Measurement and Modeling of the Solubility of NH4VO3 in the

Article pubs.acs.org/jced

Measurement and Modeling of the Solubility of NH4VO3 in the Na2HPO4−H2O and (NH4)2HPO4−H2O Systems Xuli Gong,†,‡,§ Pengge Ning,*,†,‡ Hongbin Cao,†,‡ and Changqiao Zhang§ †

Research Centre for Process Pollution Control, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China § School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, China ABSTRACT: The solubilities of ammonium metavanadate (NH4VO3) in (NH4)2HPO4−H2O and Na2HPO4−H2O systems were measured in the temperature range from 298.15 to 338.15 K by the isothermal dissolution method. The experimental data indicate that the solubility of NH4VO3 increases with the addition of Na2HPO4, while it first decreases and then increases with the addition of (NH4)2HPO4. The common ion effect and chemical equilibrium were used to explain the solubility tendencies. Two models, the Bromley−Zemaitis model and Pitzer model, were selected to correlate the solubilities of NH4VO3 in the above systems. The parameters of the new model referring to four ion−ion pairs and one ion−molecule pair were obtained via the regression of the experimental data, and the results agreed well with the experimental values. The new chemical model was then applied to analyze the main vanadium-bearing species distribution in the systems mentioned above. All of this work will develop the thermodynamics for an industrial application in the precipitation of NH4VO3.

1. INTRODUCTION Vanadium is a significant national strategic resource with properties such as high tensile strength, hardness, high melting point, fatigue resistance, and good corrosion resistance to acids and alkalis. Therefore, it can be widely used in the steel industry, car manufacture, aerospace, the electronics industry, the ceramic industry, and the nuclear industry.1−4 Since vanadium occurs in combination with various minerals, it is necessary to pay attention to the separation and purification processes.1 Ion exchange, chemical precipitation, and solvent extraction have been used to separate and recover vanadium from vanadium-bearing resources. Solvent extraction is a widely used method with the advantage of high separation efficiency, low cost, and high recovery.5−9 The solvent extraction process includes three main stages: extraction, stripping, and precipitation. The vanadium is enriched in the vanadium-containing aqueous solution after extraction and stripping and then is transformed as ammonium metavanadate (NH4VO3) in the precipitation step. However, the vanadium-enriched solution usually contains impurities such as HPO4−, SO42−, Cl−, NH4+, Na+, etc., which affect the purity of the products of vanadium. Thus, it is quite worth studying and developing the precipitation process.7,10,11 The solubility and phase equilibrium of NH4VO3 in electrolyte aqueous solutions are significant for the development, optimization, and operation of the precipitation process. In order to understand better the precipitation behavior in the vanadium-containing solution, it is necessary to have further studies of the solubility of NH4VO3 in salt solutions. There © 2015 American Chemical Society

have been several investigations of the solubility of NH4VO3 in different systems. Trypuć and co-workers reported the solubilities of NH4VO3 in the NaVO3−H2O,12 NH3−H2O,13 KVO3−H2O,14 NH4HCO3−H2O,15 NaVO3−NH3−H2O,16 and CO(NH2)2−H2O17 systems over the temperature range from 293 to 323 K. Liu and co-workers10 measured the solubilities of NH 4 VO 3 in the (NH 4 ) 2 SO 4 −H 2 O, NH 4 Cl−H 2 O, and (NH4)2SO4−NH3−H2O systems and correlated the experimental data using the Bromley−Zemaitis model and the Pitzer model. Trypuć and co-workers also investigated the mutual solubility in the NH4+−VO3−−NO3−−H2O,18 NH4+−Na+− VO3−Cl−−H2O,19 and NH4+−Na+−VO3−−NO3−−H2O20,21 systems and made phase diagrams. The hydrogen phosphate salt that usually exists in vanadium-bearing solutions also affects the purity of NH4VO3 in the precipitation process. However, solubility data for NH4VO3 in the (NH4)2HPO4−H2O and Na2HPO4−H2O systems and their thermodynamic model have not been reported. The present work focuses on a systematic determination of the solubilities of NH4VO3 in the (NH4)2HPO4−H2O and Na2HPO4−H2O systems. The Bromley−Zemaitis model and Pitzer equation were used to model the solubilities of NH4VO3 in the above systems. New model parameters were obtained by regression of the experimental solubility data. With the new Received: September 12, 2015 Accepted: December 7, 2015 Published: December 21, 2015 628

