A Novel Selective Oxygen Pressure Leaching for Zinc Extraction from Hemimorphite in Acid-Free Solutions

Abstract

A novel acid-free oxygen pressure leaching for the extraction of zinc from hemimorphite was proposed in this study. Green vitriol (FeSO₄·7H₂O), as one of the important industrial by-products, was used as the leaching reagent to separate zinc from silicon and iron. The effect of leaching conditions, including Fe/Zn molar ratio, leaching temperature, pressure, and reaction time, on the leaching efficiency of zinc, Fe, and Si was investigated systematically. The results showed that the molar ratio of Fe/Zn and leaching temperature play a pivotal role in determining the leaching efficiency rate of Zn. Under the optimized leaching conditions (Fe/Zn molar ratio = 6:1, 150 °C, 1.8 × 10⁶ Pa, and leaching time of 2 h), the leaching efficiency of Zn reached 98.80% and the leaching efficiencies of Fe and Si were 0.76% and 16.80%, respectively. In addition, the shrinking core model was established to represent the relationship between the rate control step and the leaching conditions. The leaching process was controlled by chemical reaction and diffusion, and the activation energy of the leaching process is 97.14 kJ/mol.

1. Introduction

Zinc (Zn) is thought to be one of the pivotal non-ferrous metals. Due to the effective separation of sulfides from gangue by conventional flotation techniques, it is predominantly derived from zinc sulfide ores [1,2]. However, the accelerated consumption of zinc has led to a rapid depletion of zinc sulfide ores. This burgeoning interest is propelled not only by the diminishing availability of zinc sulfide ores but also by escalating restrictions on sulfur emissions [3,4].

Hemimorphite, which accounts for approximately 30% of the oxidized ore, is the main mineral component of zinc oxide ore with commercial value [3]. At present, pyrometallurgy and hydrometallurgy have been extensively studied to treat these ores [2,4,5,6]. Compared with pyrometallurgical processes, hydrometallurgy has more economic efficiency. In practice, there are various acid or alkaline leaching lixiviants used in hydrometallurgical processes [7,8,9,10]. Sulfuric acid is the most versatile leaching agent used for leaching high-grade zinc oxide ore [11,12]. However, impurities such as iron can be significantly dissolved [5,13]. Thus, researchers proposed some processes of leaching with an alkaline solution. In practice, the dissolution of SiO₂ in an alkaline solution will increase the load of leachate purification. Moreover, SiO₂ dissolved from hemimorphite would consume too much of the alkaline leaching reagent [14,15,16]. Rao et al. [17] employed iminodiacetic acid for the leaching of hemimorphite, achieving a zinc leaching rate of 88.15%. Meanwhile, iminodiacetic acid can be reused by adding dilute sulfuric acid, underscoring the environmentally sustainable nature of this method. The recovery of zinc in hemimorphite reached 97.15% by trichloroacetic acid (TCAA) leaching [18]. The utilization of organic acids as leaching reagents not only maintained the leaching solution at a low acidity level but also mitigated the risk of environmental contamination by waste acids. Nevertheless, it is imperative to acknowledge that the costs associated with organic acids for zinc leaching surpass those of inorganic acids. Therefore, it is considered imperative to explore an environmentally friendly leaching reagent with excellent selectivity and lower costs for the zinc leaching from hemimorphite.

