Solubility Isotherms of Gypsum, Hemihydrate, and Anhydrite in the

Article pubs.acs.org/jced

Solubility Isotherms of Gypsum, Hemihydrate, and Anhydrite in the Ternary Systems CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn) at T = 298.1 K to 373.1 K Wenlei Wang,†,‡ Dewen Zeng,*,‡ Hang Zhou,† Xiaofu Wu,† and Xia Yin§ †

Downloaded by UNIV OF NEBRASKA-LINCOLN on September 11, 2015 | http://pubs.acs.org Publication Date (Web): September 10, 2015 | doi: 10.1021/acs.jced.5b00454

College of Science, College of Environmental Science and Engineering, Central South University of Forestry and Technology, Changsha 410004, P. R. China ‡ College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, P. R. China § College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, P. R. China S Supporting Information *

ABSTRACT: The solubilities of anhydrite in the ternary systems CaSO4 + MSO4 + H2O (M = Co, Ni) were determined through isothermal solution saturation at 348.1 K and 363.1 K. At low bivalent metal sulfate concentrations, anhydrite solubility decreases until it eventually reaches a minimum. Anhydrite solubility subsequently increases with the amount of heavy metal sulfate to a maximum. At this point, further increases in the concentration of metal sulfate decreases the solubility of anhydrite until saturation of the added bivalent metal sulfate. A Pitzer thermodynamic model was selected to predict isopiestic data including calcium sulfate solubilities of the ternary systems CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn) from 298.1 K to 373.1 K. The functional dependencies of the MSO4 (M = Ni, Cu, Zn) ion interaction parameters with temperature were determined, and the third virial parameters were given. The calculated solubilities are in agreement with the available experimental data. Using the Pitzer model and parameters, the solubility isotherms of metastable solid-phase hemihydrate, as well as gypsum and anhydrite, in the CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn) systems were predicted over a wide range of temperatures and concentrations.

1. INTRODUCTION Calcium sulfate, with its high scaling potential, is one of the most common inorganic salts encountered in hydrometallurgical processes.1 Calcium sulfate exists as two different hydrates: gypsum (CaSO4·2H2O), hemihydrate (CaSO4·0.5H2O) and the anhydrous phase anhydrite (CaSO4). The stability regions of CaSO4 hydrates depend on the solution conditions. Each crystalline phase can be stable, metastable or unstable at a certain temperature and for a given solution composition. In water, gypsum is the stable phase at temperatures below 42 °C and above this temperature, calcium sulfate transforms into anhydrite; hemihydrate is metastable at all temperatures.2 To estimate the scaling potential of calcium sulfate in industrial processes that employ electrolytes, a complete understanding of the solubility of all three hydrates of calcium sulfate in MSO4 (M = Mn, Co, Ni, Cu, Zn) aqueous solutions is of practical importance. Previously, a considerable amount of experimental work has been conducted to study gypsum solubility under atmospheric pressure at 298.15 K in water or in MSO4 solutions (M = Mn, Co, Ni, Cu, Zn).3−10 Several experimental studies have also examined the solubility of gypsum and anhydrite in MSO4 (M = Mn, Ni, Cu, Zn) aqueous solutions at higher temperatures, as described in our previous work.11 However, the literature contained no data © XXXX American Chemical Society

for either anhydrite in NiSO4 and CoSO4 aqueous solutions or for hemihydrate in MSO4 (M = Mn, Co, Ni, Cu, Zn) aqueous solutions over a wide temperature range, particularly at elevated temperatures. Azimi4,10 applied a mixed solvent electrolyte (MSE) model to represent solubility of gypsum in NiSO4 and ZnSO4 aqueous solutions at different temperatures. This model is especially suitable to express molecule−molecule interactions mostly resulted from the multiple solvent components. For representation and prediction of solubility phase diagram of the single solvent systems CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn), a more concise Pitzer model may be sufficient. Therefore, we performed solubility determinations of anhydrite in solutions of CoSO4 and NiSO4 at 348.1 and 363.1 K. Additionally, a Pitzer thermodynamic model was selected to simulate the properties of the studied binary and ternary systems. The model was subsequently used to predict the solubility isotherms of gypsum, hemihydrate and anhydrite in the CaSO4+MSO4+H2O (M = Mn, Co, Ni, Cu, Zn) systems over a wide range of temperatures and concentrations. Received: June 3, 2015 Accepted: September 3, 2015

A

DOI: 10.1021/acs.jced.5b00454 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Descriptions of the Chemicals Used chemical name CaSO4 CoSO4·7H2O


NiSO4·6H2O

source

initial mass fraction purity

purification method

final purity

analysis method

not measured > 0.995

none recrystallization

> 0.999 > 0.999

titration and X-ray diffraction ICP-OES and X-ray diffraction

> 0.985

recrystallization

> 0.999

ICP-OES and X-ray diffraction

synthesis China National Pharmaceutical Industry Co., Ltd., China China National Pharmaceutical Industry Co., Ltd., China

