SO32

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Solid−Liquid Equilibrium of the Quaternary System Ca2+, Mg2+// SO32−, SO42−-H2O at 298.15 K Xianze Meng,‡ Xiaozhen Wu,‡ and Junsheng Yuan*,†,‡ †

School of chemical engineering and materials, Quanzhou Normal University, Quanzhou 362000, China School of Chemical Engineering and Technology, Hebei University of Technology, Tianjin 300130, China

‡

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S Supporting Information *

ABSTRACT: Solid−liquid equilibria of the quaternary system (Ca2+, Mg2+//SO32−, SO42−-H2O) and its ternary systems (Ca2+//SO32−, SO42−-H2O; Mg2+//SO32−, SO42−H2O and Ca2+, Mg2+//SO32−-H2O) at 298.15 K were investigated via isothermal solution saturation method. Furthermore, the phase diagrams of these systems were constructed. The results show that the quaternary diagram contains three invariant points, seven univariant curves, and five crystallization fields corresponding to MgSO4·7H2O, MgSO3· 6H2O, CaSO3·0.5H2O, Ca(SO3)0.89(SO4)0.11·0.5H2O, and CaSO4·2H2O. The crystallization field of Ca(SO3)0.89(SO4)0.11·0.5H2O is the largest compared with the others. In addition, crystal complex Ca(SO3)0.89(SO4)0.11·0.5H2O also appears in the ternary system (Ca2+//SO32−, SO42−-H2O), which contains two invariant points, three invariant curves, and three crystallization fields. Both of the other two ternary diagrams contain one invariant point, two invariant curves, and two crystallization fields. The Pitzer model was applied to calculate salt solubilities, and the results agree well with the experimental data. Binary and ternary ionic interaction parameters (θSO4,SO3, ψMg,SO4,SO3, ψCa,SO4,SO3, and ψCa,Mg,SO3) and ion pair parameters (CaSO3 and MgSO3) are presented in this work based on the solubilities of these ternary systems.

1. INTRODUCTION Seawater flue gas desulfurization (SFGD) is the most widely used technology in coal-fired power plants for SO2 absorption due to its high removal rate, simple process, and environmental friendliness based on the acid−base buffering capacity of marine. During the SFGD process, sulfur oxides could be absorbed by seawater effectively and converted into insoluble calcium salts and magnesium salts after aeration oxidation.1 However, the traditional SFGD products, MgSO4 and CaSO4, are generally attached to the pipes and the inner walls of the desulfurization equipment, causing a serious scaling problem. Compared with MgSO4 and CaSO4, the solubilities of MgSO3 and CaSO3 are much lower, and more importantly, the latter salts are looser and easier to clean.2 Thus, without the aeration oxidation process in SFGD, calcium and magnesium ions in seawater will be significantly reduced after desulfurization treatment by inhibiting the oxidation of sulfite. In this case, the problems of scaling consumption in the desulfurization process will be solved. Solid−liquid phase equilibrium data of related systems are the foundation for overcoming the above issues. Since the wet-residue method for phase equilibrium research was put forward by Schreinermark in 1893, many works2−4 have been done in various water−salt systems. Stephen summarized the solubility data for calcium sulfate, calcium sulfite, magnesium sulfate, and magnesium sulfite in water at various temperatures.5 Wurz and Swoboda report the solubility of calcium sulfite in calcium sulfate solution at 293, 313, 333, and 353 K, but the existence of the crystal complex has not been mentioned.6 In our © XXXX American Chemical Society

previous study, the determination method of sulfate and sulfite in seawater by ion chromatography was established.7 This method is suitable for low concentration determination of sulfite and sulfate in seawater. Cameron has measured the phase equilibria of the ternary system Ca2+, Mg2+//SO42−-H2O at 298.15 K.8 Harvie has predicted the solubilities of the ternary system Ca2+, Mg2+//SO42−-H2O at 298.15 K using the widely recognized Pitzer model, and the predicted results are in excellent agreement with the experimental data.9 Numerical data has been reported for the ternary system Mg2+//SO32−, SO42−-H2O at 288, 308, 328, and 348 K.6 But there are no phase equilibrium data of the quaternary system Ca2+, Mg2+//SO32−, SO42−-H2O and its ternary systems Ca2+//SO32−, SO42−-H2O; Mg2+//SO32−, SO42−-H2O; and Ca2+, Mg2+//SO32−-H2O at 298.15 K so far. Moreover, the ion pair parameters and the ionic interaction parameters for salts are the necessary parameters for the theoretical prediction. Rosenblatt has calculated the ion pair parameters of CaSO3 and MgSO3 by analyzing those of other salts and obtained the interpolation and ion pair parameter through extrapolation estimation.10 However, the estimated parameters lack the support of experimental data; besides, the ionic interaction parameters and solubilities of relevant ternary systems have not been reported before. Received: May 11, 2018 Accepted: November 9, 2018

A

DOI: 10.1021/acs.jced.8b00385 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Descriptions of Chemical Samples Used in This Research chemical name

sourcea

initial mass fraction purity

purification method

final mass fraction purity

anlysis methodb

CaSO4·2H2O MgSO4·7H2O MgCl2·6H2O CaSO3 Na2SO3 MgSO3·6H2O

T.F.R. T.F.R. T.F.R. B.C. A.C. synthesis

0.99 0.99 0.99 0.98 0.98 0.98

recrystallization recrystallization recrystallization none recrystallization recrystallization

0.995 0.996 0.995 0.995 0.995

IC for SO42− IC for SO42− IC for Cl− IC for SO32− IC for SO32− IC for SO32−

a

T.F.R., Tianjin First Reagent Co., Ltd., China; B.C., Bellancom Chemistry Co., Ltd., China; A.C., Aladdin Chemistry Co., Ltd., China. bIC, ion chromatography.

originally prepared with one kind of excess salt and subsequently the second salt was added to it. Furthermore, the mixture of salts was dissolved by a quantitative water in a conical flask reactor and stirred continuously in a thermostatic bath until the solution components were constant, i.e., reaching thermodynamic equilibrium. Each sample was prepared by weighing 100 g of corresponding mixture in 150 mL of conical flask for solubility experiments. Additionally, the weights of the liquid phase and solid phase samples are measured by analytical balance. The experimental results showed that the ternary systems needed more than 10 h to reach equilibrium state, whereas the quaternary system needed 35 h. The data used to determine the equilibrium time of the quaternary system are listed in Table S1 in the Supporting Information. The solid−liquid phase was separated by filtration progress with 0.22 μm microporous membrane, and then analyzed, respectively. 2.3. Analytical Approach. The chemical analysis of ions in equilibrium liquid phase and wet residue were conducted with an ion chromatography system (ICS-1000, Thermo Fisher Scientific Dionex; ISO 7980:1986) and atomic absorption spectroscopy (TAS-990 super, Beijing Purkinje General Instrument Co., Ltd.).7,12,13 The detection limits and relative standards for calcium and magnesium are 0.02/0.002 mg/L and 0.05/−0.3%, while the detection limits for sulfite and sulfate are 0.03 mg/L and 0.04 mg/L with relative standard of 0.20− 2.07%. Before determining the compositions of the solid phase, the wet residue was completely dissolved in water. The water content was calculated by subtraction. The crystalline type of the wet residue was identified by X-ray diffraction (D8 Focus, Bruker Co.) and an FTIR spectrum (Nexus 470, Thermo Fisher Nicolet).14

