Measurement and Modeling for Molybdenum Extraction from the

Article pubs.acs.org/IECR

Measurement and Modeling for Molybdenum Extraction from the Na2MoO4−H2SO4−H2O System by Primary Amine N1923 Xinyue Zhang,†,‡,§ Pengge Ning,*,† Hongbin Cao,† and Yi Zhang†,‡,§ †

Research Centre for Process Pollution Control, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ School of Chemical Engineering and Technology, National Engineering Research Center of Distillation Technology, Tianjin University, Tianjin 300072,China § Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, China ABSTRACT: In this study, the liquid−liquid equilibrium (LLE) system N1923−Na2MoO4−H2SO4 was investigated. Within different molybdenum concentration ranges, the extraction reactions were determined using the slope method at 293.15 K based on the molybdenum phase diagram. The slopes for Mo(VI) extracted with N1923 were determined as 1 and 4, respectively. Mo(VI) was extracted as H2MoO4·(RNH2) and H6Mo7O24·(RNH2)4. The thermodynamic models were established with the Pitzer equation for aqueous phase and organic Pitzer as well as Margules equations for organic phase optimized by the General Algebraic Modeling System. Two chemical equilibrium constants and their corresponding interaction parameters were regressed from experimental LLE data. The correlated results were in good agreement with the experimental data. Furthermore, this model can also be used to predict the equilibrium composition and equilibrium pH in the aqueous phase. In addition, the mean ionic activity coefficients for Na2MoO4 and Na6Mo7O24 at 293.15 K were calculated with the Pitzer parameters. The chemical structures of the extraction complex were also proposed to illustrate the association.

1. INTRODUCTION Molybdenum has been widely used in metallurgical applications in recent decades. The common usage of this element is due to its intrinsic characteristics, such as its ability to withstand extreme temperatures without significantly expanding or softening, its ability to significantly resist corrosion, its high degree of weld ability, and its low density.1 In addition, its high-purity products are vital for developing advanced materials.2 However, it is frequently associated,3 in mineral deposits and recycled materials, with impurities, including arsenic, phosphorus, silicon, tungsten, etc.4 Therefore, recovering molybdenum cleanly and efficiently with low-cost from the natural minerals for the highvalue products is important and particularly important for utilizing the resources. Among the commonly used separation methods, such as adsorption,5 precipitation,6 ion exchange,7 and solvent extraction, solvent extraction is considered promising for metal separation with the merits of pure product and little pollution. There are some advantages for the liquid−liquid extraction: (I) Liquid−liquid extraction can be operated in large-scale industrial separation processes in the inorganic, organic, pharmaceutical, and biochemical industries, especially in the dilute polar solution. (II) On the basis of the high selectivity of the extractant, the special molecules can be obtained while others are retained in the solutions. (III) The valuable material is obtained without producing other hazardous byproducts.8 Thus, solvent extraction is used in this study to efficiently separate molybdenum from other elements. Extraction of metallic anions with amines is a common method for the recovery of tungsten and other elements. Among amine extractants widely used for the separation of molybdenum, primary amine (N1923) has been proven to be efficient and is commercially available. Yu et al.9 © 2016 American Chemical Society

proved the mechanism of molybdenic extraction by primary amine to be hydrogen bond association with the solvation process. Although many extraction processes of molybdenum and other elements have been studied,4,10,11 the thermodynamic model and chemical equilibrium constants for molybdenum extraction have not yet been reported. However, the corresponding fundamental thermodynamic parameters are quite requisite for serving as the basis for simulating and designing extraction processes. To research these parameters in detail, a thermodynamic model needs to be constructed. The construction of such a model would greatly aid in predicting the extraction performance under various initial conditions without requiring additional experiments. According to the phase diagram of Mo(VI) reported in the literature, 12 the anionic polynuclear species, such as Mo7O21(OH)3−, Mo7O23(OH)5−, and Mo7O246−, dominate in the pH range between 2 and 6, while mononuclear anionic species MoO42− is predominant at pH > 5, which leads to difficultly establishing a thermodynamic model and determining the respective species in organic phase at equilibrium for molybdenum extraction. To date, there has been no systematic research on the thermodynamics of N1923 in the separation of molybdenum from sulfate aqueous solution. Considering the importance of thermodynamic modeling and the related prediction of the system, we have attempted to develop the N1923−toluene Received: Revised: Accepted: Published: 1427

September 26, 2015 January 12, 2016 January 14, 2016 January 28, 2016 DOI: 10.1021/acs.iecr.5b03612 Ind. Eng. Chem. Res. 2016, 55, 1427−1438

Article

Industrial & Engineering Chemistry Research

degree of standard curve ≥99.99%. Before analysis, the aqueous phase was diluted by doubly distilled water to the required concentration. The solubilities of the primary amine N1923 and toluene in the aqueous phase, as well as water in the organic phase, were small and therefore neglected. 2.3. Determination of Extraction Conditions. The molybdenum species and their corresponding chemical equilibrium equations and thermodynamic constants13 are listed in Table 2. Using these constants, Figure 1 was made, which shows the species within different concentration and pH ranges. The

system to separate molybdenum and determine the composition of the complex in equilibrated organic phase. In this work, the experimental data for the equilibrium system N1923−toluene− Na2MoO4−H2SO4 was investigated, and the thermodynamic modeling was chosen to determine the chemical equilibrium constants. In this model, the nonideality of both aqueous and the organic phases was considered. For the aqueous phase, the Pitzer equation was used to calculate the activity of the ionic species with well-known Pitzer interaction parameters. For the organic phase, the organic Pitzer and Margules equations were used to regress the interaction parameters to calculate separately the activity of the neutral solute species.

Table 2. Chemical Equilibrium Equation and Constants for Molybdenum Species

2. EXPERIMENTAL SECTION 2.1. Materials. The extractant primary amine N1923 was C19−C23 secondary alkyl primary amine with the average molar mass 310.30 g·mol−1. The source and mass purity of all the reagents used in this experiment are listed in Table 1. The

species

substance

molecular mass

Na2MoO4· 2H2O toluene

241.95

N1923

310.30

sulfuric acid

92.14

98.08

source Beijing Chemical Works, Beijing, China Beijing Chemical Works, Beijing, China Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences Sinopharm Chemical Reagent Co., Ltd., Shanghai, China

MoO4 2 − + H+ ↔ HMoO4 −

H2MoO4

MoO4 2 − + 2H+ ↔ H 2MoO4

Mo7O24

6−

HMo7O24

Table 1. Source and Purity of Chemicals mass purity ≥99%

chemical equilibrium equation

HMoO4−

5−

7MoO4

2−

+

+ 8H ↔ Mo7O24 +

log10 K 3.89 7.50

6−

+ 4H 2O

62.14

7MoO4

H2Mo7O244−

7MoO4

2−

+ 4H 2O

65.68

H3Mo7O243−

7MoO4 2 − + 11H+ ↔ H3Mo7O24 3 − + 4H 2O

68.21

MoO3(s)