DOI: 10.1021/acs.jced.5b00780 J. Chem. Eng. Data 2016, 61, 628−635

Journal of Chemical & Engineering Data

Article

and then subjected to X-ray diffraction (XRD) analysis (Empyrean, PANalytical B.V., Holland) to prove that the solid phase was not altered by phase transformation. All of the experiments were repeated three times to reduce the errors. The experimental values reported are the averages of the replicates. 2.3. Determination of the Experimental Conditions. To determine the appropriate equilibrium time, the solubilities of NH4VO3 in the Na2HPO4−H2O and (NH4)2HPO4−H2O systems at 298.15 K were investigated and analyzed by ICPOES. Figure 1 shows the solubilities of NH4VO3 in 0.30 mol·

parameters, a chemical model was established and then applied to analyze the speciation distribution in the above two systems.

2. EXPERIMENTAL SECTION 2.1. Materials. NH4VO3 with a mass-fraction purity higher than 0.99 was purchased from Xilong Chemical Company (Guangdong, China). The general properties, sources, and mass-fraction purities for all of the reagents used in this work are listed in Table 1. All of the materials were of high purity and Table 1. Sources and Mass-Fraction Purities of the Materials Used in the Experiment material

mass fraction purity declared by supplier

NH4VO3

≥0.99

(NH4)2HPO4

≥0.99

Na2HPO4

≥0.99

source Xilong Chemical Co., Ltd. (China) Sinopharm Chemical Reagent Co., Ltd. (China) Sinopharm Chemical Reagent Co., Ltd. (China)

purification method none none none

were used without further purification. The water used in this work was doubly distilled water with specific conductivity of less than 0.1 μS·cm−1. 2.2. Experimental Method. The solubilities of NH4VO3 in the (NH4)2HPO4−H2O and Na2HPO4−H2O systems were measured from 298.15 to 338.15 K at atmospheric pressure using the isothermal dissolution method, which is described by Tian et al.22 The contents of vanadium and phosphorus were analyzed by inductively coupled plasma optical emission spectroscopy (ICP-OES) on a Thermo Scientific iCAP 6300 spectrometer; the correlation accuracy of the standard curve exceeded 99.99% at the wavelengths of 309.311 and 214.914 nm. The procedure is given as follows. A 250 mL jacketed glass vessel connected to a thermostat (SDC-6, SCIENTZ, China) was used in this work. Distilled water of known mass was added to the vessel, followed by the addition of a certain mass of (NH4)2HPO4 or Na2HPO4 known with a precision of ±0.001 g. Then an excess amount of NH4VO3 was added into the vessel, and a magnetic stirring bar was provided to afford vigorous agitation. The vessel was closed with ground stoppers. The temperature was measured simultaneously with a mercury thermometer. The variation of the system temperature was estimated to be within ±0.1 K. Continuous stirring lasted several hours for the NH 4 VO 3 −Na 2 HPO 4 −H 2 O and NH4VO3−(NH4)2HPO4−H2O systems to reach equilibrium. After the solid−liquid equilibrium was achieved, stirring was stopped to permit NH4VO3 to settle. The supernatant solution was withdrawn and immediately filtered using a syringe with a 0.2 μm membrane filter. The clear filtrate was immediately diluted with doubly distilled water into a 100 mL volumetric flask, and then the vanadium and phosphorus contents of the diluted solution were measured. The molar solubilities (in units of mol·L−1) were obtained according to the law of conservation of mass with a relative deviation of 1.48%. To get the molal solubilities (in units of mol·kg−1 in water), the molar solubilities obtained from the vanadium and phosphorus analyses were converted using the water density at the operating temperature with a relative deviation of 1.26%. The relative standard uncertainty in the molality was 0.0274. The equilibrated NH4VO3 in solution was filtered, dried at 333.15 K for 24 h,

Figure 1. Effect of equilibrium time on the solubilities of NH4VO3 in salt solutions at 298.15 K: ■, solubility in 0.30 mol·kg−1 Na2HPO4 solution; ●, solubility in 0.30 mol·kg−1 (NH4)2HPO4 solution.