Due to the acid leaching process, acidic waste will be produced; environmentally friendly leaching processes should be developed. Given the notable hydrolytic capabilities exhibited by Fe³⁺ or Fe²⁺ ions, an appropriate acidic environment can be maintained by controlling the hydrolytic degree. The acidic environment engendered through the hydrolysis of ferric ions serves to curtail acid consumption and alleviate the burden on waste acid treatment. In the industrial production process, plenty of by-products containing acidic iron are produced, which can be applied to leach hemimorphite. Babu, M.N. et al. [19] investigated the oxidative leaching of zinc from sphalerite concentrate using ammonium, sodium, and potassium persulfates in a sulfuric acid medium. Under optimized conditions (333 K, 5% (v/v) H₂SO₄, and 20% (w/v) ammonium persulfate (APS)), 95% of zinc was extracted from the −150 μm concentrate within 5 h. Souza, A.D. et al. [20] investigated the dissolution kinetics of iron-rich zinc sulfide concentrate in acidic ferric sulfate media, revealing a distinct two-stage leaching mechanism: an initial surface chemical reaction-controlled stage followed by a subsequent diffusion-controlled stage through elemental sulfur layers. At present, acidic ferric salts such as ferric chloride and ferric sulfate have been used as inorganic lixiviants for leaching sphalerite [21,22,23,24,25]. It is widely acknowledged that the erosion of the sphalerite by ferric sulfate plays a crucial role in the whole process [26]. The reactivity of sphalerite is contingent upon its iron content in the solution; a higher iron concentration renders the sphalerite lattice more susceptible to opening [27]. It is due to the ferric iron having a high oxidation potential of 0.77 V, which can serve as an oxidant during the sphalerite leaching process. However, if the acidic ferric salts are used to treat hemimorphite, the zinc leaching mainly depends on the hydrogen ions generated by the dissociation of water molecules. In this context, iron ions act as a hydrolytic agent to produce an acidic solution.

To verify the viability of employing acidic ferric salts as an environmentally friendly leaching agent for hemimorphite treatment, the industrial by-product Green vitriol (FeSO₄·H₂O) was used to leach zinc from hemimorphite by the oxidative pressure leaching method. Herein, the parameters of the ferrous sulfate-to-hemimorphite mass ratio, leaching temperature, leaching duration, and reaction pressure were investigated to assess their effects on the leaching efficiency of Zn. The leaching efficiency of Fe and Si was also measured to evaluate the potential for the separation of iron and zinc. In addition, a kinetic model was established, which is beneficial to interpret the reaction mechanism and provide a theoretical basis.

2. Experimental Section

2.1. Materials and Procedure

The mineral hemimorphite concentrate was obtained from Yunnan Province, China. The chemical composition analysis results of the ore samples, as determined by X-ray fluorescence spectrometry (XRF, Rigaku, Japan), were presented in

Table 1. The main chemical composition of hemimorphite.

Compositions	Zn	O	Si	Mg	Fe	Al	Ca	K	LOI *
contents	38.24	37.37	8.77	3.85	3.77	3.28	1.46	1.05	2.21

* LOI: Loss of Ignition.

. The mineral phase of hemimorphite was identified by X-ray powder diffraction (XRD, Rigaku). The microstructure and element distribution of the sample were identified by scanning electron microscopy and energy dispersive X-ray spectroscopy (SEM-EDS, Apreo S HiVac, USA). The XRD pattern was shown in Figure 1a, revealing hemimorphite as the predominant mineral phase, accompanied by cordierite (Mg₂Al₄Si₅O₁₈), quartz (SiO₂), and hematite (Fe₂O₃) identified as principal gangue components. As shown in Figure 1b, the size distribution of hemimorphite particles was measured by a laser particle size analyzer (LPS; Malvern MasterSizer2000, UK). It is indicated that the size of the particles ranged from 1.290 μm to 40.306 μm (d₁₀–d₉₀). The measured value of the mean diameter of the ore powder (d_m) was 5.012 μm, while the median diameter of the ore powder (d₅₀) is 6.148 μm. The SEM-EDS analysis displayed in Figure 1c indicated that the hemimorphite ore exhibited an irregular morphology with particle sizes ranging approximately from 5 to 20 μm. EDS analysis revealed that Zn was predominantly enriched together with Si and O, suggesting that the main mineral phase present was hemimorphite. Additionally, the co-enrichment of Mg, Al, Si, and O indicated the presence of cordierite as the main impurity phase. These observations were fully consistent with the results obtained from both PSD analysis and XRD pattern, thereby corroborating the mineralogical composition and phase identification of the sample. The leaching reagent ferrous sulfate (FeSO₄·7H₂O) used in the experiment was obtained from Sinopharm Chemical Reagent Co., Ltd., Beijing, China.