MoO24 − + 2H+ ↔ MoO3(s) + H 2O

12.06

+ 9H ↔ HMo7O24 +

5−

57.74

2−

+ 10H ↔ H 2Mo7O24

+ 4H 2O 4−

≥99.5% ≥98% 95−98%

extractant primary amine N1923 was prepared by mass using an analytical balance (Mettler ML104, 0.0001 g) and was diluted with toluene by volume without the addition of any other modifier. The aqueous phase in the process of extraction was Na2MoO4 solution prepared by dissolving sodium molybdate dihydrate (Na2MoO4·2H2O) in the doubly distilled water with specific conductivity less than 0.1 μS·cm−1. Dilute sulfuric acid prepared from concentrated sulfuric acid was used as the pH modifier in aqueous phase. These chemicals were used without further purification. 2.2. Liquid−Liquid Phase Equilibrium Experiments. In our experiments, the following procedures were employed. The aqueous solution of Na2MoO4 was prepared by dissolving Na2MoO4·2H2O in distilled water; then sulfuric acid was added to the Na2MoO4 solution to adjust the initial pH. A pH meter (Delta320, Mettler, Switzerland) with an uncertainty of 0.01 was used to measure the pH value of the aqueous phase. The extractant N1923 was diluted by toluene. Equal volumes (10 mL) of aqueous molybdenum solution and organic extractant solution were added to the equilibrium vessel. The vessel was maintained at the temperature of 293.15 K using a thermostat within ±0.1 K (DC0510, Ningbo Scientz Biotechnology Polytron Technologies Inc., China) for 1 h. A magnetic stirrer (B4-1A, Shanghai Sile Instrument Co., Ltd., China) was used to provide vigorous agitation for the solution in the vessel with a constant frequency of 1040 r/min. Then the aqueous and organic phases were transferred into the separating funnel and kept standing for stratification for 0.5 h. After that, the aqueous phase was obtained and analyzed. The content of molybdenum in the aqueous phase was analyzed using an OPTIMA 5300DV inductively coupled plasma-optical emission spectrometer (ICP-OES, PerkinElmer, United States) at the wavelength of 209.86 nm with the correlation

Figure 1. Phase diagram for molybdenum (Mo) species in aqueous phase.

lines in Figure 1 represent conditions under which the predominant species in adjacent regions contain equal amounts of Mo(VI). According to the result of Figure 1, we can estimate the species within given concentration and pH. The effect of reaction time on the extraction yield at 293.15 K is illustrated in Figure 2. It can be seen that the extraction yield increased with increasing extracting time and leveled off up to 20 min and longer time. For the reliability of experimental results, the extraction time was fixed at 60 min for the purpose of reaching equilibrium. Figure 3 shows the effect of pH0 on the molybdenum extraction yield with initial molybdenum concentrations of 0.01001 and 0.52193 mol/kg. It is evident that pH0 has a significant effect on the extraction yield. The extraction yield increased with the decrease of the initial pH, indicating that the extraction process was consuming H+. However, as is shown in Figure 1, MoO3 tends to form with too much acid, which is not beneficial for extraction. Therefore, pH0 is set greater than 2.5. To determine the equilibrium pH and extraction yield at different conditions, the influence of initial N1923 concentration on pHe value was investigated. As shown in Figures 4 and 5, the extraction yield increased sharply but then leveled off from a certain value because of the limited amount of H+. 1428

DOI: 10.1021/acs.iecr.5b03612 Ind. Eng. Chem. Res. 2016, 55, 1427−1438

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Figure 5. Effect of N1923 concentration on the equilibrium pH. The initial molybdenum concentration is 0.52078 mol/kg, and the pH0 is 4.00.

Figure 2. Effect of extraction time on molybdenum extraction yield. The initial N1923 concentration is 0.06164 mol/kg for 0.01001 mol/kg initial concentration of element molybdenum, and the initial pH is 3.95.

K1

org 2H+ + MoO24 − + x1RNH org 2 ⇄ H 2MoO4 · x1RNH 2

(1)

where superscript org represents the organic phase. The equilibrium constant of reaction 1 is designated as K1. The basis of calculation in this paper will be molality-based equilibrium constant, which is defined as follows: K1 = =

a Horg2MoO4 ·x RNH2 org a H2+a MoO4 2−(a RNH )x1 2

m Horg2MoO4 ·x RNH2γHorgMoO ·x RNH 2

4

2

org a H2+ ·m MoO4 2−γMoO 2−·(m RNH γ org )x1 2 RNH 4

2

(2)

where mi and γi represent the molality and activity coefficient, respectively, and aH+ is the activity of H+. The distribution coefficient of molybdenum, DMo, in the aqueous and organic phases is taken as

Figure 3. Effect of the initial pH on molybdenum extraction yield. The initial N1923 concentration is 0.06164 mol/kg and 0.38176 mol/kg for 0.01001 mol/kg and 0.52193 mol/kg (initial concentration of element molybdenum), respectively.

DMo =

m Horg2MoO4 ·x RNH2 m MoO4 2−

=

org x1 γ 2 −· γ RNH 2 2 org x1 MoO4 K1a H+(m RNH2) org γH MoO ·x RNH 2 4 1 2

(3)

When the logarithm of eq 3 is taken and the activity coefficient terms are neglected (γi = 1), the equation can be simplified as follows: org lgDMo + 2pH e = x1lgmRNH + lgK m ,1 2

(4)

where morg RNH2 represents the concentration of free RNH2 in the equilibrium organic phase; Km,1 is the extraction equilibrium constant without consideration of activity coefficient; and pHe is the equilibrium pH value in the aqueous phase. According to eq 4, a plot of lg DMo + 2pHe versus lg morg RNH2 should be linear. From the slope, the stoichiometric ratio x1 can be obtained. From the intercept, the value lg Km,1 is obtained simultaneously. However, due to the nonideality, equilibrium constants with consideration of activity coefficients should be obtained from the thermodynamic model.

Figure 4. Effect of N1923 concentration on the extraction yield. The initial molybdenum concentration is 0.52078 mol/kg, and the pH0 is 4.00.

2.4. Determination of Extraction Reactions with the Slope Method. In the Na2MoO4 solution, there exist several molybdenum species, such as MoO42−, HMoO4−, Mo7O246−, HMo7O245−, and H2Mo7O244−. Based on the plot of log10 mMo versus pH in Figure 1,12 MoO42− is the dominant species in the dilute molybdenum solution. Thus, the extraction reaction equation with N1923 is expressed as eq 1.

