Selective Recovery of Molybdenum Over Rhenium from Molybdenite Flue Dust Leaching Solution Using PC88A Extractant

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Article Selective Recovery of Molybdenum over Rhenium from Molybdenite Flue Dust Leaching Solution Using PC88A Extractant

Ali Entezari-Zarandi 1,2,*, Dariush Azizi 1,3, Pavel Anatolyevich Nikolaychuk 4 , Faïçal Larachi 1 and Louis-César Pasquier 3 1 Department of Chemical Engineering, Université Laval, Québec, QC G1V 0A6, Canada; [email protected] (D.A.); [email protected] (F.L.) 2 Centre Technologique des Résidus Industriels (CTRI), Rouyn-Noranda, QC J9X 0E1, Canada 3 Center Eau Terre Environnement, Institut National de la recherche scientiﬁque (INRS), Québec, QC G1K 9A9, Canada; [email protected] 4 Lehrstuhl für Thermodynamik und Energietechnik, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany; [email protected] * Correspondence: [email protected]; Tel.: +1-819-762-0931 (ext. 1737)

Received: 31 August 2020; Accepted: 23 October 2020; Published: 26 October 2020

Abstract: Selective solvent extraction of molybdenum over rhenium from molybdenite (MoS2) flue dust leaching solution was studied. In the present work, thermodynamic calculations of the chemical equilibria in aqueous solution were first performed, and the potential–pH diagram 2 for the Mo–Re–SO4−–H2O system was constructed. With the gained insight on the system, 2-ethylhexyl phosphonic acid mono-(2-ethylhexyl)-ester (PC88A) diluted in kerosene was used as the extractant agent. Keeping constant the reaction temperature and aqueous-to-organic phase ratio (1:1), organic phase concentration and pH were the studied experimental variables. It was observed that by increasing the acidity of the solution and extractant concentration, selectivity towards Mo extraction increased, while the opposite was true for Re extraction. Selective Mo removal (+95%) from leach solution containing ca. 9 g/L Mo and 0.5 g/L Re was achieved when using an organic phase of 5% PC88A at pH = 0. No rhenium was coextracted during 10 min of extraction time at room temperature. Density functional theory (DFT) calculations were performed in order to study the interactions of organic extractants with Mo and Re ions, permitting a direct comparison of calculation results with the experimental data to estimate selectivity factors in Mo–Re separation. For this aim, PC88A and D2EHPA (di-(2-ethylhexyl) phosphoric acid) were simulated. The interaction energies of D2EHPA were shown to be higher than those of PC88A, which could be due to its stronger capability for complex formation. Besides, it was found that the interaction energies of both 2+ 2 extractants follow this trend considering Mo species: MoO2 > MoO4−. It was also demonstrated through DFT calculations that the interaction energies of D2EHPA and PC88A with species are based 2+ 2 2+ 2 on these trends, respectively: MoO2 > MoO4− > ReO4− and MoO2 > ReO4− > MoO4−, in qualitative agreement with the experimental findings.

Keywords: rhenium; molybdenum; solvent extraction; separation; hydrometallurgy

1. Introduction Molybdenum (Mo) is a strategic metal that has an extensive demand in diﬀerent branches of the industry. Rhenium (Re) is also a strategic metal, although less common with wide applications in the oil industry (e.g., production of reforming catalyst) and in heat-resistant alloys (e.g., aerospace). Typically, in Mo sulphide concentrates (molybdenite, MoS2), Re coexisting with varying concentrations

Metals 2020, 10, 1423; doi:10.3390/met10111423 www.mdpi.com/journal/metals Metals 2020, 10, 1423 2 of 19 ranging from 0.001% to 0.1% is identified [1]. Upon roasting, molybdenite transforms into technical-grade Mo oxide, while Re content escapes the reactor in the form of Re2O7, which partly deposits in the filters alongside the flue dust. Scrubbing the flue gases and leaching flue dusts are effective methods to recover Re values. Such solutions typically have 5–10 g/L Mo and 0.4–0.9 g/L Re. Due to similar chemical properties, Mo–Re separation is a challenge, and a number of studies have been devoted to introducing ad hoc technologies in this regard. Ion exchange and solvent extraction are the most used separation methods [2]. However, the separation of Mo and Re from liquors obtained from leaching molybdenite roasting flue dust is an essential step in order to produce high-purity final products, such as ammonium perrhenate and ammonium (para) molybdate. The following hydrolysis and acidic reactions illustrate the reactants/products involved in the leaching of flue dust [3,4]:

MoO (s) + H O (l) H MoO (aq) ∆rG◦ = 31.9 kJ/mol (1) 3 2 2 4 − + 2+ H MoO (aq) + 2H (aq) MoO (aq) + 2H O (l) ∆rG◦ = 2.79 kJ/mol (2) 2 4 2 2 − + Re O (s) + H O (l) 2ReO− (aq) + 2H (aq) ∆rG◦ = 64.4 kJ/mol (3) 2 7 2 4 − + ReO− (aq) + H (aq) HReO (aq) ∆rG◦ = 1465.8 kJ/mol (4) 4 4 −

At high acid concentration, the anionic oxyspecies of rhenium (i.e., perrhenate ion (ReO4−)) is highly stable, and other possible short-life species readily hydrolyse to it. On the other hand, molybdenum 2+ forms cationic oxyspecies (MoO2 ) at high acid concentration, evolving into neutral and anionic species with increasing pH [5]. Many attempts have been made on Mo and Re separation. Solvating extractant TBP (tributyl phosphate) is used for Re removal in near-zero pH, followed by Mo removal employing commercial extractant LIX984N [6]. Stepwise removal of Mo with TBP was conducted at pH near 2, and afterwards, Re was removed at pH lower than 0 [7]. Similarly, the coextraction of molybdenum and rhenium by N235 (tri-octyl amine) and their separation from stripping solution by using D201 ion-exchange resin (containing quaternary ammonium group [N-(CH3)2C2H4OH]) has been reported [8]. Selective extraction of rhenium over molybdenum from alkaline solutions has also been studied by employing an organic phase composed of 20% N235 and 30% TBP diluted in kerosene [9]. An organic phase composed of 5 vol% N235 (in kerosene) was found to selectively recover Re over Mo at equilibrium pH 0.0 [10]. Table1 lists recent attempts to separate Re and Mo from their aqueous mother liquor. The use of appropriate solvents is a challenging problem. The commercially available extractant Cyanex 923 has been shown to be an appropriate choice for the purpose of rhenium recovery [11]. The lower solubility of Cyanex 923 in water compared with that of TBP (0.05 to 0.4 g/L at 25 ◦C, respectively) and its complete miscibility with diluents at low temperature are mentioned as some of its advantages over other solvents such as TOPO (trioctylphosphine oxide) and Aliquat 336. Pathak et al.[12] studied the extraction behaviour of molybdenum from acidic radioactive wastes using PC88A. They found that by increasing HNO3 concentration in the aqueous phase, Mo extraction decreases, while increasing the organic concentration until 0.15 M causes an increase in metal extraction. In the present work, the application of PC88A (2(ethylhexyl)phosphonic acid mono-2(ethylhexyl)-ester) extractant was studied on Mo–Re separation in solutions obtained from leaching molybdenite ﬂue dust under various conditions of organic concentration and aqueous solution acidity. Next, the performance of PC88A was compared with that of D2EHPA using both experimentation and density functional theory simulations. Metals 2020, 10, 1423 3 of 19

Table 1. Literature on Mo and Re solvent extraction.

Extractant/Diluent Acidity Selectivity Ref. Re over Mo N235 + TBP/kerosene pH = 9 15 g/L Mo + 0.1 g/L Re [9] 97.6%: 1.6% N235/kerosene pH = 0 Re over Mo [10] pH = 0 Cyanex 923/kerosene Re [11] HCl N235 + pH = 0 Re over Mo [13] isooctanol/kerosene HNO3 pH = 2–6 LIX 63/kerosene Mo over W [14] H2SO4 pH = 3–4 D2EHPA/kerosene Mo over W [15] H2SO4 pH = 2 TBP/kerosene pH = 0 Mo over ReRe over Mo [7] H2SO4 pH = 0 Re over Mo and V TBP/kerosene [16] <3.0 M HCl Re and Mo over V pH = 1.5 Mo over Re TBP/kerosene pH = 0.3 [1] − Re over Mo H2SO4 Re over Mo Alamine pH = 2–3 260–280 mg/L Re + 80–90 [17] 304-1/Anysol-150 H SO 2 4 mg/L Mo 0.1–4.0 M Mo PC88A/n-dodecane [12] HNO3 0.01 mol/L PC88A/Sulfonated pH = 0.2 ~ 0.5 − Mo [18] kerosene HCl N235 = tri-octyl amine, TBP = tributyl phosphate, Cyanex 923 = trialkylphosphine oxide, LIX 63 = 5,8-diethyl-7-hydroxy-6-dodecanone oxime, D2EHPA = di-(2-ethylhexyl)phosphoric acid, Alamine 304-1 = tri-n-dodecyl amine, PC88A = 2(ethylhexyl)phosphonic acid mono-2(ethylhexyl)-ester.