kg−1 Na2HPO4 and in 0.30 mol·kg−1 (NH4)2HPO4 at different times. It can be seen in Figure 1 that the solubility equilibrium between the solid and liquid was established within 0.5 h for the above systems. In the experimental work, a longer time of 4 h for the Na2HPO4−H2O and (NH4)2HPO4−H2O systems was applied. The solubility of NH4VO3 in pure water has been measured by many authors. Similar experiments were carried out in this work to verify the accuracy and reproducibility of the adopted procedure. The average relative deviation (ARD) was calculated using eq 1: n

ARD =

⎛1⎞ x exp − x lit ⎜ ⎟ ∑ ⎝n⎠ x exp i=1

(1) exp

lit

where n is the number of data points and x and x are the experimental and literature values of the solubility, respectively. As shown in Figure 2, the experimental solubilities of NH4VO3 in water from 298.15 to 343.15 K agree well with the data reported in refs 10 and 23, with average relative deviations of 3.23% and 4.39%, respectively. This indicates that the procedure is acceptable. The precipitated solids that were dried at 333.15 K for 24 h were subjected to XRD. Figure 3 proves that NH4VO3 is stable in the solid.

3. SOLUBILITY DISCUSSION 3.1. Solubilities of NH4VO3 in the Na2HPO4−H2O and (NH4)2HPO4−H2O Systems. The solubility results for NH4VO3 in the Na2HPO4−H2O and (NH4)2HPO4−H2O systems from 298.15 to 338.15 K are presented in Tables 2 and 3 and plotted in Figures 4 and 5. As can be observed in Figure 4, the experimental solubility of NH4VO3 in the Na2HPO4− 629



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temperature. In the (NH4)2HPO4 molality range from 0.0 to 1.2 mol·kg−1 there exists the lowest solubility of NH4VO3 at each temperature. 3.2. Chemical Equilibria of NH 4 VO 3 in the (NH4)2HPO4−H2O and Na2HPO4−H2O Systems. For the NH4VO3−(NH4)2HPO4−H2O and NH4VO3−Na2HPO4− H2O systems, there exist many species, including NH4+, H2VO4−, Na+, HPO42−, HVO42−, H2PO4−, and H3VO4(aq), and various chemical equilibria among them. Table 4 lists species and their dissociation reactions related to this system. The dissolution reaction of NH4VO3 can be expressed as NH4VO3 (s) + H 2O ⇄ NH4 + + H 2VO4 − Figure 2. Solubilities of NH4VO3 in pure water: black ■, the experimental data; blue ▲, data from ref 10; red ●, data from ref 23.

(R1)

The solubility product constant of NH4VO3 corresponding to reaction R1 is designated as KSP and can be expressed as K sp =

m NH4+γNH +m H2VO4−γH VO − 4

2

4

a H 2O

(2)

where mi is the molality and γi the activity coefficient of ion i and aH2O denotes the activity of water. In order to calculate the solubility of NH4VO3, the KSP value for NH4VO3 is needed. One method to calculate an equilibrium constant (K) is to use the standard thermodynamic relationship ln K = −

Δ r G° RT

(3)

in which ΔrG° is the standard-state reaction Gibbs free energy, R is the gas constant, and T is the absolute temperature. Another method to calculate the K is to use an empirical equation. The empirical expression for the KSP of NH4VO3 used in Liu’s work,10,24 which was adopted in our OLI Databank, is as follows: Figure 3. XRD pattern of the precipitated NH4VO3.

log10 KSP = − 9.50788 −

H2O system increases with increasing Na2HPO4 (0.0 to 0.9 mol·kg−1) and temperature (298.15 to 338.15 K). Figure 5 shows that the solubility of NH4VO3 in the (NH4)2HPO4− H2O system also increases with increasing temperature. It is clear that the solubility of NH4VO3 first decreases sharply and then increases slightly with increasing (NH4)2HPO4 at each

896.31564 + 0.04142T T

− 0.0000279194T 2

(4)

in which T is the absolute temperature. It can be observed from Figure 6that the KSP value calculated from eq 4 increases with increasing temperature, as expected since the dissolution reaction is endothermic.