The experimental equipment is shown in Figure 2. Oxygen was pumped into the leaching solution through a dedicated tube, with pressure regulated by a pressure valve. The temperature of the solution was set by a platinum resistance thermometer with an accuracy of ±0.1 °C. For each experiment, 10 g of finely ground hemimorphite powder and a certain amount of FeSO₄·7H₂O (mass calculated according to the Fe/Zn molar ratio was 3.2, 3.6, 4.0, 4.8, and 6.0) were added into the reactor with 100 mL of distilled water. Subsequently, the sealed reactor was heated to the presupposed temperature and stirred at 500 rpm. When the temperature was reached, the oxygen was bubbled into the reactor with controlled oxygen partial pressure and leaching for the required period. After the experiment, the reactor was cooled by water to collect the slurry. The leachate and the leaching residue were separated by filtration (S/L) separation. The leaching residue obtained from the separation process was oven-dried for further analysis. The content of Zn, Fe, and Si leached in solution was detected by ethylenediaminetetraacetic acid (EDTA) [28] or inductively coupled plasma-atomic emission spectrometry (ICP-AES) methods.

2.2. Analysis and Characterization

The concentration of zinc in the leachate was detected by the ethylenediaminetetraacetic acid (EDTA) titration method with methyl orange as the indicator [28]. The concentrations of Si and Fe in the leach solutions were analyzed by inductively coupled plasma-atomic emission spectrometry (ICP-AES, Optima 5300 DV, PerkinElmer, Waltham, MA, USA). The leaching efficiency of zinc and the leaching efficiency of Fe or Si in the leachate can be obtained as follows:

η = C_Zn × V/M_Zn × 100%

(1)

λ_i = C_i × V/M_i × 100%

(2)

where C_Zn is the concentration of Zn in the leachate (g·L⁻¹), C_i is the concentration of Fe or Si, V is the volume of the leachate (L), M_Zn is the weight of Zn in the ground hemimorphite powders added in the reactor (g) as determined by EDTA method, and M_i is the content of Si in the ore powders or the total amount of Fe existing in the ore powder plus the FeSO₄·7H₂O added in the reactor (g).

3. Results and Discussion

3.1. Feasibility Assessment

Due to the experiment being conducted in a sealed reactor, real-time monitoring of pH during the reaction was unfeasible. Therefore, pH measurements were conducted only at the initial stage (pH = 3.3) and the termination point (pH = 1.1) of the reaction. To further explore the thermodynamic behavior of hemimorphite treated with ferrous sulfate, the E-pH diagram of the Fe-S-H₂O system was analyzed. This thermodynamic analysis can not only systematically explain the reaction mechanisms under different conditions but also provide a theoretical basis for determining the optimal leaching parameters, thereby ensuring efficient zinc extraction. Figure 3 shows the potential E-pH diagram of the Fe-S-H₂O system. In the low-potential region (E < −0.5 V), iron was stable as Fe, and sulfur was predominantly in the form of hydrogen sulfide (H₂S). In the moderate-potential region (−0.5 V < E < 0 V), iron formed FeS₂ and FeS. In the high-potential region (E > 0 V), iron corroded to form Fe²⁺ or Fe₂O₃, and sulfur was present as HSO₄⁻. In this region, Fe²⁺ changed to Fe₂O₃ as the potential increased [29].

