NaBr + MgBr2 + CaBr2 + H2O - American Chemical Society

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(Solid + Liquid) Phase Equilibria in the Quaternary System (NaBr + MgBr2 + CaBr2 + H2O) at 298.15 K Rui-Zhi Cui,†,‡,§ Shi-Hua Sang,∥ Wu Li,*,†,‡,§ and Ya-Ping Dong†,‡,§

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 08/14/18. For personal use only.

†

Key Laboratory of Comprehensive and Highly Efficient Utilization of Salt Lake Resources, Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, People’s Republic of China ‡ Key Laboratory of Salt Lake Resources Chemistry of Qinghai Province, Xining 810008, People’s Republic of China § Qinghai Engineering and Technology Research Center of Comprehensive Utilization of Salt Lake Resources, Xining 810008, People’s Republic of China ∥ College of Materials and Chemistry and Chemical Engineering, Chengdu University of Technology, Chengdu 610059, People’s Republic of China ABSTRACT: The solubilities of salts in the (NaBr + MgBr2 + CaBr2 + H2O) system and its two ternary subsystems (NaBr + MgBr2 + H2O) and (NaBr + CaBr2 + H2O) are investigated at 298.15 K by the isothermal dissolution equilibrium method. The equilibrium phase diagrams of the three systems were obtained using the experimental results. In the three systems, neither solid solution nor double salt was found. In the two ternary phase diagrams, there are two invariant points, three dissolution equilibrium curves and three crystallization fields. The equilibrium solid phases in the (NaBr + MgBr2 + H2O) system are NaBr, NaBr·2H2O and MgBr2·6H2O, and those in the (NaBr + CaBr2 + H2O) system are NaBr, NaBr·2H2O and CaBr2·6H2O. The phase diagram of the quaternary system at 298.15 K consists of one invariant point, four solubility curves and four regions (corresponding to NaBr, NaBr·2H2O, MgBr2·6H2O, and CaBr2·6H2O). The solubilities of salts in the quaternary system and its two subsystems were calculated at 298.15 K by Pizter equation. The predicted results are in agreement with the experimental results.

1. INTRODUCTION Bromine and its compounds are important chemical materials with a variety of applications in many fields, such as flame retardation, pharmaceutics, printing and dyeing, pesticides, additives, and many others. Bromine can be extracted from bittern. Sichuan, covering an area of 2 × 105 km2, has large reserves of underground brines, which contain great amounts of sodium chloride and calcium chloride and are also rich in boron, potassium, bromine, strontium, iodine, lithium. and rubidium. The concentrations of all these elements are higher than those required for mining. In recent years, extraction of bromide was mainly from the shallow-layer brines in Laizhou Bay, Shandong. The bromine contents in these brines are 105−350 mg/L, which are much lower than those in the underground brines in Sichuan Basin. The average concentration of bromide ion is 300 mg/L with a maximum concentration of 2533−2640 mg/L, which makes bromide important mineral resources in the Sichuan Basin.1,2 Phase diagrams can describe the relationship between phase equilibria and thermodynamic variables and thus help to determine the conditions of salting out and precipitation as well as separation and extraction of various components from the brines. Phase diagrams can also help to understand how different factors affect chemical and phase equilibria of brine components in a saline lake.3 The underground brines in Sichuan Basin can be expressed as the (Na + K + Ca + Mg + Sr + Cl + Br + B4O7 + SO4 + Li + © XXXX American Chemical Society

I + H2O) system. The solubilities of salts in its quaternary subsystem (NaBr + MgBr2 + CaBr2 + H2O) at 298.15 K were studied in this work, and relevant stable phase diagrams were constructed. On the basis of Pitzer equation, the solubilities of salts in the quaternary system and its two ternary subsystems were calculated at the same temperature using published parameters. The relevant studies can provide basic data for the comprehensive utilization of the brines.