2. Experimentation

2.1. Materials and Reagents Babakan Ferromolybdenum Co. (Kerman, Iran) kindly provided molybdenite flue dust. Table2 lists the main chemical composition of the flue dust sample. Deionised water (industrial grade) was used as the leaching agent. D2EHPA and PC88A extractants were analytical-grade products kindly provided by Farapoyan Isatis Co., Yazd, Iran. Kerosene (Tehran Refinery, Tehran, Iran) was used as diluent, and sulphuric acid and sodium hydroxide (Merck) were the pH-adjusting agents used in our protocols. An iron-rich copper solvent extraction raffinate sample (NICICO, Tehran, Iran) was also used to investigate the possibility of selective separation of Mo from present metal impurities.

Table 2. Composition of ﬂue dust before leaching (ppm).

Component As Ca Cu Fe Mg Mo Na Pb Re S Se Zn Content 785 3670 3450 1720 775 36.6% 2380 1260 3980 25.2% 6650 242 Metals 2020, 10, x FOR PEER REVIEW 4 of 20

Table 2. Composition of flue dust before leaching (ppm).

Component As Ca Cu Fe Mg Mo Na Pb Re S Se Zn MetalsContent2020, 10, 1423785 3670 3450 1720 775 36.6% 2380 1260 3980 25.2% 6650 2424 of 19

2.2. Flue Dust Leaching 2.2. Flue Dust Leaching Molybdenite flue dust leaching was carried out in a 5 L glass reactor equipped with a mechanical Molybdenite flue dust leaching was carried out in a 5 L glass reactor equipped with a mechanical agitation system (600 rpm) and a water jacket. The pulp density and reaction temperature were 20 agitation system (600 rpm) and a water jacket. The pulp density and reaction temperature were 20 wt.% wt.% and 80 °C, respectively. A mixture of water and alcohols (e.g., ethyl or methyl alcohol) was and 80 C, respectively. A mixture of water and alcohols (e.g., ethyl or methyl alcohol) was found to found to◦ help in the selective leaching of rhenium over molybdenum [19]. Selective leaching has the help in the selective leaching of rhenium over molybdenum [19]. Selective leaching has the advantage advantage of separation of desired values from the very first steps of hydrometallurgical treatment of separation of desired values from the very first steps of hydrometallurgical treatment [20]. However, [20]. However, for the sake of simplicity in the current work, only deionised water of industrial for the sake of simplicity in the current work, only deionised water of industrial quality was used to quality was used to eliminate the probable effect of additives on the solvent extraction step. It is worth eliminate the probable effect of additives on the solvent extraction step. It is worth noting that the noting that the application of acidic medium for leaching is unfavourable due to excessive application of acidic medium for leaching is unfavourable due to excessive introduction of Mo and other introduction of Mo and other impurities, such as Fe, into the solution [21]. The leach liquor samples impurities, such as Fe, into the solution [21]. The leach liquor samples (5 mL without compensation) (5 mL without compensation) were withdrawn at predetermined intervals and immediately filtered were withdrawn at predetermined intervals and immediately filtered through a medium quantitative through a medium quantitative filter paper to be analysed for Re and Mo content after required filter paper to be analysed for Re and Mo content after required dilution with deionised water. The pH dilution with deionised water. The pH was monitored over the filtered samples in order to was monitored over the filtered samples in order to understand its variations during the leaching understand its variations during the leaching process (Figure 1a). After 360 min of contact, the process (Figure1a). After 360 min of contact, the remaining hot solution was filtered under gentle remaining hot solution was filtered under gentle vacuum and cooled down to room temperature in vacuum and cooled down to room temperature in order to obtain the stock solution. The solution order to obtain the stock solution. The solution underwent a series of colour changes in the course of underwent a series of colour changes in the course of leaching (AppendixA, Figure A1). It first became leaching (Appendix A, Figure A1). It first became pale yellow, then turned into green, and finally pale yellow, then turned into green, and finally dark blue. Metal recovery and pH variation profiles are dark blue. Metal recovery and pH variation profiles are presented in Figure 1b. Stock solution presented in Figure1b. Stock solution composition is listed in Table3. composition is listed in Table 3.

8 (a) 100% (b) 7 80% 6 5 60% Re 4 pH Mo 3 40% 2 Metal recovery, % recovery, Metal 20% 1 0 0% 0 100 200 300 400 0 100 200 300 400 Time, min Time, min

Figure 1. Dissolution of metal oxides from flue dust: (a) pH variations and (b) metal recovery over Figure 1. Dissolution of metal oxides from flue dust: (a) pH variations and (b) metal recovery over time. T = 85 ◦C, t = 360 min, 600 rpm. time. T = 85 °C, t = 360 min, 600 rpm. Table 3. Chemical composition of stock solution. Table 3. Chemical composition of stock solution. Element Mo Re Cu Se Fe Concentration (ppm)Element9150 455Mo Re 2.5Cu Se 6.2Fe 2000 Concentration (ppm) 9150 455 2.5 6.2 2000 2.3. Experimental Procedure 2.3. Experimental Procedure Different concentrations of PC88A diluted in kerosene (i.e., 5, 15, and 30 vol%) were Different concentrations of PC88A diluted in kerosene (i.e., 5, 15, and 30 vol%) were used to test used to test the influence of the extractant concentration on Re–Mo extraction and separation. the influence of the extractant concentration on Re–Mo extraction and separation. Likewise, various Likewise, various pH classes of stock solution (i.e., 1, 1, 0, 3, 7, and 9) were prepared using pH classes of stock solution (i.e., −1, 1, 0, 3, 7, and 9) were− prepared using sulphuric acid and sodium sulphuric acid and sodium hydroxide. All the solvent extraction experiments were performed hydroxide. All the solvent extraction experiments were performed at room temperature. For all at room temperature. For all extraction experiments, an organic-to-aqueous ratio of 1:1 (25 mL for extraction experiments, an organic-to-aqueous ratio of 1:1 (25 mL for each) was imposed. Good each) was imposed. Good contacting between phases was achieved during 10 min of mixing under contacting between phases was achieved during 10 min of mixing under magnetic stirring (600 rpm) magnetic stirring (600 rpm) with a cross-shaped magnet (3 cm in diameter) in 250 mL capacity beakers. Agitated mixtures were then transferred to a separation funnel and retained there for another 10 min before aqueous phase separation and chemical analysis. However, the phase separation time was Metals 2020, 10, 1423 5 of 19 measured to be in the order of 20 to 30 s. It is worth noting that for the case of pH values of 7 and 9, the solution was filtered before the experiment to separate formed iron precipitates.

2.4. Chemical Analysis An inductively coupled plasma optical emission spectrometer (ICP-OES) was used to determine the Re and Mo concentrations in all aqueous solutions. The Cu and Fe contents were measured by atomic absorption spectrometry (AAS) where necessary. The samples were treated prior to analysis by the addition of appropriate amounts of nitric acid, followed by dilutions to a predetermined volume.

2.5. Thermodynamic Analysis of Equilibria in Aqueous Solution Thermodynamic calculations were performed in order to identify the equilibrium aqueous species in the leaching stock solutions. According to Table3, the total contents of molybdenum and rhenium in the solution are equal to ~9 g/L (9.4 10 2 mol/L) and ~0.5 g/L (2.7 10 3 mol/L), respectively. × − × − The calculations were performed at pH values of 2, 1, 0, and 1, which correspond to the total content − of sulphuric acid ranging from 6.5 10 3 to 10.09 mol/L. The concentrations of different dissociation × − products of sulphuric acid were calculated as presented in AppendixB and used to calculate the ionic strength of the solutions. 2+ The activity coefficients of both ReO4− and MoO2 ions were calculated from the extended Debye–Hückel theory [22]. The values of the effective radii of the ions and the values for water dielectric constant were taken from references [23,24], respectively. The calculation details are presented in AppendixB. As can be seen, the average activities of molybdenum species are ~0.01 mol/L, and those of rhenium species are ~0.001 mol/L. The activities of sulphur species have no effect on the chemical equilibria. The chemical and electrochemical equilibria in the leaching stock solutions were presented in the form of convenient potential–pH diagrams. The diagrams for molybdenum [4] and sulphur [25] were constructed earlier. The thermodynamic characteristics of the reactions for rhenium were calculated using data from [26]. 2 The potential–pH diagram for the Mo–Re–SO4−–H2O system is plotted at 25 ◦C, air pressure of 1 bar and the activities of the molybdenum species 0.01 mol/L, the activities of the rhenium species 0.001 mol/L, and the activities of the sulphur species 0.1 mol/L, and presented in Figure2. Metals 2020, 10, 1423 6 of 19 Metals 2020, 10, x FOR PEER REVIEW 6 of 20