Table 2. Molal Solubilities of NH4VO3 (m1) in the Na2HPO4−H2O System at T = 298.15 to 338.15 K under a Pressure of 0.1 MPa at Various Molal Concentrations of Na2HPO4 (m2)a T = 298.15 K −1

T = 308.15 K −1

T = 318.15 K −1

−1

T = 328.15 K −1

−1

T = 338.15 K

m2/(mol·kg )

m1/(mol·kg )

m2/(mol·kg )

m1/(mol·kg )

m2/(mol·kg )

m1/(mol·kg )

m2/(mol·kg )

m1/(mol·kg )

m2/(mol·kg−1)

m1/(mol·kg−1)

0 0.0831 0.1747 0.2839 0.3839 0.4808 0.5695 0.6229 0.6961 0.7891 0.8208 0.8647 0.8857

0.0585 0.0985 0.1351 0.1768 0.2099 0.2441 0.2640 0.2737 0.2954 0.3234 0.3345 0.3434 0.3492

0 0.0874 0.1954 0.2848 0.3838 0.4769 0.5428 0.6320 0.6875 0.7486 0.8519 0.9222

0.0933 0.1375 0.2002 0.2421 0.2774 0.3109 0.3338 0.3655 0.3776 0.4060 0.4373 0.4654

0 0.0931 0.1914 0.2801 0.3559 0.4660 0.5284 0.6211 0.6705 0.7732 0.8299 0.8896

0.1322 0.1974 0.2488 0.2977 0.3469 0.3906 0.4128 0.4690 0.4896 0.5494 0.5669 0.5920

0 0.0821 0.1781 0.2820 0.4024 0.5165 0.5694 0.6503 0.6903 0.7960 0.9121

0.1774 0.2580 0.3291 0.4016 0.4747 0.5377 0.5653 0.5990 0.6357 0.6953 0.7698

0 0.0838 0.1895 0.3100 0.3899 0.4667 0.5875 0.6804 0.7442 0.8495

0.2354 0.3440 0.4397 0.5491 0.6129 0.6771 0.7895 0.8492 0.9025 0.9620

a

−1

−1

The standard uncertainties are u(T) = 0.1 K, ur(m) = 0.027, and u(p) = 0.3 kPa. 630



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Table 3. Molal Solubilities of NH4VO3 (m1) in the (NH4)2HPO4−H2O System at T = 298.15 to 338.15 K under a Pressure of 0.1 MPa at Various Molal Concentrations of (NH4)2HPO4 (m3)a T = 298.15 K −1

T = 308.15 K −1

T = 318.15 K −1

−1

T = 328.15 K −1

−1

T = 338.15 K

m3/(mol·kg )

m1/(mol·kg )

m3/(mol·kg )

m1/(mol·kg )

m3/(mol·kg )

m1/(mol·kg )

m3/(mol·kg )

m1/(mol·kg )

m3/(mol·kg−1)

m1/(mol·kg−1)

0 0.0136 0.0885 0.1914 0.5371 0.7949 0.8936 1.1769

0.0585 0.0306 0.0062 0.0045 0.0056 0.0080 0.0089 0.0119

0 0.0466 0.1025 0.1674 0.3639 0.5658 0.9014 1.1927

0.0933 0.0557 0.0159 0.0076 0.0083 0.0095 0.0135 0.0181

0 0.0151 0.0662 0.1009 0.1905 0.3642 0.5739 0.9307 1.2814

0.1322 0.0975 0.0551 0.0340 0.0178 0.0116 0.0134 0.0206 0.0297

0 0.0254 0.0254 0.1067 0.1888 0.3700 0.5410 0.5507 1.1307 1.2162

0.1774 0.1488 0.1364 0.0732 0.0411 0.0292 0.0284 0.0288 0.0401 0.0438

0 0.0237 0.0972 0.1928 0.3887 0.5555 0.8662 1.2152

0.2354 0.2036 0.1337 0.0845 0.0566 0.0486 0.0520 0.0665

a

−1

−1

The standard uncertainties are u(T) = 0.1 K, ur(m) = 0.0274, and u(p) = 0.3 kPa.

