Nitric Acid Purification of Molybdenite Concentrate: Copper-Iron Removal and Development of a Comprehensive Dissolution Kinetics Model

Abstract

The selective removal of impurities from molybdenite concentrates is crucial for producing high-purity molybdenum products. In this study, the purification of molybdenite concentrate was investigated using nitric acid as both a leaching medium and oxidizing agent. Leaching experiments were carried out under various conditions of temperature (22–78 °C) and nitric acid concentration (0.12–0.48 M). The results demonstrated that while molybdenite remained mostly undissolved, copper and iron were effectively leached, with near-complete removal at 78 °C in 0.24 M HNO₃ after 6 h. Compared with other acid systems, nitric acid leaching experiments in this study demonstrated higher efficiency and selectivity under relatively moderate conditions of concentration and temperature. Kinetic analyses were performed based on the shrinking core model (SCM) and extended by developing a comprehensive rate equation that incorporates both nitric acid concentration and reactive surface effects. Fitting the developed model to experimental data revealed distinct kinetic regimes below and above 50 °C, suggesting a mechanism shift from surface chemical reaction control to diffusion through an ash layer. The purified molybdenite was characterized by SEM-EDS and ICP-OES, confirming almost complete elimination of Cu and Fe impurities. This work highlights nitric acid as a promising and efficient medium for selective leaching of molybdenite concentrates and provides a comprehensive kinetic model applicable across different leaching conditions.

1. Introduction

Molybdenum is a soft, silverly white strategic metal which, due to its unique features such as a low thermal expansion coefficient, high thermal and electrical conductivity, excellent wear resistance, low vapor pressure, and high melting point (the sixth highest melting point among all elements [1]), has many applications in the industrial sector [2,3,4,5]. The main application of molybdenum, accounting for more than 80% of molybdenum usage [6], is in the cast iron- and steelmaking industries as an alloying agent, which can enhance the mechanical properties, such as hardenability, strength, and toughness, and the corrosion and wear resistance of super alloys in these industries [3,7]. Besides steel industries, molybdenum has vast applications in electrical and electronic devices, medical equipment, material testing equipment, high-temperature furnaces and associated equipment, thermal spray coating, aerospace and defense components, lubricants, briquettes, and pigments [1]. On the other hand, molybdenum-based catalysts play a vital role in the oil and gas industries, where they are used to reduce sulfur in liquid fuels by acting as a cracking agent [7]. Recent studies have also explored the incorporation of molybdenum in high-entropy alloys and solar cells, where it has been shown to enhance functional properties [8,9].

Although molybdenum is present in various minerals such as molybdenite (MoS₂), wulfenite (PbMoO₄), and powellite (CaMoO₄), the most crucial ore source is molybdenite, a mineral that is well suited for industrial processing [10,11]. Molybdenite is obtained as a by-product in copper mines, and besides molybdenum, it usually contains some impurities such as chalcopyrite (CuFeS₂), chalcocite (Cu₂S), covellite (CuS), and pyrite (FeS₂) [1,10,12]. Due to the fact that the presence of copper in steel-making industries can have deleterious effects on the mechanical properties of the products, it is essential to reduce the copper content of molybdenite. The highest acceptable levels of copper and iron in molybdenite concentrate to use in steelmaking industries are reported as 0.25%–0.5% [6,10,13]. Flotation is a well-known method in mineral processing which separates different minerals based on the differences between the wettability of their surfaces [14]. Although the floatation process is good for separating copper from molybdenum, it is widely recognized that it is not possible to achieve a high-grade molybdenite only through flotation [13]. To address this issue, it is necessary to use selective leaching [15] or selective bioleaching [16,17]. Due to the fact that bioleaching takes approximately 0.5–3 months [10,16,17] and it is not economical for industrial plants, most studies focus on the selective leaching of chalcopyrite from molybdenite.

In 2022, Tumen-Ulzii et al. investigated the dissolution of major impurities, i.e., copper and iron, from molybdenite concentrate using a leaching system containing sodium nitrate and sulfuric acid. They illustrated that under optimal conditions (0.6 M NaNO₃, 1.5 M H₂SO₄, at 97 °C), after 240 min, about 81.4% of copper and 74.1% of iron were removed, while molybdenum loss was minor. They found that after the process completed, the molybdenite grade increased from 81.33 wt.% to 90.73 wt.% [10]. Ruiz et al. leached copper sulfide impurities from molybdenite using sulfuric acid and sodium dichromate. Under optimal conditions (0.3 M H₂SO₄, 0.12 M Na₂Cr₂O₇, 100 °C, and reaction time of 90 min), they reported that more than 95% of the copper was dissolved with little dissolution of molybdenum [18]. In 2023, Behmadi et al. used nitric acid to remove chalcopyrite from low-grade molybdenite. They observed that after 2 h of leaching with 0.6 M HNO₃ at 80 °C, more than 95% of chalcopyrite was dissolved. However, no data were reported regarding molybdenum dissolution [19]. Padilla et al., in order to selectively remove copper while minimizing molybdenum dissolution, used a novel process involving sulfidation of molybdenite concentrate with S₂ (g) at 380 °C followed by a leaching step using H₂SO₄, NaCl, and oxygen for 90 min at 100 °C. The results of their study showed that under these conditions, 96% of copper can be selectively dissolved [13,20].