In this work, the solubilities and phase diagrams of the quaternary system Ca2+, Mg2+//SO32−, SO42−-H2O and its ternary systems were investigated. The ion pair parameters and unknown ionic interaction parameters of the corresponding salts are presented based on experimental solubilities. On this basis, the predicted solubilities by the Pitzer model are presented. The research will provide the basic data for the improvement of SFGD.

2. EXPERIMENTAL SECTION 2.1. Reagents and Instruments. All the solid−liquid phase equilibrium and subsequent analysis experiments were prepared using ultrapure water with a resistivity greater than 18.2 MΩ·cm. The descriptions of these chemical samples are presented in Table 1. Besides, magnesium sulfite was synthesized before experiment because it is unavailable on the market. 11 Magnesium chloride solution and sodium sulfite solution were mixed at the same concentration. After rapid filtration, the solution was washed with anhydrous ethanol and then dried in a nitrogen atmosphere. The chemical component of synthesized sulfite was determined by XRD (Figure S1, Supporting Information). All the peaks of the as-prepared sample are indexed as MgSO3·6H2O, while no other forms of hydrate magnesium sulfite are found. A magnetic stirring thermostatic bath (HXC-500-8A, Beijing Fortunejoy Science Technology Co., Ltd.) was used in this study. As it is shown in Figure 1, the sealed conical flask reactors, with Teflon rotors inside, were filled with nitrogen to prevent the oxidation of sulfite.

3. RESULTS AND DISCUSSION 3.1. Solubilities and Phase Diagrams. 3.1.1. Ternary System Ca2+//SO32+, SO42−-H2O at 298.15 K. The experimental and calculated solubilities of the ternary system Ca2+//SO32−, SO42−-H2O are listed in Table 2. The relative deviation (RD) between experimental and calculation values is defined as follows: RD = (mexp − mcal )/mexp

(1)

where mexp and mcal represent experimental and calculation values, respectively. The phase diagram of the ternary system Ca2+//SO32−, SO42−-H2O is plotted in Figure 2. As shown in Figure 2, the phase diagram has two invariant points: point C corresponds to the compresence of salts CaSO3·0.5H2O (Csi) and Ca(SO3)0.89(SO4)0.11·0.5H2O (Cc) with saturated solution; point D corresponds to the compresence of salts Cc and CaSO4·2H2O (Gyp) with saturated solution. The ternary system consists of five crystallization fields and one unsaturated solution field: field

Figure 1. Magnetic stirring thermostatic bath.

2.2. Experimental Methods. The equilibria data of the quaternary system Ca2+, Mg2+//SO32−, SO42− -H2O and its ternary systems were measured by isothermal solid state method at 298.15 ± 0.05 K under atmospheric pressure. The quaternary system saturated solution was originally prepared with two kinds of excess salts, and then the third one was gradually added to the mixture, whereas the ternary system saturated solution was B



Article

Table 2. Experimental and Calculated Solubilities of the Ternary System Ca2+//SO32−, SO42−-H2O at 298.15 K and 0.1 MPaa composition of liquid phase mexp (×10−3 mol/kg) 2−

SO4

14.9634 14.9666 14.9503 13.2367 10.2642 9.3156 6.5119 4.0009 2.8534 2.1780 1.7487 0.4979 0.1320 0.0439 0.0000

mcal (×10−3 mol/kg) 2−

SO3

0.0000 0.0183 0.0250 0.0317 0.0358 0.0375 0.0442 0.0583 0.0749 0.0916 0.1082 0.2331 0.3662 0.3995 0.4162

2−

SO4

14.9994 14.9846 14.9773 13.2446 10.2972 9.3399 6.5354 4.0125 2.8583 2.1894 1.7559 0.4995 0.1322 0.0441 0.0000

composition of residue (wt %)

RD

SO3

CaSO4

CaSO3

CaSO4

equilibrium solid phaseb

0.0000 0.0183 0.0250 0.0317 0.0358 0.0375 0.0442 0.0583 0.0749 0.0916 0.1082 0.2331 0.3662 0.3995 0.4162

8.7103 9.0433 7.6690 9.7201 7.7599 10.1732 8.4434 10.0562 8.8993 46.3549 -

52.6634 61.8789 64.3541 54.4535 69.3043 55.2786 72.6044 60.2290 71.7796 63.5295 -

0.0024 0.0012 0.0018 0.0006 0.0032 0.0026 0.0036 0.0029 0.0017 0.0052 0.0041 0.0032 0.0018 0.0046 0.0000

Gyp Gyp Gyp, Cc Cc Cc Cc Cc Cc Cc Cc Cc Cc Cc, Csi Csi Csi

2−

a Standard uncertainties u are u(T) = 0.1 K; u(p) = 0.005 MPa; u(m) for SO42− and SO32− are 0.0005 mmol/kg and 0.0003 mmol/kg; u(wt %) for CaSO4 and CaSO3 are 0.005 and 0.003 in mass fraction. bCsi, CaSO3·0.5H2O; Gyp, CaSO4·2H2O; Cc, Ca(SO3)0.89(SO4)0.11·0.5H2O.

Figure 3. XRD spectrum of the crystal complex (a) and CaSO3·0.5H2O (b).

Gyp and Csi prepared by Setoyama’s method,10 and salt Csi. According to the figure, OH bond stretching vibration and water molecular deformation vibration are at 3400 and 1620 cm−1, respectively. The strong absorption peak in the region 1000− 950 cm−1 and the absorption peaks at 650, 520, and 500 cm−1 are characteristic peaks of sulfite ions. The 3600−3400 cm−1 and 1700−1620 cm−1 bands are deformation vibrations of water molecules. The strong and broad absorption peaks in the ranges 1150−1100 cm−1 and 670−600 cm−1 are triple degenerate vibrations of sulfate. The weak absorption peak at 1003 cm−1 represents fully symmetric telescopic vibration of sulfate. In addition, the absorption peak at 1100 cm−1 is split because of the influence of the crystal field or other ions on sulfate, indicating the formation of a sulfate-substituted crystal complex. Composition of the crystal complex is determined by the previous chemical method. Setoyama has confirmed that the substitution rate of sulfate changes with temperature.15 By the chemical method, the substitution rate was 11% at the temperature of 298.15 K.