2. EXPERIMENTAL SECTION 2.1. Materials and Apparatus. Table 1 shows the chemicals used in this work. Gypsum was first prepared by neutralizing calcium carbonate (purity in mass fraction >0.999, China National Pharmaceutical Industry Co. Ltd., China) with sulfuric acid (G. R.). The obtained gypsum sample was air-dried at room temperature for several days and verified by X-ray diffraction (XRD). Then, the sample was placed in an oven at 760 °C for 16 h and cooled in a desiccator to prepare the anhydrite. X-ray diffraction analysis indicated that the product consisted solely of anhydrite. The X-ray diffraction result of anhydrite prepared is in Figure 1. CoSO4·7H2O and NiSO4·6H2O were purified three

within the analytical error; these ions were not analyzed in the solutions after reaching equilibrium. The concentrations of CoSO4 or NiSO4 were calculated from the weighed amounts of metal sulfate hydrate and the deionized water. The equilibrium time is set to be 120 h. At the end of each experiment, the solution was kept unstirred for 8 h and then the sup-layer clear solution is taken out into a weighed vacuum tube and analyzed. 2.3. Accuracy Analysis. The temperature stability of the water bath reaches to within 0.05 K. The Ca2+ content was analyzed by ICP-OES as described in our previous work.12 The contents of heavy metal sulfate were determined by precipitating SO42− by BaCl2 solution. For Co and Ni, the relative standard uncertainty of the solubility measurement is 0.003. For calcium, the relative standard uncertainty of the solubility measurement is 0.02 for most measurements. 2.4. Experimental Results. The experimental solubility data of anhydrite in the ternary systems CaSO4 + CoSO4 + H2O and CaSO4 + NiSO4 + H2O at T = (348.1 and 363.1) K are tabulated in Table 2 and plotted in Figure 2b and c.

3. MODELING METHODOLOGY 3.1. Model Selection. Pitzer’s equations for most pure electrolytes are valid to a maximum of 6 mol/kg of H2O with the parameters initially reported by Pitzer and co-workers. Several publications12−15 have subsequently used the Pitzer model to account for the effect of metal sulfates on calcium sulfate solubility in multicomponent solutions over a wide temperature range. In this work, a molality-based Pitzer model, as summarized by Harvie,16 was used for modeling. 3.2. Chemical Equilibrium Relationships. Typically, the solid−liquid equilibrium constant K for this reaction eq 1 is expressed by eq 2. The solubility products of CaSO4 were taken from our previous work17

Figure 1. X-ray diffraction pattern of anhydrite prepared in this work.

times by crystallization with half salt recovery of the analytical grade reagent in each case (China National Pharmaceutical Industry Co., Ltd., China). The CoSO4 and NiSO4 stock aqueous solutions were prepared by the chemical agents mentioned previously. Solution compositions were determined by BaSO4 precipitation. Doubly distilled water (σ < 1.2 × 10−4 S·m−1) was used in the experiment. A thermostat (Lauda E219, Germany) with a temperature stability up to 0.05 K at higher temperatures was used for the equilibrium experiment. The equilibrium temperature was determined by a calibrated glass thermometer (Miller & Weber, Inc., U.S.A.) with standard uncertainty in temperature of 0.01 K. A Sartorius BS224S balance with an uncertainty of 0.1 mg was used for weighing. The Ca2+ analysis was performed by the standard addition method with an inductively coupled plasma optical emission spectrometer (ICP-OES) (5300DV, PerkinElmer, U.S.A.). The hydrate solid phase in equilibrium with solution was determined by an X-ray diffractometer (D/Max-2500, Rigaku, Japan). 2.2. Experimental Procedures. Solubility isotherm measurements were performed in a ground 150 cm3 Erlenmeyer flask immersed in a thermostatic glycol−water bath. Approximately 130 g of CoSO4 or NiSO4 aqueous stock solution was placed in the Erlenmeyer flask. Then, 5 g of anhydrite was added as the saturating solid phase. For some solutions, the change in heavy metal concentration resulting from the added anhydrite was

2+ 2− CaSO4 ·nH 2O(s) = Ca(aq) + SO4(aq) + nH 2O(aq)

(n = 0, 0.5, 2)

(1)

ln K CaSO4 ·nH2O(s) = ln aCa + ln aSO4 + n ln aW (n = 0, 0.5, 2)

(2)

3.3. Parameter Regression Method. To determine the model parameters of the MSO4 + H2O (M = Ca, Mn, Co, Ni, Cu, Zn) systems, water activity (or osmotic coefficient), mean ionic activity coefficients, enthalpies of dilution and solution, heat capacity of aqueous phase and solubility data were used. At 298.1 K, the Pitzer model parameter sets were derived from osmotic and activity coefficients.18,19 With the available experimental isopiestic data at higher temperatures, such as osmotic efficient and water activity, the parameter values for each system were determined by minimizing a weighted standard deviation of all data for the system. Agreements with isopiestic data were characterized by citing the standard deviation. For isopiestic data, B



