The leaching of vanadium pentoxide using sulfuric acid and sulfite as a reducing agent

The leaching of vanadium pentoxide using sulfuric acid and sulfite as a reducing agent

Hydrometallurgy 141 (2014) 59–66 Contents lists available at ScienceDirect Hydrometallurgy journal homepage: www.elsevier.com/locate/hydromet The l...

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Hydrometallurgy 141 (2014) 59–66

Contents lists available at ScienceDirect

Hydrometallurgy journal homepage: www.elsevier.com/locate/hydromet

The leaching of vanadium pentoxide using sulfuric acid and sulfite as a reducing agent M.R. Tavakoli ⁎, S. Dornian, D.B. Dreisinger Department of Materials Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada

a r t i c l e

i n f o

Article history: Received 29 June 2013 Received in revised form 27 September 2013 Accepted 21 October 2013 Available online 2 November 2013 Keywords: Vanadium Solubility Reductive leaching Kinetics model

a b s t r a c t Vanadium has been produced from both primary and secondary sources having various compositions. One of the most available sources of vanadium is vanadium pentoxide. In this paper, vanadium pentoxide leaching was investigated using three chemistries. First, vanadium leaching and the solubility of pentavanadyl ion (VO+ 2 ) at different pHs and temperatures were investigated in the sulfuric acid system. It was shown that decreasing pH and temperature as well as increasing sulfate concentration in the solution will increase the solubility and extraction of vanadium. The extraction of vanadium (V) was found to be limited by solubility. To overcome the solubility problem of vanadium (V), the kinetics of vanadium leaching from vanadium pentoxide at mildly basic pHs and reductive leaching in the low acidic pHs were then investigated. The kinetics of leaching was reasonably fast in both cases. Moreover, the progressive-conversion model was applied to model reductive leaching of vanadium using sodium sulfite. The rate of the reaction was reported as: rate ¼ k

 þ H



ðKe þ ½Hþ Þ0:5

0:57

½SO2 total : © 2013 Elsevier B.V. All rights reserved.

1. Introduction Vanadium is a valuable rare metal found in over 50 different minerals (Gupta and Krishnamurty, 1992; Moskalyk and Alfantazi, 2003). As well as using vanadium in metal alloys, other applications such as catalysts, biological application, and vanadium batteries have recently increased the importance of vanadium (Gupta and Krishnamurty, 1992; Habashi, 1998). The increasing demand for vanadium requires increased knowledge of the possible routes to vanadium recovery from a variety of raw materials. A significant number of reports about vanadium leaching have been published in recent years. Table 1 summarizes some of the important research studies on vanadium leaching from different resources. Vanadium is produced from primary and secondary sources such as fly ash, spent catalyst, and steel slags (Izquierdo and Querol). Vanadium leaching has yielded a wide range of results. Varying conditions, such as solvent pH and temperature range as well as solid to liquid ratio, have been applied in order to obtain reasonable recovery of vanadium from different sources. In addition to this wide variety of results, some studies have shown opposite effects by varying certain parameters in the vanadium leaching process. For instance, regarding the effect of additives, Li et al. (2009) and Xiang-yang et al. (Chen et al., 2010) ⁎ Corresponding author. Tel.: +1 604 822 2676; fax: +1 604 822 3619. E-mail address: [email protected] (M.R. Tavakoli). 0304-386X/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.hydromet.2013.10.014