3. THERMODYNAMIC MODELING For the aqueous and organic phases of the equilibrium system, the nonideality of the solution should be taken into account. To keep the K value constant and to determine the molality of molybdenum in the organic phase, the activity coefficients are required. 1429


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⎡ ⎤ I 2 = −36Aφ⎢ + ln(1 + b I )⎥ ⎣1 + b I ⎦ b (1) ⎫ ⎧ 2βMo 6− + ⎪ ⎪ (0) 7O24 ,Na −α I ⎬ [1 (1 )e ] I + 2m Na+⎨βMo − + α 6− + + 2 O24 ,Na 7 αI ⎪ ⎪ ⎭ ⎩

In recent years, some extraction models have been developed for the computation of activity coefficients. The Pitzer model has been widely used to evaluate activity coefficients because of its mathematical flexibility and high accuracy.14 Li et al. used the Pitzer model for the aqueous phase and the Scatchard−Hildebrand model and Margules model for the organic phase in the quaternary extraction system.15 Pitzer first used his equation to calculate the activity coefficient of neutral species H3PO4 in aqueous solution.16 Schunk and Maurer established the thermodynamic model in systems of mineral acid {(hydrochloric, nitric, or sulfuric acid)−water−toluene} in the presence of tri-n-octylamine with the Pitzer equation both for the aqueous and organic phases.17 Due to the complicated chemical speciation in aqueous solution, there is no thermodynamic modeling for the extraction of molybdenum. In the present work, the Pitzer theory18,19 was used to correct the nonideality of the aqueous solution. The organic Pitzer17,20 and Margules21,22 equations were used for the correlation of the organic phase. 3.1. Aqueous Phase. The activity coefficient of the cation M is given by the Pitzer equation for mixed electrolytes in aqueous phase, as shown in eq 5:23 ln γM =

ln γMo

∑ ∑ mcma(z M2B′ca + z M2Cca) c

− 2mSO4 2 −m Na+

a

c

+

−

− 2mSO4 2 −m Na+

αI (1) 4βSO 2− ,Na+ 4

α 2I 2

[1 − (1 + α I + α 2I /2)e−α I ]

2

2

(9)

2

2

2

2

(10)

where the concentration of molybdenum species and free extractant in the organic phase mMo‑RNH2 and mRNH2 were obtained by mass balances. βijorg represents the binary interactions between neutral species i and j, and morg is the j molality of neutral solute species j in organic phase. Similar to the aqueous electrolyte solution, the organic solvent molecules are not interaction particles, but serve only as the medium. Its activity coefficients can also be calculated by the osmotic coefficient equation. In our system, because the solvent molecules do not participate in chemical extraction reactions, the solvent activities in the organic phase are not calculated. 3.2.2. Margules Equation. The Margules equation, which can be obtained from the simplified Scatchard−Hildebrand equation, is very useful in thermodynamics. Wang et al.24 regressed the chemical equilibrium constants and interaction parameters from experimental LLE data (water + n-dodecane + TOPO + HCl) based on the Margules equation in the organic phase. Lin et al.25 also used Pitzer−Margules equations for the extraction of tungstic acid with primary amine N1923 in thermodynamic models. For simplicity, a 2-suffix formula was used instead of a 3-suffix formula in our work. The activity coefficient of the component in the organic phase can be determined as

and Mo7O246−

⎡ ⎤ I 2 + ln(1 + b I )⎥ ln γMoO 2 − = − 4Aφ⎢ 4 ⎣1 + b I ⎦ b (1) ⎧ ⎫ 2β MoO 2 −,Na+ ⎪ (0) ⎪ 4 −α I ⎬ + 2m Na+⎨β MoO + − + I [1 (1 α )e ] + 2− 4 ,Na α 2I ⎪ ⎪ ⎩ ⎭ (1) 4β MoO + 2− 4 ,Na 2m MoO4 2 −m Na+ [1 2 2

4

α 2I 2

org βMo m org ) ‐ RNH 2·RNH 2 RNH 2

2

(6)

The activity coefficient expressions of are presented in eqs 7 and 8, respectively.

(1) 36βSO 2− + ,Na

[1 − (1 + α I + α 2I /2)e−α I ]

org org org ln γRNH = 2(βRNH m org + βRNH m org ) ·Mo ‐ RNH Mo ‐ RNH 2 ·RNH RNH 2

[1 − (1 + α I + α 2I /2)e−α I ]

MoO42−

αI

2

⎫ −α I ⎪ ⎬ − + [1 (1 α )e ] I ⎪ α 2I ⎭

α 2I 2

,Na+

org org ln γMo = 2(βMo m org ‐ RNH ‐ RNH ·Mo ‐ RNH Mo ‐ RNH 2

2βX(1) c βac(1)

2−

2 2

1

⎤ 2 I + ln(1 + b I )⎥ ⎦ b I b

− 2 ∑ ∑ mamc z X 2

7 24

Here I is the ionic strength (I = 2 ∑i mizi2 ) and β0 and β1are the Pitzer parameters for hard sphere repulsion term between ions. 3.2. Organic Phase. 3.2.1. Organic Pitzer Equation. For the extraction reaction, the solute activity coefficients in the organic phase can be expressed as eqs 9 and 10:

where zM is the charge of the subscripted species M and m is the concentration of the subscripted species in molality. Subscripts a and c refer to the anion and cation in the mixed electrolytes, respectively. When the activity coefficient of the anion X is needed, M, c, and a in the above equations are replaced by X, a, and c. By derivation, the activity coefficient of the anion X is obtained as shown in eq 6 without considering the ternary interactions Cca. ⎡ ln γX = − zX 2Aϕ⎢ ⎣1 + ⎧ ⎪ + 2 ∑ mc ⎨ β (0) + ⎪ Xc ⎩ c

(1) 36βMo O

(8)

(5)

a

6−

− 2m Mo7O246 −m Na+

1 2 z Mf ′(I ) + 2 ∑ ma[BMa + (∑ mz)CMa] 2 a +

7O24

ln f1 = A12 x 2 2 + A13x32 + (A12 + A13 − A 23)x 2x3

(11)

ln f2 = A12 x12 + A 23x32 + (A12 + A 23 − A13)x1x3

(12)

ln f3 = A13x12 + A 23x 2 2 + (A13 + A 23 − A12 )x1x 2

(13)

where f i represents the activity coefficient of species i in the organic phase and Aij is the parameter for binary interactions between species i and j; 1, 2, and 3 represent molybdenum complex, C7H8, and RNH2, respectively; xi stands for the mole fraction of component i in organic phase. In the Margules equation, the activity of species i is expressed as xi f i.