In addition to traditional inorganic acids, in recent years, increasing attention has been directed toward the use of alternative green solvents such as ionic liquids, deep eutectic solvents (DES), and organic acids for the selective dissolution of the elements of interest. These systems offer advantages in terms of reduced environmental impact and recyclability, and several studies have shown their potential for efficient metal extraction [21,22,23] However, their application at industrial scale remains limited due to challenges including high cost, viscosity-related mass transfer limitations, lower dissolution rate, and incomplete knowledge of long-term stability. In contrast, nitric acid remains a well-established lixiviant with high oxidative power, lower cost, and higher reaction rate. Thus, while green solvents represent a promising future direction, nitric acid was selected in this study as an oxidizing agent to provide fundamental insights into selective molybdenite purification.

Regarding the reviewed studies, it is evident that the presence of an oxidizing agent is essential in aqueous systems for the effective removal of chalcopyrite from molybdenite concentrate. Molybdenite is a refractory mineral, characterized by its low dissolution efficiency in acidic media unless assisted by an oxidizing agent. While nitric acid is a strong oxidative medium capable of efficiently dissolving sulfide minerals such as chalcopyrite, its use carries the risk of co-dissolution of molybdenite, potentially increasing Mo losses during the purification process. Previous studies have demonstrated that un-activated MoS₂ exhibits negligible dissolution under ambient conditions and low acid concentrations, highlighting its inherent selectivity against oxidative leaching [24].

Building on this understanding, the present study systematically investigates the selective removal of copper and iron impurities from molybdenite concentrates using nitric acid. Nitric acid was selected over other mineral acids due to its strong oxidizing capability, ability to dissolve sulfide impurities efficiently without requiring external oxidants, and its relatively selective behavior toward molybdenite under mild conditions. By optimizing leaching conditions, including acid concentration, temperature, and reaction time, this work aims to achieve near-complete purification of molybdenite while minimizing molybdenum losses. The outcomes provide critical insights into the selective oxidative leaching behavior of mixed sulfide systems and establish a foundation for developing efficient purification processes for molybdenite concentrates.

Although nitric acid is a strong oxidizing agent and has been traditionally used for the leaching of refractory sulfide minerals, it is also associated with safety and environmental concerns due to the generation of toxic NOx gases during the process. However, in the context of molybdenite purification, nitric acid offers distinct advantages over other acids, including high selectivity toward copper and iron sulfides under moderate conditions, while leaving molybdenite largely unaffected. Moreover, nitric acid regeneration represents a promising aspect, as NOx gases formed during the leaching process can be effectively captured and converted to regenerate nitric acid through proper scrubbing systems and reactors. This combination of efficiency and selectivity motivated its selection in the present study. Nonetheless, the limitations of nitric acid are acknowledged, and the mechanistic and kinetic insights gained here may also serve as a foundation for developing alternative, greener oxidative leaching systems in the future.

In addition to evaluating the selective removal of impurities, this study also investigates the dissolution kinetics of copper and iron from molybdenite concentrates in nitric acid. Traditional kinetic models, such as the shrinking core model, often assume constant acid concentration and fail to capture the complexities of multi-mineral systems. To address this limitation, a comprehensive kinetic model was developed, incorporating both the effect of nitric acid concentration and the available reactive surface area of each mineral. This approach enables the determination of reaction orders, activation energies, and potential shifts in rate-controlling mechanisms across different temperature ranges. By combining experimental leaching data with this advanced kinetic modeling, the study not only elucidates the fundamental mechanisms governing selective oxidative dissolution but also provides predictive capabilities for optimizing purification processes under varying conditions.

2. Materials and Methods

2.1. Materials

The molybdenite concentrate used in this study was obtained from the Sarcheshmeh Copper Complex in southeastern Iran. The as-received concentrate was washed with acetone and distilled water to remove residual organic compounds remaining from the flotation process [11,25]. X-ray diffraction (XRD) analysis confirmed that MoS₂ is the predominant crystalline phase. No detectable peaks corresponding to other minerals, such as chalcopyrite or pyrite, were observed, which can be attributed to their low concentrations (lower that the detectable limit of XRD) in the concentrate and the strong intensity of the molybdenite basal-plane reflections (Figure 1a). Particle size distribution of the molybdenite concentrate was investigated using a Mastersizer 2000 (Malvern Instruments Ltd., Malvern, Worcestershire, UK), and the results are given in Figure 1b.

The morphology and elemental composition of the sample were evaluated using scanning electron microscopy with energy-dispersive spectroscopy (SEM-EDS) on a Philips microscope operating at 20 kV. As shown in Figure 2, molybdenum and sulfur are the primary elements, with copper and iron present as impurities.