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Table 2. Experimental Solubility Data of Anhydrite in CaSO4 + CoSO4 + H2O and CaSO4 + NiSO4 + H2O Systems at Temperature T = (348.1 and 363.1) K and Pressure p = 0.1 MPaa molality (mol/kg of H2O)


T = 348.1 K

molality (mol/kg of H2O) T = 363.1 K

solid phase

No. 1 2 3 4 5 6 7 8 9 10 11 12 13

CoSO4 0 0.02573 0.0463 0.0666 0.0812 0.1543 0.2501 0.5105 1.0078 1.5008 2.0067 2.5096 2.9883

CaSO4 0.00854 0.00712 0.00632 0.0063 0.00672 0.00689 0.00739 0.00882 0.01021 0.01005 0.01003 0.00934 0.00893

No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

NiSO4 0 0.02328 0.04515 0.0687 0.1137 0.1622 0.2309 0.4676 0.7235 1.0188 1.5092 2.1054 2.4059 2.4557 2.5022 3.2484 3.5994 4.2008

CaSO4 0.00854 0.00669 0.00632 0.00658 0.00702 0.00756 0.00808 0.00889 0.01015 0.01056 0.01053 0.01021 0.00927 0.00896 0.00907 0.00644 0.00572 0.00455

CaSO4 + CoSO4 + H2O No. CaSO4 1 CaSO4 2 CaSO4 3 CaSO4 4 CaSO4 5 CaSO4 6 CaSO4 7 CaSO4 8 CaSO4 9 CaSO4 10 CaSO4 11 CaSO4 CaSO4 CaSO4 + NiSO4 + H2O No. CaSO4 CaSO4 1 CaSO4 2 CaSO4 3 CaSO4 4 CaSO4 5 CaSO4 6 CaSO4 7 CaSO4 8 CaSO4 9 CaSO4 10 CaSO4 11 CaSO4 12 CaSO4 13 CaSO4 CaSO4 CaSO4 CaSO4

solid phase

CoSO4 0 0.1011 0.1556 0.2498 0.5087 0.751 1.0057 1.5082 2.0901 2.2458 2.7504

CaSO4 0.00614 0.00498 0.00537 0.00572 0.00616 0.00657 0.00783 0.00816 0.00865 0.00829 0.00773

CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4

NiSO4 0 0.1179 0.1724 0.2503 0.5129 0.7523 1.1058 1.5028 2.1341 2.2507 2.8305 3.2525 3.5071 3.8422

CaSO4 0.00614 0.00535 0.00573 0.00611 0.00675 0.00757 0.00822 0.0082 0.00888 0.00844 0.00778 0.00698 0.00665 0.00589

CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4 CaSO4

a

The standard uncertainty of the measurement temperature is u(T) = 0.05 K; standard uncertainty of the measurement pressure is u(p) = 0.005 MPa; relative standard uncertainty of the measurement of Co and Ni is ur(m(CoSO4)) = ur(m(NiSO4)) = 0.003; relative standard uncertainty of the solubility measurement is ur(m(CaSO4)) = 0.02.

interaction parameters for a 2:2 electrolyte through the following relation:

the standard deviation was given in terms of the water activity (αWexp − αWcalc). In previous reports,20−22 the limited high temperature data for osmotic and activity coefficients had resulted in the use of an ioninteraction type of equation that has subsequently been demonstrated to be successful for both pure and mixed electrolytes near room temperature. This model was extended to include wide temperature ranges, enthalpy and heat capacity. For the regression analysis, the reported heat capacity data (Cp) were first converted to apparent molal heat capacities (ϕCp) using the relation ϕ

Cp =

ϕ

o C p = Cp2 ̅ + ν|z Mz X|AJ

⎡ mνMz M ϕJ ⎤ × m⎢β (0)J + g (α1I 0.5)β (1)J + g (α2I 0.5)β (2)J + C ⎥ 2 |z Mz X|0.5 ⎣ ⎦

(4)

where, v = the total number of moles of ions per mole of salt (v = vM + vX), AJ = the temperature derivative of the Debye−Hückel parameter for the apparent molal enthalpy (AH) and C̅ op1 is the apparent molal heat capacity of the solute at infinite dilution. The term β(0)J was given by

o Cp − n1Cp1 ̅

n2

ln(1 + 1.2I 0.5) − 2νMνXRT 2 2.4

(3)

β (0)J =

where, n1 and n2 refer to the number of moles of solvent and solute, respectively, and C̅ op1 refers to the molal heat capacity of pure water. ϕCp values are related to the derivatives of the

d2β (0) 2 ⎛ dβ (0) ⎞ ⎜⎜ ⎟⎟ + T ⎝ dT ⎠ dT 2

(5)

ϕJ

and the terms β , β , and C are given by analogous expressions. This regression process resulted in two integration (1)J

C

(2)J




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Figure 2. Comparison of the calculated and experimental solubilities of gypsum (Gy) and anhydrite (An) in the system CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn) at various temperatures. (a) M = Mn; (b) M = Co; (c) M = Ni; (d) M = Cu; (e) M = Zn.