Table 4. Chemical Species and Their Dissociation Reactions for the NH4VO3−Na2HPO4−H2O and NH4VO3− (NH4)2HPO4−Na2HPO4−H2O Systems

Figure 4. Solubilities of NH4VO3 in the Na2HPO4−H2O system. Solid symbols are the experimental data; lines are the OLI calculations. Black ●, 298.15 K; red ▲, 308.15 K; blue ■, 318.15 K; magenta ★, 328.15 K; green ⬟, 338.15 K; blue □, predicted values at 308.15 K; blue +, predicted values at 328.15 K; red ○, experimental values to verify the predictions at 308.15 K; magenta ☆, experimental values to verify the predictions at 328.15 K.

species

dissociation reaction

H2O NH4VO3(s) Na2HPO4(s) (NH4)2HPO4(s) NH4+ H2VO4− HVO42− H3VO4(aq) HPO42− H2PO4− H3PO4(aq)

H2O ⇄ H+ + OH− NH4VO3(s) + H2O ⇄ NH4+ + H2VO4− Na2HPO4(s) ⇄ 2Na+ + HPO42− (NH4)2HPO4(s) ⇄ 2NH4+ + HPO42− NH4+ ⇄ NH3 + H+ H2VO4− ⇄ HVO42− + H+ HVO42− ⇄ VO43− + H+ H3VO4(aq) ⇄ H2VO4− + H+ HPO42− ⇄ PO43− + H+ H2PO4− ⇄ HPO42− + H+ H3PO4(aq) ⇄ H2PO4− + H+

Figure 6. Solubility product constant of NH4VO3 as a function of temperature.

can be calculated using eq 3, in which the standard-state reaction Gibbs free energy can be obtained using eq 5:

Figure 5. Solubilities of NH4VO3 in the (NH4)2HPO4−H2O system. Solid points are the experimental data; lines are the OLI calculations. Black ●, 298.15 K; red ▲, 308.15 K; blue ■, 318.15 K; magenta ★, 328.15 K; green ⬟, 338.15 K; blue □, predicted values at 308.15 K; blue +, predicted values at 328.15 K; red ○, experimental values to verify the predictions at 308.15 K; magenta ☆, experimental values to verify the predictions at 328.15 K.

Δr G° = Δf G°(products) − Δf G°(reactants)

(5)

in which ΔfG°(reactants) and ΔfG°(products) are the standardstate Gibbs free energies of formation for the reactants and products, respectively. Table 5 shows the standard-state Gibbs free energies of formation for some molecules and ions at 298.15 K. Table 6 lists standard-state reaction Gibbs free energies for various chemical equilibria calculated from these values using eq 5 and the corresponding values of K obtained from eq 3.

3.3. Discussion of the NH4VO3 Solubility. The chemical equilibrium constants K for various reactions can be used to explain the phenomena of the NH4VO3 solubility. The K value 631



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4. REGRESSION SECTION 4.1. Bromley−Zemaitis Model and Pitzer Model. It is evident from eq 2 that the determination of the solubility is associated with the relevant ionic activity coefficients. In previous research, the ionic activity coefficients were calculated using the Pitzer model or the Bromley−Zemaitis model.24,31 Li and co-workers calculated the ionic activity coefficients for the UO2Cl2−H2O32 and UO2(NO3)2−H2O33 systems at ambient temperature using the Pitzer model. The Bromley−Zemaitis model,34 which was introduced by Bromley and modified by Zemaitis, can be applied for electrolytes with molalities of up to 30 mol·kg−1 over the temperature range from 0 to 473.15 K. In OLI Platform 9.0,35,36 the Bromley−Zemaitis model is used to calculate ion−ion interactions while the Pitzer model is used to calculate molecule−molecule and molecule−ion interactions. Liu et al.10 and Zeng et al.37 used these models to correlate the solubilities of NH4VO3 and Na2SiO3·9H2O, respectively, in different systems. The NH4VO3−(NH4)2HPO4−H2O and NH4VO3−Na2HPO4−H2O systems contain ionic and neutral species, so the Bromley−Zemaitis model and the Pitzer model were adopted. The Bromley−Zemaitis equation for the activity coefficient of cation i can be described as follows:

Table 5. Relevant Standard-State Gibbs Free Energies of Formation at 298.15 Ka species H2VO4− HVO42− H3VO4(aq) HPO42− H2PO4− H3PO4 PO43− SO42− HSO4− NH4+ NH4VO3(s) H2O NH3(aq)

ΔfG°/(kJ·mol−1)

ref

−1021.5819 −975.5710 −1043.3975 −1089.9209 −1131.0804 −1143.5195 −1019.5303 −744.9929 −756.2978 −79.5112 −878.8467 −237.3601 −26.7257

25 25 25 26 26 27 26 26 26 26 28 29 30

a The standard states for solutes, solvents, and solids are 1 mol·kg−1, the pure liquid, and the pure solid, respectively, at 298.15 K.