To quantify the molybdenum, copper, and iron contents, the concentrate was treated by chemical digestion using aqua regia. The resulting solution was analyzed by inductively coupled plasma optical emission spectrometry (ICP-OES, 5100, Agilent Technologies, Santa Clara, CA, USA).

Table 1. Chemical analysis of the molybdenite concentrate.

Component	Mo	Fe	Cu	S	Silica
Wt. %	55.6	0.96	0.58	38.23	4.63

shows the chemical composition of the molybdenite concentrate.

Analytical-grade hydrochloric acid (HCl, 37%, Sigma-Aldrich, Saint Louis, MO, USA) and nitric acid (HNO₃, 65%, Sigma-Aldrich) were used for chemical digestion and for the preparation of nitric acid leaching solutions.

2.2. Methods

Leaching experiments were carried out in nitric acid solutions under varying conditions of temperature and acid concentration, using a water-jacketed reactor connected to a thermostatic bath. A magnetic stirrer (500 rpm) ensured effective dispersion of the solid particles in solution. The temperature of the isothermal leaching tests was controlled by a digital bath equipped with a circulating pump (CRIOTERM 10-80 Thermostat). Since the focus of this study was on evaluating the effects of temperature and acid concentration, the solid-to-liquid ratio and solvent volume were kept constant across all experiments to isolate these variables. Consequently, a fixed amount of 1.3 g/L MoS₂ was employed in each experiment, corresponding to the addition of 0.13 g of concentrate into 100 mL of nitric acid solution. This solid-to-liquid ratio was selected to ensure a sufficiently low pulp density that minimizes diffusion limitations and enables precise monitoring of leaching kinetics. This value also allowed us to avoid secondary effects such as significant solution saturation, thereby ensuring that the leaching behavior of the impurities could be clearly distinguished.

After leaching, solid–liquid separation was achieved by centrifugation at 4000 rpm for 5 min. The filtrates were subsequently analyzed by ICP-OES to determine the dissolved concentrations of Mo, Fe, and Cu.

The leaching efficiency of the three elements was calculated according to Equation (1):

$$\mathrm{L}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{E}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} (\%)=100\times {\displaystyle \frac{{\mathrm{C}}_{\mathrm{M}}\times {\mathrm{V}}_{\mathrm{f}}}{{\mathrm{M}}_{\mathrm{M}}}}$$

(1)

where C_M is the metal concentration in the leaching solution (mg/L), V_f is the final volume of the solution (L), and M_M represents the initial mass of the target element in the molybdenite concentrate (mg).

In this study, each leaching test was performed once under carefully controlled conditions, and thus replicate experiments were not conducted. However, several measures were taken to ensure the reliability of the results: (1) all leaching tests were carried out carefully, using the same solid-to-liquid ratio and under strictly identical operating parameters, (2) solution analyses were performed with ICP-OES, which provides high analytical precision, and (3) mass balance checks between the solid residues and leaching solutions were performed to confirm consistency. These internal controls support the reproducibility and accuracy of the reported data.

All graphical representations of the results were prepared using Origin software version OriginPro 2021 (OriginLab, Northampton, MA, USA).

3. Results and Discussion

3.1. Thermodynamic Evaluation

For the oxidative leaching of pyrite and chalcopyrite in nitric acid, it is generally believed that the oxidation of sulfide occurs in two stages. In the first stage, elemental sulfur is formed, which is subsequently oxidized to sulfate ions in the second stage [26]. The probable reactions for dissolution of MoS₂, CuFeS₂, and FeS₂ in nitric acid solution are as follows [27,28]:

$$\mathrm{M}\mathrm{o}{\mathrm{S}}_2+6\mathrm{H}\mathrm{N}{\mathrm{O}}_3\to \mathrm{M}\mathrm{o}{\mathrm{O}}_3·\mathrm{n}{\mathrm{H}}_2\mathrm{O}+2{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4+6\mathrm{N}\mathrm{O}+(1-\mathrm{n}){\mathrm{H}}_2\mathrm{O}$$

(2)

$$\mathrm{F}\mathrm{e}{\mathrm{S}}_2+4\mathrm{H}\mathrm{N}{\mathrm{O}}_3\to \mathrm{F}\mathrm{e}{\left(\mathrm{N}{\mathrm{O}}_3\right)}_3+2{\mathrm{S}}^0+\mathrm{N}\mathrm{O}+2{\mathrm{H}}_2\mathrm{O}$$

(3)

$$2\mathrm{F}\mathrm{e}{\mathrm{S}}_2+10\mathrm{H}\mathrm{N}{\mathrm{O}}_3\to {\mathrm{F}\mathrm{e}}_2{\left(\mathrm{S}{\mathrm{O}}_4\right)}_3+10\mathrm{N}\mathrm{O}+4{\mathrm{H}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4$$

(4)

$$2\mathrm{F}\mathrm{e}{\mathrm{S}}_2+30\mathrm{H}\mathrm{N}{\mathrm{O}}_3\to {\mathrm{F}\mathrm{e}}_2{\left(\mathrm{S}{\mathrm{O}}_4\right)}_3+30\mathrm{N}{\mathrm{O}}_2+14{\mathrm{H}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4$$