3.4. Model Parameter Determination. While the thermodynamic relationship between the partial molal enthalpy and temperature derivative of the activity coefficient is wellknown, it is convenient to use the same basic equation for both. At 298.1 K, Pitzer and Mayorga19 have reviewed the available water activity, osmotic efficient and enthalpy data for MSO4 (M = Mn, Co, Ni, Cu, Zn) and have determined that an adequate description of the data was obtained by regressing only the following parameters: β(0)M−SO4, β(1)M−SO4, β(2)M−SO4, and Cϕ. For the case of MnSO4, there were no available osmotic coefficient or water activity data below 0.1 mol/kg of H2O; hence, Pitzer and Mayorga19 has not given the β(2) MnSO4 value, which was set to be zero. In the case of CoSO4, where available osmotic coefficient or

constants for each parameter, one of which was the value at the reference temperature of 298.15 K, whereas the other must be evaluated through a regression analysis of the apparent molal enthalpy data (ϕL) for MSO4 solutions at some reference temperature. Apparent molal enthalpies were given by the Pitzer formulation through the following expression: ϕ

L = ν|z Mz X|AH

ln(1 + 1.2I 0.5) − 2νMνXRT 2m 2.4

⎡ mνMz M ϕL ⎤ ×⎢β (0)L + g (α1I 0.5)β (1)L + g (α2I 0.5)β (2)L + C ⎥ 2 |z Mz X|0.5 ⎣ ⎦ (6)

where, β(0)L, β(1)L, β(2)L, and CϕL were the first temperature integrals of β(0)J, β(1)J, β(2)J, and CϕJ, respectively. D




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Figure 3. Comparison of the calculated and experimental water activity data23−25 in the MSO4−H2O (M = Mn, Co, Ni, Cu, Zn) system at various temperatures. (a) M = Mn; (b) M = Co; (c) M = Ni; (d) M = Cu; (e) M = Zn.

to experimental data from the literature.23−25 For the system MSO4−H2O (M = Mn, Ni, Cu, Zn), the calculated results are in good agreement with the experimental data. The binary parameters for MSO4 (M = Mn, Ni, Cu, Zn) reported by Pitzer and Mayorga19 were also used in this work. For the CoSO4−H2O system, the calculated results are in good agreement with the experimental data from the literature23,24 for concentrations less than 1.0 mol/kg of H2O of CoSO4 aqueous solutions, but the results deviated at higher concentrations. Therefore, the third virial coefficient Cϕca was deemed necessary. To improve the

water activity data are limited to dilute solutions (below 0.1 mol/kg of H2O), the third virial coefficient was omitted, resulting in parameter sets of CoSO4 restricted to less than 0.1 mol/kg of H2O. These parameter sets for MSO4 (M = Ni, Cu, Zn), as determined by Pitzer and Mayorga,19 can be used for near-saturated concentrations. To test the reliability of these available binary parameters, the water activities of the systems MSO4−H2O (M = Mn, Co, Ni, Cu, Zn) were recalculated with the parameter sets from Pitzer and Mayorga.19 The calculated results are presented as solid lines in Figure 3 and are compared E



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Table 3. Binary Parameters of the Pitzer Model for MSO4 (M = Mn, Co, Ni, Cu, Zn) Pitzer interaction parameters


ion interactions Mn2+

SO42−

Co2+

SO42−

Ni2+

SO42−

Ni2+

SO42−

Cu2+

SO42−

Zn2+

SO42−

coefficients*

a1Lit

a2Lit

a2this work

β(0) ca β(1) ca β(2) ca Cϕca β(0) ca β(1) ca β(2) ca Cϕca β(0) ca β(1) ca β(2) ca Cϕca β(0) ca β(1) ca β(2) ca Cϕca β(0) ca β(1) ca β(2) ca Cϕca β(0) ca β(1) ca β(2) ca Cϕca

0.201 × 10−1a 2.980a 0a 1.82 × 10−2 a 0.20 × 10−1 a 2.70a −3.07 × 101 a 2.11 × 10−2 (this work) 1.594 × 10−1 c 2.926c −4.276 × 101 c 4.06 × 10−2 c 1.702 × 10−1 a 2.907a −4.006 × 101 a 3.66 × 10−2 a 2.358 × 10−1 a 2.485 a −4.735 × 101 a −1.2 × 10−3 a 1.949 × 10−1 a 2.883a −3.281 × 101 a 2.90 × 10−2 a