investigated NaClO and MnO2, respectively, as an oxidizer to increase vanadium recovery in leaching. Furthermore, Okuwaki et al. (1988) and Li et al. (2010c) studied H2SO3 and FeSO4, respectively, as a reductive agent to increase leaching recovery. Moreover, Li et al. (2009) showed that FeSO4 has no effect on vanadium leaching while Xiangyang et al. (Chen et al., 2010) reported that FeSO4 decreases vanadium recovery. The lack of primary research on vanadium leaching as well as contradictory results in the literature has prompted an interest in studying vanadium (V) leaching in a more fundamental way. Therefore, the leaching of vanadium (V) at different pHs and reductive leaching of vanadium (V) to vanadium (IV) have been investigated. 2. Materials and methods Pure vanadium pentoxide (V2O5) from Fisher Scientific was used for leaching experiments. The purity of vanadium pentoxide was greater than 99.6% with low levels of iron (0.01% max), aluminum (0.03% max), silicon oxide (0.01% max), sulfur (0.01% max), and phosphorus (0.01% max). The phase composition of vanadium pentoxide was also confirmed by XRD analysis. The effect of impurities was not considered in our experiments. The vanadium pentoxide was screened to various particle size fractions for the study. The leaching/solubility procedure using 90 μm average (75–106 μm) particle size was performed in a Pyrex reactor equipped with a magnetic stirrer and a reflux condenser. A water bath was used for controlling the temperature. The final

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Table 1 Vanadium leaching reports in literature. No.

Source

Vanadium content (%)

Extraction (%)

Solvent

Solvent conc.

Temp. (°C)

S/L ratio (g/L)

Time (min)

1 2 3

HDS catalyst EP ash Fly ash

15 1.93–3.36 1.8

4

Fly ash

0.41 & 1.91

5

Spent petroleum catalyst

27.28 (V2O5)

6 7 8 9

Fly ash Fly ash Boiler ash Fly ash Spent catalyst Fly ash

12 13 14 15 16 17 18 19 20

Black shale mine Black shale mine Stone coal Steel slag LD convertor slag Black shale mine Calcium vanadate Spent petroleum catalyst Stone coal

3.26 (V2O5) 0.56 (V2O5) 1.09 8.46 (V2O5) 1.97 (V2O5) 6.15 (V2O5) 65.5 (V2O5) 9 1.82

H2O H2SO4 Na2CO3 NH4Cl (NH4)2CO3 H2SO4 NaOH NH4OH NH3 NaOH H2SO4 H2SO4 H2SO4 NaOH H2SO4 Water H2SO4 NaOH Na2CO3 H2SO4 H2SO4 H2SO4 NaOH H2SO4 H2SO4 Na2CO3 H2SO4 H2SO4

– 0.5 M 2M 2M 2M 2M 2M 2M 15 M pH = 8 2M 2M 0.6 M 5M 0.5 M – 0.5 M 2M 0.66 M 2M 0.87 M 1M 0.4 M 3M 2M 1.2 M 1M 0.3 M

Boiling 70 25 25 25 30 30 30 95 95 Boiling Boiling 220

10 11

1.3–3.3 3.8 (19 wt.% after burning) 20 0.93 0.93 0.42 1.6

81.8 95 63 10 20 95 75 48 90 90 80–95 97 98 80 90 90.1 98 56 60 75 86 85 90 90 70 95 80 91

– 0.125 0.2 0.2 0.2 0.2 0.2 0.2 100 100 333.34 142.85 0.5 100 100 0.5 250 250 250 833.34 250 333.34 500 0.067 14.28 40 0.1 0.833

45 420 420 420 120 120 120 1440 1440 30 60 30 5760 1440 15 1440 1440 1440 240 8640 120 350 140 60 60 120 240

solution was filtered using an ashless syringe filter paper and analyzed for vanadium content with Inductively Coupled Plasma spectroscopy (ICP, made by PerkinElmer; model Optima 7300). The pH was continuously monitored by a controller connected to the computer. The pH was kept constant (±0.01) during the leaching process by the addition of concentrated sulfuric acid from the acid stock tank on the digital scale connected to an accurate pump and controller. The vanadium extraction was confirmed using mass balance by weighting the remaining solid after each test and calculating the extent of leaching. In the second step, the kinetics of vanadium pentoxide leaching by weak acid solution (pH = 5) and dilute sodium hydroxide solution (pH = 8) was studied. In these tests, pH was kept constant by adding sodium hydroxide during the experiment. Vanadium (V) concentration was also analyzed by Inductively Coupled Plasma spectroscopy (ICP). In the third step, the kinetics of reductive leaching of vanadium (V) using sodium sulfite was also investigated. The effect of pH, temperature, and sulfite concentration on the kinetics was studied. For this part of the project, UV–Visible spectroscopy (made by PerkinElmer; model Lambda 35) was applied to analyze vanadium (IV) concentration in the solution (Kanamori et al., 1999; Yang and Gould, 2003). UV– Visible spectroscopy showed a suitable accuracy for vanadium (IV) standard solutions in sulfuric acid.