2. EXPERIMENTALS 2.1. Reagents and Instruments. The chemicals are guaranteed reagents and were listed in Table 1.The water was deionized by the Ultrapure Water Instrument (Youpute). In our phase equilibrium experiments, the SW23 Shaking Water Baths (with a temperature control precision of ±0.02 K) manufactured by JULABO Labortechnik GmbH was used. 2.2. Experimental Method. In this work, the isothermal dissolution equilibrium method was used. Briefly speaking, from the solubility at the cosaturated point in a subsystem, another salt was added at certain concentration interval followed by appropriate amounts of ultrapure water. The prepared solutions were placed in rigid plastic bottles and then Received: April 11, 2018 Accepted: July 30, 2018

A

DOI: 10.1021/acs.jced.8b00291 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

determined by EDTA titration with erichrome black-T as an indicator by adding ammonia buffer solution. In the quaternary system, the total amount of Ca2+ and Mg2+ was measured first by EDTA titration. Then, the concentration of Ca2+ was determined with an indicator of calcium and the addition of NaOH solution. As a result, Mg2+ was converted into solid Mg(OH)2 in strong alkaline solution (pH ≥ 12) without affecting the chemical reaction of Ca2+ with EDTA. The adsorption of Mg(OH)2 makes the end point of the titration insensitive. In this paper, before adding the NaOH solution, 2−3 mL of a 5% dextrin solution was first added to inhibit the adsorption of the Mg(OH)2 precipitate to Ca2+ and indicator. The amount of Mg2+ was calculated by subtracting the amount of Ca2+ from the total amount of Ca2+ and Mg2+. The concentration of Na+ was calculated by the subtraction method based on ion charge balance.

Table 1. Chemical Sample Specifications chemical name

source

sodium bromide

Shanghai Macklin Biochemical Co., Ltd. Shanghai Macklin Biochemical Co., Ltd. Shanghai Macklin Biochemical Co., Ltd.

magnesium hexahydrate bromide calcium bromide hydrate

initial mass fraction purity

purification method

analysis method

0.999

none

titration

0.999

none

titration

0.999

none

titration

were placed in the water bath shaker at (298.15 ± 0.02) K. The supernatant was sampled every other day for chemical analysis. The system was considered to reach thermodynamic equilibrium state when the chemical composition of solution did not change in 3 consecutive days. After equilibrium, chemical composition of the liquid phase was analyzed. 2.3. Analytical Methods. The concentration of Br− was determined by mercury nitrate volumetric method. In the two ternary systems, the concentration of Ca2+ or Mg2+ was

3. RESULTS AND DISCUSSIONS 3.1. Results. For the (NaBr + MgBr2 + CaBr2 + H2O) system, its two subsystems (NaBr + MgBr2 + H2O) and (NaBr + CaBr2 + H2O) at 298.15 K have been published.4,5 Because

Table 2. Experimental Results of Phase Equilibria in the (NaBr + MgBr2 + H2O) System at 298.15 K and 0.077406 MPaa composition of liquid phase 100·w(B)

composition of wet residue 100·w(B)

no.

w(NaBr)

w(MgBr2)

w(NaBr)

w(MgBr2)

equilibrium phase solids

1, B 2 3 4 5 6 7 8 9, E2 10 11, E1 12 13 14 15, A

48.57 46.00 44.17 37.15 30.19 26.09 17.73 10.75 7.16 5.41 3.52 1.89 1.02 0.72 0.00

0.00 2.20 3.99 10.66 17.35 20.63 30.07 38.31 42.76 46.26 47.95 49.16 49.79 50.18 50.61

71.94 65.59 64.39 61.75 60.64 60.64 59.89 66.25 67.65 11.68 0.87 0.23 0.05

0.38 1.26 2.75 4.98 6.15 6.70 9.25 11.13 16.39 53.02 56.45 60.58 59.73

NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O + NaBr NaBr NaBr + MgBr2·6H2O MgBr2·6H2O MgBr2·6H2O MgBr2·6H2O MgBr2·6H2O

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.00015 MPa, u[w(Na+)] = 0.005, u[w(Mg2+)] = 0.003, u[w(Br−)] = 0.003.