2.30 × 10−4b 2.513 × 10−2 b 4.497 × 10−1b −3.916 × 10−4 b

2.30 × 10−4 2.513 × 10−2 4.497 × 10−1 −3.916 × 10−4 2.072 × 10−4 2.99 × 10−2 4.506 × 10−1 2.115 × 10−4

6.17 × 10−4 c 1.38 × 10−2 c −3.34 × 10−1 c −2.61 × 10−4 c 2.1882 × 10−4d 2.208 × 10−2 d 4.713 × 10−1d −2.587 × 10−4d 6.17 × 10−4 b 1.38 × 10−2 b −3.34 × 10−1 b −2.61 × 10−4 b −3.66 × 10−3 b 2.33 × 10−2 b −3.33 × 10−1 b 3.97 × 10−3 b

2.1882 × 10−4 2.208 × 10−2 4.713 × 10−1 −2.587 × 10−4 2.01 × 10−4 1.508 × 10−2 3.33 × 10−1 1.0 × 10−4 1.877 × 10−4 3.11 × 10−2 −4.667 × 10−1 −3.601 × 10−4

a The parameter sets were determined by Pitzer and Mayorga.19 bThe parameter sets were determined by Silvester and Pitzer.26 cThe parameter sets were determined by Reardon.21 dthe parameter sets were determined by Holmes and Mesmer.27 *X(T/K) = a1 + a2(T/K − 298.15). The (1) (2) ϕ temperature dependency of the Pitzer parameters (X(T) = β(0) ca , βca , βca , and Cca) in activity coefficient equations was defined in this work.

experimental data at higher concentrations. Holmes and Mesmer27 have re-evaluated the parameters for NiSO4−H2O by regressing the water activity of the system at 383.15 K, and then derived the parameters with respect to temperature. Additionally, we calculated the water activity of the binary system; the results are presented as solid lines in Figure 3c and compared to the experimental data from Yang.25 The calculated results of Holmes and Mesmer27 are in good agreement with the experimental data. The binary parameters for NiSO4 reported by Holmes and Mesmer27 were used in this work. To simplify the fitting procedure, we refitted the parameters for MSO4 (M = Mn, Co, Cu, Zn) at 323.1 K by regressing the experimental water activity data from Yang25 and obtained the parameters as a function of temperature (see Table 3). As a demonstration of the consistency of the derived expressions for the MSO4 interaction parameters with respect to the thermodynamic data, a comparison of the measured activity coefficient data with the values calculated using the determined parameters is presented in Figure 3. The calculated water activity with the newly obtained parameter sets agreed well with the experimental data (See Figure 4). This demonstrated the reliability of this model, which enabled the newly obtained parameters to be extrapolated to 373.1 K. 3.5. Solubility Isotherms Prediction. The solubility of gypsum in the MSO4 (M = Mn, Co, Ni, Cu, Zn) aqueous solution at various temperatures was measured by several researchers.4,19 The solubility of anhydrite in the MSO4 (M = Mn, Cu, Zn) aqueous solution was measured at higher temperatures in our previous work.11 In this work, we continued to determine the anhydrite solubility in MSO4 (M = Co, Ni) at 348.1 K and 363.1 K. All of the experimental solubility data formed a basis for

application range of parameters, we re-evaluated these (1) (2) parameters for CoSO4. The values for β(0) ca , βca , and βca from 19 Pitzer and Mayorga were used in this work, whereas only Cϕca of their former set was adjusted. The comparison of the calculated and experimental water activity data in Figure 3b show the improvement in representing the activity coefficients with the parameters obtained in this study. The functional dependencies of the MSO4 (M = Cu, Zn) and NiSO4 ion interaction parameters with temperature were determined from an analysis of reported enthalpy and heat capacity data for relevant metal solutions by Silvester and Pitzer26 and Reardon,21 respectively (see Table 3). For the regression analysis, the reported heat capacity data (Cp) were first converted to apparent molal heat capacities. To obtain expressions for the (1) (2) ϕ variation of β(0) ca , βca , βca , and Cca with temperature, eq 3 through eq 6 must be integrated twice. This produced two integration constants for each parameter, one of which was the parameter value at the reference temperature of 298.1 K, whereas the other must be evaluated through a regression analysis of apparent molal enthalpy data for metal sulfate solutions at a reference temperature. Applying the reported temperature derivative of each parameter for MSO4 (M = Ni, Cu, Zn), we recalculated the water activity of the MSO4−H2O (M = Cu, Zn) system at 323.15 K and the NiSO4−H2O system at 323.15 K and 383.15 K. The calculated results are plotted as dashed lines in Figure 3. As described in Silvester’s work,26 the reported parameter sets can be used for concentrations less than 1.0 mol/kg of H2O, as demonstrated by the agreement between the calculated results and the experimental data reported by Yang25 (see Figures 3d and 3e). However, the calculated results strongly deviated from the F