22− Figure 2. The potential–pH diagram for the Mo–Re–SO −–H O system is plotted at 25 C, air pressure Figure 2. The potential–pH diagram for the Mo–Re– SO44 –H22O system is plotted at 25 °C,◦ air pressure of 1 bar and the activities of molybdenum, rhenium, and sulphur species equal to 0.01, 0.001, of 1 bar and the activities of molybdenum, rhenium, and sulphur species equal to 0.01, 0.001, and 0.1 and 0.1 mol/L, respectively. mol/L, respectively. 2.6. DFT Computational Details 2.6. DFT Computational Details Density functional theory (DFT)-based simulations were conducted using Dmol3 module implementedDensity functional in Material theory Studio (DFT)-based 2016 software simulations package. were The conducted structures using of nonsolvated Dmol3 module and 2 2+ water-solvatedimplemented in forms Material of MoO Studio−, MoO 2016 software, and ReO pa−ckage.were optimisedThe structures in the of aqueous nonsolvated pregnant and solution. water- − 4 2 − 4 For the interactions in the2 organic phase,2+ only the optimised structures of MoO2 , MoO2+, and ReO , solvated forms of MoO4 , MoO2 , and ReO4 were optimised in the aqueous4− pregnant2 solution.4− deprived of their inner-sphere water molecules, were considered [26]. Similarly,2 the− structures2+ of ForPC88A the andinteractions D2EHPA in were the optimisedorganic phas in thee, only organic the phase.optimised The complexationstructures of (orMoO interaction)4 , MoO energies2 , and − in the aqueous (EC/w) and organic (EC/o) phases of the complex species were determined as follows [27]: ReO4 , deprived of their inner-sphere water molecules, were considered [26]. Similarly, the structures of PC88A and ED2EHPA= E were optimisedE in the organicE phase. The complexation (or(5) C/w Species + Reagent/w − Species/w − Reagent/o interaction) energies in the aqueous (EC/w) and organic (EC/o) phases of the complex species were determined as follows [27]:E = E E E (6) C/o Species + Reagent/o − Species/o − Reagent/o where ESpecies+Reagent/w is the totalEC/w energy= ESpecies+Reagent/w after complex − ESpecies/w formation − EReagent/o in the aqueous phase between(5) water-solvated species aqua-complexes and two reagent (PC88A and D2EHPA) species; ESpecies+Reagent/o EC/o = ESpecies+Reagent/o − ESpecies/o − EReagent/o (6)

Metals 2020, 10, 1423 7 of 19 is the total energy after complex formation between species and two reagent (PC88A and D2EHPA) 2 2+ species in the organic phase; ESpecies/w is the energy of optimised solvated MoO4−, MoO2 , and ReO4− 2 2+ aqua-complexes; ESpecies/o is the energy of optimised MoO4−, MoO2 , and ReO4− species in the organic phase; and Ereagent/o is the energy of solvated PC88A and D2EHPA optimised in the organic phase. Note the “w” and “o” index solvent parameterizations in Equations (5) and (6) for the conductor-like screening model (COSMO) used as an implicit solvation model to account for the aqueous, interfacial, and organic environments of the simulated structures. In this regard, dielectric constant was considered to be 78.54 (water) [24] and 1.8 (kerosene) for simulations in the aqueous phase and the organic phase, respectively. The generalised gradient approximation (GGA) with Perdew-Burke-Ernzerhof exchange-correlation density functional (PBEsol) was used to describe the exchange correlation interactions. The double numerical plus polarization (DNP) basis was selected. The self-consistent field (SCF) convergence was fixed to 2 10 6 (0.005 kJ/mol), and the convergence criteria for the × − energy, maximum force, and maximum displacement were set to 2 10 5 Ha (0.05 kJ/mol), 0.05 Ha/Å, × − and 0.002 Å, respectively. No special treatment of core electrons was considered, and all the electrons were included in the calculations. In addition, a smearing value was fixed at 5 10 3 through × − calculation. In the spin-unrestricted condition, the calculation was performed by the use of various orbitals for different spins. Besides, the initial value for the number of unpaired electrons for each atom was taken from the formal spin introduced for each atom. In this situation, the starting value can be subsequently optimised throughout the calculations. Maximum SCF interactions and calculation interactions were set at 2000 and 1000, respectively, and calculation of the interactions step was set to 0.3 Å. It is worth mentioning that different initial positions were considered for all cases during DFT simulations, and only the most stable configuration and results have been reported. Besides, it is worthy to mention that similar studies in rhenium/ molybdenum solvent extraction have not been conducted based on the authors’ best of knowledge.

3. Results and Discussion

3.1. Eﬀects of pH and Organic Phase Concentration 2 A potential–pH equilibrium diagram for the Mo–Re–SO4−–H2O system is presented in Figure2. It can be inferred that soluble perrhenate (ReO4−) ion is the dominant species over the whole pH range. However, for the case of Mo, several cationic and anionic species may be present depending on the 2 solution pH. In a neutral to alkaline region, MoO4− is the predominant species, while moving towards the acidic region, complex anionic species will form. The precipitation of molybdenum oxide MoO3 in the acidic media was not experimentally observed because of the formation of complex compounds of molybdenum (VI) with sulphate anions [28,29]. Variation of oxidation states of Mo over pH could simply be presented as follows [30]:

2 pH < 6 6 pH < 5 4 pH < 1 MoO − Mo O − Mo O − 4 → 7 24 → 8 26 → (7) pH < 1 2 c (H2SO4) > 0.3M 2+ Mo O (SO ) − MoO → 2 5 4 2 → 2 These complexes of molybdenum (VI) with sulphate were not included in the thermodynamic calculations due to lack of information on their stability constants. PC88A, a close analog of D2EHPA, is an acidic organophosphorus extractant that is typically present as a dimer with a noticeable potential to extract cationic molybdenum species through ion exchange. The highly hydrophobic organic anion forms an organic neutral complex with the metal ions that are present in the aqueous phase:

n+ + Me (aq) + m (HX)2 (org) Me(HX)2m n (org) + n H (aq) (8) → − Metals 2020, 10, x FOR PEER REVIEW 8 of 20

+ + Men (aq)+→ m() HX (org) Me() HX (org) + n H (aq) (8) Metals 2020, 10, 1423 22mn− 8 of 19 where ()HX represents the dimeric form of PC88A. Due to the formation of several oxidation states where (HX)2 represents the dimeric form of PC88A. Due to the formation of several oxidation states in the aqueous2 phase, molybdenum chemistry is rather complicated. Depending on the acidity of the in the aqueous phase, molybdenum chemistry is rather complicated. Depending on the acidity of aqueous solution, the size and type of molybdenum ion change [31]. However, the cationic the aqueous solution, the size and type of molybdenum ion change [31]. However, the cationic molybdenum may form at a low pH range that describes the high Mo extraction values in Figure 3a. molybdenum may form at a low pH range that describes the high Mo extraction values in Figure3a. Conversely, little amounts of Re are extracted at the same low pH range, which is correlated to the Conversely, little amounts of Re are extracted at the same low pH range, which is correlated to the − existenceexistence of of Re Re in in its its ReOReO4−4 form formthat that isis notnot extractableextractable byby PC88A (Figure3 3b).b). It can be inferred from FigureFigure 3a,b3a,b that by keeping keeping the the concentration concentration of of PC88A PC88A constant constant and and changing changing proton proton concentration, concentration, selectivityselectivity increases increases towards towards Mo Mo extraction extraction over over Re. Re.