(5)

$$\mathrm{C}\mathrm{u}\mathrm{F}\mathrm{e}{\mathrm{S}}_2+10\mathrm{H}\mathrm{N}{\mathrm{O}}_3\to \mathrm{C}\mathrm{u}{\left(\mathrm{N}{\mathrm{O}}_3\right)}_2+\mathrm{F}\mathrm{e}{\left(\mathrm{N}{\mathrm{O}}_3\right)}_3+2{\mathrm{S}}^0+5{\mathrm{H}}_2\mathrm{O}+5\mathrm{N}{\mathrm{O}}_2$$

(6)

$$3\mathrm{C}\mathrm{u}\mathrm{F}\mathrm{e}{\mathrm{S}}_2+20\mathrm{H}\mathrm{N}{\mathrm{O}}_3\to 3\mathrm{C}\mathrm{u}\mathrm{S}{\mathrm{O}}_4+\mathrm{F}\mathrm{e}{\left(\mathrm{N}{\mathrm{O}}_3\right)}_3+{\mathrm{F}\mathrm{e}}_2{\left(\mathrm{S}{\mathrm{O}}_4\right)}_3+17\mathrm{N}\mathrm{O}+10{\mathrm{H}}_2\mathrm{O}$$

(7)

$$\mathrm{S}+2\mathrm{H}\mathrm{N}{\mathrm{O}}_3\to {\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4+2\mathrm{N}\mathrm{O}$$

(8)

Equation (2) demonstrates the leaching reaction of MoS₂ in nitric acid solution, yielding hydrated molybdic oxide as the main product, which may precipitate due to its limited solubility [24]. The leaching reactions of pyrite (Equations (3)–(5)) depend on the stoichiometric ratio of nitric acid. At lower acid ratios, elemental sulfur is the main product (Equation (3)), whereas higher acid ratios promote the conversion of sulfur to sulfate ions and the formation of ferric sulfate (Equations (4) and (5)). A similar trend is observed for chalcopyrite, with elemental sulfur produced under lower acid ratios (Equation (6)) and sulfate formation favored at higher concentrations (Equation (7)). Finally, elemental sulfur may also be converted into sulfuric acid, as shown in Equation (8).

To assess the feasibility of these reactions, Gibbs free energy (ΔG) calculations were performed at different temperatures, as this approach is widely applied in metallurgical systems [29,30,31,32]. In this study, HSC Chemistry 10 software was used to calculate ΔG values for the dissolution reactions of MoS₂, FeS₂, and CuFeS₂ in nitric acid (Equations (2)–(8)) as a function of temperature. The results, presented in Figure 3, indicate that all reactions exhibit negative Gibbs free energy values throughout the investigated temperature range, confirming that the leaching reactions for chalcopyrite and pyrite dissolution are thermodynamically feasible under the studied temperature range (0–100 °C).

3.2. Leaching Results

Purification experiments were conducted at different temperatures and nitric acid concentrations. Different nitric acid levels (0.12 to 0.4 M) were selected to evaluate the stoichiometric oxidant demand of the impurity sulfides (chalcopyrite and pyrite) at the applied pulp density, while remaining well below conditions that promote appreciable MoS₂ dissolution. Specifically, 0.12 M approximates the minimum oxidant requirement for impurity dissolution, whereas 0.4 M provides more than threefold excess to test oxidant sufficiency and kinetic sensitivity without resorting to strongly acidic conditions. The removal efficiencies of Cu and Fe, together with the co-dissolution of Mo, are presented in Figure 4. To evaluate the effect of temperature, leaching tests were carried out at a fixed nitric acid concentration of 0.24 M, which corresponds to approximately twice the minimum tested acid concentration. As shown in Figure 4a, temperature had a significant effect on copper removal. After 30 min of reaction, the removal efficiency of Cu increased from ~16% at 22 °C to ~55% at 78 °C. Prolonging the reaction time further enhanced removal efficiency, reaching ~99% after 4 h at 78 °C, compared with only ~20% at 22 °C. The effect of acid concentration at different temperatures is presented in Figure 4b, where it can be seen that varying nitric acid concentration at 30, 50, and 70 °C had only a minor effect on copper removal.

A similar trend was observed for iron removal. At a constant nitric acid concentration of 0.24 M, increasing temperature significantly improved the removal efficiency of Fe (Figure 4c). After 4 h at 78 °C, ~99% of iron was removed. As with copper, the nitric acid concentration had little effect on iron removal efficiency across the tested temperatures (Figure 4d). These results are promising, as ~80% of Cu and ~90% of Fe could still be removed after 6 h of leaching at 70 °C, even at a low acid concentration of 0.12 M.

In addition to Cu and Fe removal, as expected according to negative ΔG values of Equation (2) (Figure 3), partial co-dissolution of Mo occurred. As shown in Figure 4e, the extent of Mo dissolution was relatively low, reaching a maximum of ~12% after 6 h at 78 °C. Temperature exerted the strongest effect on Mo dissolution, while acid concentration showed lower effect in comparison with temperature (Figure 4f).