− (1 + α I + α 2I /2)e−α I ]

[1 − (1 + α I + α 2I /2)e−α I ] (7) 1430


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Table 3. Experimental Results for Model Regression on the Extraction of Mo by Primary Amine N1923 Diluted in Toluene at T = 293.15 K under Pressure of 0.1 MPaa m(Mo)0 (mol/kg)

a

m(RNH2)0 (mol/kg)

0.009791 0.009341 0.008347 0.009722 0.009155 0.009611 0.005067 0.009331

0.06164 0.06164 0.04860 0.06164 0.06164 0.06164 0.002917 0.06164

0.5208 0.5208 0.5208 0.5208 0.5208 0.5155 0.5173 0.5219

0.1243 0.1901 0.2586 0.3299 0.4041 0.5100 0.5100 0.5100

m(Mo)e (mol/kg)

pHe

DMo

Data for Regression with eq 14 0.004182 6.49 1.34 0.003745 6.44 1.49 0.003146 6.35 1.65 0.003247 6.40 1.99 0.002350 6.40 2.89 0.002063 6.25 3.65 0.002535 5.60 0.998 0.0003013 5.80 29.88 AARD of lgK values (%) Data for Regression with eq 15 0.3510 5.50 0.461 0.2939 5.81 0.735 0.2425 6.01 1.093 0.2047 6.15 1.470 0.1735 6.35 1.907 0.1785 6.52 1.89 0.1699 6.48 1.95 0.1322 6.45 2.81 AARD of lgK values/%

E (%)

lgK (Pitzer)

lgK (Margules)

57.18 59.81 62.31 66.52 74.27 78.48 92.85 96.76

14.63 14.57 14.54 14.63 14.77 14.60 14.87 14.61 0.865

13.88 13.82 13.80 13.88 14.04 13.86 14.09 13.89 0.540

31.54 42.38 52.21 59.52 65.60 65.37 66.08 73.74

48.44 48.50 48.48 48.47 48.56 48.50 48.45 48.53 0.0644

50.05 49.94 50.09 50.05 50.47 50.21 50.10 50.33 0.269

Phase ratio, O/A = 1; equilibrium time, 1 h; standing time, 0.5 h.

4. RESULTS AND DISCUSSION 4.1. Determination of Extraction Reactions. According to Figure 1, the dominant species is MoO42− when the equilibrium molybdenum concentration is below 0.01 mol/kg with the equilibrium pH ranging from 5.3 to 7.0. The equilibrium data is listed in Table 3. As is seen in Figure 1,13 equilibrium pH is expected to remain constant to form as unique species as possible. To avoid the error from repeated titration of H2SO4 in the extraction process, the concentration of primary amine as well as initial pH were adjusted simultaneously before extraction. On the basis of this, when lg DMo + 2pHe versus lg mRNH2 is plotted (Figure 6), the slope x1 equals 1, which shows the

extraction reaction is performed as eq 14 in this molybdenum concentration range. K1

org 2H+ + MoO4 2 − + RNH org 2 ⇄ H 2MoO4 · RNH 2

(x1 = 1) (14)

When the equilibrium molybdenum concentration is above 0.1 mol/kg with equilibrium pH ranging from 5.0 to 6.5, the dominant species is Mo7O246−.Thus, the relationship of lg DMo + 6pHe versus lg mRNH2 was plotted in Figure 7, and the slope x2 is 4. The stoichiometric ratio was determined with good correlation. The extraction reaction is performed as eq 15 in the above-mentioned range. With the slope method, the intercept represents the lg Km value (see eq 4). So the lg Km values for reactions in eqs 14 and 15 are 14.577 and 41.566, respectively. (Km is the extraction equilibrium constant without consideration of activity coefficient.) K2

org 6H+ + Mo7O24 6 − + 4RNH org 2 ⇄ H6Mo7 O24 · 4RNH 2

(x 2 = 4) (15)

4.2. Regression of Parameters with Thermodynamic Models. In Tables 3 and 4, the LLE results were classified with different extraction reactions in the system. Tables 3 and 4 show the experimental data used for regression and prediction, respectively. A detailed explanation of the error analysis is very necessary for the evaluation and characterization of the experimental data, which encompass both inherent error and random error. As to inherent error, the factors causing inherent error and the relative uncertainty for m(Mo)0, m(Mo)e, and m(RNH2)0 are listed in Tables 5 and 6. The values for m(Mo)0 and m(Mo)e are obtained from the ICP-OES instrument with the correlation degree of standard curve ≥99.99%. Therefore, relative uncertainty due to standard curve deviation is 0.01%. The second uncertainty results from the dilution process for reading error. The third uncertainty is the density error of water caused by temperature. Experiments were carried out at 293.15 K, but

Figure 6. Slope of extraction reaction (eq 14) on the basis of MoO42−. Experimental conditions: at 293.15 K, the initial molality of element Mo is 0.0105 mol/(kg·H2O). ur(Mo)0 = 0.17%. The initial pH values are 2.99, 4.00, 4.54 and 5.03, respectively. ur(a(H+)) = 2.276%. The initial molalities of RNH2 are 0.003026, 0.006329, 0.008772, and 0.01398 mol/(kg·toluene), respectively. The standard uncertainties ur(m(RNH2)) are 3.59%, 3.33%, 3.27%, and 3.20%, respectively.

stoichiometric ratio of H2MoO4·RNH2 is 1, and the correlation degree is excellent (R2 = 0.989). Thus, it is concluded that the 1431


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Table 5. Relative Uncertainty for m(Mo)0 and m(Mo)e factors for error analysis

relative uncertainty

standard curve deviation reading error in dilution process density error of water caused by temperature total

0.01% 0.05% 0.11% 0.17%

Table 6. Relative Uncertainty for m(RNH2)0

Figure 7. Slope of extraction reaction (eq 15) on the basis of Mo7O246−. Experimental conditions: at 293.15 K, the initial molality of element Mo is 0.5622 mol/(kg·H2O). ur(Mo)0 = 0.17%. The initial pH is 4.0. ur(a(H+)) = 2.276%. The initial molalities of RNH2 are 0.1038, 0.1557, 0.2076, and 0.2594 mol/(kg·toluene), respectively. The standard uncertainties ur(m(RNH2)) are all 3.10%.

factors for error analysis

relative uncertainty

impurity of N1923 impurity of toluene reading error in dilution process density error of toluene caused by temperature analytical balance error

2% 0.5025% 0.05% 0.5451% changing with m(RNH2)