Figure 2. Phase diagram of the ternary system Ca2+//SO32−, SO42−H2O at 298.15 K and 0.1 MPa.

WBDCA corresponds to unsaturated solution; field ACE corresponds to the salt Csi with saturated solution; field BDF corresponds to the salt Gyp with saturated solution; field CDG corresponds to the salt Cc with saturated solution; field CGE corresponds to the salt Csi and Cc with saturated solution; and field DFG corresponds to the salt Gyp and Cc with saturated solution. Figure 3 is the XRD spectrum for the wet residue of salts Cc and Csi. The results show that the crystal structures of the two salts are similar, while the characteristic peak of Cc shifted slightly to small angle. This shift may be the result of partial replacement of sulfite by sulfate, since the ionic radius of sulfate is greater than sulfite. Figure 4 represents the IR spectrum corresponding to salt Gyp and salt Cc obtained by this experiment, the mixture of salt C



Article

Figure 5. Phase diagram of the ternary system Mg2+//SO32−, SO42−H2O at 298.15 K and 0.1 MPa.

Figure 4. IR spectrum: salt CaSO4·2H2O (a), crystal complex (b), mixture of salt CaSO4·2H2O and CaSO3·0.5H2O (c), crystal complex prepared by the Setoyama method (d), and CaSO3·0.5H2O (e).

solution. The dissolvability of Eps in water is huge, so Eps has the smallest crystalline field. Figure 6 is the X-ray spectrogram of point C, which contrasted with the PDF-2004 standard cards using MDI-Jade software. Salts Msh and Eps coexist at the invariant point C. It demonstrates that no solid solution and crystal complex are found at 298.15 K for the ternary system. Figure 7 is the solubility data of MgSO3 in MgSO4 solutions at different temperatures.6 Comparing the solubility data of previous studies (288, 308, 328, and 348 K), the solubility trend of MgSO3 obtained from the experiment is similar. In the gradual increase of the MgSO4 concentration, the equilibrium concentration of MgSO3 increased at first and then decreased, and the equilibrium solid phase is the same as 288 and 308 K. When the temperature rises to 328 K, the equilibrium solid phase changes from MgSO3·6H2O to MgSO3·3H2O. It is

3.1.2. Ternary system Mg2+//SO32+, SO42−-H2O at 298.15 K. The experimental and calculated solubilities of the ternary system Mg2+//SO32−, SO42−-H2O are listed in Table 3. On the basis of the data in Table 3, the phase diagram is plotted in Figure 5. As the figure shows, the ternary system has an invariant point C, which corresponds to the compresence of salts MgSO3· 6H2O (Msh) and MgSO4·7H2O (Eps) with the saturated solution. There are one unsaturated field and three crystallization fields: field WBCA corresponds to the unsaturated solution; field ACD corresponds to the compresence of solids Eps with saturated solution; field BEC corresponds to the compresence of solids Msh with saturated solution; and field CED corresponds to the compresence of solids Msh and Eps with saturated

Table 3. Phase Equilibrium Data of Ternary System Mg2+//SO32−, SO42−-H2O at 298.15 K and 0.1 MPaa composition of liquid phase mexp (mol/kg)

mcal (mol/kg)


RD

SO32−

SO42−

SO32−

SO42−

MgSO3

MgSO4

SO42−


0.0000 0.0262 0.0464 0.0500 0.0539 0.0570 0.0593 0.0582 0.0542 0.0538 0.0539 0.0553 0.0625

3.0120 3.0095 2.9812 2.6054 2.1957 1.8319 1.1384 0.8308 0.3176 0.2119 0.1691 0.0838 0.0000

0.0000 0.0262 0.0464 0.0500 0.0539 0.0570 0.0593 0.0582 0.0542 0.0538 0.0539 0.0553 0.0625

3.0259 3.0164 3.0095 2.6370 2.2206 1.8343 1.1398 0.8330 0.3186 0.2142 0.1705 0.0844 0.0000

0.1154 15.1426 16.1577 20.1114 18.6748 20.6397 18.6752 14.7564 17.6992 16.2425 -

36.0152 16.5809 14.0913 10.7199 7.5104 5.2997 2.2948 1.7501 1.2832 0.6724 -

0.0046 0.0023 0.0094 0.0120 0.0112 0.0013 0.0012 0.0026 0.0030 0.0107 0.0084 0.0067 0.0000

Eps Eps Eps, Msh Msh Msh Msh Msh Msh Msh Msh Msh Msh Msh

a

Standard uncertainties u are u(T) = 0.1 K; u(p) = 0.005 MPa; u(m) for SO42− and SO32− are 0.0005 mol/kg and 0.0003 mol/kg; u(wt %) for MgSO4 and MgSO3 are 0.005 and 0.005 in mass fraction. bEps, MgSO4·7H2O; Msh, MgSO3·6H2O. D



Article

Figure 6. XRD spectrogram of the saturation point of the ternary system Mg2+//SO32−, SO42−-H2O at 298.15 K and 0.1 MPa.

Figure 8. Phase diagram of the ternary system Ca2+, Mg2+//SO32−-H2O at 298.15 K and 0.1 MPa.

noteworthy that the equilibrium concentration of MgSO3 is negatively correlated with low range MgSO4 at experimental temperature. There is no description of this change in former data, which might be related to the selection of saturation point. 3.1.3. Ternary system Ca2+, Mg2+//SO32−-H2O at 298.15 K. The experimental and calculated solubilities of ternary system Ca2+, Mg2+//SO32−-H2O are given in Table 4, and the phase diagram is plotted in Figure 8. As shown in Figure 8, the phase diagram consists of an invariant point C. Point C corresponds to the compresence of salt Msh and Csi with the saturated solution. There are three crystallization fields and an unsaturated field: field ACD corresponds to the compresence of solids Msh with saturated solution; field BEC corresponds to the compresence of solids Csi with saturated solution; field CED corresponds to the compresence of solids Msh and Csi with saturated solution; and field WBCA corresponds to unsaturated solution.

Figure 7. Solubility of magnesium sulfite in aqueous magnesium sulfate solutions.