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363.1 K, which were calculated by the ternary parameters, are presented as solid curves in Figure 2. At other temperatures, the solubility isotherms predicted by the binary and ternary parameters are in good agreement with the experimental solubility data in most cases (see the dash-dotted lines in Figure 2). The agreement between calculated results and experimental data for solubility in the ternary system shows the consistency of thermodynamic properties measured by different research groups and the reliability of the newly obtained binary and ternary parameters. As is well known, hemihydrate is metastable in aqueous solutions at various temperatures. It remains a difficult task to determine the solubility of hemihydrate accurately. In this work, the Pitzer model was used to predict the solubility of hemihydrate. Applying the binary and ternary parameters listed in Table 3 and Table 4, solubility isotherms of gypsum, hemihydrate and anhydrite in the ternary systems CaSO4−MSO4−H2O (M = Mn, Co, Ni, Cu, Zn) were predicted over a wide temperature range from 298.1 K to 373.1 K. As is illustrated in Figures S1−S3, Supporting Information, and Figure 5, the influences of M2+ (M = Mn, Co, Ni, Cu, Zn), MSO4 (M = Mn, Co, Ni, Cu, Zn) concentration, and temperature were very remarkable. For all ternary systems, the solubilities of gypsum, hemihydrate, and anhydrite decreased at low concentrations of bivalent metal sulfate until a minimum was reached, at which point the concentrations rose with increasing amounts of heavy metal sulfate to a maximum. Further increasing the metal sulfate concentration decreased the mineral solubility until saturation of the added bivalent metal sulfate was reached. From the diagrams, it can be observed that the influence of each M2+ was similar. No obvious difference could be observed on the influence of M2+ at lower concentrations. At higher concentrations, the difference became more pronounced with increasing temperatures. At 298.1 K, gypsum was the least soluble of the hydrates for a given metal sulfate concentration. At a higher temperature, the anhydrite solubility was the least. For all temperatures, the hemihydrate solubility was highest. A striking difference was that gypsum solubility increased with temperature, whereas hemihydrate solubility and anhydrite solubility decreased, (see Figure 6). The anhydrite solubility decreased in lower than about 3.5 mol/kg of H2O of MSO4 aqueous solutions but increased at higher concentrations. Additionally, the anhydrite solubility was much lower than that of gypsum and hemihydrate at higher temperatures.

Figure 4. Deviation plot for the water activity of the MSO4−H2O systems (M = Mn, Co, Ni, Cu, Zn) at 323.15 K. (αWexp − αWcalc) was calculated from the experimental water activity αWexp of MSO4 and from αWcalc values obtained with the Pitzer model and the parameter sets of this work: □, M = Mn; ○, M = Co; △, M = Ni; ◇, M = Cu; ☆, M = Zn.

determining the solubility phase diagram of the studied systems. To obtain a model that better represented the solubility isotherms of gypsum in the ternary systems CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn) at 298.15 K, the ternary parameters θCa−M and ψCa−M−SO4 (M = Cu, Zn, Ni) were introduced to fit the experimental data.15 Consequently, the calculated solid lines with the ternary parameters yielded a moderately better fit. Furthermore, we at first predicted the solubility isotherms of gypsum in the CaSO4 + CoSO4 + H2O system using only binary parameters(the third virial parameters θCa−Co and ψCa−Co−SO4 were set to zero), obtaining the predicted dash lines shown in Figure 2b, which are in good agreement with the experimental data. To simplify the fitting procedure and improve the prediction ability of the thermodynamic model, we evaluated the mixing parameters θCa−M and ψCa−M−SO4 for 363.1 K by regressing the solubilities of anhydrite in the system CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn) at 363.1 K. The obtained mixing parameters, along with the mixing parameters θCa−M and ψCa−M−SO4 for 298.1 K, are presented as a function of temperature and listed in Table 4. In the regression process, the third virial parameter ψCa−M−SO4 was found to be important for fitting the solubility data at higher concentrations. The solubility isotherms of gypsum at 298.1 K and anhydrite at