Overall, the results indicate that nearly complete removal of Cu and Fe (>99%) can be achieved by leaching for 6 h at 78 °C in 0.24 M nitric acid, with Mo co-dissolution limited to ~12%. Shortening the leaching time to 4 h reduced Mo dissolution to ~9% while still ensuring ~99% removal of Cu and Fe.

The results of this study are encouraging when compared with previous reports. For instance, Padilla et al. [13] demonstrated that, after sulfidation at 380 °C followed by leaching in a 0.6 M H₂SO₄-NaCl solution with an oxygen flow rate of 1 L/min at 100 °C, ~96% of Cu and <20% of Fe were removed. In a different system using sulfuric acid and sodium dichromate, Ruiz et al. showed that with stoichiometric H₂SO₄ and 0.12 M Na₂Cr₂O₇, ~95% of Cu was dissolved after 90 min at 100 °C [18]. More recently, Tumen-Ulzii et al. [10] reported that only 81.4% of Cu and 74.1% of Fe were removed from concentrate after 240 min of leaching in an H₂SO₄-NaNO₃ solution (1.5 M H₂SO₄ + 0.6 M NaNO₃) at 97 °C.

It should be noted that, although the removal efficiencies for Cu and Fe in this study were nearly complete, the observed Mo co-dissolution of up to ~12% after 6 h of leaching could be economically significant at an industrial scale. Such losses would directly impact molybdenum recovery and process profitability. However, as mentioned earlier, by shortening the leaching duration to 4 h at 78 °C, Mo losses can be reduced to ~9% while still maintaining ~99% Cu and Fe removal. This suggests that careful optimization of leaching time and acid concentration offers a practical strategy for balancing impurity removal with molybdenum preservation. Additional approaches, such as staged leaching or coupling nitric acid leaching with a secondary purification step, could further reduce Mo dissolution. It should also be noted that the dissolved Mo cannot be considered as an absolute loss, since it can be subsequently recovered from the leach solution using well-established hydrometallurgical techniques such as precipitation or electrowinning. Therefore, while nitric acid leaching demonstrates strong selectivity under moderate conditions, optimization strategies must be implemented to ensure minimal economic impact from Mo losses in industrial applications.

3.3. Kinetics Study

3.3.1. Shrinking Core Model Fitting

To investigate the dissolution kinetics of impurities, the leaching results for iron and copper (Figure 3) were analyzed. The shrinking core model (SCM) kinetic equations which are commonly applied in solid–liquid hydrometallurgical reactions were fitted to the experimental data [33]. According to this model, the reaction initiates at the particle surface and progresses inward as the reaction interface moves toward the core.

Two scenarios are possible. In the first, one of the reaction products is a solid, which accumulates as a layer on the particle surface. For sulfide minerals, in the absence of a suitable oxidant, elemental sulfur may form on the surface. The dissolution of chalcopyrite in sulfuric acid is a classic example of this behavior, where sulfur passivation occurs during the progress of reaction [34,35]. In this case, diffusion of reactants through the ash layer is the rate-controlling step, and the process follows Equation (9) [33]:

$$1-3{\left(1-\mathrm{X}\right)}^{{\displaystyle \frac{2}{3}}}+2\left(1-\mathrm{X}\right)=\mathrm{k}\mathrm{t}$$

(9)

where X is the fractional conversion, t is time, and k is the rate constant. It should be noted that, although the unreacted core shrinks over time, the overall particle size changes little due to the formation of the ash layer.

In the second scenario, all reaction products are soluble, and the particle size decreases continuously until complete dissolution. Here, the rate-controlling step may be either diffusion of species through the fluid film surrounding the particle (Equation (10)) or the surface chemical reaction (Equation (11)) [33]:

$$1-{\left(1-\mathrm{X}\right)}^{{\displaystyle \frac{2}{3}}}=\mathrm{k}\mathrm{t}$$

(10)

$$1-{\left(1-\mathrm{X}\right)}^{{\displaystyle \frac{1}{3}}}=\mathrm{k}\mathrm{t}$$

(11)

In systems with limited stirring or stagnant fluid, film diffusion may dominate. However, at sufficiently high stirring speeds, the fluid film becomes thin and diffusional resistance is negligible [36].

The Arrhenius equation can be used to calculate activation energy:

$$\mathrm{k}={\mathrm{k}}_0·{\mathrm{e}}^{\left({\displaystyle \frac{-\mathrm{E}}{\mathrm{R}\mathrm{T}}}\right)}$$

(12)

where k₀ is the frequency factor, E is the activation energy, and T is the absolute temperature. By plotting lnk versus 1/T, the activation energy can be derived from the slope.

Considering the dissolution reactions of chalcopyrite, pyrite, and molybdenite in nitric acid (Equations (2)–(8)), elemental sulfur formation (ash layer) or its subsequent oxidation to soluble sulfate ions is possible, depending strongly on the nitric acid concentration.