0.01, the relative uncertainty for the activity of H+ is uniform. ur(H+) = 1 − 10−0.01 = 2.276%. The extraction coefficient, D, and extraction percentage, E, are calculated from the main measured experimental variables. Therefore, the propagation of errors from the individual uncertainties to the calculated values has also been listed with partial derivation as follows:

the measurement process is under 298.15 K. In summary, the total relative uncertainty for m(Mo)0 and m(Mo)e are both 0.17%. For the value of m(RNH2)0, its inherent errors come from the five parts. They are the errors from the impurity of reagents including primary amine and toluene. The reading error in dilution is also 0.05%. The density error of toluene caused by temperature is 0.867/0.8623 − 1 = 0.5451%. The relative uncertainty for primary amine due to the analytical balance change with molalities. For the 1 g/L and 50 g/L primary amine samples, primary amine is diluted in 25 and 100 mL flask, respectively. For example, the molality of primary amine is 0.06164 mol/kg, and the relative uncertainty is 0.024%. When the molality of primary amine is 0.51 mol/kg, the relative uncertainty is 0.003%. Because the uncertainty of the pH meter is

⎛ ∂D ⎞ ⎛ ∂D ⎞ Mo ⎟ Mo ⎟ ΔDMo = ⎜⎜ ⎟Δm(Mo)0 + ⎜⎜ ⎟Δm(Mo)e ⎝ ∂m(Mo)0 ⎠ ⎝ ∂m(Mo)e ⎠

(16)

aq aq ⎛ Δm(Mo)e ΔDMo 1 ⎜ Δm(Mo)0 = ⎜ + ur (DMo) = aq aq DMo E ⎝ m(Mo)0 m(Mo)e

⎞ ⎟ ⎟ ⎠

=

1 (|ur(m(Mo)0)| + |ur(m(Mo)e)|) E (17)

Table 4. Experimental Results for Model Prediction on the Extraction of Mo by Primary Amine N1923 Diluted in Toluene at T = 293.15 K under Pressure of 0.1 MPaa m(Mo)0 (mol/kg)

m(RNH2)0 (mol/kg)

0.0100 0.0051 0.0083 0.0105 0.0083 0.0105 0.0098

0.0616 0.0033 0.0299 0.0162 0.0369 0.0101 0.0616

0.5622 0.5622 0.5622 0.5622 0.5475

0.0636 0.1237 0.2570 0.3290 0.3290

m(Mo)e (mol/kg)

pHe

DMo

Data for Prediction with eq 14 0.0070 6.69 0.43 0.0026 5.65 0.91 0.0031 6.23 1.69 0.0039 5.92 1.69 0.0030 6.24 1.75 0.0038 5.75 1.76 0.0027 6.26 2.59 AARD of lgK values (%) Data for Prediction with eq 15 0.4582 5.28 0.13 0.3882 5.70 0.26 0.2843 6.03 0.56 0.2418 6.24 0.76 0.2219 6.11 0.84 AARD of lgK values (%)

E (%)

lgK (Pitzer)

lgK (Margules)

30.16 47.72 62.78 62.83 63.60 63.71 72.11

14.56 14.97 14.68 14.58 14.60 14.81 14.62 0.93

13.75 14.19 13.86 13.75 13.78 13.99 13.73 1.04

18.50 30.95 49.43 56.99 59.46

49.34 49.12 48.51 48.87 48.10 0.924

51.69 51.62 50.17 50.57 49.62 1.59

a

Phase ratio, O/A = 1; equilibrium time, 1 h; standing time, 0.5 h. m(Mo)0 and m(RNH2)0 represent the initial concentration of element molybdenum in aqueous phase and N1923 in organic phase, respectively. m(Mo)e represents the concentration of element molybdenum in the equilibrium aqueous phase. DMo and E represent the distribution coefficient and extraction yield of molybdenum, respectively. K is the equilibrium constant considering activity coefficient. The standard uncertainties are u(T) = 0.1 K, u(P) = 3 kPa, ur(mMo0) = 0.17%, ur(mMoe) = 0.17%, ur(aH+) = 2.276%, ur(average)(mRNH20) = 3.152%, ur(average)(DMo) = 0.6744%, ur(average)(E) = 0.4602%. ur(average) is the average relative uncertainty. The unit mol/kg represents mol (in elemental molybdenum)/(kg·H2O) in aqueous phase or mol (in free RNH2)/(kg·toluene) in organic phase. 1432


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Industrial & Engineering Chemistry Research Table 7. Regression Results of MoO42− and Mo7O246− with Pitzer−Pitzer Model at 293.15 K species 2−

MoO4 Mo7O246−

β0aq

β1aq

βorg MoR,MoR

βorg MoR,R

βorg R,R

lg K

AARD (%)

0.15429 3.3696

0.49919 22.797

11.679 8.8199

−1.2168 −0.94995

0.6697 0.6697

14.74 48.50

9.9 5.54

Table 8. Regression Results of MoO42− and Mo7O246− with Pitzer−Margules Model at 293.15 K species 2−

MoO4 Mo7O246−

β0aq

β1aq

Aorg MoR,R

Aorg MoR,tol

Aorg R,tol

lg K

AARD (%)

0.15429 3.36964

0.49919 22.7965

−43.601 −80.099

−1.1834 −1.7018

0.5535 0.5535

13.90 50.15

9.66 5.69

⎛ ∂E ⎞ ⎛ ∂E ⎞ ⎟⎟Δm(Mo)0 + ⎜⎜ ⎟⎟Δm(Mo)e ΔE = ⎜⎜ ⎝ ∂m(Mo)0 ⎠ ⎝ ∂m(Mo)e ⎠ u r (E ) =

aq aq ⎛ Δm(Mo)e ΔE 1 ⎜ Δm(Mo)0 = + aq aq E DMo ⎜⎝ m(Mo)0 m(Mo)e

m H2MoO4 ·RNH2 + m RNH2 = (m RNH2)initial

2mSO4 2− + 2m MoO4 2− = m Na+

(18)

⎞ ⎟ ⎟ ⎠

(24)

The equations of mass and charge balances for Mo7O24 presented in eqs 25−28. m Na+ = 2·7(m Mo7O24 6−)initial

1 = (|ur(m(Mo)0)| + |ur(m(Mo)e)|) DMo

mcalcd Mo

7

⎡ m calcd − m exptl ⎤2 ⎫ ⎪ ∑ ⎢⎢ Mo exptl Mo ⎥⎥ ⎬⎪ mMo ⎦⎭ i=1 ⎣

2

8

(26)

1/2

(20)

where and represent the calculated and experimental elemental molality of molybdenum in aqueous phase, respectively. In the calculation of ionic strength, three ions, Na+, SO42−, and molybdenum ions, should be considered in the aqueous phase. For eqs 7 and 8, the concentrations of Na+ and MoO42− were obtained by mass balances, while SO42− was estimated according to the charge balance in solution. The equations of mass and charge balances for MoO42− are expressed as follows (eqs 21−24): m Na+ = 2(m MoO4 2−)initial