a

Table 3. Experimental Results of Phase Equilibria in the (NaBr + CaBr2 + H2O) System at 298.15 K and 0.077406 MPa composition of liquid phase 100·w(B) no.

w(NaBr)

w(CaBr2)

1, C 2 3 4 5 6 7 8, E4 9 10 11, E3 12 13 14, B

48.57 45.71 40.41 33.10 28.91 23.47 14.03 8.61 3.65 0.88 0.76 0.47 0.18 0.00

0.00 2.87 8.31 14.20 19.95 25.26 36.77 44.60 51.66 59.31 59.34 59.69 60.23 60.25

composition of wet residue 100·w(B) w(NaBr)

w(CaBr2)

68.57 67.19

0.51 1.72

60.22 74.86 79.66

8.58 7.79 10.69

equilibrium phase solids NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O NaBr·2H2O + NaBr NaBr NaBr NaBr + CaBr2·6H2O CaBr2·6H2O CaBr2·6H2O CaBr2·6H2O

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.00015 MPa, u[w(Na+)] = 0.005, u[w(Ca2+)] = 0.003, u[w(Br−)] = 0.003.

a

B



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Figure 4. X-ray diffraction photograph at the invariant point E2 of the (NaBr + MgBr2 + H2O) system at 298.15 K [NaBr·2H2O + NaBr].

Figure 1. Phase diagram of the (NaBr + MgBr2 + H2O) system at 298.15 K; ●, liquid phase composition; ▲, wet residue composition; −, solubility isotherm curve; ···, wet residue line.

Figure 5. X-ray diffraction photograph at the invariant point E3 of the (NaBr + CaBr2 + H2O) system at 298.15 K [CaBr2·6H2O + NaBr].

Figure 2. Phase diagram of the (NaBr + CaBr2 + H2O) system at 298.15 K; ●, liquid phase composition; ▲, wet residue composition; −, solubility isotherm curve; ···, wet residue line.

Figure 6. X-ray diffraction photograph at the invariant point E4 of the (NaBr + CaBr2 + H2O) system at 298.15 K [NaBr·2H2O + NaBr].

The results from the salt solubility measurements in the (NaBr + MgBr2 + H2O) and (NaBr + CaBr2 + H2O) systems at 298.15 K are listed in Table 2 and 3, respectively. Their stable phase diagrams are plotted (see Figures 1 and 2) based on the corresponding compositions of liquid phase and wet residue in Tables 2 and 3. Figures 3, 4, 5, and 6 are the XRD photographs of the invariant points in the two systems. Crystallographic forms of equilibrium solids were determined by Schreinemakers residue method and X-ray diffraction method. The experiment results are consistent with those previously reported. Under this temperature condition, besides NaBr·2H2O and MgBr2·6H2O or CaBr2·6H2O, the anhydrous salt NaBr is simultaneously present in two systems. Both ternary systems belong to the hydrate II type. It can be found that there are three dissolution equilibrium curves, two invariant points, and three fields of crystallization in each of two ternary phase diagrams. Points E1and E2 are the invariant points of the (NaBr + MgBr2 + H2O) system (Table 1) at which the solutions are

Figure 3. X-ray diffraction photograph at the invariant point E1 of the (NaBr + MgBr2 + H2O) system at 298.15 K [MgBr2·6H2O + NaBr].

of the particularity of the experimental results of quaternary system at 298.15 K, its two ternary subsystems at 298.15 K were studied again in this work to verify the accuracy and reliability of experimental results. C



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Table 4. Experimental Results of Phase Equilibria in the (NaBr + MgBr2 + CaBr2 + H2O) System at 298.15 K and 0.077406 MPaa,b Jänecke index J/(g/100 g)

composition of solution w(B) × 100

J(NaBr) + J(MgBr2) + J(CaBr2) = 100 g

no.

w(NaBr)

w(MgBr2)

w(CaBr2)

J(NaBr)

J(MgBr2)

J(CaBr2)