It is important to note that Equations (9)–(11) assume constant acid concentration over time [33]. Therefore, only the leaching data obtained at a fixed nitric acid concentration of 0.24 M and varying temperatures (22, 50, 70, and 78 °C) were used for kinetic fitting. The 0.24 M HNO₃ concentration was selected as the primary fitting concentration to ensure sufficient oxidizing capacity while maintaining moderate acid levels. This concentration corresponds to approximately twice the minimum tested concentration (0.12 M), allowing meaningful comparisons across the studied temperature range without reaching excessively high acid strengths that could obscure the selectivity of the process.

Figure 5 presents the linear fittings of copper and iron removal efficiencies to the three SCM models. The obtained R² values indicate poor fits, particularly at lower temperatures. This suggests that the dissolution of impurities in molybdenite concentrate cannot be fully described by the assumptions of the SCM. The presence of multiple sulfide minerals, their potential interactions, and the dependence of dissolution reactions on nitric acid concentration likely complicate the mechanism of Cu and Fe dissolution. As suggested earlier (Equations (2)–(8)), lower ratio of nitric acid concentration may lead to elemental sulfur formation, which can be followed by its subsequent dissolution to sulfate, further deviating from the SCM assumptions.

Therefore, the purification mechanism in this system appears to be more complex than predicted by the standard SCM. In the following section, a modified kinetic model is developed to account for the influence of nitric acid concentration on the rate equation.

3.3.2. Model Development

Traditional kinetic models, such as the SCM, have been widely used to describe sulfide leaching processes, as evaluated in the previous section. However, these models rely on assumptions such as constant acid concentration and fixed reactive surface area. These simplifications often limit their applicability, especially in systems where acid consumption and mineral’s reactive surface are changes play a critical role. To overcome these limitations, this study develops and validates a comprehensive kinetic model that explicitly incorporates both the instantaneous acid concentration and the evolution of the reactive surface area. This approach provides a more accurate representation of the leaching mechanism and allows prediction of dissolution behavior across a broader range of operational conditions.

In the conventional SCM, it is assumed that the acid concentration remains constant throughout the reaction. However, in the real system, the acid concentration decreases as leaching progresses. Moreover, the earlier kinetic fitting was performed using data obtained at a fixed acid concentration and varying temperatures (Figure 5). Therefore, a more comprehensive model is required which can account for both temperature and acid concentration simultaneously and thus be applicable across a wider range of leaching conditions.

It should also be noted that Cu and Fe originate from two distinct sulfide minerals, chalcopyrite and pyrite, respectively. Consequently, the dissolution kinetics should be considered separately for each mineral, rather than as overall element removal. Furthermore, the influence of acid concentration must be incorporated into the rate expressions, since as indicated by Equations (2)–(8), variations in nitric acid concentration can shift the reaction pathway, favoring either the formation of a sulfur passivation layer or the production of soluble sulfate ion.

By considering the leaching data of Fe and Cu and the initial composition of the concentrate and applying mass balance calculations, the contributions of chalcopyrite and pyrite dissolution can be differentiated. Figure 6 presents the separated leaching efficiencies of chalcopyrite and pyrite under different temperatures and nitric acid concentrations. The results reveal a distinct increase in leaching efficiency above 50 °C, suggesting a possible change in the dissolution mechanism. This observation also may explains the reason for the poor fit of the experimental results to the classical SCM models (Figure 5).

To incorporate the effect of nitric acid concentration on the dissolution rate, the following general rate expression was applied:

$$\mathrm{r}={\displaystyle \frac{\mathrm{d}\mathrm{X}}{\mathrm{d}\mathrm{t}}}=\mathrm{k}·{\mathrm{C}}^{\mathrm{m}}$$

(13)

where k is the rate constant, C is the instantaneous nitric acid concentration, and m is the reaction order with respect to acid concentration. Thus, the dissolution rate depends not only on temperature (through k), but also on the nitric acid concentration.

The instantaneous acid concentration can be estimated from the balance between the initial nitric acid amount and the quantity consumed during the leaching reaction. At any given time, the consumed amount corresponds to the fraction of reaction completed (X) multiplied by the stoichiometric acid requirement. Accordingly, the instantaneous nitric acid concentration can be expressed as follows:

$$\mathrm{C}={\mathrm{C}}_0-\mathrm{X}{\mathrm{C}}_{\mathrm{S}}$$

(14)

where C₀ is the initial acid concentration, C_S is the stoichiometric concentration, and X is the fractional conversion.