100% (a) 100% (b) 5% 80% 15% 80% 30% 60% 60%

40% 40% Re Extraction, % Extraction, Re Mo Extraction,% 20% 20%

0% 0% -10123456789 -10123456789 pH pH

100% (c) 100% (d)

80% 80%

60% 60%

40% 40% Fe Extraction, % Fe Extraction, 20% % Extraction, Cu 20%

0% 0% -10123456789 -10123456789 pH pH

Figure 3. Metal extraction profiles as a function of pH and organic phase concentration: (a) Re, (b) Mo, Figure 3. Metal extraction profiles as a function of pH and organic phase concentration: (a) Re, (b) (c) Fe, and (d) Cu. Mo, (c) Fe, and (d) Cu. Likewise, the effect of PC88A concentration on the extraction of Mo and Re was studied. Likewise, the effect of PC88A concentration on the extraction of Mo and Re was studied. However, for the case of Fe and Cu extraction, this effect was not studied (one-time test using 30% However, for the case of Fe and Cu extraction, this effect was not studied (one-time test using 30% PC88A). It is clear that in the pH range of 1 to 3, increasing extractant concentrations does effectively PC88A). It is clear that in the pH range of 1 to 3, increasing extractant concentrations does effectively change the Mo–Re extraction help in a better separation, notably near pH = 1. change the Mo–Re extraction help in a better separation, notably near pH = 1. 3.2. Effect of Extractant 3.2. Effect of Extractant The organophosphoric acid reagents PC88A and D2EHPA are close analogs. Metal extraction at pH =The1, 3,organophosphoric and 7 was performed acid usingreagents an organic PC88A phaseand D2EHPA composed are of close 15% D2EHPAanalogs. Metal diluted extraction in kerosene at pHto be= compared1, 3, and with7 was PC88A. performed Experimental using an results organic show phase that PC88Acomposed is highly of 15% selective D2EHPA in the diluted extraction in keroseneof Mo over to Rebe atcompared pH = 1, whilewith PC88A. D2EHPA Experimental is more capable results of providing show that anoticeable PC88A is separationhighly selective at neural in thepH extraction (Table4). of Mo over Re at pH = 1, while D2EHPA is more capable of providing a noticeable separation at neural pH (Table 4).

Metals 2020, 10, 1423 9 of 19 Metals 2020, 10, x FOR PEER REVIEW 9 of 20 Metals 2020, 10, x FOR PEER REVIEW 9 of 20

TableTable 4. ComparisonComparison of of PC88A PC88A and and D2EHPA D2EHPA capabi capabilitylity of separation between Re and Mo. Table 4. Comparison of PC88A and D2EHPA capability of separation between Re and Mo.

ExtractantExtractantExtractant pHpH pH Org.Org. Conc.Conc. Org. Conc.MoMo RecoveryRecovery Mo Recovery (%)(%) ReRe (%) RecoveryRecovery Re Recovery (%)(%) (%) PC88APC88APC88A 11 11515 1595.4895.48 95.483.193.19 3.19 D2EHPAD2EHPAD2EHPA 11 11515 1581.5181.51 81.5115.3515.35 15.35 PC88A 3 15 45.32 22.45 PC88APC88A 33 1515 45.3245.32 22.4522.45 D2EHPAD2EHPA 3 315 1557.23 57.234.3 4.3 PC88AD2EHPA 3 715 1557.23 25.944.3 27 D2EHPAPC88APC88A 77 71515 1525.9425.94 90.082727 14.1 D2EHPAD2EHPA 77 1515 90.0890.08 14.114.1

Such observed behaviours could could be be attributed attributed to to the the Re and Mo species properties and the propertiesSuch observed of the extractants behaviours (PC88A could and be D2EHPA) attributed over to thethe entireRe and range Mo of species studied properties pH. To disclose and the the propertiesproperties ofof thethe extractantsextractants (PC88A(PC88A andand D2EHPA)D2EHPA) ovoverer thethe entireentire rangerange ofof studiedstudied pH.pH. ToTo disclosedisclose theeﬀects effects of these of these parameters parameters on the on separation the separation of Mo overof Mo Re, over ﬁrst, Re, the propertiesfirst, the properties of the two of extractants the two thewere effects studied of these via DFT parameters calculations. on the Figures separation4 and 5of display Mo over the Re, converged first, the structuresproperties ofof thethe twotwo extractantsextractants werewere studiedstudied viavia DFTDFT calculations.calculations. FiguresFigures 44 andand 55 displaydisplay thethe convergedconverged structuresstructures ofof theextractants two extractants along with along thedistributions with the distributions of their highest of their occupied highest molecular occupied orbitals molecular (HOMOs) orbitals and thelowest two unoccupied extractants molecular along with orbitals the (LUMOs).distributions of their highest occupied molecular orbitals (HOMOs)(HOMOs) andand lowestlowest unoccupiedunoccupied molecularmolecular orbitalsorbitals (LUMOs).(LUMOs).

Figure 4. (a) Optimised structure of D2EHPA, (b) distribution of highest occupied molecular orbitals FigureFigure 4. 4. (a) (Optimiseda) Optimised structure structure of D2EHPA, of D2EHPA, (b) distribution (b) distribution of highest of highestoccupied occupied molecular molecular orbitals (HOMOs) of D2EHPA, and (c) distribution of lowest unoccupied molecular orbitals (LUMOs) of (HOMOs)orbitals (HOMOs) of D2EHPA, of D2EHPA, and (c) anddistribution (c) distribution of lowest of lowest unoccupied unoccupied molecular molecular orbitals orbitals (LUMOs) (LUMOs) of D2EHPA. D2EHPA.of D2EHPA.

Figure 5. (a) Optimised structure of PC88A, (b) distribution of highest occupied molecular orbitals Figure 5. (a) Optimised structure of PC88A, (b) distribution of highest occupied molecular orbitals (HOMOs)Figure 5. (ofa) PC88A, Optimised and structure(c) distribution of PC88A, of lowest (b) distribution unoccupied ofmolecular highest occupiedorbitals (LUMOs) molecular of PC88A. orbitals (HOMOs) of PC88A, and (c) distribution of lowest unoccupied molecular orbitals (LUMOs) of PC88A. (HOMOs) of PC88A, and (c) distribution of lowest unoccupied molecular orbitals (LUMOs) of PC88A. As seen, HOMOs and LUMOs are mostly located around their P = O and P − O groups, which AsAs seen, seen, HOMOs and LUMOsLUMOs areare mostly mostly located located around around their their P =P O= O and and P P O− groups,O groups, which which are areare consideredconsidered polarpolar electronelectron donordonor groupsgroups inin thethe structurestructure ofof thesethese extractants.extractants.− Furthermore,Furthermore, aa Hirshfeldconsidered charge polar electronanalysis donorwas performed groups in to the assess structure the electronic of these extractants. charge of O Furthermore, atoms in P = a O Hirshfeld and P − Hirshfeldcharge analysis charge was analysis performed was performed to assess the to electronicassess the charge electronic of O charge atoms inof PO= atomsO and in P P =O O groups and P as− O groups as presented in Table 5. − Opresented groups as in presented Table5. in Table 5. Table 5. Charge properties of PC88A and D2EHPA. Table 5. Charge properties of PC88A and D2EHPA.

ExtractantsExtractants ActiveActive GroupGroup ChargeCharge (e)(e) AverageAverage ChargeCharge (e)(e) PP == OO −−0.5510.551 D2EHPAD2EHPA −−0.5520.552 PP −− OO −−0.5530.553 PP == OO −−0.540.54 PC88APC88A −−0.5450.545 PP −− OO −−0.530.53