During the oxygen pressure leaching process, the primary reactions conducted can be expressed as the following equations. Firstly, FeSO₄·7H₂O dissolved in distilled water and dissociated into Fe²⁺ and SO₄²⁻ (Equation (4)). Meanwhile, a portion of Fe²⁺ underwent oxidation either by dissolved O₂ (aq) (Equation (3)) in the solution or by pumped O₂ (g) bubbles (Equation (5)), converting into Fe³⁺. Subsequently, according to Figure 3, Equations (6) and (7) were achievable under experimental conditions. The generated Fe³⁺ was further hydrolyzed in water and produced a significant quantity of H⁺ ions and Fe₂O₃ (Equations (6) and (7)). The resultant H⁺ ions contributed to the development of pronounced acidity in the leachate, which was beneficial for the zinc in hemimorphite to leach in lixivium (Equation (8)). Meanwhile, zinc can be separated from silicon simultaneously due to the silica in silicate ores being dissolved first and then agglomerated into colloidal silica by adjusting the pH value to 4–5.5 [2]. Therefore, zinc can be extracted from hemimorphite using Green vitriol as a selective leaching reagent. The entire complex process was aptly elucidated through the reaction Equation (9). It should be noted that there are some secondary reactions conducted in the intricate leaching process, which would generate some by-products as shown in Equations (10) and (11). Compared with the general acid leaching, the FeSO₄·7H₂O leaching process was more economical and environmentally friendly.

O2(g) = O2(aq)		(3)
FeSO4·7H2O = Fe2+ + SO42− + 7H2O		(4)
4Fe2+ + O2(g) + 4H+ = 4Fe3+ + 2H2O	ΔrGmθ = 0.25944T − 401.301 kJ/mol	(5)
2Fe3+ + 3H2O = Fe2O3 + 6H+	ΔrGmθ = −0.0514T − 180.617 kJ/mol	(6)
4Fe2+ + 4H2O + O2(g) = 2Fe2O3 + 8H+	ΔrGmθ = 0.15664T − 762.534 kJ/mol	(7)
Zn4(Si2O7)(OH)2 + 8H+ = 4Zn2+ + 2H4SiO4 + H2O	ΔrGmθ = 0.044T − 363.78 kJ/mol	(8)
4Fe2+ + O2(g) + Zn4(Si2O7)(OH)2 = 4Zn2+ + 2SiO2 + H2O + 2Fe2O3	ΔrGmθ = 0.158T − 1116.70 kJ/mol	(9)
H4SiO4 = 2H2O + SiO2	ΔrGmθ = 4.811 − 0.0232T kJ/mol	(10)
M2SO4 + 3Fe2(SO4)3 + 12H2O = 2MFe3(SO4)2(OH)6 + 6H2SO4 (M = K,Na)		(11)

3.2. Effect of the Fe/Zn Molar Ratio

Due to the acidity of the solution being mainly determined by the hydrolysis of FeSO₄·7H₂O, the content of FeSO₄·7H₂O was very critical for the Zn leaching process. According to Equations (6)–(8), the leaching process was performed at 150 °C for 2 h with leaching pressure at 1.5 MPa. The influence of the Fe/Zn molar ratio on the leaching efficiency of Zn, Fe, and Si was illustrated in Figure 4. The leaching efficiency of Zn, Fe, and Si was calculated according to Equations (1) and (2). The leaching efficiency of Zn increased from 71.29% to 94.8% as the Fe/Zn molar ratio elevated from 3.2 to 4.0. Beyond this point, a plateau was discerned, signifying that despite the Fe/Zn molar ratio further increasing from 4.0 to 4.8, the leaching efficiency of Zn stabilized. This phenomenon arose from the fact that the concentration of H⁺ generated through the hydrolysis of Fe²⁺ or Fe³⁺ became insufficient to facilitate the decomposition of the hemimorphite concentrate. With the increase in the Fe/Zn molar ratios, a greater participation of Fe²⁺ or Fe³⁺ in the hydrolysis reaction occurred, thereby fostering the production of H⁺. It is beneficial for the leaching of Zn from hemimorphite concentrate particles. Meanwhile, the decomposition of hemimorphite would liberate zinc and silica simultaneously, leading to the formation of silica gel, which would wrap the concentrate particles and prevent the decomposition from continuing. Whereas, it should be noted that the leaching efficiency of Si remarkably increased when the Fe/Zn molar ratio increased from 4.0 to 4.8. It can be attributed to the bonding of silica gel, which may be broken to release monomeric silica in a strong acidic solution. In addition, the leaching efficiency of iron exhibited a discernible increase, particularly notable at a Fe/Zn molar ratio of 6. A possible explanation for this observation lies in the fact that the hydrolysis reaction could not be conducted continuously when most of the hemimorphite had decomposed. It led to excessive FeSO₄·7H₂O dissolved in solution and the leaching efficiency of Fe increased.