Ambient 80–90 Ambient Ambient Ambient 180 95 95 240 70 150 80 30 150

Ref. Biswas et al. (1985) (Okuwaki et al. (1988) Akita et al. (1995) Akita et al. (1995) Akita et al. (1995) Tsai and Tsai (1998) Tsai and Tsai (1998) Tsai and Tsai (1998) Villarreal et al. (1999) Villarreal et al. (1999) Vitolo et al. (2000) Vitolo et al. (2001) Amer (2002) Guibal et al. (2003) Guibal et al. (2003) Chen et al. (2006) Navarro et al. (2007) Navarro et al. (2007) Navarro et al. (2007) Li et al. (2009) Li et al. (2010a) Chen et al. (2010) Xiao et al. (2010) Aarabi-Karasgani et al. (2010) Li et al. (2010b) Wang-xing et al. (2010) Mishra et al. (2010) Deng et al. (2010)

amounts of sulfuric acid which should be neutralized by sodium hydroxide before the purification step. The solubility of VOþ was studied at different pHs from 0.3 to 1.4 and 2 at various temperatures. Fig. 2 represents vanadium extraction versus time in different pHs at 90 °C. The limiting concentration reached in each experiment after 8 h of leaching represents the solubility of pentavalent vanadium in solution. The same calculations have been made for temperatures 30, 50 and, 70 °C and the results were reported in Table 2. The results show that the kinetics of leaching vanadium to VOþ is 2 fast, but that this species suffers from low solubility. Thermodynamic data was studied for comparison with the experimental results. Table 3 shows the thermodynamics data for the following reaction which can occur in acidic media: þ

þ

V2 O5 þ 2H ¼ 2VO2 þ H2 O:

ð1Þ

3. Results and discussion 3.1. Solubility The kinetics of V2O5 leaching at different solid to liquid ratios was studied. As Fig. 1 shows, the kinetics of vanadium (V) leaching is fast at 90 °C. However, at a high solid to liquid ratio, the leaching halted abruptly after a short time, apparently because the vanadium solution had reached its solubility limit. In fact, the solution has been saturated by vanadium to the same concentration for the experiments performed at 5 and 10 g/L solid to liquid ratio. This means that when there is enough sulfuric acid in solution, the leaching can be completed quickly. However, acid concentration must be kept high through the leaching process. This suggests that the final leach solution will have significant

Fig. 1. The effect of solid to liquid ratio on V2O5 leaching (30 g/L H2SO4, 90 °C, 90 μm and 600 rpm).

M.R. Tavakoli et al. / Hydrometallurgy 141 (2014) 59–66

Fig. 2. The effect of pH on vanadium leaching at 90 °C (at 10 g/L V2O5, 90 μm and 600 rpm).

As shown, the solubility of this cation is affected significantly by temperature and pH. Considering thermodynamic data and Le Chatelier's principle, it would be expected that by decreasing pH and temperature, solubility of VOþ increases. However, the experimental data reported 2 higher values for solubility than thermodynamics would suggest. This can be explained with reference to activity coefficients and the complexation of vanadium in sulfate media. In a solution containing sulfate/bisulphate anions, a monosulfate complex VO2HSO− 4 is formed according to the following reactions: þ

−2



VO2 þ SO4 ¼ VO2 SO4 þ

ð2Þ



VO2 þ HSO4 ¼ VO2 HSO4 :