J(H2O)

equilibrium solids

1, E2 2 3 4 5 6 7 8 9, E1 10 11 12 13 14 15, E3 16 17 18, E5 19, F1 20, E4 21 22

7.16 7.39 7.51 7.80 7.70 7.74 7.73 7.82 3.52 3.62 3.56 4.32 2.92 2.40 0.76 0.76 0.67 0.00 0.59 8.61 8.23 8.04

42.76 41.08 35.64 30.13 27.43 23.35 19.33 9.33 47.95 45.65 42.32 36.30 27.85 19.72 0.00 1.43 3.76 5.92 5.89 0.00 2.83 6.90

0.00 1.52 6.30 12.55 16.49 20.28 24.58 36.06 0.00 3.13 7.00 12.36 23.18 33.45 59.34 57.26 56.37 54.37 54.16 44.60 42.44 38.82

14.35 14.78 15.19 15.45 14.91 15.06 14.97 14.70 6.84 6.91 6.73 8.15 5.41 4.32 1.26 1.27 1.11 0.00 0.97 16.19 15.38 14.96

85.65 82.17 72.08 59.69 53.15 45.46 37.44 17.53 93.16 87.11 80.03 68.52 51.63 35.49 0.00 2.40 6.18 9.81 9.72 0.00 5.30 12.83

0.00 3.05 12.73 24.86 31.95 39.47 47.59 67.76 0.00 5.98 13.23 23.33 42.96 60.19 98.74 96.32 92.71 90.19 89.31 83.81 79.32 72.21

100.32 100.00 102.23 98.10 93.72 94.67 93.64 87.90 94.29 90.83 89.10 88.76 85.38 79.96 66.39 68.23 64.45 65.88 64.90 87.94 86.90 86.03

NB2 + NB NB2 + NB NB2 + NB NB2 + NB NB2 + NB NB2 + NB NB2 + NB NB2 + NB MB6 + NB MB6 + NB MB6 + NB MB6 + NB MB6 + NB MB6 + NB CB6 + NB CB6 + NB CB6 + NB MB6 + CB6 MB6 + CB6 + NB NB2 + NB NB2 + NB NB2 + NB

Abbreviations: NB = NaBr, NB2 = NaBr·2H2O, MB6 = MgBr2·6H2O, CB6 = CaBr2·6H2O. bStandard uncertainties u are u(T) = 0.02 K, u(p) = 0.00015 MPa, u[w(Na+)] = 0.005, u[w(Mg2+)] = 0.003, u[w(Ca2+)] = 0.003, u[w(Br−)] = 0.003. a

Figure 8. Water contents of saturated solutions in the (NaBr + MgBr2 + CaBr2 + H2O) system at 298.15 K.

Figure 7. Phase diagram of the (NaBr + MgBr2 + CaBr2 + H2O) system at 298.15 K; ●, equilibrium liquid composition; −, solubility isotherm curve.

phase diagram (Figure 7) and the water content diagram (Figure 8) were plotted using the Jänecke indices in Table 4, which are defined as follows:

saturated with MgBr2·6H2O + NaBr and NaBr·2H2O + NaBr, respectively. The two invariant points of ternary system (NaBr + CaBr2 + H2O) are labeled as points E3 and E4. The saturated salts are CaBr2·6H2O + NaBr and NaBr·2H2O + NaBr, respectively. The liquid composition at each invariant points are shown in Tables 2 and 3. Those results are consistent with experimental data in literature within the measurement uncertainties.4 The experimental results of the (NaBr + MgBr2 + CaBr2 + H2O) system at 298.15 K were given in Table 4. The equilibrium

w(s) = w(NaBr) + w(MgBr2) + w(CaBr2) J(B) =

100·w(B) w(s)

(B = NaBr, MgBr2, CaBr2, or H 2O)

As can be seen from Table 4 and Figure 7, there is no solid solution or double salt formed between three end-member components in this quaternary system. Compared with its D