The leaching residues were characterized via XRD which is shown in Figure 5. The main mineral phases in the leaching residues were hematite and jarosite. Moreover, there are discernible diffraction peaks corresponding to unreacted hemimorphite (Zn₄Si₂O₇(OH)₂), cordierite (Mg₂Al₄Si₅O₁₈), and formed SiO₂. With the increase in the Fe/Zn molar ratio, the intensity of the diffraction peaks corresponding to hemimorphite decreased, indicating that the decomposition of hemimorphite increased as the Fe/Zn molar ratio rose. It can be attributed to the oxidation and hydrolysis of Fe²⁺ would generate H⁺, which can largely improve the acidity of the solution and promote the decomposition of hemimorphite. Meanwhile, the intensity of hematite increased correspondingly, indicating that most of the Green vitriol (FeSO₄·7H₂O) was converted into hematite simultaneously with the help of the dissolution of hemimorphite (Equation (9)), which is consistent with Figure 5.

3.3. Effect of the Leaching Temperature

To investigate the effect of temperature on the leaching efficiency of Zn, Fe, and Si, the experiments at different temperatures were conducted at 1.5 MPa for 2 h with a Fe/Zn molar ratio of 6. The results were shown in Figure 6, it was indicate that the leaching efficiency of Zn increased obviously from 94.80% to 95.58% when the leaching temperature ranged from 120 °C to 150 °C. It may be due to the high temperature being conducive to the hydrolysis of Green vitriol, resulting in an increased generation of H⁺. However, the leaching efficiency of Zn decreased slightly above 150 °C. The reason was that the crystallization of FeSO₄·7H₂O occurred when the temperature further increased, which inhibited the oxidative hydrolysis of Fe²⁺ to a certain extent and caused the concentration of H⁺ in the solution to fluctuate. However, this change was relatively inconspicuous when compared to the variation of leaching efficiency of Fe and Si, which decreased from 2.81% to 1.12% and from 17.57% to 10.19%, respectively. It can be attributed to the high temperature being advantageous for the transformation of jarosite and cordierite into Fe₂O₃ and SiO₂, leading to a noticeable decrease in the leaching efficiency of Fe and Si in the leachate.

The XRD patterns of the leaching residue were depicted in Figure 7. This indicated that Fe was mainly deposited as jarosite and yellow iron oxide at temperatures ranging from 120 °C to 150 °C. However, as the temperature reached 180 °C, the diffraction peak intensity of Fe₂O₃ increased while the diffraction peaks of jarosite and Fe₂O₃·H₂O gradually weakened. It indicates that these metastable precipitates (jarosite and iron oxide yellow) would convert into stable hematite (Fe₂O₃) at relatively high leaching temperatures. In addition, the diffraction peak intensity of SiO₂ increased correspondingly, suggesting that more gangue cordierite was decomposed into SiO₂ with the rising temperature. It is consistent with the change trend shown in Figure 6.

3.4. Effect of the Reaction Pressure

The influence of the reaction pressure on the leaching process of hemimorphite was investigated under leaching conditions at 150 °C for 2 h and a Fe/Zn molar ratio of 6. The leaching efficiency of Zn, as depicted in Figure 8, indicated that almost all the leaching efficiencies exceeded 96%, showing minimal variation under different reaction pressures. However, the leaching efficiency of Fe and Si exhibited a slight increase with the rising reaction pressure. It might be attributed to the fact that the reaction pressure was primarily related to the oxygen partial pressure. The acidity of the solution will improve due to the augmentation of oxygen partial pressure, which will enhance the hydrolytic degree of Fe ions. It is beneficial for the decomposition of formed precipitates such as jarosite and SiO₂, leading to the leaching efficiency of Fe and Si increasing slightly.