61

Some techniques have been known to study speciation in the solution. Raman spectroscopy is one of the well-known methods that characterize the speciation in the solution (Bal et al., 2004; Chagnes et al., 2010; Hurley et al., 2011; Tomikawa and Kanno, 1998; Tracy et al., 2007). This technique has been used to detect different cations in vanadium solutions formed with various acids and complexing salt additions. The final solutions after leaching at pH = 1 by hydrochloric acid with no salt and 0.55 M sodium sulfate as well as sulfuric acid with no additive were characterized by Raman spectroscopy. As Fig. 4 shows, when the matrix is hydrochloric acid, soluble vanadium only appears as one cation, VOþ . However, when sulfate is available in the solution, 2 vanadium has been confirmed to complex as VO2SO− 4 . Lastly, with the addition of sodium sulfate to the hydrochloride acid solution, the formation of VO2SO− 4 increases. As discussed above, acid leaching of vanadium pentoxide suffers from the low solubility of vanadium. However, it was shown that, by increasing the sulfate concentration in the system, the vanadium solubility will increase due to complexation. Two alternate strategies for overcoming the low solubility of vanadium have been investigated. Leaching at higher pHs and reductive leaching have been applied to change the vanadium species in solution in the hopes of increasing solubility. 3.2. Leaching of vanadium in pH 5–8 solution The kinetics of vanadium leaching using mildly acidic or mildly basic solution was investigated. According to vanadium speciation calculations, vanadium (V) can form the decavanadate anion in solution at pH = 5. The formation of decavanadate can proceed by the following reaction: 5V2 O5 þ 5OH



−5

¼ HV10 O28 þ 2H2 O

ΔG



298 K

¼ −648:02 kJ=mol: ð4Þ

ð3Þ

The equilibrium constant (Log β1) for reaction (2) has been reported as 9.7 (Ivakin, 1966), 1.3 (Rakib and Durand, 1996), and 1.72 (Puigdomenech, 2004). Besides, the equilibrium constant (Log β1) for reaction (3) was also reported −0.136 (Ivakin, 1966). In fact, in a non-complexing aqueous acidic solution, the pentavanadyl ion (VOþ ) 2 is the only dominant cation in the solution. However, the formation of vanadium sulfate complex can increase solubility of vanadium in sulfuric acid media. To investigate in more detail, the solubility of vanadium in different acid media and the effect of ionic strength and complexation have been studied. Fig. 3 shows vanadium solubility in sulfuric acid, nitric acid, and hydrochloric acid. It can be seen that the solubility of vanadium in nitric and hydrochloric acid is almost the same at pH = 1 and 30 °C. However, the solubility of vanadium in sulfuric acid is greater. To investigate the effect of added salt on vanadium solubility considering ionic strength and complexation (Butler, 1998), solubility of vanadium in hydrochloric acid was studied by adding 0.33 and 1.65 M sodium chloride and 0.11 and 0.55 M sodium sulfate separately. The results shown in Fig. 3 confirm that by increasing the sulfate concentration in solution, the solubility of vanadium increases. This is believed to be due to the complexation of vanadyl ion by sulfate. Table 2 Experimental solubility of vanadium as a function of pH and temperature. Temperature

Vanadium solubility (mM) (±3% error)

(°C)

pH = 0.3

pH = 0.6

pH = 1

pH = 1.4

30 50 70 90

102.6 82.6 42.4 32.9

62.8 39.3 26.1 20.6

26.9 16.1 10.5 8.4

8.9 6.0 3.2 1.8

This reaction is highly favorable. The equilibrium solubility of decavanadate in water has been calculated ( LogaHV10 O−5 ðTb100  CÞ≅75 ). 28

Therefore solubility limits should not impede leaching of vanadium under conditions to form decavanadate. During the leaching process, the pH was kept constant by adding sodium hydroxide to the solution. Fig. 5 shows the effect of temperature on vanadium leaching. Temperature has a significant effect on vanadium leaching. Vanadium pentoxide was nearly completely leached in 90 min at 90 °C. However, less than 40% of the vanadium was leached in that same time at 30 °C. Moreover, leaching at higher pH has also been studied. Reactions (5) and (6) show the chemical reactions that form the two anion species that dominate at pH = 8 (Pourbaix, 1949; Puigdomenech, 2004): 3V2 O5 þ 6OH