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to those of the (NaBr + MgBr2 + H2O) system. The phase diagrams of this ternary system at 288.15, 298.15, and 323.15 K have three crystallization regions, three dissolution equilibrium curves two and invariant points. The system belongs to the hydrate I type at 348 K. That is, its diagram only has one invariant point, two crystallization regions, and two dissolution equilibrium curves. The sodium bromide hydrate are NaBr· 2H2O at (288.15, 298.15, and 323.15) K, whereas its crystal water is lost at 348.15 K. For calcium bromide hydrates, the number of crystal water decreases with the temperature increasing. At 288.15 and 298.15 K, the number of crystal water is six, at 323.15 K it is four, and at 348.15 K it becomes two. In the phase diagrams at the four temperatures, the crystallization form of calcium bromide hydrates is the smallest due to its maximal solubility. Meanwhile, the crystallization field of NaBr gets bigger and bigger as temperature increases. The solid−liquid phase equilibria in ternary system (MgBr2 + CaBr2 + H2O) at 273.15, 298.15, 323.15 and 348.15 K have been published.10−12 At 273.15 and 298.15 K, it is of hydrate I type, whose hydrates are has MgBr2·6H2O and CaBr2·6H2O. At 323.15 and 348.15 K, a new solid phase 2MgBr2·CaBr2· 12H2O was found, so the ternary phase diagrams contain two invariant points, three crystallization regions, and three dissolution equilibrium curves. The measurements and calculation of phase equilibria in quaternary system at 348.15 K have been reported.13 Compared with the phase diagrams at 298.15 K, the phase field of NaBr·2H2O disappears, and the double salt 2MgBr2·CaBr2·12H2O forms at 348.15 K. The calcium bromide hydrate is CaBr2·6H2O at 298.15 K and becomes CaBr2·2H2O at 348.15 K. The phase diagram of the (NaBr + MgBr2 + CaBr2 + H2O) system at 348.15 K has two invariant points, five dissolution equilibrium curves, and four crystallization regions (three single salts NaBr, MgBr2·6H2O, CaBr2·2H2O, and one double salt 2MgBr2·CaBr2·12H2O). In the phase diagrams of the (NaBr + MgBr2 + CaBr2 + H2O) system at the two temperatures, the phase field of calcium salt is the smallest, whereas the sodium salt has the biggest phase field. It means that the solubility of sodium salt is the lowest, and it is easily crystallized from solution in this quaternary system. For the invariant points E1 and E2 of the ternary system NaBr + MgBr2 + H2O and the invariant points E3 and E4 of the NaBr + CaBr2 + H2O system, the experimental data of the liquid phase composition are basically the same in terms of the error range reported in the literature.4 However, the experimental data for the invariant point E5 of the MgBr2 + CaBr2 + H2O system were somewhat different from those previously reported.14 In addition to the errors of reagents, instruments, and pressure conditions used in the experiments, errors in the judgment of titration end point of the Ca2+ content titration due to the adsorption of Mg(OH)2 should also be included, and this error would also be carried over to determining the Mg2+ content.

Figure 9. X-ray diffraction photograph at the invariant point F1 of the (NaBr + MgBr2 + CaBr2 + H2O) system at 298.15 K [CaBr2·6H2O + MgBr2·6H2O + NaBr].

Table 5. Single-Salt Parameters of the (NaBr + MgBr2 + CaBr2 + H2O) System at 298.15 K salt

β(0)

β(1)