Table 4. Phase Equilibrium Data of Ternary System Ca2+, Mg2+//SO32−-H2O at 298.15 K and 0.1 MPaa composition of liquid phase −3

mexp (×10

mol/kg)

mcal (×10−3 mol/kg)


RD

Ca2+

Mg2+

Ca2+

Mg2+

CaSO3

MgSO3

Mg2+


0.0000 0.0168 0.0319 0.0402 0.0567 0.1424 0.1849 0.2690 0.3132 0.3540 0.4747

61.8547 61.9673 62.1236 23.9271 10.4844 2.2134 1.4390 0.7262 0.5065 0.3443 0.0000

0.0000 0.0168 0.0319 0.0402 0.0567 0.1424 0.1849 0.2690 0.3132 0.3540 0.4747

62.4858 62.4859 62.4860 24.0111 10.5117 2.2232 1.4565 0.7282 0.5078 0.3449 0.0000

0.0001 41.7662 45.3981 44.4907 46.3068 33.5964 35.4126 39.9524 -

20.6974 0.1338 0.0543 0.0117 0.0074 0.0048 0.0032 0.0020 -

0.0101 0.0083 0.0058 0.0035 0.0026 0.0044 0.0120 0.0028 0.0025 0.0017 0.0000

Msh Msh Msh, Csi Csi Csi Csi Csi Csi Csi Csi Csi

a

Standard uncertainties u are u(T) = 0.1 K; u(p) = 0.005 MPa; u(m) for Ca2− and Mg2− are 0.0005 mmol/kg and 0.0003 mmol/kg; u(wt %) for CaSO3 and MgSO3 are 0.005 and 0.0002 in mass fraction. bMsh, MgSO3·6H2O; Csi, CaSO3·0.5H2O. E



Article

ELKJI is ascribed to the salt of Cc; and field AFLE is ascribed to the salt of Csi. In Figure 11, the XRD characterization corresponding to the invariant points J, K, and L are presented. The figure shows that salts Gyp + Cc + Eps coexist at the invariant point J, salts Cc + Eps + Msh coexist at the invariant point K, and salts Cc + Csi + Msh coexist at the invariant point L. 3.2. Calculation of Solubilities. Debye and Hü kel proposed an electrolyte solution theory for a single strong electrolyte dilute solution with a concentration of less than 0.1 mol/kg. Pitzer extended the scope of this theory to higher concentrations (5−6 mol/kg). Pitzer theory is a semiempirical thermodynamic model of electrolyte solution.19 The formula uses the ionic strength of the electrolyte solution as a bond to establish a mathematical relationship between the excess Gibbs free energy of the solution and the electrolyte activity coefficient and the solution permeability coefficient of the solution. The single electrolyte thermodynamic parameters and the mixed dielectric thermodynamic parameters are used to mix the electrolyte solution. The relationship between the thermodynamic parameters and the change in electrolyte ion concentration is precisely explained. Pitzer theory has become a widely used theoretical calculation model for electrolyte solutions. The small solubility of CaSO3 (0.0053 g/100g H2O) at 298.15 K determines that it should be viewed as a dilute solution in such condition. The activity coefficient was calculated with Debye−Hükel theory by the following equation.20

Figure 9. XRD spectrogram of the saturation point of the ternary system Ca2+, Mg2+//SO32−-H2O at 298.15 K and 0.1 MPa.

Figure 9 shows the X-ray spectrogram of point C, which contrasted with the PDF-2004 standard cards using MDI-Jade software. Salts Msh and Csi coexist at the invariant point C. It shows that no solid solution and crystal complex are found at 298.15 K for the ternary system. 3.1.4. Quaternary system Ca2+, Mg2+//SO32+, SO42−-H2O at 298.15 K. The experimental composition results of liquid phase and wet residue of the reciprocal quaternary system Ca2+, Mg2+//SO32−, SO42−-H2O are listed in Table 5. The phase diagram of the reciprocal quaternary system was plotted using the Jänecke index. The Jänecke indexes for ions are expressed in dry salt mole indexes, which were calculated using the following eqs 2−7.

lgγi = −AϕZi 2I1/2

where γ, Aφ, Z, and I correspond to ion activity coefficients, Debye−Hü kel coefficient for osmotic coefficient, charge number, and ionic strength. In addition, ionic interaction parameters and activity coefficients constants of MgSO3·6H2O are acquired by the regression of reliable solubility data. The activity coefficients9,19 of various solutes are calculated by the following eqs 9−19:

w(H 2O) = 100 − w(Ca 2 +) − w(Mg 2 +) − w(SO32 −) − w(SO24 −)

(2)

Jt = w(SO32 −)/80.0632 + w(SO24 −)/96.0626

(3)

J(Ca 2 +) = w(Ca 2 +)/(40.0780 × Jt )

(4)

2+

2+

J(Mg ) = w(Mg )/(24.3050 × Jt )

J(SO32 −) = w(SO32 −)/(80.0632 × Jt ) J(SO42 −) = w(SO42 −)/(96.0626 × Jt )

(8)

NA

ln γM = ZM 2F +

(5)

∑ mA(2BMA + ZCMA) ij

iA = 1

(6)

+

NA

j k

iC = 1

(7)

iA = 1

NC

NA − 1

z {

NA

mA m A′ψAA′M

iA = 1 j A′ = iA − 1

NA

∑ ∑ mC mACCA

+ |ZM|

Based on the Jänecke index in Table 5, the phase diagram of the reciprocal quaternary system Ca2+, Mg2+// SO32−, SO42−H2O is plotted in Figure 10. Points F, G, and H are the invariant points of the ternary systems (Ca2+, Mg2+//SO32−-H2O; Mg2+// SO32−, SO42−-H2O and Ca2+, Mg2+//SO42−-H2O) at 298.15 K, respectively. The ternary system Ca2+//SO32−, SO42−-H2O is a complex type phase diagram with two invariant points E and I. Point J corresponds to the existence of the solids of Gyp, Cc, and Eps with saturated solution; point K indicates the existence of solids of Cc, Msh, and Eps with saturated solution; and point L indicates the existence of solids of Cc, Csi, and Msh with saturated solution. The reciprocal quaternary system is divided by seven invariant curves into five crystallization fields. Field IJHD is ascribed to the salt of Gyp; field JKGCH is ascribed to the salt of Eps; field KLFBG is ascribed to the salt of Msh; field

yz

∑ mC jjjjj2ΦMC + ∑ mAψMCAzzzzz + ∑ ∑ NC

(9)

iC = 1 iA = 1

NA

∑ mC (2BCX

+ ZCCX ) +

iC = 1 NC − 1

+

ij

∑ ∑

j k

iA = 1

NC

NC

mC mC′ψCC′X + |ZX |

iC = 1 jC′ = iC − 1

yz

∑ mAjjjjj2ΦXA + ∑ mC ψXAC zzzzz

NC

ln γX = ZX 2F +

NC

iC = 1

z {

NA

∑ ∑ mC mACCA iC = 1 iA = 1

(10)

F = − Aϕ[I1/2/(1 + 1.2I1/2) + 2 ln (1 + 1.2I1/2)/1.2] NC

+

NC − 1

NA

iC = 1 iA = 1 NA − 1

+

mC mC′Φ′CC′

iC = 1 jC = iC + 1

NA

∑ ∑ iA = 1 jA = iA + 1

F

NC

′ ∑ ∑ mC mABCACA + ∑ ∑ mA m A′Φ′AA′

(11) DOI: 10.1021/acs.jced.8b00385 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 5. Phase Equilibrium Data of the Quaternary System Ca2+, Mg2+//SO32−, SO42−-H2O at 298.15 K and 0.1 MPaa composition of liquid phase (wt %) no.