−3

¼ 2V3 O9 þ 3H2 O

ΔG



298 K

¼ −221:9 kJ=mol ð5Þ

(Barner and Scheueman, 1978; HSC) 2V2 O5 þ 4OH



−4

¼ V4 O12 þ 2H2 O



ΔG

298 K

¼ −208:6 kJ=mol

ð6Þ

(Barner and Scheueman, 1978; HSC). According to the thermodynamic data, all of these anion species in the solution have high solubility. Therefore, the effect of temperature on the kinetics of vanadium leaching in mildly basic media was investigated. Fig. 6 represents the effect of temperature on vanadium leaching. It was observed that the temperature had a significant effect on vanadium leaching in mildly basic media. Moreover, the molar ratio of sodium hydroxide consumption to vanadium pentoxide was determined to be 2.091 for leaching at pH = 8 at 90 °C. This value is very close to the predicted ratio from reactions (5) and (6). In addition, it was shown that by increasing the pH from 5 to 8, the kinetics of vanadium leaching was improved drastically.

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Table 3 Thermodynamic data for Eq. (1) (Barner and Scheueman, 1978; Evans and Garrels, 1958; HSC; Tracy et al., 2007; Wanty and Goldhaber, 1992) calculated solubility assuming unit activity coefficients. Temperature

ΔH

ΔS

ΔG

(°C)

(kJ)

(J/°K)

(kJ)

30 50 70 90

−35.18 −38.06 −40.70 −43.34

−147.73 −156.95 −164.89 −172.35

9.60 12.65 15.87 19.24

K

2.21 9.01 3.83 1.70

3.3. Reductive leaching Since vanadium (IV) has higher solubility than vanadium (V) in acidic pH media (Puigdomenech, 2004), reductive leaching can be applied to increase vanadium extraction at modest pH and hence decrease acid consumption in the leach process. The kinetics of reductive vanadium pentoxide leaching using sodium sulfite was investigated. The effect of varying temperature, particle size, stirring speed, pH, and sodium sulfite concentration was studied. For the kinetic study, since pure vanadium pentoxide was used and all spherical particles were shrunk through the leaching process (without formation of an “ash” layer”), the progressive-conversion model (PCM) has been used to describe the reductive leaching of vanadium (Levenspiel, 1998). The leach model has been defined by evaluating the thermal function k(T), the chemical function f(C) surrounding sulfite concentration, and the topological function g(1 − X) indicating the changing vanadium pentoxide grain topology in the following generalized topological leach model: dX ¼ kðTÞ·f ðCÞ·gð1−XÞ: dt

ð7Þ

3.3.1. Effect of temperature Fig. 7 illustrates the effect of temperature on vanadium extraction. It shows that, by increasing the temperature, the rate of the reaction will also increase. The chemical control model based on Stokes regime for small particles has been applied for describing the kinetic model: h i 2 dX n ¼ k′ ½SO2  1−ð1−XÞ3 : dt

ð8Þ

Calculated vanadium solubility (mM)

× × × ×

−2

10 10−3 10−3 10−3

pH = 0.3

pH = 0.6

pH = 1

pH = 1.4

74.57 47.56 31.03 20.68

37.37 23.83 15.55 10.36

14.87 9.49 6.19 4.13

5.92 3.77 2.46 1.64

relationship with extrapolation through the origin. So, it can be concluded that the reductive leaching of vanadium using sulfite is controlled by the reaction at the surface of the particle. Using the data obtained at the various temperatures, the apparent activation energy of the reaction using an Arrhenius relationship has been obtained. It can be seen in Fig. 8 that an activation energy of 33.47 kJ/mol is calculated for the reaction. The particles were studied during leaching by taking intermediate samples and observing using SEM (Hitachi model S-3000N). Fig. 9 shows SEM pictures for particle shape after 20 min of leaching at pH = 1 at temperatures of 30 and 90 °C. It was shown that the particles are roughly round. As the leaching rate increases with temperature, the particles shrink and the porosity on the surface increases. 3.3.2. Effect of particle size The fraction reacted versus time plots are shown in Fig. 10(a) for different initial particle sizes. As shown, the kinetics of the leaching reaction increased with decreasing particle size. A shrinking particle model was used to analyze the experimental data. The linear relation between reaction rate and 1/d in Fig. 10(b) confirms that the reaction control mechanism for reductive leaching conforms to the following equation: dX ¼ dt

