	0.69	9.50	12.79	0.85
21	120	60	-	0.52	9.22	12.67	0.82
22	120	120	-	0.18	7.66	12.42	0.82
23	120	180	-	0.12	7.40	12.38	0.79
24	120	300	-	0.02	7.00	12.31	0.78
25	160	120	-	0.01	6.31	12.38	0.74
26	200	120	-	0.01	2.16	12.38	0.64
27	105	120	2.10	4.09	6.39	14.40	0.79
28	120	0	3.95	5.77	19.30	19.50	1.15
29	120	10	3.16	4.85	12.99	17.10	0.99
30	120	20	2.46	4.19	8.23	14.80	0.85
31	120	30	2.19	4.06	6.66	14.30	0.82
32	120	40	2.08	3.86	5.52	13.90	0.79
33	120	50	2.01	3.79	4.95	13.40	0.77
34	120	60	1.94	3.70	4.40	13.40	0.76
35	120	120	1.67	3.37	2.93	12.80	0.73
36	120	180	1.64	3.17	2.49	12.50	0.70
37	120	300	1.58	3.31	2.03	12.50	0.68
38	160	120	1.42	2.29	0.39	12.00	0.65
39	200	120	1.35	1.90	0.28	12.30	0.64

.

The reduction in the amount of silver precipitated into jarosite was found to decrease from 53% to 37% at a temperature of 160 °C and to 31% at a temperature of 200 °C. This result indicates a decrease in the effectiveness of the influence of potassium salts in the initial solutions on the yield of silver in the solid phase. With rising temperature, the silver content in the solid phase of jarosite increased.

3.2. Determination of Thermodynamic Parameters

In order to provide a theoretical basis for the formation of jarosite, the following conjugated chemical reactions are expressed in Equations (6)–(8). The equilibrium constants and Gibbs energies of solid precipitation formation are calculated:

Fe₂(SO₄)₃ + K₂SO₄ + 12H₂O ⇆ 2KFe₃(SO₄)₂(OH)₆↓ + 6H₂SO₄

(6)

3Fe₂(SO4)₃ + 2AgNO₃ + 12H₂O ⇆ 2AgFe₃(SO₄)₂(OH)₆↓ + 5H₂SO₄ + 2HNO₃

(7)

3Fe₂(SO₄)₃ + 14H₂O ⇆ 2(H₃O)Fe₃(SO₄)₂(OH)₆↓ + 5H₂SO₄

(8)

These equations are written in the reduced ionic form (Equations (9)–(11)):

3Fe³⁺ + 2SO₄²⁻ + K⁺ + 6H₂O ⇆ KFe₃(SO₄)₂(OH)₆↓ + 6H⁺

(9)

3Fe³⁺ + 2SO₄²⁻ +Ag⁺ + 6H₂O ⇆ AgFe₃(SO₄)₂(OH)₆↓ + 6H⁺

(10)

3Fe³⁺ + 2SO₄²⁻ + 7H₂O ⇆ (H₃O)Fe₃(SO₄)₂(OH)₆↓ + 5H⁺

(11)

The results of the chemical analysis of equilibrium solutions and mineralogical analysis (

Table A3. Distribution of coefficients in mineral formula of jarosite calculated by Topas 5 program (T = 120 °C, time = 300 min).

Series No.	K	Ag	H3O
1	0.92	0.00	0.08
2	0.00	0.80	0.20
3 1	0.66	0.34	0.00

¹ Due to the peculiarities of the calculation in the Topas 5 program and the results obtained in the PDXL 2 program, the coefficients in the formula of jarosite containing K⁺, Ag⁺, and H₃O⁺ at the same position were calculated.

) of solid products have allowed the following compositions of the investigated samples to be established (

Table 3. Chemical and mineralogical composition of obtained jarosite.

Series No.	Content of Solid Phase Elements, %				Compound Formula Based on Mineralogy Results
	K	Ag	Fe	S
1	6.52	0.00	30.20	12.00	K0.92(H3O)0.08Fe3(SO4)2(OH)6
2	0.00	15.11	30.20	10.99	Ag0.80(H3O)0.2Fe3(SO4)2(OH)6
3	4.61	4.80	29.00	11.42	K0.6Ag0.27(H3O)0.13Fe3(SO4)2(OH)6

).