The XRD patterns of the corresponding leaching residues were displayed in Figure 9. It is indicated that the main precipitates were jarosite, hematite, and SiO₂ at comparatively low pressure (1.0–1.5 MPa). As the reaction pressure increased from 1.5 MPa to 2.0 MPa, the diffraction peaks corresponding to jarosite and SiO₂ disappeared, while some weak diffraction peaks indexed to yellow iron oxide emerged. It is suggested that the decomposition of jarosite prefers to convert into yellow iron oxide rather than hematite at high reaction pressure.

3.5. Effect of the Leaching Time

The oxygen leaching of hemimorphite was performed at 150 °C with a Fe/Zn molar ratio of 6 and a reaction pressure of 1.5 MPa for different leaching times. The results were depicted in Figure 10. It was observed that the leaching efficiency of Zn and Fe remained stable with the extension of leaching time, ranging from 96.54% to 98.12% and from 0.72% to 1.61%, respectively. However, the leaching efficiency of Si exhibited a noticeable decreasing trend with the extension of leaching time, varying from 33.32% to 10.90%. It might be due to the silicate in gangue dissolving and forming silicic acid in acid solution, which is further converted into SiO₂ as the leaching time is extended. In addition, impurity ions such as Mg and Al may react with the dissolved Si to form some undissolved silicate, contributing to the decrease in the leaching efficiency of Si.

The XRD patterns of the leaching residues are presented in Figure 11. It is evident that the primary phases were jarosite and iron oxide yellow at 0.5 h. With the extension of the reaction time beyond 1 h, the diffraction intensity of Fe₂O₃ enhanced while the diffraction peaks of jarosite and Fe₂O₃·H₂O gradually weakened. It is indicated that these phases will convert into hematite. Meanwhile, it is noteworthy that the diffraction peak intensity of SiO₂ initially increased with prolonged reaction time, showing an enhancement after 2 h, but subsequently decreased with further extension of leaching time. It is attributed to the fact that during the initial leaching stage (within 2 h), the decomposition of hemimorphite released Si⁴⁺, which formed silica gel encapsulating the mineral particle surfaces in the weakly acidic system, leading to increased silicon content in the leach residue. When the leaching time exceeded 2 h, the acidity of the solution intensified, causing the silica gel to gradually dissociate and regenerate Si²⁺ that returned to the leaching solution.

3.6. Analysis of Leaching Kinetics

Based on the aforementioned analysis, it is known that leaching temperature was the primary factor influencing the dissolution of FeSO₄ [24]. To explore the reaction mechanism of FeSO₄ leaching of hemimorphite, the influence of reaction temperatures on zinc leaching efficiency as a function of reaction time was investigated under a molar ratio of 6:1. The results were depicted in Figure 12.

The results showed that the reaction temperature exerted a predominant influence on zinc leaching. The leaching efficiency increased with a rise in leaching temperature. For instance, at 135 °C, a 75.21% zinc leaching efficiency was achieved in 30 min, which escalated to 84.85% by increasing the temperature to 180 °C in just 5 min. The effects of temperature on zinc leaching efficiency varied significantly within the first 10 min, while the changes became more gradual beyond this initial period. Hence, it is reasonable to affirm that the majority of zinc leaching occurred within the initial 10 min, emphasizing the significance of the leaching kinetics for zinc during this initial period, which had a crucial impact on the entire process.