  h i bKs MV2 O5 2 n k½SO2  1−ð1−XÞ3 : ρR

ð9Þ

R∘ is the average radius of spherical particle, ρ is the molar density of V2O5, b is the stoichiometric coefficient of the reaction, Ks is the rate constant for surface reaction, and M is the molecular weight of V2O5.

tion. The model fit was excellent. The data fit the required linear

3.3.3. Effect of stirring speed In order to rule out mass transfer as a possible rate control mechanism, the effect of stirring speed variation on vanadium reductive leaching was investigated at 500, 600, and 700 rpm. It was found that stirring speed has no significant effect on the kinetics of leaching. Therefore, considering the obtained results for activation energy, particle size

Fig. 3. The effect of different solvents and adding different salts on vanadium solubility (at 10 g/L V2O5, 90 μm 30 °C, pH = 1 and 600 rpm).

Fig. 4. Raman test for vanadium solution to confirm vanadium complexation in the presence of sulfate (leaching conditions: 10 g/L V2O5, 90 μm 30 °C, pH = 1 and 600 rpm).

By integration of the rate Eq. (8), slopes were obtained by plotting   1 1−ð1−XÞ3 versus time in constant pH and sodium sulfite concentra-

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63

Fig. 5. The effect of temperature on vanadium leaching at pH = 5 (10 g/L, 90 μm and 600 rpm).

Fig. 7. The effect of temperature on vanadium reductive leaching (at 10 g/L V2O5, 10.39 g/L Na2SO3, 90 μm, pH = 1 and 600 rpm).

and stirring speed, it can be positively claimed that the kinetics of leaching is controlled by chemical reaction rate, not mass transfer.

3.3.6. Chemistry and electrochemistry of the reaction The reduction of V2O5 by sodium sulfite in an aqueous solution can be considered as an electrochemical reaction. Sodium sulfite can form sulfur dioxide (SO2aq) and bisulfite in solution (HSO− 3 ) and they are − oxidized to sulfate (SO−2 4 ) and bisulphate (HSO4 ) by vanadium (HSC; Puigdomenech, 2004). The overall reaction can be represented by two half cell reactions. The cathodic half cell would be the dissolution of V2O5:

3.3.4. Effect of sodium sulfite concentration To investigate the effect that reductive additive concentration had on leaching efficiency, 10 g/L of V2O5 was leached using different amounts of sodium sulfite. The temperature was set at 70 °C, pH = 1, and stirring speed was adjusted to 600 rpm. As shown in Fig. 11(a), by increasing the amount of sulfite the leaching rate also increased. The order of dependence of rate on initial sodium sulfite concentration has been investigated by plotting Log k versus Log[SO2]initial. As shown in Fig. 11(b), the slope obtained was 0.57 which shows the order of dependence of reductive agent on the kinetics of the reaction. 3.3.5. Effect of pH The effect of pH on leaching is seen in Fig. 12 which indicates that pH has a significant effect on vanadium reductive leaching rates. The leaching process was completed in less than 30 min at pH = 0.5 and around 1 h at pH = 1. However, less than 70% of the vanadium was dissolved at pH 1.5 after an hour. Since pH can have an effect on the leaching reaction and can change the sulfite species as a reductive additive in the solution, it can be considered an independent parameter. Therefore, to investigate the effect pH has on the kinetics of vanadium leaching, both chemistry and electrochemistry have been considered for vanadium reductive leaching.

Fig. 6. The effect of temperature on vanadium leaching at pH = 8 (10 g/L, 90 μm and 600 rpm).