Ca2+ (×10−3)

Mg2+

SO32−

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

1.9758 1.7123 1.3607 1.0942 0.7475 0.4240 0.1549 0.1513 0.1465 0.1478 0.1426 0.1496 0.1514 0.1526 0.1543 0.2167 0.2570 0.3111 0.5594 3.2315 3.2446 3.2969 3.2354 2.5320 0.0000 16.6800 16.4758 17.4988 57.3023 56.1498 54.4470 52.6911 52.4490 48.2602 47.4347 46.4258 42.3617 33.4556 29.0094 22.7239 59.1709

0.0000 0.0005 0.0013 0.0023 0.0041 0.0108 0.2009 0.1564 0.1583 0.1654 0.1690 0.1797 0.1832 0.1868 0.1939 0.2250 0.2791 0.3663 0.6154 3.9757 4.0755 4.3231 5.4258 5.4351 5.4466 5.4036 5.3977 5.3944 0.0052 0.0089 0.0152 0.0233 0.0311 1.6440 1.9603 2.2328 2.9626 3.8958 4.2903 4.8399 0.0000

0.0029 0.0038 0.0052 0.0072 0.0109 0.0265 0.4832 0.5155 0.4954 0.4926 0.4918 0.4888 0.4877 0.4870 0.4850 0.4776 0.4713 0.4644 0.4563 0.3708 0.3640 0.3452 0.2554 0.2652 0.2714 0.0405 0.0225 0.0000 0.0002 0.0002 0.0002 0.0003 0.0003 0.0107 0.0130 0.0151 0.0202 0.0276 0.0307 0.0356 0.0001

composition of wet residue (wt %)

Jänecke index

SO42−

Ca2+ (×10−3)

Mg2+

SO32−

SO42−

Mg2+

SO42−

H2O (×103)


0.0013 0.0015 0.0022 0.0031 0.0049 0.0119 0.2146 0.0000 0.0316 0.0630 0.0782 0.1241 0.1393 0.1544 0.1848 0.3168 0.5382 0.8913 1.8862 15.2763 15.6790 16.6803 21.1461 21.1695 21.2014 21.3485 21.3463 21.3627 0.1577 0.1695 0.1903 0.2180 0.2483 6.6005 7.8459 8.9180 11.7866 15.4448 16.9896 19.1409 0.1417

4.5471 5.0663 7.4175 11.7475 21.1626 0.4781 0.9018 1.4069 1.8176 1.6926 1.5957 2.0833 2.3705 2.4773 2.8219 2.9420 3.1334 3.5388 4.6857 5.0130 1.7293 1.6316 23.6803 21.4758 76.9471 77.2864 74.9684 76.2392 73.4490 54.2124 39.0634 33.9318 27.9681 26.9835 35.8172 25.3084 -

0.0003 0.0007 0.0004 0.0020 0.0094 0.3439 0.7693 1.3839 1.7765 1.3102 1.5091 1.6116 1.7321 1.7234 1.8460 2.1523 2.2181 3.9757 4.5807 4.9048 6.2593 6.1908 5.9947 6.1203 0.0044 0.0035 0.0097 0.0147 0.0146 0.0658 0.4574 0.7754 0.8385 0.8822 1.2600 1.0807 -

0.0045 0.0088 0.0109 0.0158 0.0207 0.9542 2.5190 4.5353 5.8269 4.2587 4.8771 5.2092 5.5816 5.6329 6.0392 6.9821 7.0258 9.9256 9.6292 10.0267 0.5627 0.8953 0.0166 0.0140 0.0005 0.0006 0.0008 0.0011 0.0015 0.0017 0.0589 0.1387 0.2409 0.2674 0.3279 0.3625 -

0.0068 0.0042 0.0064 0.0171 0.0630 0.2120 0.0124 0.0174 0.0164 0.0594 0.1013 0.1080 0.1368 0.0412 0.0378 0.1145 0.3219 3.7724 6.5156 7.3171 24.0041 23.3347 23.6690 24.1618 0.2011 0.1984 0.2169 0.2394 0.2317 0.3873 1.8261 2.9716 3.0837 3.2217 4.6595 3.8859 -

0.0000 33.9004 62.2848 79.4480 89.9174 97.6603 99.9531 99.9624 99.9599 99.9585 99.9580 99.9561 99.9557 99.9552 99.9541 99.9523 99.9506 99.9484 99.9448 99.9506 99.9516 99.9537 99.9638 99.9717 100.0000 99.8127 99.8147 99.8031 12.9646 20.6126 31.4893 42.0746 49.3720 98.2464 98.5501 98.7515 99.1381 99.4806 99.5906 99.7153 0.0000

23.0579 23.3999 23.8564 24.9795 26.5113 26.7780 26.8468 0.0000 4.7663 9.4066 11.4642 17.2259 19.0161 20.6721 23.8896 35.4356 48.6284 61.4354 77.4485 97.1631 97.2832 97.5705 98.5681 98.5155 98.4832 99.7723 99.8736 100.0000 99.8714 99.8670 99.8612 99.8543 99.8538 99.8054 99.8017 99.7973 99.7942 99.7852 99.7829 99.7768 99.8763

1666.2500 1377.1894 1033.6390 741.8923 490.1637 202.6370 11.0482 14.8114 14.5289 13.7992 13.4637 12.5477 12.2693 12.0043 11.5059 9.7291 7.6761 5.7186 3.2872 0.4106 0.3980 0.3693 0.2735 0.2729 0.2722 0.2738 0.2741 0.2743 45.2990 42.5420 38.3452 33.9199 30.0382 1.1067 0.9156 0.7937 0.5765 0.4165 0.3696 0.3168 49.6582

Cc, Csi Cc, Csi Cc, Csi Cc, Csi Cc, Csi Cc, Csi Cc, Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Cc, Msh Cc, Msh Cc, Msh Cc, Msh Cc, Msh Cc, Msh Cc, Msh Cc, Msh, Eps Eps, Msh Eps, Msh Cc, Eps, Gyp Eps, Gyp Eps, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp

Standard uncertainties are u(T) = 0.1 K; u(p) = 0.005 MPa; u(wt %) for Ca2+, Mg2+, SO32−, and SO42− of liquid phase are 0.003 × 10−3, 0.05 × 10−3, 0.003 × 10−3, and 0.2 × 10−3 in mass fraction, respectively; u(wt %) for Ca2+, Mg2+, SO32−, and SO42− of wet residue are 0.005 × 10−3, 0.03 × 10−3, 0.02 × 10−3, and 0.3 × 10−3 in mass fraction, respectively. bGyp, CaSO4·2H2O; Eps, MgSO4·7H2O; Csi, CaSO3·0.5H2O; Msh, MgSO3·6H2O; Cc, Ca(SO3)0.89(SO4)0.11·6H2O. a

ÅÄÅ o o o ÅÅÅÅ ϕ 3/2 ÅÅ− A I /(1 + 1.2I1/2) + 2 m o Å o o o ÅÅÅÇ n

−1l

yz ij ϕ − 1 = jjjj∑ mi zzzz z j { k i

yz z + ZCCA zzzz + z { NA − 1

+

NC − 1

NA ϕ mC mC′(ΦCC ′ +

iC = 1 jC′ = iC + 1

∑ mAψCC A) iA = 1

′

NC

NA

∑ ∑

similar definitions; F is the function of Debye−Hükel term and the derivatives of the second Viral coefficient to ionic strength; 55.51 refers to the molar amount of 1 kg of H2O; ψ is considered the ternary ion interaction parameters; and Φφ, Φ, and Φ′ correspond to second virial coefficients that are only related to ionic strength. The activity coefficients of water isare based on the osmotic coefficient φ by the following equation:

NA

iC = 1 iA = 1

NC

∑ ∑

iA = 1 j A′ = iA + 1

NC

ϕ ∑ ∑ mC mA(BCA

mA m A′(ΦϕAA′ +

∑ mC ψAA′C)]} iC = 1

(12)

ln αw = −ϕ ∑ (mi /55.51)

The activity coefficient of water is related to the osmotic coefficient and was obtained by the following equation. C/C′ and A/A′ are considered as cations and anions; mC and ZC refer to molality and charge number of cation C; anions also have

(13)

The unknown parameters noted above are acquired from the following equations: G



Article

Table 6. Activity Coefficients of Salts at 298.15 K and 0.1 MPa species and mineral semihydrated calcium sulfitea six-hydrated magnesium sulfitea gypsum16 epsomite17 solid solutiona a

activity coefficients

formula CaSO3·0.5H2O

0.1644 × 10−6

MgSO3·6H2O

0.1917 × 10−3

CaSO4·2H2O MgSO4·7H2O Ca(SO3)0.89(SO4)0.11·0.5H2O

0.2630 × 10−4 0.1320 × 10−1 0.1138 × 10−6

Experimental data.

Table 7. Pitzer Parameters of Calcium Sulfite and Magnesium Sulfite electrolyte CaSO3·0.5H2O CaSO3·0.5H2O18 MgSO3·6H2Oa MgSO3·6H2O18 CaSO4·2H2O19 MgSO4·7H2O19 a

a

Figure 10. Phase diagram of the quaternary system Ca2+, Mg2+//SO32−, SO42−-H2O at 298.15 K and 0.1 MPa.

β(1)

β(2)

CΦ

0.200 0.180 0.200 0.200 0.200 0.221

3.768 2.380 3.372 3.000 2.650 3.343

60.051 −61.300 −14.173 −41.000 −55.700 −37.230

0 0 0 0 0 0.025

Experimental data.

Z= ϕ CMX = CMX /(2|ZMZX |1/2 )

β(0)

∑ |Zi|mi

(15)

i

(14)

Bϕ = β (0) + β (1) exp( −1.4 I ) + β (2) exp(− 12 I ) (16)

Figure 11. XRD spectrogram of the three saturation points of the quaternary system Ca2+, Mg2+//SO32−, SO42−-H2O at 298.15 K and 0.1 MPa. H



Article

Table 8. Ionic Interaction Parameters Pitzer parameters values

θMg,Ca

θSO4,SO3

ψCa,Mg,SO3

ψCa,SO4,SO3

ψMg,SO4,SO3

ψCa,Mg,SO4

0.0071

0.0049

0.0240

0.0012

0.0020

0.0240

Table 9. Calculated and Experimental Results of Solubility for the Quaternary System Ca2+, Mg2+// SO32−, SO42−-H2O at 298.15 K and 0.1 MPaa composition of liquid phase −3

mexp (×10

mcal (×10−3 mol/100 g solution)

mol/100 g solution)

RD

no.

Ca2+

Mg2+

SO32−

SO42−

Ca2+

Mg2+

SO32−

SO42−

Ca2+

Mg2+

SO32−

SO42−

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0.0493 0.0427 0.0340 0.0273 0.0187 0.0106 0.0039 0.0038 0.0037 0.0037 0.0036 0.0037 0.0038 0.0038 0.0038 0.0054 0.0064 0.0078 0.0140 0.0806 0.0810 0.0823 0.0807

0 0.0206 0.0535 0.0946 0.1687 0.4444 8.2658 6.4349 6.5131 6.8052 6.9533 7.3935 7.5375 7.6857 7.9778 9.2574 11.4832 15.0710 25.3199 163.5754 167.6815 177.8688 223.2380

0.0362 0.0475 0.0649 0.0899 0.1361 0.3310 6.0352 6.4387 6.1876 6.1526 6.1426 6.1052 6.0914 6.0827 6.0577 5.9653 5.8866 5.8004 5.6992 4.6313 4.5464 4.3116 3.1900

0.0135 0.0156 0.0229 0.0323 0.0510 0.1239 2.2340 0.0000 0.3290 0.6558 0.8141 1.2919 1.4501 1.6073 1.9237 3.2978 5.6026 9.2783 19.6351 159.0244 163.2165 173.6399 220.1283

0.0485 0.0414 0.0330 0.0268 0.0181 0.0104 0.0038 0.0037 0.0036 0.0038 0.0036 0.0036 0.0037 0.0037 0.0037 0.0053 0.0065 0.0079 0.0143 0.0810 0.0897 0.0838 0.0804

0.0000 0.0204 0.0537 0.0910 0.1725 0.4502 8.3044 6.3027 6.3214 6.8347 6.9846 7.3200 7.3672 7.7238 7.8740 9.2227 11.5901 15.2121 25.7679 161.8779 168.2118 177.0158 223.6405

0.0363 0.0466 0.0645 0.0877 0.1388 0.3357 6.0765 6.3064 6.0035 6.1963 6.1873 6.0440 5.9294 6.1327 5.9642 5.9210 5.9519 5.8220 5.6215 4.7422 4.6592 4.3335 3.2457