Since three sulfide minerals (MoS₂, FeS₂, and CuFeS₂) are simultaneously dissolved during leaching, all their contributions to acid consumption must be considered. Therefore, Equation (14) can be extended as follows:

$$\mathrm{C}={\mathrm{C}}_0-{\left(\mathrm{X}{\mathrm{C}}_{\mathrm{S}}\right)}_{{\mathrm{M}\mathrm{o}\mathrm{S}}_2}-{\left(\mathrm{X}{\mathrm{C}}_{\mathrm{S}}\right)}_{{\mathrm{F}\mathrm{e}\mathrm{S}}_2}-{\left(\mathrm{X}{\mathrm{C}}_{\mathrm{S}}\right)}_{{\mathrm{C}\mathrm{u}\mathrm{F}\mathrm{e}\mathrm{S}}_2}$$

(15)

In addition to acid concentration, the effect of reactive surface area should also be incorporated into the model. As dissolution progresses, the available surface area decreases, reducing the reaction rate. This dependence can be introduced by relating the reaction rate to the unreacted fraction of the mineral. If X is the fractional conversion, the remaining mineral, and hence the available surface, is proportional to (1 − X). The rate equation can then be written as follows:

$$\mathrm{r}={\displaystyle \frac{\mathrm{d}\mathrm{X}}{\mathrm{d}\mathrm{t}}}=\mathrm{k}·{\left(1-\mathrm{X}\right)}^{\mathrm{n}}$$

(16)

where n is the reaction order with respect to the remaining mineral (chalcopyrite or pyrite).

Therefore, considering the above Equations (13)–(16) and combining the effects of both nitric acid concentration and reactive surface area, the general rate expression becomes the following:

$$\mathrm{r}={\displaystyle \frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}}=\mathrm{k}·{\mathrm{C}}^{\mathrm{m}}·{\left(1-\mathrm{X}\right)}^{\mathrm{n}}$$

(17)

The Arrhenius equation can be expressed in the following form:

$$\mathrm{k}=\exp \left({\displaystyle \frac{-\mathrm{E}}{\mathrm{R}\mathrm{T}}}+\mathrm{b}\right)$$

(18)

where b is a model parameter defined as follows:

$$\mathrm{b}=\mathrm{e}\mathrm{x}\mathrm{p}\left({\mathrm{k}}_0\right)$$

(19)

with k₀ representing the pre-exponential (frequency) factor.

This comprehensive model accounts for both temperature and acid concentration, making it applicable across a wide range of leaching conditions.

The model was fitted to all experimental leaching data using the least-squares method. To solve the equation and plot X versus t, numerical integration of Equation (17) was performed with the fourth-order Runge–Kutta method (RK4) to obtain X as a function of t. The results of model fitting are plotted in Figure 7.

As expected from the leaching results of chalcopyrite and pyrite (Figure 6), the initial fitting suggested separating the leaching data into two groups according to temperature: one below 50 °C and the other above 70 °C. This distinction, as noted earlier, indicates a possible change in the dissolution mechanism. Accordingly, the fitting process was carried out separately for these two temperature ranges, and the results are summarized in

Table 2. Constants of the fitted model for the leaching experiments along with the activation energy value and R² values obtained from fitting the rate equation in each case.

Mineral	Model Parameters		Temp. - Conc.	R2
FeS2	b	14.2	22 – 0.24	0.9204
	m	0.35	30 – 0.12	0.9203
	n	6	30 – 0.36	0.8592
	E (J/mol)	43,500	50 – 0.24	0.9895
			50 – 0.41	0.9805
	b	11.5	70 – 0.24	0.9583
	m	0.4
	n	1	78 – 0.24	0.9900
	E (J/mol)	43,500
CuFeS2	b	16.5	22 – 0.24	0.8942
	m	0.3	30 – 0.12	0.8940
	n	13.5	30 – 0.36	0.9596
	E (J/mol)	51,000	50 – 0.24	0.9389
			50 – 0.41	0.9322
	b	14.1	70 – 0.24	0.9721
	m	0.4
	n	1.5	78 – 0.24	0.9838
	E (J/mol)	51,000

. Figure 7 and the corresponding R² values in Table 2 confirm that the developed model provides a good fit to all leaching tests, even at lower temperatures and under different acid concentrations.

The results in Table 2 also show that, while the overall activation energy for each mineral can be assumed to be constant across both temperature ranges, the model parameter n (the reaction order with respect to the mineral’s available surface) exhibits the most significant change. Specifically, for both minerals, n decreases markedly as the temperature increases. This suggests that the dissolution mechanism is sensitive to surface availability at lower temperatures, whereas at higher temperatures, the reaction rate becomes less dependent on the reactive surface area.

This interpretation is supported by the fact that, according to reactions (Equations (3) and (6)), oxidative leaching of chalcopyrite and pyrite in nitric acid can produce elemental sulfur. The precipitation of sulfur on the mineral surface can form a passivating layer, reducing the accessibility of fresh surface to the leaching agent. This is consistent with the decrease in n at higher temperatures, indicating a lower dependence on available surface area.

Based on this observation, it can be inferred that at lower temperatures, the dissolution process is primarily controlled by surface chemical reactions at the solid–liquid interface. However, as temperature increases, a shift toward ash-layer diffusion control likely occurs. Since sufficient agitation was applied during the leaching tests, external fluid-film diffusion can be excluded as the rate-controlling step. Therefore, the mechanism most likely transitions between chemical reaction control at lower temperatures and ash-layer diffusion control at higher temperatures. This conclusion is also consistent with the calculated activation energy values, which lie within the range typically reported for these two mechanisms.