Metals 2020, 10, 1423 10 of 19

Table 5. Charge properties of PC88A and D2EHPA. Metals 2020, 10, x FOR PEER REVIEW 10 of 20 Extractants Active Group Charge (e) Average Charge (e) As illustrated in the Table 5, moreP = Oelectronic charges0.551 accumulate in both polar groups of D2EHPA − 0.552 D2EHPA, which are responsible for theP complexO formation0.553 through solvent −extraction. This means that D2EHPA can be considered a stronger− extractant, while− PC88A has a potential for being a more P = O 0.54 PC88A − 0.545 selective reagent through solvent extraction.P O Such behaviour0.53 of these two extractants− has already − − been reported in the literature [32]. Considering that the pKa of D2EHPA and that of PC88A are around 3.01 and 4.21, respectively [33], this implies that these extractants will lie in their molecular As illustrated in the Table5, more electronic charges accumulate in both polar groups of D2EHPA, forms for pH ≤ pKa and will be dissociated into their ionic forms outside this pH range. In addition which are responsible for the complex formation through solvent extraction. This means that D2EHPA to extractant properties, Re and Mo species and properties are varied at studied pH as demonstrated can be considered a stronger extractant, while PC88A has a potential for being a more selective reagent in Figure 2. Variations in pH should play a critical role through complex formations in the present through solvent extraction. Such behaviour of these two extractants has already− been reported in the solventliterature extraction [32]. Considering system. In that this the regard, pKa of as D2EHPA seen in Figure and that 2, ofwhile PC88A ReO are4 aroundcan be 3.01considered and 4.21, a respectively [33], this implies that these extractants will lie in their2+ molecular forms for6− pH pKa and4− dominated Re species over the entire range of studied pH, MoO at pH = 1, Mo O and≤ Mo O will be dissociated into their ionic forms outside this pH range.2 In addition to extractant724 properties,826 2− atRe pH and = Mo3, and species MoO and4 properties at natural arepH variedare regarded at studied as domina pH as demonstratedted Mo species. in Water-solvated Figure2. Variations forms in pH should− play a2− critical role through2+ complex formations in the present solvent extraction system. of ReO4 , MoO4 , and MoO2 were studied by DFT calculations (Figure 6) to disclose more In this regard, as seen in Figure2, while ReO4− can be considered a dominated Re species over the entire range of studied pH, MoO2+ at pH = 1, Mo O6 and Mo O4 at− pH = 3,2− and MoO2 at2+ natural pH are details about these Re and 2Mo species. It was7 found24− that 8ReO26− , MoO , and MoO4− are solvated 4 4 2 22+ regarded as dominated Mo species. Water-solvated forms of ReO−, MoO −, and MoO were studied with five, four, and seven water molecules, respectively. It was4 also realised4 that bond2 lengths of by DFT calculations (Figure6) to disclose more details about these Re and Mo species. It was found − ReO 2 2+ water-that ReO4−, MoO4 are4 −less, and thanMoO others2 are (Table solvated 6), indicating with ﬁve, stronger four, and interactions seven water between molecules, water respectively. molecules − It was also realised that bond lengths of water-ReO4− are less than others (Table6), indicating stronger and ReO4 as compared with those involved with the Mo species. Besides, Hirshfeld charge analysis interactions between water molecules and ReO4− as compared with those involved with the Mo species. wasBesides, performed Hirshfeld to compare charge analysischarges of was Re performedand Mo in these to compare three species charges after of Resolvation. and Mo It in was these realised three thatspecies changes after solvation.in the charge It was of Re realised are higher that changescompared in with the charge those of Mo Reare after higher solvation compared (water) with of these those threeof Mo species after solvation as presented (water) in of Table these three6, indicating species ashigher presented interaction in Table between6, indicating water higher molecules interaction and − between water molecules and ReO− as already established through bond length assessments. ReO4 as already established throug4 h bond length assessments.

2+ 2− − Figure 6. Optimised structures of (a) MoO 2+, (b) MoO2 , and (c) ReO . Figure 6. Optimised structures of (a) MoO2 2 ,(b) MoO44−, and (c) ReO4−. 4 Table 6. Charge analysis and bond length of solvated Re and Mo species in the aqueous phase. Table 6. Charge analysis and bond length of solvated Re and Mo species in the aqueous phase. Charge e (Re or Mo) Charge e (Re or Mo) Water Bond SpeciesCharge e (Re or Mo) Charge e (Re or Mo) Changes (e) Species Nonsolvated Solvated Changes (e) Water Bond LengthLength (Å) (Å) Nonsolvated Solvated 2 0.83 0.61 0.22 2.3 MoO2− 4− MoO4 2+ 0.83 0.890.61 0.60.22 0.292.3 2.3 MoO2 2+ 0.74 0.4 0.34 2.2 ReO4− MoO2 0.89 0.6 0.29 2.3 − 0.74 0.4 0.34 2.2 ReOAs4 seen in Table4, PC88A performance in Mo extraction decreased once pH increased. At pH 2+ = 1, PC88A is in molecular form, but positively charged Mo species, MoO2 , with relatively low As seen in Table 4, PC88A performance in Mo extraction decreased once pH increased. At pH = 2+ 1, PC88A is in molecular form, but positively charged Mo species, MoO2 , with relatively low interaction with water molecule is the prevailing species. Therefore, making bond between PC88A

Metals 2020, 10, 1423 11 of 19 interaction with water molecule is the prevailing species. Therefore, making bond between PC88A and 2+ 6 MoO2 occurred. On the other hand, at pH = 3, relatively bulky species of Mo, including Mo7O24− 4 and Mo8O26−, are predicted to be the dominant forms in the solution, while the extractant is in its molecular form. It may be speculated that hindrance effects prevent bond formations between Mo 2 species and PC88A, thus the declining recovery of Mo. Finally, at pH = 7, negatively charged MoO4− forms along with PC88A dissociated into its ionic moieties. In this situation, it is suggested that electrostatic repulsions hinder the bond formation. Such effect can be more pronounced when it is noticed that PC88A is not a strong extractant based on DFT calculations. However, the case of Re is different as its recovery increased with increasing pH. Over the entire range of studied pH, Re is in the form of ReO4−, showcasing strong interactions with water molecules. PC88A dissociates in its ionic constituents with a potential for bond formation only at pH 7. Hence, it can be speculated that at pH 7, PC88A was more likely to create bonds with the Re species. Even in this situation, it is worthy to mention that PC88A is not a strong extractant based on DFT calculations; thus, although enhancement in Re recovery occurred through pH evolution, generally, its recovery is relatively lower than that of Mo in all ranges of pH. This could be due to the strength degree of PC88A in bond formation and the stability of ReO4− in interaction with water molecules. In the case of D2EHPA, hindrance effect at pH = 3 and repulsion at pH = 7 are less pronounced through Mo separation due to its stronger capability in complex formation (according to DFT calculations). In order to confirm these explanations for the solvent extraction system, the interaction energy of the extractants with the Re and Mo species were obtained and are reported in Table7. Interactions in both the organic and aqueous phases were taken into consideration since complexations could occur in both environments. In the case of aqueous phase calculations, the water-solvated forms of the species were considered. As seen in Table7, the interaction energies of D2EHPA are higher than those of PC88A, which could be due to its stronger capability for complex formation. Besides, it can be seen that the interaction energies of both extractants follow this trend considering the Mo species: 2+ 2 MoO2 > MoO4−. This trend is in line with the observation in Table4. Besides, the interaction energies 2+ 2 of D2EHPA and PC88A with the species are based on these trends, respectively: MoO2 > MoO4− 2+ 2 > ReO4− and MoO2 > ReO4− > MoO4−. These are also in line with observed recovery at different pH values.

Table 7. Interaction energy (kJ/mol) species with extractants in the organic and aqueous phases.

PC88A D2EHPA Species Organic Aqueous Organic Aqueous

MoO2 178.1 138.1 321.3 237.5 4− − − − − MoO2+ 411.4 321.1 372.1 221.8 2 − − − − ReO 189.1 155.3 195.3 157.1 4− − − − −

4. Conclusions PC88A was found to be a suitable solvent extraction candidate for selectively removing Mo over Re from molybdenite flue dust leach solutions. Acidifying the leach solution with H2SO4 at pH = 0–1 and employing an organic phase composed of 10–15% PC88A diluted in kerosene led to an ultimate separation between Mo and Re, transferring ca. 97% of Mo to the organic phase and leaving ca. 98% of Re in the leach solution. DFT simulations also indicated that the interaction energies of metals with D2EHPA were stronger than those with PC88A, thus explaining a different capability for complex formation. Besides, considering the Mo species, it was found that the interaction energies of both 2+ 2 extractants followed the trend MoO2 > MoO4− in line with the experimental observations. It was also confirmed via DFT simulations that the interaction energies of D2EHPA and PC88A with the metal 2+ 2 2+ 2 oxyspecies follow the trends MoO2 > MoO4− > ReO4− and MoO2 > ReO4− > MoO4−, respectively. These are also in line with observed recoveries at different pH values. Metals 2020, 10, x FOR PEER REVIEW 12 of 20

2+ 2− extractants followed the trend MoO2 > MoO4 in line with the experimental observations. It was also confirmed via DFT simulations that the interaction energies of D2EHPA and PC88A with the 2+ 2− − 2+ − 2− Metalsmetal2020 oxyspecies, 10, 1423 follow the trends MoO2 > MoO4 > ReO4 and MoO2 > ReO4 > MoO124 of 19 , respectively. These are also in line with observed recoveries at different pH values.

AuthorAuthor Contributions: Contributions: Conceptualization,Conceptualization, A.E.-Z.; A.E.-Z.; data data curation, curation, A.E.-Z., A.E.-Z., D.A., P.A.N., D.A., F.L., P.A.N., and F.L.,L.-C.P.; and formal L.-C.P.; formalanalysis, analysis, A.E.-Z. A.E.-Z. and D.A.; and methodology, D.A.; methodology, A.E.-Z.; pr A.E.-Z.;oject administration, project administration, F.L.; software, F.L.; P.A.N.; software, writing— P.A.N.; writing—originaloriginal draft, A.E.-Z.; draft, A.E.-Z.;writing—review writing—review and editing, and editing,D.A., P.A.N., D.A., F.L., P.A.N., and F.L., L.-C.P. and All L.-C.P. authors All authorshave read have and read andagreed agreed to tothe the published published version version of the of themanuscript. manuscript.

Funding:Funding:This This research research received received no no externalexternal funding.funding.