(21)

m H2MoO4 ·RNH2ρC H = ((m MoO4 2−)initial − m MoO4 2−)ρH O 8

4m H6Mo7O24 ·4RNH2 + m RNH2 = (m RNH2)initial

(27)

2mSO4 2− + 6m Mo7O24 6− = m Na+

(28)

where subscript “initial” represents the initial value. ρC7H8 and ρH2O at 293.15 K are 867 and 998.2 kg/m3, respectively.26 As the Pitzer parameters for Na2MoO4 at 293.15 K have been regressed with solubility data,27 the values for β0Na2MoO4 and β1Na2MoO4 are 0.15429 and 0.49919, respectively. Therefore, the Pitzer parameters for Na2MoO4 were considered as fixed values and used directly in our extraction system. However, there do not exist Pitzer parameters for Na6Mo7O24 mainly because of its complexity, which needs to be regressed simultaneously with those in the organic phase. The thermodynamic model was established through regression of the experimental data with the Pitzer−Pitzer model and Pitzer−Margules model by the GAMS. The regression results are shown in Tables 7 and 8, respectively. The average absolute relative deviation (AARD) value stands for average absolute relative deviation between experimental molality and calculated molality of elemental molybdenum in aqueous phase. Because the model selected in aqueous phase was the same, β0Na2MoO4 and β1Na2MoO4 kept constant. The Pitzer−Pitzer and Pitzer−Margules models seemed to have approximate deviation. The AARD of Mo7O246− was smaller than that of MoO42−, which meant the solution of Mo7O246− was more unlikely to be mixed with other Mo(VI)−OH− species. The Pitzer model for the organic phase is empirical, and Pitzer parameters cannot be used to do theoretical explanation, while the 2-suffix Margules model in organic phase, which is deduced from Scatchard−Hildebrand (regular solution) theory, has obvious physical meanings. Aij (Aij = Cii + Cjj − 2Cij, where C is the attractive interactions between molecules) can demonstrate the difference of attractions between like molecules and unlike molecules.23 The more negative the Aij value, the stronger the attraction between 6− species i and j. For instance, the Aorg MoR,R for Mo7O24 is −80.099 and is more negative than that of MoO42−, which shows that the primary amine has more attraction for H6Mo7O24 than for H2MoO4. Similarly, the attraction between primary amine and toluene is so small that the Aorg R,tol value is positive.

mexptl Mo

7

are

7mH6Mo7O24·4RNH2ρC H = 7((m Mo7O246−)initial − m Mo7O246−)ρH O

Random errors in experimental measurements are caused by unknown and unpredictable changes in the experiment. These changes may occur in the measuring instruments or in the environmental conditions. For m(Mo)0 and m(Mo)e, the standard deviation for the instrument (ICP-OES) that was used to measure the concentration of molybdenum are random errors. The ICPOES has replications itself, and the relative standard deviation is between 0.1%−0.5%. For example, when the average value for m(Mo)0 is 44.38 g/L, the replication values are 44.32, 44.30, and 44.53 g/L. The standard deviation is 0.13 g/L, and relative standard deviation is 0.293%. When the average value for m(Mo)e is 0.2254 g/L, the replication values are 0.2250, 0.2260, and 0.2253g/L. The standard deviation is 0.0005 g/L, and relative standard deviation is 0.222%. While for m(RNH2)0, weighing error with replications is the random error. For example, when m(RNH2)0 is 0.04860 mol/kg, the mass of primary amine with replicated measurements are 0.3245, 0.3213, and 0.3202 g. In this situation, the standard deviation is 0.0022 g and the relative standard deviation is 0.694%. After the extraction reactions were determined, by use of the experimental data presented in Table 3, the thermodynamic model was built. Two sets of parameters were obtained by the General Algebraic Modeling System (GAMS). The objective function is n

6−

(25)

(19)

⎧ ⎪1 min F = ⎨ ⎪n ⎩

(23)

2

(22) 1433


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Figure 8. Experimental and calculated values at equilibrium in aqueous phase with Pitzer−Pitzer model at 293.15 K: (a) molality of MoO42− for eq 14, (b) equilibrium pH in aqueous phase for eq 14, (c) molality of Mo7O246− for eq 15, and (d) equilibrium pH in aqueous phase for eq 15.

activity coefficient γ±. Because Pitzer parameters are of intrinsic parameters for a definite electrolyte, these parameters also can be applied to single Na2MoO4 and Na6Mo7O24 aqueous solutions without SO42−.Thus, the mean ionic activity coefficient of the pure solution was obtained through the Pitzer equation. We will consider Na2MoO4 as an example. According to charge balance in single Na2MoO4 aqueous solution, eq 29 is obtained.

In addition, when different reference states are selected, the K values differ. It is known that different models need different concentration units (such as Pitzer model and Margules model), so the reference state for the Pitzer model is infinite dilution for solutes, while that for the Margules model is pure solute and solvent. This would be the reason why ln K differs with various models for the same species. Although DMo of MoO42− is bigger than that of Mo7O246− (see Table 3), ln K for Mo7O246− is larger because of the effect of α6H+ as expressed in eq 15. 4.3. Validation of the Model. 4.3.1. Calculation with Regressed Parameters. To verify the reliability of the established model, the equilibrium molality of elemental molybdenum and equilibrium pH of all experimental data in aqueous phase were recalculated and drawn in Figures 8 and 9. The ln K values for Pitzer−Pitzer and Pitzer−Margules models of all the experimental data were also calculated as shown in Tables 3 and 4. It can be seen from Figures 8 and 9 that there were reasonable deviations between the prediction values and the experimental values, which resulted from more complex species generated. The calculated lg K values kept almost constant around the regressed lg K values, which proved the reliability of the extraction reaction mechanism and also the model parameters. The AARD values between experimental data and calculated data were shown in Table 9, from which the reliability of the models was clearly reflected. 4.3.2. Mean Ionic Activity Coefficients for Na2MoO4 and Na6Mo7O24. To verify more completely, the mean ionic activity coefficients for Na2MoO4 and Na6Mo7O24 were calculated with the obtained parameters. The nonideality of a single electrolyte solution is conventionally represented in terms of the mean ionic

mNa+ = 2mMoO4 2−

(29)

The ionic strength of Na2MoO4 solution is shown in eq 30. I=

1 2

∑ mizi2 = 3mMoO

2−

4

(30)

i

For a single Na2MoO4 solution,23 the mean ionic activity coefficient of Na2MoO4 is given by eq 31. ⎡ I1/2 ⎤ 2 + ln(1 + bI1/2)⎥ ln γ± = −2Aϕ⎢ 1/2 b ⎣ 1 + bI ⎦ 1 ⎧ 2βNa 1 4m ⎪ 0 2MoO4 ⎨2βNa MoO + + m2(25/2)C ϕ + 2 4 ⎪ 2 3 ⎩ α 2I ⎫ ⎡ 1/2 ⎤⎪ ⎛ 1 ⎞ × ⎢1 − ⎜1 + αI1/2 − α 2I ⎟e−αI ⎥⎬ ⎝ ⎦⎪ ⎣ 2 ⎠ ⎭

(31)

When the Pitzer parameter values for Na2MoO4 (β0MoO42−,Na+ = 0.15429, β1MoO42−,Na+ = 0.49919) were applied to eq 31, the mean 1434


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Figure 9. Experimental and calculated data at equilibrium in aqueous phase with Pitzer−Margules model at 293.15 K: (a) molality of MoO42− in eq 14, (b) equilibrium pH in aqueous phase in eq 14, (c) molality of Mo7O246− in eq 15, and (d) equilibrium pH in aqueous phase in eq 15.