Table 4. Ternary Parameters of the Pitzer Model for the CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn) Systems Pitzer interaction parameters ion interactions

coefficients

a

a1

Cu Zn2+ Co2+ Ni2+ Mn2+ Cu2+

θcc′ θcc′ θcc′ θcc′ θcc′ ψSO42−

1.0 × 10 4.0 × 10−3

Ca2+

Zn2+

ψSO42−

−0.013

2+

2+

2+

Ni

ψSO4

Ca2+

Co2+

ψSO42−

2+

2+

Ca Ca

Mn

ψSO4

1.0 × 10−2

2−

resources

a2 −3

Ca Ca2+ Ca2+ Ca2+ Ca2+ Ca2+

2+

−3

2.462 × 10 2.525 × 10−4 1.938 × 10−3 1.938 × 10−3 8.092 × 10−4 −7.846 × 10−4

this work this work this work this work this work this work

8.6 × 10−4

this work

−8.01 × 10−4

this work

−1.301 × 10−3

this work

−4

2.03 × 10

2−

this work

X(T/K) = a1 + a2(T/K − 298.15). The temperature dependency of the Pitzer parameters (X(T) = θcc and ψSO4) in activity coefficient equations defined in this work. a

G




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Figure 5. Predicted solubility isotherms of gypsum, hemihydrate and anhydrite in the systems CaSO4−MSO4−H2O (M = Mn, Co, Ni, Cu, Zn): black, Mn; red, Co; blue, Ni; magenta, Cu; purple, Zn. (a) T = 298.1 K; (b) T = 323.1 K; (c) T = 348.1 K; (d) T = 373.1 K.

MSO4 concentrations possessed a similar effect on the solubilities of gypsum, hemihydrate, and anhydrite: hydrate solubilities decreased at low concentrations of bivalent metal sulfate until a minimum was reached. The solubilities subsequently increased with increasing amounts of heavy metal sulfate and eventually reached a maximum. With a further increase in metal sulfate concentration, the hydrate solubilities again decreased until a the added bivalent metal sulfate reached saturation. At low concentrations of hydrate, no obvious difference could be observed with respect to the influence of M2+ on the solubility of the three calcium sulfates. For higher concentrations, the difference became more obvious as the temperature increased. Gypsum was the stable solid phase at lower temperatures, whereas anhydrite was stable at higher temperatures. With increasing temperature, gypsum solubility increased over a wide metal sulfate concentration range; in contrast, hemihydrate solubility and anhydrite solubility decreased. At higher temperatures, the anhydrite solubility was considerably lower than that of gypsum and hemihydrate. This knowledge can be used to develop an economical and effective approach for avoiding calcium sulfate scaling in hydrometallurgical processes.

Figure 6. Predicted solubility isotherms of gypsum, hemihydrate, and anhydrite in 1.5 mol/kg of H2O of MnSO4 aqueous solution from 298.1 K to 373.1 K: , gypsum; ---, hemihydrate; ···, anhydrite.

4. CONCLUSIONS The solubilities of anhydrite were determined for the CaSO4 + MSO4 + H2O (M = Co, Ni) systems at 348.1 K and 363.1 K. On the basis of the temperature-dependent equation and the Pitzer thermodynamic model, the dissolution equilibrium for the ternary systems CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn) were predicted. The consistency between predicted values and available experimental data demonstrated the reliability of the Pitzer model-based temperature-dependent equations, as well as the sets of binary and ternary parameters that were determined. For all ternary systems mentioned, the influence of

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00454. Predicted solubility isotherms of gypsum, hemihydrate and anhydrite in the systems CaSO4 + MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn). (PDF) H



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(18) Pitzer, K. S.; Mayorga, G. Thermodynamics of Electrolytes. II. Activity and Osmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent. J. Phys. Chem. 1973, 77, 2300−2308. (19) Pitzer, K. S.; Mayorga, G. Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2−2 electrolytes. J. Solution Chem. 1974, 3, 539−546. (20) Silvester, L. F.; Pitzer, K. S. Thermodynamics of electrolytes. X. Enthalpy and the effect of temperature on the activity coefficients. J. Solution Chem. 1978, 7, 327−337. (21) Reardon, E. L. Ion interaction model applied to equilibria in the NiSO4−H2SO4−H2O system. J. Phys. Chem. 1989, 93, 4360−4363. (22) Alai, M.; Sutton, M.; Carroll, S. Evaporative evolution of a Na− Cl−NO3−K−Ca−SO4−Mg−Si brine at 95 °C: experiments and modeling relevant to Yucca Mountain, Neada. Geochem. Trans. 2005, 6, 31−45. (23) Robinson, R. A.; Stokes, R. H. Eletrolyte Solutions, 2nd ed., 5th Revised Impression; Butterworth: London, 1970. (24) Malatesta, F.; Zamboni, R. Activity and Osmotic coefficients from EMF of Liquid Membrane Cells. VI-ZnSO4, MgSO4, CaSO4, and SrSO4 in water at 25 °C. J. Solution Chem. 1997, 26, 791−815. (25) Yang, H. T.; Zeng, D. W.; Voigt, W.; Hefter, G.; Liu, S. J.; Chen, Q. Y. Isopiestic measurements on aqueous solutions of heavy metal sulfates: MSO4+H2O (M = Mn, Co, Ni, Cu, Zn). 1. T = 323.15 K. J. Chem. Eng. Data 2014, 59, 97−102. (26) Silvester, L. F.; Pitzer, K. S. Thermodynamics of electrolytes. X. Enthalpy and the effect of temperature on the activity coefficients. J. Solution Chem. 1978, 7, 327−337. (27) Holmes, H. F.; Mesmer, R. E. Isopiestic studies of aqueous solutions at elevated temperatures VII. MgSO4 and NiSO4. J. Chem. Thermodyn. 1983, 15, 709−719.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86 13618496806. Fax: +86 731 88879616. Funding