0.0133 0.0152 0.0221 0.0301 0.0518 0.1249 2.2317 0.0000 0.3215 0.6422 0.8009 1.2796 1.4415 1.5948 1.9135 3.3069 5.6448 9.3980 20.1607 157.2167 163.6423 172.7661 220.4752

0.0172 0.0300 0.0309 0.0179 0.0321 0.0189 0.0256 0.0263 0.0270 0.0270 0.0000 0.0270 0.0263 0.0263 0.0316 0.0185 0.0156 0.0103 0.0243 0.0050 0.1074 0.0182 0.0037

0.0000 0.0107 0.0032 0.0381 0.0225 0.0131 0.0047 0.0205 0.0294 0.0043 0.0045 0.0099 0.0226 0.0050 0.0130 0.0038 0.0093 0.0094 0.0177 0.0104 0.0032 0.0048 0.0018

0.0030 0.0189 0.0059 0.0240 0.0198 0.0142 0.0068 0.0205 0.0298 0.0071 0.0073 0.0100 0.0266 0.0082 0.0154 0.0074 0.0111 0.0037 0.0136 0.0239 0.0248 0.0051 0.0174

0.0148 0.0256 0.0349 0.0690 0.0157 0.0081 0.0010 0.0000 0.0227 0.0208 0.0162 0.0095 0.0060 0.0078 0.0053 0.0028 0.0075 0.0129 0.0268 0.0114 0.0026 0.0050 0.0016

24 25 26

0.0632 0.0000 0.4162

223.6207 224.0938 222.3246

3.3124 3.3898 0.5059

220.3719 220.7040 222.2353

0.0643 0.0000 0.4143

224.4300 225.8815 223.6311

3.3349 3.6195 0.5067

221.1594 222.2620 223.5387

0.0174 0.0000 0.0046

0.0036 0.0080 0.0059

0.0068 0.0678 0.0016

0.0036 0.0071 0.0059

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

0.4111 0.4366 1.4298 1.4010 1.3585 1.3147 1.3087 1.2042 1.1836 1.1584 1.0570 0.8348 0.7238 0.5670 1.4764

222.0819 221.9461 0.2139 0.3662 0.6254 0.9587 1.2796 67.6404 80.6542 91.8659 121.8926 160.2880 176.5192 199.1319 0.0000

0.2810 0.0000 0.0025 0.0025 0.0025 0.0037 0.0037 0.1336 0.1624 0.1886 0.2523 0.3447 0.3834 0.4446 0.0012

222.2124 222.3831 1.6416 1.7645 1.9810 2.2694 2.5848 68.7104 81.6749 92.8353 122.6971 160.7785 176.8597 199.2544 1.4751

0.4219 0.4321 1.4287 1.3943 1.3482 1.3181 1.3069 1.2145 1.1492 1.1523 1.0574 0.8331 0.7196 0.5564 1.4787

223.2783 223.1893 0.2138 0.3677 0.6226 0.9559 1.2861 68.3439 79.3571 93.2254 122.7411 158.3097 176.7636 198.3031 0.0000

0.2783 0.0000 0.0024 0.0025 0.0025 0.0036 0.0038 0.1354 0.1688 0.1966 0.2555 0.3376 0.3871 0.4491 0.0012

223.4219 223.6214 1.6401 1.7594 1.9684 2.2704 2.5893 69.4230 80.3375 94.1811 123.5430 158.8052 177.0961 198.4104 1.4773

0.0263 0.0103 0.0008 0.0048 0.0076 0.0026 0.0014 0.0086 0.0291 0.0053 0.0004 0.0020 0.0058 0.0187 0.0016

0.0054 0.0056 0.0007 0.0040 0.0044 0.0029 0.0051 0.0104 0.0161 0.0148 0.0070 0.0123 0.0014 0.0042 0.0000

0.0096 0.0000 0.0400 0.0000 0.0000 0.0270 0.0162 0.0135 0.0394 0.0424 0.0127 0.0206 0.0097 0.0101 0.0000

0.0054 0.0056 0.0009 0.0029 0.0064 0.0005 0.0017 0.0104 0.0164 0.0145 0.0069 0.0123 0.0013 0.0042 0.0015

equilibrium solid phaseb Cc, Csi Cc, Csi Cc, Csi Cc, Csi Cc, Csi Cc, Csi Cc, Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Csi, Msh Cc, Msh, Eps Eps, Msh Eps, Msh Cc, Eps, Gyp Eps, Gyp Eps, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp Cc, Gyp

a

Standard uncertainties are u(T) = 0.1 K; u(p) = 0.005 MPa; u(mexp) for Ca2+, Mg2+, SO32−, and SO42− of liquid phase are 0.0002 mmol/100 g, 0.003 mmol/100 g, 0.0002 mmol/100 g and 0.002 mmol/100 g, respectively. bGyp, CaSO4·2H2O; Eps, MgSO4·7H2O; Csi, CaSO3·0.5H2O; Msh, MgSO3·6H2O; Cc, Ca(SO3)0.89(SO3)0.11·0.5H2O.

I



Article

B = β (0) + 2β (1)[1 − (1 + 1.4 I ) exp( − 1.4 I )] 2

XRD spectrum of synthesized magnesium sulfite (Figure S1) and liquid phase composition for the quaternary system Ca2+, Mg2+//SO32−, SO42−-H2O at 298.15 K (Table S1) (PDF)

(2)

/(1.4 I ) + 2β [1 − (1 + 12 I ) exp( − 12 I )] /(12 I )2

(17)

■

B′ = β (0) − 2β (1)[1 − (1 + 1.4 I + 0.98I )

Corresponding Author

exp( − 1.4 I )]/(1.4 I )2

*E-mail: [email protected]. Tel.: +86-02260204598. Fax: +86-022-60204274. Address: No. 398 Donghai Road, Quanzhou Normal University, Quanzhou, Fujian Provence, 362000, China.

− 2β (2)[1 − (1 + 12 I + 72I ) exp( − 12 I )] /(12 I )2

(18)

where Bφ and B are the second virial coefficients, while B′ is the differential of ionic strength. By analyzing eqs 8−18, Kap of each salt can be expressed as a linear function of β(0), β(1), β(2), CΦ, θ, and ψ. Kap =

αwn

∑ i

Cicγic

∑

Aiaγia

i

ORCID

Junsheng Yuan: 0000-0002-3107-9570 Funding

Financial support from National Key Technology Research and Development Program (2015BAB09B00, 2016YFB0600500), Science and Technology Project of Hebei Province (17273101D), Chinese Postdoctoral Science Foundation (2017M611142), High-tech Marine Industry Development Project of Fujian Provence (201513), and Joint Innovation Project of Industrial Technology in Fujian Provence (2015489).