Table 9. AARD Values between Experimental Data and Calculated Data for pH and Molality of Elemental Molybdenuma regression-Mo

regression-7Mo

prediction-Mo

prediction-7Mo

AARD (%)

P−P

P−M

P−P

P−M

P−P

P−M

P−P

P−M

m pH

9.9 0.469

9.66 0.440

5.54 0.438

5.69 0.591

9.77 1.02

9.44 1.00

5.30 0.601

4.53 0.971

a P−P represents Pitzer model in aqueous phase and Pitzer model in organic phase. P−M represents Pitzer model in aqueous phase and Margules model in organic phase

4.4. Structure Prediction of the Extraction Complex. It was mentioned that MoO42− and Mo7O246− have the same structure in both solid and liquid phase.30 The structure for MoO42− is regular tetrahedron. However, after the structure of secondary molybdate crystals was investigated with X-ray analysis, it was found that Mo7O246− is made up of octahedrons.30 Therefore, the proposed structures are based on the structures of molybdate crystals. In Yu and Chen,9 the extraction complex structure of vanadium was represented, and the slope method corresponded very well with the structure. For one molecule of primary amine, there exist one activated nitrogen atom and two activated hydrogen atoms to form three hydrogen bonds. For one molecule of H6Mo7O24, there are 12 possible positions to bond with RNH2. Therefore, one H6Mo7O24 molecule associates with four primary amine molecules, which is consistent with the result

ionic activity coefficients with various molalities of Na2MoO4 without SO42− were obtained as Figure 10a. For 6:1 electrolyte Na6Mo7O24, the method was the same. To verify the reliability of the Pitzer parameters, the mean ionic activity coefficients for electrolytes with similar valences were calculated and compared. Mo and W are both transition elements and have similar characteristics. Therefore, they were compared. Kim and Frederick28 have regressed Pitzer parameters from osmotic coefficients of Goldberg’s29 for Na2WO4 at 298.15 K (β0 = 0.20318, β1 = 0.87616). Studies on Pitzer parameters for high valence are quite few. Data for Na5P3O10 at 298.15 K23 (β0 = 1.1214, β1 = 21.66) was used to compare with Na6Mo7O24. From Figure 10a we can see that Na2MoO4 correlates quite excellent with Na2WO4. Although in Figure 10b there is some deviation with Na6Mo7O24 and Na5P3O10, it is true the mean ionic activity coefficients with higher valence are lower. 1435


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Figure 10. Effect of ionic strength on the mean ionic activity coefficients in single solution without SO42−. (a) The comparison of mean ionic activity coefficients between Na2MoO4 at 293.15 K and Na2WO4 at 298.15 K.28 (b) The comparison of mean ionic activity coefficients between Na6Mo7O24 at 293.15 Kand Na5P3O10 at 298.15 K.23

Figure 11. Schematic representation of extraction species−primary amine extraction of H6Mo7O24. R represents alkyl group; “....” represents hydrogen bond; hydrogen atoms surrounded by dashed lines represent free active atoms that have not bonded with RNH2 because of steric hindrance effect.

associates with one primary amine molecule, which is consistent with the result from the slope method, as shown in Figure 12.

from the slope method. Due to the steric hindrance effect, one primary amine molecule can use only two activated atoms to form hydrogen bonds with the H6Mo7O24 molecule, as shown in Figure 11. For one molecule of H2MoO4, there are four possible positions to bond with RNH2. Therefore, one H2MoO4 molecule

5. CONCLUSIONS The LLE data of molybdenum extraction from sodium molybdenate solution in sulfuric acid by primary amine N1923 were obtained at 293.15 K. The extraction reactions were determined with the slope method at 293.15 K within different molality ranges based on the molybdenum phase diagram. It was assumed that there are mainly two extraction complexes generated in the organic phase, and the stoichiometric ratios are 1 and 4 for H2MoO4·RNH2 and H6Mo7O24·(RNH2)4, respectively. Thermodynamic parameters were obtained with Pitzer−Pitzer and Pitzer−Margules models. The prediction for equilibrium molality and equilibrium pH in aqueous phase and the calculated ln K values excellently verified the parameters. Then the mean ionic activity coefficients for Na2MoO4 and Na6Mo7O24 were calculated and compared with similar ionic species. Finally, the microstructures of the complexes were

Figure 12. Schematic representation of extraction species−primary amine extraction of H2MoO4. R represents alkyl group; “....” represents hydrogen bond; hydrogen atoms surrounded by dashed lines represent free active atoms that have not bonded with RNH2 because of steric hindrance effect. 1436