Reaction R1 is the main reaction in the two researched systems. The K for this reaction is the solubility product constant (KSP) of NH4VO3, which is equal to 2.2562 × 10−3 at 298.15 K. In order to explain the solubility tendencies, it is necessary to compare the K values for some other reactions in the solid−liquid equilibrium systems. For the NH4VO3−Na2HPO4−H2O system, the solubility of NH4VO3 increases with increasing Na2HPO4. This phenomenon may be caused by reaction R3. As can be seen in Table 6, the value of K for this reaction is 0.1413, which is larger than the Ksp of NH4VO3. Therefore, reaction R3 can happen, and it causes the increase in the solubility of NH4VO3 with increasing Na2HPO4. In regard to the NH4VO3−(NH4)2HPO4−H2O system, the dissolution of (NH4)2HPO4 forms NH4+ ion. Therefore, the solubility of NH4VO3 initially decreases with increasing (NH4)2HPO4 as a result of the common ion effect. The subsequent increase in the solubility of NH4VO3 can be explained by reaction R3. In the above two researched systems, the solubility of NH4VO3 increases with increasing temperature. For the NH4VO3−(NH4)2SO4−H2O system,10 the solubility of NH4VO3 decreases with increasing (NH4)2SO4, which can be explained by the common ion effect. There is no increase in the solubility with continued increases in (NH4)2SO4. The reason for this is that the K values for reactions R5 and R8 are smaller than the KSP value of NH4VO3, and therefore, these reactions have little influence on the dissolution reaction of NH4VO3.

log γi = −

AZ i 2 I + 1+ I

⎡ 0.06 + 0.6B |Z Z | ij i j

∑⎢ j

⎢⎣ (1 + 1.5I /|Z iZj|)2

+ Bij + C ijI

⎤ ⎛ |Z | + |Z | ⎞ 2 i j + DijI 2 ⎥ × ⎜ ⎟ mj ⎥⎦ ⎝ 2 ⎠

(6)

where the sum over j runs over all of the anions in the solution; A is the Debye−Hückel parameter; I is the ionic strength of the solution; Bij, Cij, and Dij are temperature-dependent empirical coefficients; and Zi and Zj are the cation and anion charges, respectively. The coefficients Bij, Cij, and Dij can be expressed by eqs 7, 8, and 9, respectively: Bij = B1ij + B2ijT + B3ijT 2

(7)

C ij = C1ij + C2ijT + C3ijT 2

(8)

Dij = D1ij + D2ijT + D3ijT 2

(9)

where B1ij, B2ij, B3ij, C1ij, C2ij, C3ij, D1ij, D2ij, and D3ij are temperature-independent adjustable parameters. In the case of neutral species in aqueous solution, the expression proposed by Pitzer is applied to obtain the activity coefficient.10,31 The Pitzer model can be expressed as follows: ln γaq = 2βo(m − m)mm + 2βo(m − s)ms

(10)

Table 6. Standard-State Reaction Gibbs Free Energies and Corresponding Values of K for Various Reactions at 298.15 K ΔrG°/(kJ·mol−1)

reaction −

+ H2VO4 (R1) NH4VO3(s) + H2O ⇄ H2VO4− + H2PO4− ⇄ H3PO4 + HVO42− (R2) H2VO4− + HPO42− ⇄ H2PO4− + HVO42− (R3) H2VO4− + PO43− ⇄ HPO42− + HVO42− (R4) H2VO4− + SO42− ⇄ HSO4− + HVO42− (R5) H2VO4− + NH4+ ⇄ H3VO4 + NH3 (R6) HPO42− + NH4+ ⇄ H2PO4− + NH3 (R7) SO42− + NH4+ ⇄ HSO4− + NH3 (R8) NH4+

15.1137 33.5718 4.8514 −24.3797 34.7060 30.9699 11.6260 41.4806 632

K 2.2562 1.3126 0.1413 1.8680 8.3068 3.7498 9.1854 5.4014

× 10−3 × 10−6 × × × × ×

104 10−7 10−6 10−3 10−8



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Table 7. Newly Regressed Parameters for the Bromley−Zemaitis Model and the Pitzer Model Bromley−Zemaitis