(19)

The Kap of different solutions with same wet residue are equal. Corresponding parameters and Kap is obtained by substituting the solubility data of the ternary systems into the equations. The activity coefficients of Csi, Gyp, Msh, Eps, and Cc are listed in Table 6, and the interaction parameters are listed in Table 7 and Table 8. Obtaining interaction parameters through the interpolation method has some practical significance. However, in this paper, the parameters obtained by regression of experimental data will provide another option for practical applications. For the parameter β(2), it is an additional item derived from the ion association effect of type 2−2 electrolyte. The discrepancy between the experimental values and the literature values is acceptable, because the contribution of β(2) is quite small in the equation of Kap. The purpose of this part is to provide a reference for the parameters by experiment, not only by assumption through interpolation method. The solubilities and the calculation values in molality of these systems are presented in Tables 2−4 and 9. As shown in Table 2−4 and 9, it is found that Pitzer model is feasible to calculate the liquid−solid phase equilibrium with a relative error less than 5%.

Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Oikawa, K.; Yongsiri, C.; Takeda, K.; Harimoto, T. Article seawater flue gas desulfurization: Its technical implications and performance results. Environ. Prog. 2003, 22 (1), 67−73. (2) Song, L.; Xu, Y.; Yang, C.; Guo, H.; Si, T. Measurement and application of a solid-liquid equilibrium for the ternary NaCl + Na2S2O3 + H2O System. Ind. Eng. Chem. Res. 2015, 54, 3976−3980. (3) Zhong, Y.; Yang, H.; Wang, H.; Ge, H.; Wang, M. Solid-liquid phase equilibrium in the ternary system MgSO4 + MgCl2 + H2O at 263.15 K. J. Chem. Eng. Data 2018, 63, 1300−1303. (4) Zhang, X.; Ren, Y.; Li, P.; Ma, H.; Ma, W.; Liu, C.; Wang, Y.; Kong, Y.; Shen, W. Solid-liquid equilibrium for the ternary systems (Na2SO4 + NaH2PO4 + H2O) and (Na2SO4 + NaCl + H2O) at 313.15 K and atmospheric pressure. J. Chem. Eng. Data 2014, 59 (12), 3969−3974. (5) Stephen, H.; Stephen, T. Solubilities of Inorganic and Organic Compounds; Pergamon Press: 1963; Vol. 1, pp 236−249. (6) Kertes, A. S.; Masson, M. R.; Lutz, H. D.; Engelen, B. Sulfites, Selenites and Tellurites; IUPAC SDS (ONLINE); National Institute of Standards and Technology: 1986; Vol. 26, pp 153−220. (7) Meng, X.; Yuan, J.; Li, J. Simultaneous determination of sulfate and sulfite in seawater by ion chromatography. J. Analyt. Sci. 2018, 34 (2), 294−296. (8) Cameron, F. K.; Bell, J. M. The solubility of gypsum in magnesium sulphate solutions. J. Phys. Chem. 1906, 10 (3), 210−215. (9) Harvie, C. E.; Eugster, H. P.; Weare, J. H. Mineral equilibria in the six-component seawater system, Na-K-Mg-Ca-SO4-Cl-H2O at 25°C. Geochim. Cosmochim. Acta 1982, 46 (9), 1603−1618. (10) Rosenblatt, G. M. Estimation of activity coefficients in concentrated sulfite-sulfate solutions. AIChE J. 1981, 27 (4), 619−626. (11) Lidong, W.; Yongliang, M.; Wendi, Z.; Qiangwei, L.; Yi, Z.; Zhanchao, Z. Macrokinetics of magnesium sulfite oxidation inhibited by ascorbic acid. J. Hazard. Mater. 2013, 258−259, 61−69. (12) Yin, L.; Yuan, D.; Guo, J.; Liu, X. Determination of sulfite in flue gas desulfurization with seawater by ion chromatography. Chin. J. Chromatogr. 2009, 27 (6), 825−828. (13) Shimizu, K.; Suzuki, K.; Saitoh, M.; Konno, U.; Kawagucci, S.; Ueno, Y. Simultaneous determinations of fluorine, chlorine, and sulfur in rock samples by ion chromatography combined with pyrohydrolysis. Geochem. J. 2015, 49 (1), 113−124. (14) Damian Risberg, E.; Eriksson, L.; Mink, J.; Pettersson, L. G. M.; Skripkin, M. Y.; Sandström, M. Sulfur X-ray absorption and vibrational

4. CONCLUSION (1) The solubilities of the quaternary system Ca2+, Mg2+// SO32−, SO42− -H2O at 298.15 K and its ternary systems were measured, and the phase diagrams of these systems were plotted. The phase diagrams of the quaternary system and the ternary system Ca2+//SO32−, SO42− -H2O contain a field of crystal complex Ca(SO3)0.89(SO4)0.11·0.5H2O. The calculated solubilities are in excellent agreement with the experimental data. Pitzer theory is feasible to calculate the solubilities of these systems. (2) Ionic interaction parameters and Kap values of CaSO3· 0.5H2O and MgSO3·6H2O are regressed from the experimental data of the ternary systems. Compared with the Pitzer parameters obtained by interpolation method, the values of β(0) and β(1) are similar, but β(2) have serious discrepancies. The parameters obtained in this paper provide a new choice for practical application.

■

AUTHOR INFORMATION

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00385. J



Article

spectroscopic study of sulfur dioxide, sulfite, and sulfonate solutions and of the substituted sulfonate ions X3CSO3- (X = H, Cl, F). Inorg. Chem. 2007, 46 (20), 8332−8348. (15) Setoyama, K.; Takahashi, S. Solid solution of calcium sulfite hemihydrate and calcium salfate. Yogyo Kyokaishi 1978, 86 (5), 244− 250. (16) Lilley, T. H.; Briggs, C. C. Activity Coefficients of Calcium Sulphate in Water at 25 degrees C. Proc. R. Soc. London, Ser. A 1976, 349 (1658), 355−368. (17) Li, Z.; Deng, T.; Liao, M. Solid−liquid metastable equilibria in the quaternary system Li2SO4+MgSO4+Na2SO4+H2O at T = 263.15 K. Fluid Phase Equilib. 2010, 293 (1), 42−46. (18) Rodríguez-Sevilla, J.; Ä lvarez, M.; Díaz, M. C.; Marrero, M. C. Absorption equilibria of dilute SO2 in seawater. J. Chem. Eng. Data 2004, 49 (6), 1710−1716. (19) Pitzer, K. S.; Mayorga, G. Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2−2 electrolytes. J. Solution Chem. 1974, 3 (7), 539−546. (20) Debye, P.; Hü ckel, E. Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Phys. Z. 1923, 24 (9), 185−206.

K


SO32

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