þ



V2 O5 þ 6H þ 2e

¼ 2VO

þ2

þ 3H2 O:

ð10Þ

While the anodic half cell may be presented as sodium sulfite oxidation in solution as per any of the following four reactions: −2

þ

SO2 ðaqÞ þ 2H2 O ¼ SO4 þ 4H þ 2e −

þ



ð11Þ



SO2 ðaqÞ þ 2H2 O ¼ HSO4 þ 3H þ 2e

ð12Þ



−2

þ 3H þ 2e

þ



ð13Þ





þ



ð14Þ

HSO3 ðaqÞ þ H2 O ¼ SO4

HSO3 ðaqÞ þ H2 O ¼ HSO4 þ 2H þ 2e :

Fig. 8. Arrhenius plot for activation energy calculation.

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Fig. 9. SEM image for the initial particle (a) and after 20 min of leaching at 30 °C (b) and 90 °C (c) (at 10 g/L V2O5, 10.39 g/L Na2SO3, 90 μm, pH = 1 and 600 rpm).





þ HSO4 þ H2 O

ð15Þ

28

C

ð17Þ ! ! where nc and na are the total charge transfer, kc , kc , ka ,and ka are the rate constant for forward and reverse reactions for the cathodic and anodic, respectively. Zc and Za are the number of electrons transferred in the charge transfer process. αc and αa are the transfer coefficients for reactions (16) and (17) that represent the symmetry of the activation barrier for the cathodic and anodic charge-transfer reactions. It was assumed that the potential difference is large enough that the backward reaction would be unfavorable and slow and can be →

Keq@25

þ2

¼ 9:47  10 ðHSCÞ:

Eqs. (10) and (12) represent half cell cathodic and anodic reactions, respectively. The Butler–Volmer equation for these reactions can be written in the following form (Bard and Faulkner, 2000):     h i !h þ2 i α Z FE −ð1−αc ÞZc FE þ −nc Fkc H exp exp c c ic ¼ nc Fkc VO RT RT



þ

V2 O5 þ SO2ðaqÞ þ 3H ¼ 2VO

    ! α Z FE −ð1−αa ÞZa FE − ia ¼ na F ka ½SO2 aq exp a a −na Fka ½HSO4  exp RT RT →

In the simplest form, the overall reaction at low pH can be presented by:



ð16Þ

Fig. 10. The effect of particle size on vanadium reductive leaching (a) and the rate of dissolution of vanadium (b) (at 70 °C, 10 g/L V2O5, 10.39 g/L Na2SO3, pH = 1 and 600 rpm).

Fig. 11. The effect of sulfite concentration on vanadium reductive leaching (a) and the rate of dissolution of vanadium (b) (at 70 °C, 10 g/L V2O5, 90 μm, pH = 1 and 600 rpm).

M.R. Tavakoli et al. / Hydrometallurgy 141 (2014) 59–66

65

And the total concentration of SO2 would be: −

½SO2 total ¼ ½HSO3  þ ½SO2 aq :

ð27Þ

Combining Eqs. (26) and (27): ½SO2 aq ¼

½SO2 total : K 1 þ þe ½H 

ð28Þ

Considering Eqs. (24) and (28), the rate of vanadium pentoxide dissolution would be:

− Fig. 12. The effect of pH on vanadium reductive leaching (at 70 °C, 10 g/L V2O5, 10.39 g/L Na2SO3, 90 μm and 600 rpm).

neglected. Therefore, cathodic and anodic reactions can be rewritten as below:   h i −ð1−αc ÞZc FE þ ic ¼ −2 Fkc H exp RT

ð18Þ

  ! α Z FE ia ¼ 2F ka ½SO2 aq exp a a : RT

ð19Þ

dnV2 O5 dt

0 10:5  þ h i0:5 ½SO  H þ  0:5 2 total A @ ¼k H ¼k ½SO2 total : ð29Þ ðKe þ ½Hþ Þ0:5 1 þ ½HKþe  

Eq. (29) predicts the rate of the overall reaction in terms of concentration of total SO2 and H+ in an aqueous solution due to electrochemical analysis. It can be seen that electrochemical analysis reports onehalf-order dependence on SO2 concentration which is consistent with the experimental results. Based on the electrochemical analysis, the following equation shows the rate dependence of vanadium leaching on pH. This equation has been used to compare experimental with predicted theoretical results considering the effect of pH.