Pitzer

interaction parameter

NH4 −H2VO4−

NH4+−HPO42−

B1 B2 B3 C1 C2 C3 D1 D2 D3

8.183098 −0.1400895 5.9667183 × 10−4 −2.784653 2.8697972 × 10−2 1.6555811 × 10−4 0.3025922 −1.1039595 × 10−4 −5.9241117 × 10−5

−1.990713 2.1590567 × 10−2 1.9439171 × 10−4 4.2894492 × 10−2 1.3565661 × 10−5 −1.4474614 × 10−4 9.4729506 × 10−4 8.4098216 × 10−4 1.0297288 × 10−6

+

interaction Na

−H2VO4−

+

−1.734773 −2.4151125 × 10−3 −7.4164463 × 10−4 0.8811208 1.0142114 × 10−2 3.5416249 × 10−4 −6.3649067 × 10−2 −3.3090052 × 10−3 −5.1301878 × 10−5

NH4+−H2PO4− 118.3438 −9.9093580 −2.0172984 −0.7731085 −2.4291774 −4.6117973 −4.7389571 −8.7181302 −1.8683934

× 10−2 × 10−3 × × × × ×

10−3 10−4 10−3 10−4 10−5

parameter

NH4+−H3VO4

B01 B02 B03 B11 B12 B13

2.107637 −0.1055455 1.5528931 × 10−3 −6.436872 5.3642924 × 10−2 −1.8309132 × 10−3

Figure 7. Speciation distributions of dominant “V”-bearing species as functions of temperature: (a) in pure water; (b) for a solution containing 0.5 M Na2HPO4; (c) for a solution containing 0.6 M (NH4)2HPO4.

where βo(m−m) and βo(m−s) are adjustable parameters for the molecule−molecule and molecule−ion interactions, respectively, and mm and ms denote the molalities of the neutral and ionic species, respectively. βo(m−m) and βo(m−s) are expressed as shown in eqs 11 and 12, respectively: βo(m − m) = B01ij + B02ijT + B03ijT 2

(11)

βo(m − s) = B11ij + B12ijT + B13ijT 2

(12)

9.0, the prediction values were not in agreement with the experimental data. Therefore, new model parameters had to be obtained by regression of the experimental data. 4.2. Model Parameters. To model the solubilities of NH4VO3 in the Na2HPO4−H2O and (NH4)2HPO4−H2O systems using the OLI platform, the parameters of the Bromley−Zemaitis model and the Pitzer model had to be determined by regression of the experimental data. As mentioned in Table 4, the main aqueous species in the systems are NH4+, Na+, H2VO4−, H3VO4, HPO42−, and H2PO4−. The main equilibrium condition is to calculate the values of γNH4+ and γH2VO4− from eq 2 to keep the value of KSP constant. For γNH4+, the NH4+−H2VO4−, NH4+−HPO42−, NH4+−H2PO4−, and NH4+−H3VO4 interaction terms should be considered, and for γH2VO4−, the NH4+−H2VO4− and Na+−H2VO4− interactions must be included. Thus, the Bromley−Zemaitis parameters for

In the OLI platform, the properties of the liquid phase are calculated from the above two activity coefficient models, which account for ion−ion, ion−molecule, and molecule−molecule interactions. In the regression, the parameters of the Bromley− Zemaitis model and the Pitzer model are determined by minimizing the sum of squared deviations between the experimental and correlated values. According to OLI Platform 633



Article

Figure 8. Speciation distributions of dominant “V”-bearing species at 318.15 K as a function of (a) the Na2HPO4 concentration and (b) the (NH4)2HPO4 concentration.