According to the analysis results, two conjugated reactions (9) and (11) are observed during the formation of potassium jarosite. The following solid phases are formed: KFe₃(SO₄)₂(OH)₆ and (H₃O)Fe₃(SO₄)₂(OH)₆ (Figure S1 of the Supplementary Materials). The total equation has the following form (Equation (12)):

6Fe³⁺ + 4SO₄²⁻ + K⁺ + 13H₂O ⇆ KFe₃(SO₄)₂(OH)₆↓+ (H₃O)Fe₃(SO₄)₂(OH)₆↓ + 11H⁺

(12)

In the synthesis of argentojarosite, the solid precipitates are AgFe₃(SO₄)₂(OH)₆ and (H₃O)Fe₃(SO₄)₂(OH)₆ (Figure S2 of the Supplementary Materials) formed by the following reaction (Equation (13)):

6Fe³⁺ + 4SO₄²⁻ + Ag⁺ + 13H₂O ⇆ AgFe₃(SO₄)₂(OH)₆↓ + (H₃O)Fe₃(SO₄)₂(OH)₆↓ + 11H⁺

(13)

In the co-presence of silver and potassium ions, three solid phases are formed: KFe₃(SO₄)₂(OH)₆, AgFe₃(SO₄)₂(OH)₆, and (H₃O)Fe₃(SO₄)₂(OH)₆ (Figure S4 of the Supplementary Materials). The equation of the reaction has the following form (Equation (14)):

9Fe³⁺ + 6SO₄²⁻ + Ag ⁺ + K⁺ + 19H₂O ⇆ KFe₃(SO₄)₂(OH)₆↓ + AgFe₃(SO₄)₂(OH)₆↓ + (H₃O)Fe₃(SO₄)₂(OH)₆↓ + 17H⁺

(14)

Since this study considers a heterogeneous system, modeled on a real technological process and comprising weighted concentrations of components, the activity method was utilized to calculate the equilibrium constants. The activity coefficients were calculated using the equation of the third approximation of the Debye–Hückel theory (Equation (15)):

$$\log \gamma =-{\displaystyle \frac{h\left|z_{+·}{z}_{-}\right|\sqrt{I}}{1+a·B·\sqrt{I}}}+CI,$$

(15)

• h—constant depending on the dielectric permittivity of the solution ε and temperature T;
• z⁺, z^–—charges of cation and anion;
• I—ionic strength of the solution;
• a—distance of the greatest convergence of electric centers of ions;
• B—parameter depending on temperature and dielectric permittivity of the medium;
• C—a constant coefficient that takes into account the decrease in dielectric permittivity near the ion as a result of the polarization of dipole molecules of the solvent.
• ε—dielectric constant of sulfuric acid.

The obtained activity coefficients according to the calculations are presented in

Table 4. Thermodynamic parameters of jarosite formation reactions at 120 °C.

Equations	I mol/L	h (K3·kg/mol)0.5	B m−1·mol−0.5·kg·K0.5	C L/mol	log(γ)	γ	Keq.	ΔGT kJ/mol
12	1.12	0.23	2.52 × 109	−0.0206	−0.158	0.695	3.38 × 107	−56.66
13	1.51	0.23	2.52 × 109	−0.0194	−0.175	0.668	3.05 × 106	−48.81
14	1.08	0.23	2.52 × 109	−0.0204	−0.156	0.699	1.31 × 1013	−98.72

.

The Gibbs energy value of argentojarosite formation has been determined to be higher than that of jarosite formation. This finding indicates that the formation of basic iron–potassium sulfates is more favorable, thus determining the preferred mineralogical outcome. In accordance with the principle of additivity, the Gibbs energy of formation of basic iron–potassium–silver sulfates is calculated as the sum of the Gibbs energies of the individual reactions (12) and (13). The total Gibbs energy of the process is −104 kJ/mol, which is in satisfactory agreement with the value of −98.72 kJ/mol calculated from reaction (14) on the basis of experimental studies.

The findings of this study corroborate the extant literature data [34] on the possibility of using potassium in the process of hydrothermal synthesis of jarosite to reduce the concentration of silver in the solid phase. Potassium has a salting effect on the content of silver ions in the crystal lattice of jarosite, a phenomenon attributable to its substantial electrochemical potential, which, in comparison with the Ag⁺ ion, is determined by a smaller hydrated radius. For the reactions under investigation that occur in sulfuric acid solution under autoclave conditions, it is likely that metal cations in the solid phase are in hydrated form.