Acknowledgments:Acknowledgments:The The authors are are grateful grateful to tothe the Babakan Babakan Ferromolybdenum Ferromolybdenum Co. and Co. Ali andAmirarmand Ali Amirarmand (Yazd (Yazd Science and Technology Park) for providing the materials. Science and Technology Park) for providing the materials. Conﬂicts of Interest: The authors declare no conﬂict of interest. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Appearance of the Leaching Solution Appendix A. Appearance of the Leaching Solution

Figure A1. The solution colour changes in the course of molybdenite flue dust leaching. It first became Figure A1. The solution colour changes in the course of molybdenite flue dust leaching. It first became pale yellow (right), then turned into green, and finally dark blue (left). pale yellow (right), then turned into green, and finally dark blue (left).

AppendixAppendix B B. Details Details of of the the Thermodynamic Thermodynamic Calculations In order to construct the potential–pH diagram (Figure 2), the thermodynamic activities of ionic In order to construct the potential–pH diagram (Figure2), the thermodynamic activities of ionic species in the solution should be calculated. To do it, the composition of the leaching solution should species in the solution should be calculated. To do it, the composition of the leaching solution should be estimated first. The leaching reactions of molybdenite flue dust are described by Equations (1)– be estimated ﬁrst. The leaching reactions of molybdenite ﬂue dust are described by Equations (1)–(4). 2+ − (4). According to them, the primary aqueous species for Mo and Re 2are+ MoO and ReO , According to them, the primary aqueous species for Mo and Re are MoO2 and ReO2 4−, respectively.4 Sulphuricrespectively. acid Sulphuric is used to acid maintain is used the to desiredmaintain pH the value. desired However, pH value. it isHowever, dibasic; it is does dibasic; not dissociateit does completelynot dissociate and completely may form sulphateand may andform hydrosulphate sulphate and hydrosulphate ions and undissociated ions and undissociated H2SO4 in the H solution2SO4 accordingin the solution to the according following to equations: the following equations: −+ + + H24 SO (aq) HSO 4 (aq) H (aq), K 1 (A1) H2SO4 (aq) HSO4− (aq) + H (aq),K1 (A1)

−−+22 + HSO4− (aq)(aq) SO4− (aq)+ + H (aq),K2 (A2) HSO44 (aq) (aq) SO (aq) H (aq), K 2 (A2) The dissociation constants are presented in Table A1. The dissociation constants are presented in Table A1.

Table A1. Dissociation constants of sulphuric acid at 25 C. Table A1. Dissociation constants of sulphuric acid at 25 °C.◦ Step i K , mol/L Reference Step i Ki, mol/Li Reference 11 1000 1000 [34] [34] 22 0.012 0.012 [35] [35]

o Let c be the initial concentration of sulphuric acid and cH2SO4 , cHSO , and c 2 the equilibrium H2SO4 4− SO4− concentrations of diﬀerent species. Then the following equations for the equilibrium constants may be written: c 2 c + SO − H K = 4 · (A3) 2 c HSO4−

cHSO c + 4− · H K1 = (A4) cH2SO4 Metals 2020, 10, 1423 13 of 19

o = + + c cH2SO4 cHSO c 2 (A5) H2SO4 4− SO4− Rearranging Equations (A3) and (A4) and substituting them into Equation (A5) yields

+ cSO2 cH = 4− · cHSO− (A6) 4 K2

c c + SO2 H 4− · 2 c c + + c 2 c + HSO− H K cH SO − H c = 4 · = 2 · = 4 · (A7) H2SO4 K K K K 1 1 1 · 2 2 + cSO2 c + cSO2 cH o = 4− · H + 4− · + cH SO cSO2 (A8) 2 4 K K K 4− 1 · 2 2 Rearranging Equation (A8) gives

 2   c + c +  o =  H + H +  cH SO cSO2  1 (A9) 2 4 4− · K K K  1 · 2 2

 2   c + K1 c + K K  o =  H + · H + 1 2  cH SO cSO2  ·  (A10) 2 4 4− · K K K K K K  1 · 2 1 · 2 1 · 2 2 c + + K1 cH+ + K1 K2 o = H · · cH SO cSO2 (A11) 2 4 4− · K K 1 · 2 o 2 = + + + K1 K2 cH SO cSO2 c + K1 cH K1 K2 (A12) · · 2 4 4− · H · · o K1 K2 c · · H2SO4 c 2 = (A13) SO4− 2 c + + K c + + K K2 H 1 · H 1 · The equilibrium concentrations of hydrosulphate ions and undissociated sulphuric acid might be obtained by substituting Equation (A13) into Equations (A6) and (A7):

o K1 K2 c · · H2SO4 c + o c 2 c + 2 + + H K c + c SO − H c + K1 cH+ K1 K2 · 1 H H SO c = 4 · = H · · = · · 2 4 (A14) HSO4− 2 K2 K2 c + + K c + + K K2 H 1 · H 1 ·

o K1 K2 c · · H2SO4 2 2 c 2 o c 2 c + c2 +K c +K K + c c SO − H + 1 H+ 1 2 · H + H SO c = 4 · == H · · = H · 2 4 (A15) H2SO4 2 K1 K2 K1 K2 c + + K c + + K K2 · · H 1 · H 1 · Let us introduce the mole fractions of the three species in the solution:

n 2 c 2 c 2 SO4− V = const SO4− SO4− x 2 = = = o (A16) SO4− + + + + nH2SO4 nHSO n 2 cH2SO4 cHSO c 2 c 4− SO4− 4− SO4− H2SO4 n c c HSO4− V = const HSO4− HSO4− xHSO = = = (A17) 4− + + + + o nH2SO4 nHSO n 2 cH2SO4 cHSO c 2 c 4− SO4− 4− SO4− H2SO4

nH SO V = const cH SO cH SO x = 2 4 = 2 4 = 2 4 (A18) H2SO4 + + + + o nH2SO4 nHSO n 2 cH2SO4 cHSO c 2 c 4− SO4− 4− SO4− H2SO4 Metals 2020, 10, 1423 14 of 19

Consequently,

o K1 K2 c · · H2SO4 2 cSO2 c +K1 c + +K1 K2 4− H+ · H · K1 K2 x 2 = o = o = · (A19) SO4− 2 c c c + + K1 c + + K1 K2 H2SO4 H2SO4 H · H ·

o K1 c + c · H · H2SO4 c 2 + + HSO− c + K1 cH+ K1 K2 K1 c + x = 4 = H · · = · H (A20) HSO4− o o 2 c c c + + K1 c + + K1 K2 H2SO4 H2SO4 H · H · 2 o c + c H · H2SO4 2 + + 2 cH SO c + K1 cH+ K1 K2 c + x = 2 4 = H · · = H (A21) H2SO4 o o 2 c c c + + K1 c + + K1 K2 H2SO4 H2SO4 H · H · It is worth noting that + + = xH2SO4 xHSO x 2 1 (A22) 4− SO4−

If the pH value is predetermined and the values of the equilibrium constants K1 and K2 (see Equations (A3) and (A4)), are known, the mole fractions of the three species in the solution might be unambiguously calculated. The dependency of the mole fractions of the species on pH value is called theMetals speciation 2020, 10, x diagram. FOR PEER TheREVIEW speciation diagram for the sulphuric acid is presented in Figure A215. of 20

2 ( ) Figure A2. The speciation diagram for the sulphuric acid in the pH range from 1 to 2. (1)—SO4− aq , − 2− (2)—HSO− (aq), (3)—H2SO4 (aq). Figure A2.4 The speciation diagram for the sulphuric acid in the pH range from −1 to 2. (1)— SO4 (aq) Because pH− is not an independent variable and is determined by the addition of sulphuric acid, , (2)— HSO4 (aq) , (3)—H2SO4 (aq). one needs to estimate the relationship between the total content of sulphuric acid in the solution and the pHBecause value. TopH do is it,not the an material independent balance variable equations and shouldis determined be considered. by the addition of sulphuric acid, oneIn needs the ﬁrstto estimate dissociation the relationship step (Equation between (A1)), the to lettal the content initial of concentrationsulphuric acid ofin sulphuricthe solution acid and be co . Let x moles of free acid per litre of solution dissociate to hydrosulphate ions. the HpH2SO value.4 To do it, the material balance equations should be considered. x Consequently,In the first the dissociation equilibrium stepconcentration (Equation of(A1)), the let hydrosulphate the initial concentration ions is equal of tosulphuric. From acid the be reaction stoichiometry, it follows that the equilibrium concentration of hydrogen ions according to that co . Let x moles of free acid per litre of solution dissociate to hydrosulphate ions. Consequently, dissociationHSO24 step is also equal to x. the Inequilibrium the second dissociationconcentration step of (Equationthe hydrosulphate (A2)), let y ions moles is of equal hydrosulphate to x. From ions the per litrereaction of solutionstoichiometry, dissociate it furtherfollows to that sulphate the ions.equilibrium Consequently, concentration the equilibrium of hydrogen concentration ions according of the sulphate to that ionsdissociation is equal tostep y. Fromis also the equal reaction to x. stoichiometry, it follows that the equilibrium concentration of hydrogenIn the ions second according dissociation to that dissociation step (Equation step (A2)), is also let equal y moles to y. of hydrosulphate ions per litre of solution dissociate further to sulphate ions. Consequently, the equilibrium concentration of the sulphate ions is equal to y. From the reaction stoichiometry, it follows that the equilibrium concentration of hydrogen ions according to that dissociation step is also equal to y. Considering both dissociation steps, one might notice that the equilibrium concentration of hydrogen ions according to both dissociation steps equals x + y, the equilibrium concentration of o hydrosulphate ions equals x − y, and the equilibrium concentration of free acid equals cx− (see HSO24 Table A2).