It is worth noting that while sufficient stirring (500 rpm) in the present study minimizes external diffusion effects, in industrial reactors, agitation efficiency may vary depending on the reactor design and operating conditions. In such cases, elemental sulfur accumulation could promote ash-layer diffusion control at elevated temperatures, whereas optimized agitation could help prolonging the predominance of surface chemical reaction control.

As observed, this model improvement enables the model to fit experimental data across a wider range of leaching conditions (temperature and acid concentration), providing a more realistic description of the dissolution process.

In this kinetic model, the stoichiometric acid consumption parameters were determined directly from the balanced leaching reactions for MoS₂, FeS₂, and CuFeS₂ considering the highest acid value (Equations (2), (5) and (7)), assuming complete oxidation under the respective conditions. While these values provide a robust framework for quantifying instantaneous acid concentration, it should be noted that uncertainties in stoichiometry, particularly in cases where elemental sulfur may form (Equations (3) and (6)), can affect the precision of the calculated acid consumption. To address this, a sensitivity check was performed during the fitting, and it was observed that small variations in stoichiometric values did not significantly affect the overall model predictions. This is also reflected in the m values in Table 2, which indicate lower sensitivity of the rate equation to acid concentration compared with the n parameter (reaction order with respect to surface area), thereby confirming the model’s relative robustness.

Regarding intermediate temperatures (50–70 °C), the model remains applicable in this intermediate region. However, fitting in this range may reflect mixed-control behavior, leading to slightly lower R² values compared to the two distinct regimes.

Finally, the purified molybdenite concentrate obtained after leaching in 0.24 M nitric acid for 6 h at 78 °C was examined by SEM-EDS to evaluate the remaining impurities. As shown in Figure 8, in contrast to the initial concentrate (Figure 2), no detectable traces of Cu or Fe are observed, indicating that these impurities were almost completely removed under the applied conditions. The chemical purity of the product was further quantified by ICP-OES, with the results expressed as the relative proportion of total dissolvable cations (Mo, Cu, and Fe) before and after purification (Figure 8c,d). These analyses clearly confirm the significant enhancement in Mo purity following nitric acid treatment.

4. Conclusions

This study demonstrated that nitric acid is a highly effective oxidizing medium for the selective purification of molybdenite concentrates. Under optimized conditions (0.24 M HNO₃, 78 °C, 6 h), nearly complete removal of copper and iron was achieved, while molybdenite co-dissolution was limited to ~12%. The kinetic investigation revealed that conventional shrinking core models were insufficient to describe the process due to variations in acid concentration and mineral specific behavior. A new comprehensive kinetic model was therefore developed, incorporating both acid concentration and reactive surface area effects. This model successfully fitted the experimental data across a wide range of leaching conditions and revealed a probable transition in the controlling mechanism from chemical reaction control at lower temperatures to ash-layer diffusion at higher temperatures. SEM-EDS and ICP-OES analyses confirmed the high purity of the final product, highlighting the practical applicability of the method.

What distinguishes this work is that the applied process not only achieves nearly complete removal of Fe and Cu impurities but also does so under relatively moderate conditions of temperature and acid concentration compared to conventional sulfuric acid or mixed-oxidant systems. Moreover, the integration of a comprehensive kinetic model that accounts for both nitric acid concentration and reactive surface area provides a more realistic description of the leaching process than the traditional SCM approach. This dual achievement of highly efficient purification and the development of a generalized kinetic framework represents a major step forward in understanding and optimizing nitric acid-based purification of molybdenite concentrates. The combination of experimental validation (SEM-EDS, ICP-OES) and theoretical modeling not only demonstrates the feasibility of this approach but also shows the potential for further scale-up and industrial application.

From a scalability perspective, while the process demonstrates strong selectivity and efficiency at laboratory scale, industrial implementation would require careful consideration of safety and environmental aspects associated with nitric acid, particularly NOx gas management. Integration into existing hydrometallurgical flowsheets is feasible, as nitric acid leaching could be positioned as a pre-treatment stage for impurity removal, followed by conventional downstream molybdenum recovery processes. It should be noted that dissolved molybdenum in solution should not be regarded as an irretrievable loss, since it can be recovered by established hydrometallurgical techniques such as precipitation or electrowinning.

Nevertheless, the toxicity and environmental concerns of nitric acid should be acknowledged. Future work may therefore focus on evaluating greener oxidative alternatives such as deep eutectic solvents or ionic liquids systems, guided by the mechanistic insights and kinetic framework established in this study. Such efforts would strengthen the sustainability and industrial relevance of selective impurity removal from molybdenite and other complex sulfide concentrates.

Overall, the findings not only establish nitric acid leaching as a promising route for the selective purification of molybdenite but also introduce a robust kinetic framework that can be extended to other complex sulfide systems. By addressing both scientific mechanisms and practical considerations, this work contributes toward bridging laboratory-scale insights with industrially viable purification strategies.