3.3. Determination of Kinetic Parameters

The reaction orders of the occurring processes in each series of experiments at a temperature of 120 °C were calculated. Given the involvement of iron (III) cations in all reactions, it was decided to utilize the dependence of the concentration of this metal on the duration of the experiment.

The reaction orders were calculated using the graphical method of determination. The time dependencies of iron concentration for reaction orders 1, 2, and 3 were utilized (

Table A4. Dependencies for calculation of reaction orders.

Reaction Order	Integrated Rate Law	Plot Needed for Linear Fit of Rate Data
1	$\ln \left[\mathrm{A}\right]=-kt+\ln \left[{\mathrm{A}}^0\right]$	$\ln \left[\mathrm{A}\right]\mathrm{v}\mathrm{s}.\mathrm{t}$
2	${\displaystyle \frac{1}{\left[A\right]}}=kt+\left({\displaystyle \frac{1}{\left[A^0\right]}}\right)$	${\displaystyle \frac{1}{\left[\mathrm{A}\right]}}\mathrm{v}\mathrm{s}.\mathrm{t}$
3	${\displaystyle \frac{1}{{\left[A\right]}^2}}=kt+\left({\displaystyle \frac{1}{{\left[A^0\right]}^2}}\right)$	${\displaystyle \frac{1}{{\left[\mathrm{A}\right]}^2}}\mathrm{v}\mathrm{s}.\mathrm{t}$

). The reaction order was determined based on the highest regression coefficient for each linear dependence.

The results are presented in Figure 7, Figure 8 and Figure 9.

The analysis conducted revealed that the formation of jarosite, argentojarosite, and potassium–silver jarosite follows a third-order reaction. This indicates that the rate-limiting stage is the chemical interaction between the reactants, as the first, second, and third orders of reaction are independent of diffusion and depend solely on the concentration of the reactants. The formation of each jarosite is thus determined by the alteration in the concentrations of three distinct reactant substances.

4. Conclusions

The issue that is currently being encountered pertains to the formation of silver compounds that exhibit resistance to cyanide leaching, specifically argentojarosite, during the processing of silver–copper raw materials by means of pressure oxidation.

The issue at hand can be resolved through the incorporation of a metal salt that exhibits a higher binding affinity for the group of basic iron sulfates than that of silver. To illustrate this approach, consider the addition of potassium sulfate to the autoclave leaching reactor during the processing of raw materials.

The findings of laboratory tests have indicated the precipitation of three types of compounds with structures belonging to the group of jarosite—jarosite, argentojarosite, and hydroniumjarosite—at temperatures ranging from 105 to 200 °C during the process. This outcome is consistent with the findings of previous literature studies.

In the presence of jarosite and argentojarosite, hydroniumjarosite is precipitated under specified conditions. This precipitation can be attributed to the incorporation of hydroniumjarosite from the sulfuric acid solution into the crystal lattice of the primary compounds that were the subject of this study.

The investigation revealed that the formation of potassium compounds is more favorable during the co-precipitation of jarosite and argentojarosite. This finding is corroborated by the calculated equilibrium constants and Gibbs energies of formation of basic sulfates.

The present study has enabled the establishment of the order of reactions in the co-formation of K-Ag-jarosite, which has been determined to be equal to 3. This finding indicates that the limiting stage of the process is the rate of chemical interaction between the reactants (at 120 °C).

The co-deposition of jarosite and argentojarosite at a molar ratio of 2:1 and a temperature of 120 °C has been shown to reduce the amount of silver deposited in argentojarosite by 53% in comparison with the experiment conducted without the addition of potassium salts. Furthermore, at process temperatures of 160 °C and 200 °C, the reduction in the amount of silver precipitated into jarosite was found to be 37% and 31%, respectively. This suggests that the efficiency of the effect of potassium salt addition on the precipitation of argentojarosite decreases with increasing temperature.

In order to achieve the most efficient reduction in silver precipitation as jarosite, the optimal conditions are as follows: a temperature of 120 °C, a molar ratio of potassium to silver of 2:1, and a potassium-to-iron ratio of 1:3. However, it should be taken into account that in industry, a process temperature of 200 °C is employed, which results in a lower efficiency of potassium addition. The actual raw material contains less silver than is discussed in this article, and therefore, the potassium-to-iron ratio should be focused on in further studies.