Table A2. Material balance of sulphuric acid dissociation.

− + HSO(aq)  H(aq) 24 HSO4 (aq) + co Initial state HSO24 0 0

o Equilibrium state cx− x x HSO24

− 2− +  H(aq) HSO4 (aq) SO4 (aq) + Initial state x 0 x Equilibrium state x − y y x + y

If the pH value is known, the ratio of equilibrium concentrations of sulphate and hydrosulphate ions is constant. The following system of equations may be written:

Metals 2020, 10, 1423 15 of 19

Considering both dissociation steps, one might notice that the equilibrium concentration of hydrogen ions according to both dissociation steps equals x + y, the equilibrium concentration of hydrosulphate ions equals x y, and the equilibrium concentration of free acid equals co x − H2SO4 − (see Table A2).

Table A2. Material balance of sulphuric acid dissociation.

( ) + H2SO4 (aq) HSO4− aq + H (aq) Initial state co 0 0 H2SO4 Equilibrium state co x x x H2SO4 − ( ) 2 ( ) + ( ) HSO4− aq SO4− aq + H aq Initial state x 0 x Equilibrium state x y y x + y −

If the pH value is known, the ratio of equilibrium concentrations of sulphate and hydrosulphate ions is constant. The following system of equations may be written:

pH cH+ = 10− = x + y (A23)

cHSO− x y 4 = − (A24) c 2 y SO4− Rearranging Equation (A24) yields c x y x HSO− − = 1 = 4 (A25) y y − c 2 SO4− c x HSO− = 4 + 1 (A26) y c 2 SO4−   cHSO−   4  x = y  + 1 (A27) ·  c 2  SO4−     cHSO−  cHSO−   4   4  cH+ = x + y = y  + 1 + y = y  + 2 (A28) ·  c 2  ·  c 2  SO4− SO4− c + y = H (A29) cHSO 4− c + 2 SO2 4− Obviously, the ratio of equilibrium concentrations of sulphate and hydrosulphate ions is equal to the ratio of their mole fractions: c x HSO− HSO− K1 c + K K K1 c + c + 4 = 4 = · H : 1 2 = · H = H . (A30) 2 2 · cSO2 xSO2 c + + K1 c + + K1 K2 c + + K1 c + + K1 K2 K1 K2 K2 4− 4− H · H · H · H · · Substituting Equation (A30) into Equation (A29) gives

cH+ cH+ K2 cH+ y = c 2 = = = · (A31) SO − cHSO cH+ 4 4− + 2 cH+ + 2 K2 c + 2 K2 · SO2 4− Metals 2020, 10, 1423 16 of 19

Substituting Equation (A31) into Equations (A6) and (A7) yields

K2 cH+ c 2 c + · c + 2 SO − H c + +2 K H c + 4 · H · 2 · H cHSO = = = (A32) 4− K K c + + 2 K 2 2 H · 2 K c 2 2 H+ 2 3 c 2 c · c SO − + c + +2 K + c + 4 · H H · 2 · H H cH SO = = = (A33) 2 4 K K K K c + K + 2 K K 1 · 2 1 · 2 H · 1 · 1 · 2 Therefore, by using Equations (A5) and (A31)–(A33), the equilibrium concentrations of diﬀerent species and the total content of sulphuric acid at the given pH value might be calculated straightforwardly. The calculated concentrations for pH values equal to 2, 1, 0, and 1 are presented in − Table A3.

Table A3. Equilibrium concentrations of various aqueous sulphuric acid species and total concentration of sulphuric acid at diﬀerent pH values.

o PH c , mol/L c , mol/L c 2 , mol/L c , mol/L H2SO4 HSO4− SO4− H2SO4 2 2.94 10 8 0.00294 0.00353 0.00647 × − 1 8.06 10 6 0.0806 0.00968 0.0903 × − 0 0.000977 0.977 0.0117 0.989 1 0.0998 9.976 0.0119 10.088 −

The leaching reactions of molybdenite ﬂue dust are given by reactions (1) through (4). 2+ According to them, the aqueous species to molybdenum and rhenium in the leaching liquor are MoO2 and ReO4−, respectively. According to Table3, the total content of molybdenum in a solution equals:

g g mol c = 9 : 95.94 = 0.094 (A34) [Mo] L mol L The total content of rhenium equals:

g g mol c = 0.5 : 186.207 = 0.0027 (A35) [Re] L mol L The parameters of the extended Debye–Hückel equation are:

T = 298.15 K (A36) ε = 87.74 0.4008 (T 273.15)+ − · − (A37) + 9.398 10 4 (T 273.15)2 + 1.41 10 6 (T 273.15)3 = 78.3294 · − · − · − · − 1 1.825 106 1.825 106 L 2 = = = A · 3 · 3 0.5114 1 (A38) (ε T) 2 (78.3294 298.15) 2 mol 2 · · 1 5.029 1011 5.029 1011 L 2 = = = 9 B · 1 · 1 3.291 10 1 . (A39) (ε T) 2 (78.3294 298.15) 2 · m mol 2 · · · The electrostatic radii of the individual ions are presented in Table A4.

Table A4. Electrostatic radii of individual ions.

Ion ai,Å

ReO4− 4.5 2+ 4.5 MoO2 Metals 2020, 10, 1423 17 of 19

The ionic strength of the solution is calculated as follows:

2 2 2 2 2 C z + C 2+ z + C 2 z + C z + C + z ReO− MoO 2+ SO − 2 HSO− H + 4 · ReO4− 2 · MoO 4 · SO − 4 · HSO4− · H I = 2 4 (A40) 2 The activity coeﬃcients of molybdenum and rhenium ions in a solution are calculated according to the extended Debye–Hückel equation. The thermodynamic activities are calculated straightforwardly:

√I lg γ = A z2 (A41) ReO− ReO 4 − · 4− · √ 1 + B aReO I · 4− · γ ReO− aReO = c[Re] 10 4 (A42) 4− ·

2 √I lg γ 2+ = A z (A43) MoO MoO2+ 2 − · 2 · + + √ 1 B aMoO2 I · 2 · γ + MoO2 + = 2 aMoO2 c[Mo] 10 (A44) 2 · The calculated values are presented in Table A5.

Table A5. Activity coeﬃcients and thermodynamic activities of molybdenum and rhenium species in leaching stock solution at diﬀerent pH values.

pH I, mol/L lg γ a , mol/L lg γ 2+ a 2+ , mol/L ReO4− ReO4− MoO2 MoO2 2 0.20288 0.138 0.00196 0.553 0.0263 − − 1 0.299 0.155 0.00189 0.618 0.0226 − − 0 1.096 0.214 0.00165 0.855 0.0131 − − 1 10.201 0.285 0.00140 1.140 0.0068 − − −

As can be seen, the average activities of the molybdenum species are ~0.01 mol/L, and those of the rhenium species are ~0.001 mol/L. The activities of the sulphur species have no inﬂuence on the position of the lines on the diagram. 2 The potential–pH diagram for the Mo–Re–SO4− system (Figure2) is plotted at 25 ◦C, air pressure of 1 bar and the activities of the molybdenum species 0.01 mol/L, the activities of the rhenium species 0.001 mol/L, and the activities of the sulphur species 0.1 mol/L.