Many authors consider that the shrinking core model can explain the heterogeneous kinetics of acidic leaching of most metals [23]. For the solid reactant particles, the chemical reaction was gradually promoted from the outside to the inside, and there is a shrinking core composed of unreacted substances in the ore until the end of the reaction. The product layer was attached to the reactants, and the shape and volume of the product layer were almost the same as that of the raw ore, which can be negligible. Based on the shrinking core model theory, the reaction rate was mainly determined by two aspects: the chemical reaction at the reaction interface (chemical reaction control) and the diffusion of the fluid phase in the boundary layer and product layer (diffusion control).

Figure 13 shows the SEM images of samples obtained after leaching for 2 min at 150 °C under the condition of a molar ratio of 3.2. It is known from Figure 13a that Zn was surrounded by Si and Fe, and the part of the Si and Fe product layer in contact with Zn₄(Si₂O₇)(OH)₂ formed the reaction interface. This indicated that hemimorphite was decomposed with the help of an acid solution generated by the hydrolysis of Fe³⁺ according to Equation (8). Figure 13b shows the variation of the compositions of the main elements in different layers of the obtained samples tested by EDS spectra. It is indicated that the content of Zn gradually increased as the line scanning direction changed to reach a stable state. The content of Si gradually decreased near Zn₄(Si₂O₇)(OH)₂. The overall content of Fe was also reduced with some fluctuation. It is due to the hydrolysis of Fe³⁺ to generate H₂SO₄ and Fe₂O₃, and some of the generated Fe₂O₃ was mixed into H₄SiO₄. As a result, the Fe content exhibited fluctuations, although they were not as pronounced as the decreasing trend of Si.

Based on the above analysis and in conjunction with the SEM image in Figure 13, it is reasonable to confirm that the leaching process of Zn₄(Si₂O₇)(OH)₂ in hemimorphite by FeSO₄·7H₂O was a typical shrinking core model. The solid products SiO₂ and Fe₂O₃ will gradually wrap around the reactants, and the size of the unreacted Zn₄(Si2O₇)(OH)₂ will gradually decrease.

To further explain the kinetics of the leaching process, the reaction rate constant and apparent activation energy can be obtained by establishing the kinetic equations, which is an essential method to optimize the leaching conditions.

When the reaction rate is restricted by the diffusion of the reagents within the boundary layer or reaction product layer, the zinc leaching efficiency at any time can be described by Equations (12) and (13):

1 − (1 − α)^2/3 = k₁t

(12)

1−2/3α − (1 − α)^2/3 = k₂t

(13)

The zinc leaching efficiency at any time, under a system, is limited by the chemical reaction and can be obtained as Equation (14):

1 − (1 − α)^1/3 = k₃t

(14)

When the regime is constrained by the diffusion and chemical reaction simultaneously, the zinc leaching efficiency at any time can be calculated according to Equation (15):

1/3ln((1 − α)) − [1 − (1 − α)^−1/3] = k₄t

(15)

where $\mathsf{\alpha }$ is the zinc recovery (%); t is the reaction time (min); k₁, k₂, k_3, and k₄ represent the apparent rate constants (min⁻¹).

Regarding kinetic analysis, various rate-controlling steps within the shrinking core model were estimated. The values of the apparent rate constant (k) and the correlation coefficient (R²) obtained by fitting the unreacted shrinking core model for different control processes (Equations (12)–(15)) are exhibited in

Table 2. Relevant parameters under different kinetic controlling steps.

Controlling Step	1 − (1 − α)2/3		1 − 2/3α − (1 − α)2/3		1 − (1 − α)1/3		1/3ln(1 − α) − [1 − (1 − α)−1/3]
Correlation Coefficient/Rate Constant	R2	k1	R2	k2	R2	k3	R2	k4
135 °C	0.819	0.0325	0.939	0.00332	0.837	0.0182	0.957	0.0026
150 °C	0.820	0.0562	0.964	0.0107	0.865	0.0354	0.993	0.0137
165 °C	0.714	0.0592	0.917	0.0130	0.779	0.0390	0.995	0.0208
180 °C	0.765	0.0808	0.968	0.0266	0.901	0.0681	0.995	0.0526

. The results derived from the data presented in Table 2 demonstrated that the leaching kinetics governing the dissolution of hemimorphite conformed to the mixed control model as delineated by Equation (15). The study demonstrated that this rate was determined by both chemical reaction kinetics and reagent diffusion. The rate of this intricate process reflected the reaction order regarding the hydrolysis of Fe³⁺ and the decomposition of hemimorphite.