This work was financially supported by the Hunan Provincial Innovation Foundation for Postgraduates (CX2012B118), the National Nature Science Foundation of China (21176261) and the Youth Scientific Research Foundation of Central South University of Forestry and Technology (104|0329). Notes

The authors declare no competing financial interest.


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REFERENCES

(1) Azimi, G.; Papangelakis, V. G. Mechanism and kinetics of gypsumanhydrite transformation in aqueous electrolyte solutions. Hydrometallurgy 2011, 108, 122−129. (2) Freyer, D.; Voigt, W. Crystallization and phase stability of CaSO4 and CaSO4−based salts. Monatsh. Chem. 2003, 134, 693−719. (3) Power, W. H.; Fabuss, B. M. Transient solubilities in the calcium sulfate water system. J. Chem. Eng. Data 1964, 9, 437−442. (4) Azimi, G.; Papangelakis, V. G.; Dutrizac, J. E. Modelling of calcium sulphate solubility in concentrated multi-component sulphate solutions. Fluid Phase Equilib. 2007, 260, 300−315. (5) Dutrizac, J. E.; Kuiper, A. The solubility of calcium sulphate in simulated nickel sulphate-chloride processing solutions. Hydrometallurgy 2006, 82, 13−31. (6) Farrah, H. E.; Lawrance, G. A.; Wanless, E. J. Solubility of calcium sulfate salts in acidic manganese sulfate solutions from 30 to 105 °C. Hydrometallurgy 2007, 86, 13−21. (7) Wollmann, G.; Voigt, W. Solubility of gypsum in MSO4 solutions (M = Mg, Mn, Co, Ni, Cu, Zn) at 298.15 and 313.15 K. J. Chem. Eng. Data 2008, 53, 1375−1380. (8) Dutrizac, J. E.; Kuiper, A. The solubility of calcium sulphate in simulated copper sulphate electrorefining solutions. Hydrometallurgy 2008, 92, 54−68. (9) Campbell, A. N.; Yanick, N. S. The system NiSO4−CaSO4−H2O. Trans. Faraday Soc. 1932, 28, 657−661. (10) Azimi, G.; Papangelakis, V. G. Thermodynamic modeling and experimental measurement of calcium sulfate in complex aqueous solutions. Fluid Phase Equilib. 2010, 290, 88−94. (11) Zeng, D. W.; Wang, W. L. Solubility phenomena involving CaSO4 in hydrometallurgical process concerning heavy metals. Pure Appl. Chem. 2011, 83, 1045−106. (12) Wang, W. L.; Zeng, D. W.; Yin, X.; Chen, Q. Y. Prediction and measurement of gypsum solubility in the systems CaSO4+HMSO4+H2SO4+H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K. Ind. Eng. Chem. Res. 2012, 51, 5124−5134. (13) Zhelnin, B. I.; Gorshtein, G. I.; Bezprozvannaya, L Kh. Solubility of calcium sulfate dihydrate in manganese sulfate solutions. Zhur. Prikl. Khim. 1973, 46, 506−510. (14) Umetsu, Y.; Mutalala, B. K.; Tozawa, K. Solubility of CaSO4 in solutions of Zinc, Magnesium, Copper and Cobalt sulfates over a temperature range of 25 to 200 °C. J. Min. Metall. 1989, 6, 13−22. (15) Wang, W. L.; Zeng, D. W.; Wang, J. T.; Li, H. L.; Wu, L. C. Experimental determination and modeling of the solubility of CaSO4· 2H2O and CaSO4 in the quaternary system CaSO4+MgSO4+H2SO4+H2O. Ind. Eng. Chem. Res. 2014, 53, 12839− 12847. (16) Harvie, C. E.; Moller, N.; Weare, J. H. The prediction of mineral solubilities in natural waters: the Na−K−Mg−Ca−Cl−SO4−OH− HCO3−CO3−CO2−H2O system from zero to high concentration at 25 °C. Geochim. Cosmochim. Acta 1984, 48, 723−751. (17) Wang, W. L.; Zeng, D. W.; Chen, Q. Y. Experimental determination and modeling of gypsum and insoluble anhydrite solubility in the system CaSO4−H2SO4−H2O. Chem. Eng. Sci. 2013, 101, 120−129. I


Solubility Isotherms of Gypsum, Hemihydrate, and Anhydrite in the

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