Rate of the reaction ¼ f

The net current density is zero at the mixed potential: yields

iðEm Þ ¼ 0 → −ic ðEm Þ ¼ ia ðEm Þ:

ð20Þ

Then, the exchange current density can be derived by the following relationship:     h i ! −ð1−αc ÞZc FEm α Z FE þ iÅ ¼ 2 Fkc H exp ¼ 2 F ka ½SO2 aq exp a a m RT RT

! ka ½SO2 aq →

kc ½Hþ 

  ðαc −αa −1ÞFEm : ¼ exp RT

! ka ½SO2 aq →

kc ½Hþ 

¼ exp

RpH¼1 ¼ RpH¼1:5

  −FEm : RT

ð23Þ

Considering Faraday's low, the rate of the overall electrochemistry reaction can be obtained as:

dnV2 O5 dt

dnSO2aq dt →

dt

¼

¼

h

¼ Ac ic kc H

Ac ic nc F þ

i

ð24Þ

  h i −FEm þ exp ¼ Ac ic kc H 2RT →



dnV2 O5

h i0:5  þ 0:5 ¼k H ½SO2 aq :

! ka ½SO2 aq →



kc ½Hþ 

!0:5 ð25Þ

On the other hand, SO2 can be considered as a weak acid in the solution that dissociates as follows: þ



SO2ðaqÞ þ H2 O ¼ H þ HSO3 ; Ke ¼

RpH¼1 ¼ RpH¼0:5

ð22Þ

By assuming αc = αa = 0.5:

 þ − H ½HSO3  ½SO2 0:5 aq

:

ð26Þ

ðKe þ ½Hþ Þ0:5

:

ð30Þ

The reaction constant for dissociation of SO2, Ke, using thermodynamic data and Criss-Cobble technique generated a value of 4.317 × 10−3 at 70 °C. Then, the reaction rate ratio can be derived from the following equations:



ð21Þ

!

 þ H

10−1 −1

0:5 10 þ 4:37  10−3

10−0:5 10−0:5 þ 4:37  10−3

10−1:5

ð31Þ

¼ 2:44:

ð32Þ

0:5

10−1 −1

0:5 10 þ 4:37  10−3

¼ 0:53

0:5 10−1:5 þ 4:37  10−3

Considering Fig. 12, the rate of the reaction in different pH tests was obtained. RpH = 1/RpH = 0.5 and RpH = 1/RpH = 1.5 are found to be 0.51 and 2.57, respectively. The predicted ratios in electrochemical analysis are consistent with the experimental results. 4. Conclusions This study has been done in three steps. First, it was found that V2O5 can be leached quickly in sulfuric acid. However, pentavanadyl cation ( VOþ ) suffers from low solubility in solution. On the other 2 hand, it was reported that the solubility can be raised by increasing the sulfate concentration in the solution. Secondly, it was shown that V2O5 can be leached in water and mild sodium hydroxide solution at constant pH. At 90 °C and pH = 5, approximately all of V2O5 can be leached in less than 2 h as decavanadate. Whereas for pH = 8 and maintained at the same temperature, 90 °C, vanadium can be leached completely as metavanadate after about an hour. It was found that temperature can significantly affect both the water and mild basic leaching.

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Thirdly, it was observed that using reductive agents in acidic pH range can increase leaching efficiency significantly. The kinetics of reductive leaching of vanadium pentoxide using sodium sulfite was then studied using a progressive conversion model (PCM). It was shown that the reductive leaching is a chemical control regime by activation energy of 33.47 kJ/mol. Finally, the following rate equation has been offered for leaching prediction for vanadium reductive leaching: dnV2 O5 dt



¼k

h

0

1

0:5 i þ 0:5 @½SO2 total A H 1 þ ½HKþe 

¼k



 þ H ðKe þ ½Hþ Þ0:5

0:57

½SO2 total :

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