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(3) Kholmogorov, A. G.; Kononova, O. N. Processing Mineral Raw Materials in Siberia: Ores of Molybdenum, Tungsten, Lead and Gold. Hydrometallurgy 2005, 76, 37−54. (4) Ning, P. G.; Cao, H. B.; Zhang, Y. Selective Extraction and Deep Removal of Tungsten from Sodium Molybdate Solution by Primary Amine N1923. Sep. Purif. Technol. 2009, 70, 27−33. (5) Lv, Y.; Sun, F. Study of Separation of Tungsten and Molybdenum from High W-Containing Molybdenum Acid Sodium Solution by Fe(OH)3 Adsorption. Rare Met. Cem. Carbides 2005, 33, 1−3. (6) Cheresnowsky, M. J.; Towanda, P. Method for separation Tungsten from Molybdenum. U.S. Patent 4999169, 1988. (7) Blokhin, A. A.; Kaloshin, J. I.; Lyubman, H. R. Removing Tungsten and Purifying Ammonia Molybdate by Catechol Cationexchange Resin. Russ. J. Appl. Chem. 2005, 78, 425−427. (8) Rydberg, J.; Cox, M.; Musikas, C.; Choppin, G. R. Solvent Extraction Principles and Practice, 2nd ed.; CRC Press: New York, 2004. (9) Yu, S. Q.; Chen, J. Y. Solvent Extraction of Transition Metals Cr, Mo, W, V by Amines. Acta Metal. Sin. 1982, 18 (2), 187−199. (10) Nguyen, T. H.; Lee, M. S. Separation of Vanadium and Tungsten from Sodium Molybdate Solution by Solvent Extraction. Ind. Eng. Chem. Res. 2014, 53, 8608−8614. (11) Guan, W. J.; Zhang, G. Q.; Gao, C. J. Solvent Extraction Separation of Molybdenum and Tungsten from Ammonium Solution by H2O2-complexation. Hydrometallurgy 2012, 127−128, 84−90. (12) Nekovár,̌ P.; Schrötterová, D. Extraction of V (V), Mo (VI) and W (VI) Polynuclear Species by Primene JMT. Chem. Eng. J. 2000, 79, 229− 233. (13) Baes,C. F.; Mesmer, R. E. The Hydrolysis of Cations; Wiley: New York, 1976. (14) Lu, J. F.; Yu, Y. X.; Li, Y. G. Modification and Application of the Mean Spherical Approximation Method. Fluid Phase Equilib. 1993, 85, 81−100. (15) Li, Y. G.; Teng, T.; Cheng, Z. H.; Zhang, L. P. An Investigation of the Thermodynamics of Solvent-Extraction of Metals.2.Calculation of the Activity-Coefficient of Non-Electrolytes in the UO2(NO3)2(C7H15)2SO System. Hydrometallurgy 1982, 8, 273−287. (16) Pitzer, K. S.; Silvester, L. F. Thermodynamics of Electrolytes.VI.Weak Electrolytes Including H3PO4. J. Solution Chem. 1976, 5, 269−278. (17) Schunk, A.; Maurer, G. Distribution of Hydrochloric, Nitric, and Sulfuric Acid between Water and Organic Solutions of Tri-n-octylamine Part I. Toluene as Organic Solvent. Fluid Phase Equilib. 2003, 207 (1− 2), 1−21. (18) Pitzer, K.; Mayorga, G. Thermodynamics of Electrolytes. II. Activity and Osmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent. J. Phys. Chem. 1973, 77 (19), 2300−2308. (19) Pitzer, K. S. Activity Coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, FL, 1991. (20) Schunk, A.; Maurer, G. Distribution of Hydrochloric, Nitric, and Sulfuric Acid between Water and Organic Solutions of Tri-n-octylamine Part II. Methylisobutylketone as Organic Solvent. Fluid Phase Equilib. 2003, 211, 189−209. (21) Shacham, M.; Wisniak, J.; Brauner, N. Error Analysis of Linearization Methods in Regression of Data for the Van Laar and Margules Equations. Ind. Eng. Chem. Res. 1993, 32, 2820−2825. (22) Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth Publishers: London, 1985. (23) Li, Y. G. Thermodynamics of Solvent Extraction of Metals; Tsinghua University Press: Beijing, 1988. (24) Wang, H. P.; Qin, W.; Li, Y. G.; Fei, W. Y. Distributions of Hydrochloric Acid between Water and Organic Solutions of Tri-noctylphosphine Oxide: Thermodynamic Modeling. Ind. Eng. Chem. Res. 2014, 53, 12111−12121. (25) Lin, X.; Ning, P. G.; Xu, W. F.; Cao, H. B.; Zhang, Y. Thermodynamic Models Based on Pitzer-NRTL and Pitzer-Margules Equations for the Extraction of Tungstic Acid with Primary Amine N1923. Sci. China: Technol. Sci. 2015, 58, 935−942. (26) Lide, D. R. CRC Handbook of Chemistry and Physics 82th; CRC Press: Boca Raton, FL, 2000.

proposed to demonstrate the reaction mechanism in molybdenum extraction.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86-010-82544879. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors gratefully thank the National Natural Science Foundation (Grants 21206168 and 51425405) for financial support of this work.

■

NOMENCLATURE Aφ = Debye−Hückel parameter of water AARD = average absolute relative deviation Aij = Margules parameter for binary interactions between species i and j aH+ = activity of H+ DMo = distribution coefficient of elemental molybdenum f i = activity coefficient of the component i for Margules equation I = ionic strength K1 = chemical equilibrium constant for H2MoO4·RNH2 K2 = chemical equilibrium constant for H6Mo7O24·(RNH2)4 Km,1 = chemical equilibrium constant for H2MoO4·RNH2 without considering activity coefficients Km,2 = chemical equilibrium constant for H6Mo7O24·(RNH2)4 without considering activity coefficients mi = molality of species i pH0 = initial pH pHe = equilibrium pH RNH2 = primary amine x1 = the slope for eq 14 x2 = the slope for eq 15 xi = mole fraction of component i for Margules equation zi = number of charges of species i

Greek Letters (1) β(0) ij , βij = Pitzer binary interaction parameters between solute species i and j γi = activity coefficient of species i for Pitzer equation ρC7H8 = density of toluene at 293.15 K ρH2O = density of water at 293.15 K

Superscripts

org = organic phase aq = aqueous phase Subscripts

a = anion c = cation X = anion M = cation

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REFERENCES

(1) Xu, W. F.; Ning, P. G.; Cao, H. B.; Zhang, Y. Thermodynamic Model for Tungstic Acid Extraction from Sodium Tungstate in Sulfuric Acid Medium by Primary Amine N1923 Diluted in Toluene. Hydrometallurgy 2014, 147−148, 170−177. (2) Oertel, C. G.; Huensche, I.; Skrotzki, W.; Knabl, W.; Lorich, A.; Resch, J. Plastic Anisotropy of Straight and Cross Rolled Molybdenum Sheets. Mater. Sci. Eng., A 2008, 483−484, 79−83. 1437


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Industrial & Engineering Chemistry Research (27) Xu, W. F. Thermodynamic Study on the Tungsten Extraction by Primary Amine and Aqueous Solution of Tungsten and Molybdenum. Master Degree Dissertation, Tianjin University, Tianjin, China, 2014. (28) Kim, H. T.; Frederick, W. J. Evaluation of Pitzer Ion Interaction Parameters of Aqueous Electrolytes at 25°C. 1. Single Salt Parameters. J. Chem. Eng. Data 1988, 33, 177−184. (29) Goldberg, R. N. Evaluated Activity and Osmotic Coefficients for Aqueous Solutions: Thirty-Six Uni-Bivalent Electrolytes. J. Phys. Chem. Ref. Data 1981, 10, 671−764. (30) Zhang, X. L. Complex Compound Chemistry; Metallurgical Industry Press: Beijing, 1979.

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Measurement and Modeling for Molybdenum Extraction from the

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