The fitting results derived from the application of the mixed control model are shown in Figure 14. It is discernible that the slope of the fitting line (k) experienced an increase with an elevation in temperature. This phenomenon was attributable to the positive correlation between the apparent rate constant, the reaction rate constant, and the diffusion coefficient. Both the reaction rate and diffusion exhibited an upward trend with increasing leaching temperatures.

To determine the activation energy (E_a), the relationship between the apparent rate constant (k) and temperature (T) is calculated according to the Arrhenius formula (Equation (16)) [26], in which the plot of lnk against 1/T forms a straight line with a slope of −E_a/R and the intercept of ln k (Figure 15).

$$\mathrm{l}\mathrm{n}\mathrm{k}=-{\displaystyle \frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}\mathrm{T}}}+\mathrm{l}\mathrm{n}\mathrm{A}$$

(16)

where k is the apparent rate constant, A is the pre-exponential factor, R is the universal gas constant, and T is the reaction temperature [26].

Thus, the leaching process of Zn from hemimorphite by FeSO₄·7H₂O conformed to the shrinking core model of mixed control. And the activation energy (${\mathrm{E}}_{\mathrm{a}}$) was 97.14 kJ/mol. The equation elucidating the leaching kinetics of hemimorphite can be expressed as follows:

1/3ln((1 − α)) − [ 1 − (1 − α)^−1/3] = 8.965 × 10⁹ e^−97142/RT t

This study revealed that the leaching of hemimorphite in ferrous sulfate (FeSO₄·7H₂O) solution exhibited a high activation energy of 97.14 kJ/mol, significantly exceeding values reported for acidic and alkaline leaching systems [30,31,32]. From a kinetic perspective, such a high activation energy indicated that the dissolution of hemimorphite in ferrous sulfate solution was thermodynamically more challenging. This characteristic may lead to slower Zn extraction rates, potentially affecting overall production efficiency in industrial applications. However, from a sustainability standpoint, the ferrous sulfate leaching system offered distinct advantages. First, it eliminated the need for strong acids commonly used in conventional leaching processes, significantly reducing environmental hazards. Second, ferrous sulfate was an economical and widely available industrial by-product, ensuring cost-effectiveness. Moreover, this approach aligned with the principles of green metallurgy, as it operated under mild conditions with minimal environmental impact. These features made ferrous sulfate leaching a promising method for future zinc leaching efficiency processes.

4. Conclusions

Industrial by-product Green vitriol (FeSO₄·7H₂O) was used as the leaching reagent; Zn was selectively extracted from hemimorphite in acid-free solution by the oxygen pressure leaching method. The leaching parameters, such as leaching reagent amount, leaching temperature, and reaction pressure of oxygen, exerted a significant influence on the zinc leaching efficiency. The optimum reaction conditions were a Fe/Zn molar ratio of 6:1, 150 °C, 1.8 MPa, and a leaching time of 2 h. In those conditions, the leaching efficiency of Zn reached 98.80% and the leaching efficiencies of Si and Fe were only 0.76% and 16.80%, respectively. Hence, Green vitriol proved to be a viable and economic leaching agent. In addition to the high selective leaching efficiency of Zn, a more important benefit of using Green vitriol to leach hemimorphite is that the leaching process is environmentally protective.

Moreover, the shrinking core model was established to express the relationship between the rate-controlling steps and the leaching conditions. The leaching process was controlled by chemical reaction and diffusion, and the activation energy of the leaching process is 97.14 kJ/mol. This research will present a novel idea and provide a theoretical foundation for the efficient environmental extraction of Zn from other oxidized zinc ores.