References

1. Habashi, F. Handbook of Extractive Metallurgy; Wiley-VCH: Weinheim/Heidelberg, Germany, 1997. 2. Virolainen, S.; Laatikainen, M.; Sainio, T. Ion exchange recovery of rhenium from industrially relevant sulfate solutions: Single column separations and modeling. Hydrometallurgy 2015, 158, 74–82. [CrossRef] 3. Srivastava, R.R.; Lee, J.-C.; Kim, M.-S. Complexation chemistry in liquid–liquid extraction of rhenium. J. Chem. Technol. Biotechnol. 2015, 90, 1752–1764. [CrossRef] 4. Cheema, H.A.; Ilyas, S.; Masud, S.; Muhsan, M.A.; Mahmood, I.; Lee, J.-C. Selective recovery of rhenium from molybdenite ﬂue-dust leach liquor using solvent extraction with TBP. Sep. Purif. Technol. 2018, 191, 116–121. [CrossRef] 5. Nikolaychuk, P.A.; Tyurin, A.G. Utoˇcnënnaâ diagramma Purbe dlâ molibdena. Butlerovskie Soobseniˆ â 2011, 24, 101–105. 6. Khoshnevisan, A.; Yoozbashizadeh, H.; Mohammadi, M.; Abazarpoor, A.; Maarefvand, M. Separation of rhenium and molybdenum from molybdenite leach liquor by the solvent extraction method. Miner. Metall. Process. 2013, 30, 53–58. [CrossRef] Metals 2020, 10, 1423 18 of 19

7. Alamdari, E.K.; Darvishi, D.; Haghshenas, D.F.; Yousefi, N.; Sadrnezhaad, S.K. Separation of Re and Mo from roasting-dust leach-liquor using solvent extraction technique by TBP. Sep. Purif. Technol. 2012, 86, 143–148. [CrossRef] 8. Cao, Z.F.; Zhong, H.; Jiang, T.; Liu, G.Y.; Wang, S. Selective electric-oxidation leaching and separation of Dexing molybdenite concentrates. Zhongguo Youse Jinshu Xuebao/Chin. J. Nonferrous Met. 2013, 23, 2290–2295. 9. Zhan-fang, C.; Hong, Z.; Zhao-hui, Q. Solvent extraction of rhenium from molybdenum in alkaline solution. Hydrometallurgy 2009, 97, 153–157. [CrossRef] 10. Kang, J.; Kim, Y.U.; Joo, S.H.; Yoon, H.S.; Kumar, J.R.; Park, K.H.; Shin, S.M. Behavior of Extraction, Stripping, and Separation Possibilities of Rhenium and Molybdenum from Molybdenite Roasting Dust Leaching Solution Using Amine Based Extractant Tri-Otyl-Amine (TOA). Mater. Trans. 2013, 54, 1209–1212. [CrossRef] 11. Srivastava, R.R.; Kim, M.-S.; Lee, J.-C.; Ilyas, S. Liquid–liquid extraction of rhenium (VII) from an acidic chloride solution using Cyanex 923. Hydrometallurgy 2015, 157, 33–38. [CrossRef] 12. Pathak, S.K.; Singh, S.; Mahtele, A.; Tripathi, S.C. Studies on extraction behaviour of molybdenum (VI) from acidic radioactive waste using 2 (ethylhexyl) phosphonic acids, mono 2 (ethylhexyl) ester (PC-88A)/n-dodecane. J. Radioanal. Nucl. Chem. 2010, 284, 597–603. [CrossRef] 13. Wang, Y.; Jiang, K.; Zou, X.; Zhang, L.; Liu, S. Recovery of metals from molybdenite concentrate by hydrometallurgical technologies. In TT Chen Honorary Symposium on Hydrometallurgy, Electrometallurgy and Materials Characterization; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2012; pp. 315–322. 14. Nguyen, T.H.; Lee, M.S. Separation of molybdenum (VI) and tungsten (VI) from sulfate solutions by solvent extraction with LIX 63 and PC 88A. Hydrometallurgy 2015, 155, 51–55. [CrossRef] 15. Morís, M.A.A.; Díez, F.V.; Coca, J. Solvent extraction of molybdenum and tungsten by Alamine 336 and DEHPA in a rotating disc contactor. Sep. Purif. Technol. 1999, 17, 173–179. [CrossRef] 16. Truong, H.T.; Lee, M.S. Separation of rhenium (VII), molybdenum (VI), and vanadium (V) from hydrochloric acid solution by solvent extraction with TBP. Geosyst. Eng. 2017, 20, 224–230. [CrossRef] 17. Kim, H.S.; Park, J.S.; Seo, S.Y.; Tran, T.; Kim, M.J. Recovery of rhenium from a molybdenite roaster fume as high purity ammonium perrhenate. Hydrometallurgy 2015, 156, 158–164. [CrossRef] 18. Xiao, C.; Zeng, L.; Xiao, L.; Zhang, G. Solvent Extraction of Molybdenum (VI) from Hydrochloric Acid Leach Solutions Using P507. Part I: Extraction and Mechanism. Solvent Extr. Ion Exch. 2017, 156, 130–144. [CrossRef] 19. Entezari, A.; Karamoozian, M.; Eskandari Nasab, M. Investigation on selective rhenium leaching from molybdenite roasting flue dusts. J. Min. Environ. 2013, 4, 77–82. 20. Entezari-Zarandi, A.; Larachi, F. Selective dissolution of rare-earth element carbonates in deep eutectic solvents. J. Rare Earths 2019, 37, 528–533. [CrossRef] 21. Keshavarz Alamdari, E. Selective Leaching-Recovery of Re and Mo from Out-Gas Dust of Molybdenite Roasting Furnace. Trans. Indian Inst. Met. 2017, 70, 1995–1999. [CrossRef] 22. Debye, P.; Hückel, E. Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Phys. Z 1923, 24, 185–206. 23. Kielland, J. Individual activity coefficients of ions in aqueous solutions. J. Am. Chem. Soc. 1937, 59, 1675–1678. [CrossRef] 24. Coolidge, W. Dielektrische Untersuchungen und elektrische Drahtwellen. Ann. Phys. 1899, 305, 125–166. [CrossRef] 25. Nikolaychuk, P. Das revidierte pourbaix-diagramm für schwefel. In Materialien Zum Wissenschaftlichen Seminar der Stipendiaten der Programme „Mikhail Lomonosov“ und „Immanuel Kant“; Deutscher Akademischer Austausch Dienst und Ministerium für Bildung und Wissenschaft der RF: Moscow, Russia, 2015; pp. 72–76. 26. Wagman, D.D.; Evans, W.H.; Parker, V.B.; Schumm, R.H.; Halow, I. The NBS tables of chemical thermodynamic

properties. Selected values for inorganic and C1 and C2 organic substances in SI units, National Standard Reference Data System. J. Phys. Chem. Ref. Data 1982, 11, 37–38. 27. Azizi, D.; Larachi, F. Behavior of bifunctional phosphonium-based ionic liquids in solvent extraction of rare earth elements-quantum chemical study. J. Mol. Liq. 2018, 263, 96–108. [CrossRef] 28. Palant, A.; Iatsenko, N.; Petrova, V. Solvent extraction of molybdenum (VI) by diisododecylamine from sulphuric acid solution. Hydrometallurgy 1998, 48, 83–90. [CrossRef] Metals 2020, 10, 1423 19 of 19

29. Loewenschuss, A.; Shamir, J.; Ardon, M. Vibrational spectra of binuclear molybdenum sulfate complexes of high bond order. Inorg. Chem. 1976, 15, 238–241. [CrossRef] 30. Alamdari, E.K.; Sadrnezhaad, S.K. Thermodynamics of extraction of from aqueous sulfuric acid media with TBP dissolved in kerosene. Hydrometallurgy 2000, 55, 327–341. [CrossRef] 31. Kholmogorov, A.G.; Kononova, O.N.; Panchenko, O.N. A Review of the Use of Ion Exchange for Molybdenum Recovery in Russia. Can. Metall. Q. 2004, 43, 297–304. [CrossRef] 32. Shi, Q.; Zhang, Y.; Huang, J.; Liu, T.; Liu, H.; Wang, L. Synergistic solvent extraction of vanadium from leaching solution of stone coal using D2EHPA and PC88A. Sep. Purif. Technol. 2017, 181, 1–7. [CrossRef] 33. Cheng, C.Y.; Barnard, K.R.; Zhang, W.; Robinson, D.J. Synergistic solvent extraction of nickel and cobalt: A review of recent developments. Solvent Extr. Ion Exch. 2011, 29, 719–754. [CrossRef]

34. Sue, K.; Uchids, M.; Adschiri, T.; Arai, K. Determination of sulfuric acid ﬁrst dissociation constants to 400 ◦C and 32 MPa by potentiometric pH measurements. J. Supercrit. Fluids 2004, 31, 295–299. [CrossRef] 35. Wu, Y.C.; Feng, D. The second dissociation constant of sulfuric acid at various temperatures by the conductometric method. J. Solut. Chem. 1995, 24, 133–144. [CrossRef]

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