the NH4+−H2VO4−, NH4+−HPO42−, Na+−H2VO4−, and NH4+−H2PO4− interactions and the Pitzer parameters for the NH4+−H3VO4 interactions were chosen to be regressed. The newly obtained parameters are tabulated in Table 7. The newly correlated data are plotted in Figures 4 and 5, which show the good agreement between the calculated data and experimental data, with the average relative deviations of 7.56% and 11.67%, respectively. In Figures 4 and 5 some predicted solubility points are shown to be in good agreement with experimental values. 4.3. Application of the New Model Parameters. The newly obtained model parameters were applied to analyze the effect of temperature and the concentration of Na2HPO4 or (NH4)2HPO4 on the speciation distribution in the NH4VO3− Na2HPO4−H2O and NH4VO3−(NH4)2HPO4−H2O systems with OLI Analyzer Studio 9.0. Figure 7 reveals the relative concentrations of the dominant vanadium-bearing (“V”-bearing) species, namely, H2VO4−, H3VO4(aq), and HVO42−, as functions of temperature. It is obvious from Figure 7a,b that H2VO4− is the major “V”-bearing species in pure water and 0.5 M Na2HPO4 solution at the researched temperatures. Figure 7c shows the speciation distribution for the NH4VO3-saturated solution containing 0.6 M (NH4)2HPO4. The relative concentration of H2VO4− increases from 14.0% to 93.5% while the relative concentration of H3VO4(aq) decreases from 43.3% to 6.0% over the temperature range from 298.15 to 338.15 K. The relative concentration of H3VO4(aq) in the (NH4)2HPO4 system is higher than that in the Na2HPO4 system as a result of reaction R6. For HVO42−, the relative concentration decreases from 42.7% to 0.5% at the researched temperatures. The relative concentration of HVO42− is higher in the (NH4)2HPO4 system because of reactions R1, R3, R6, R7, and R2, whereas in the Na2HPO4 system this is due only to reactions R1, R3, and R2. However, the real concentrations of H3VO4 and HVO42− are very low in the (NH4)2HPO4−H2O system, even in the low temperature range. The effects of concentration on the speciation distributions for the NH 4 VO 3 −Na 2 HPO 4 −H 2 O and NH 4 VO 3 − (NH4)2HPO4−H2O systems at 318.15 K are plotted in Figure 8. Figure 8a shows that the relative concentration of H2VO4− increases slightly and then decreases slightly while the relative concentrations of H3VO4(aq) and HVO42− decrease slightly then increase slightly with increasing Na2HPO4 concentration. As can be seen in Figure 8b, the relative concentration of H2 VO4 − decreases and then increases with increasing

(NH4)2HPO4 concentration, while for H3VO4(aq) and HVO42− the contrary trend can be observed. The complexity of the curves in Figure 8b is due to the ionic activity coefficient, common ion effect, and reactions R1, R3, R6, R7, and R2, while in Figure 8a only the ionic activity efficient and reactions R1, R2, and R3 are involved. From Figures 7 and 8 it can be concluded that the dominant “V”-bearing species is H2VO4− in the solid−liquid phase equilibrium.

5. CONCLUSIONS The solubilities of NH4VO3 in the (NH4)2HPO4−H2O and Na2HPO4−H2O systems from 298.15 to 338.15 K have been measured by the isothermal dissolution method. In the Na2HPO4−H2O system, the solubility of NH4VO3 increases with increasing Na2HPO4. The chemical equilibrium H2VO4− + HPO42− ⇄ H2PO4− + HVO42− causes more NH4VO3 to be dissolved. For the (NH4)2HPO4−H2O system, the solubility of NH4VO3 decreases sharply and then increases slightly with increasing (NH4)2HPO4. This phenomenon can be explained by the common ion effect and the chemical equilibria H2VO4− + HPO42− ⇄ H2PO4− + HVO42− and H2VO4− + NH4+ ⇄ H3VO4 + NH3. The solubility of NH4VO3 increases with increasing temperature in both of the above systems. The Bromley−Zemaitis parameters for four ion−ion pairs and the Pitzer parameters for one molecule−ion pair were obtained by regression of the experimental data. The calculated results were in good agreement with the experimental data. Furthermore, speciation distributions for the NH4VO3−Na2HPO4−H2O and NH4VO3−(NH4)2HPO4−H2O systems have been calculated using the new model parameters with the aid of OLI Analyzer Studio 9.0. The results generated from this study may provide the thermodynamic basis for industrial applications to the precipitation step in solvent extraction of vanadium.

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AUTHOR INFORMATION

Corresponding Author

*Tel./fax: +86 1082544845. E-mail: [email protected]. Funding

Financial support from the National Natural Science Foundation of China (Grants 51178446 and 21202068) is acknowledged. Notes

The authors declare no competing financial interest. 634



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Measurement and Modeling of the Solubility of NH4VO3 in the

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