Cϕ

reference source

NaBr MgBr2 CaBr2

0.120914 0.434520 0.335714

0.061475 1.734634 2.906156

−0.002820 0.002684 0.008975

16 17 8

ternary subsystems, new solid phase was not found in this quaternary system. The order of size of crystallization fields is NaBr·2H2O (DE2E4) > NaBr (E1E2E4E3) > MgBr2·6H2O (GE1F1E5) > CaBr2·6H2O (E5F1E3H). Because the phase diagrams of both ternary subsystems contain crystallization fields of NaBr·2H2O and NaBr at 298.15 K, this quaternary is somewhat special. In its phase diagram, the crystallization field of NaBr·2H2O is isolated by the cosaturation curve of NaBr and NaBr.2H2O. Therefore, the quaternary system only contains four dissolution equilibrium curves (curves E2E4, E1F1, E1E3, and E5F1) and one invariant point (point F1). According to the powder XRD photograph (Figure 9), at the invariant point F1, the solution is saturated with three single salts NaBr + MgBr2·6H2O + CaBr2·6H2O (Table 3). 3.2. Discussions. The (NaBr + MgBr2 + CaBr2 + H2O) system includes three ternary subsystems, (NaBr + MgBr2 + H2O), (NaBr + CaBr2 + H2O), and (MgBr2 + CaBr2 + H2O). A series of experimental solubility data of these systems have been reported within the temperature range from 273.15 to 348.15 K.4−9 The stable phase equilibrium data in ternary system (NaBr + MgBr2 + H2O) are available at 273.15, 298.15, 323.15, and 348.15 K.4−6 The phase diagram of this system contains only one invariant point, two crystallization fields (NaBr·2H2O and MgBr2·6H2O) and two dissolution equilibrium curves at 273.15 K. At 298.15 and 323.15 K, it contains two invariant points, three dissolution equilibrium curves, and three crystallization fields (NaBr, NaBr·2H2O and MgBr2·6H2O). It transforms into the hydrate I type at 348.15 K, as the phase field of sodium bromide dihydrate disappears. The phase diagrams of ternary system (NaBr + CaBr2 + H2O) at 288.15, 298.15, 323.15, and 348.15 K5,7−9 are similar

4. PREDICTION OF SOLUBILITY For the calculation of the phase equilibria in salt-water systems, the commonly used model is the semiempirical theoretical

Table 6. Debye−Hückel Constant (Aϕ) and Mixing Ion-Interaction Parameters of the (NaBr + MgBr2 + CaBr2 + H2O) System at 298.15 K parameter

θNa,Mg

θNa,Ca

θMg,Ca

ΨNa,Mg,Br

ΨNa,Ca,Br

ΨMg,Ca,Br

Aϕ

value reference

0.07 5

0.05 8

0.007 11

0.004322 5

−0.012755 8

0.00088 11

0.391475 18

E



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Table 7. Dissolution equilibrium constants of salts in the (NaBr + MgBr2 + CaBr2 + H2O) system at 298.15 K parameter

ln K(NaBr)

ln K(NaBr·2H2O)

ln K(CaBr2·6H2O)

ln K(MgBr2·6H2O)

value reference

6.7032 16

4.6433 16

13.1965 8

12.2010 17

Figure 10. Comparison of the experimental and calculated phase diagrams of the (NaBr + MgBr2 + H2O) system at 298.15 K; ●, experimental result; ···○···, calculated result.

Figure 12. Comparison of the experimental and calculated phase diagrams of the (NaBr + MgBr2 + CaBr2 + H2O) system at 298.15 K; ●, experimental result; ···○···, calculated result.

Figure 11. Comparison of the experimental and calculated phase diagrams of the (NaBr + CaBr2 + H2O) system at 298.15 K; ●, experimental phase diagram; ···○···, calculated phase diagram.

three systems at 298.15 K, no solid solution was found. For the calculation of invariant points and boundary points (invariant points of subsystems), the nonlinear equations are established with Pitzer equation and solid−liquid equilibrium conditions. The equations are solved using MatLab software and Particle Swarm Optimization (PSO) algorithm. The calculation can give the molality of each ion and then the corresponding Jänecke dry salt indices can be calculated. On each dissolution equilibrium curves of the quaternary system, the solution is saturated with two equilibrium solid phases. The concentration of a certain ion was given equally spaced to calculate the concentrations of the other ions at each point, and the dissolution equilibrium curve can be obtained with the method mentioned above. Using experimental data and calculated results, the

model of electrolyte solutions proposed by Pitzer.15 With the improvement of many scholars, Pitzer model can be successfully applied to electrolyte solutions up to high temperatures, high pressures, and high concentrations, which basically solves the problem of the thermodynamic calculation of the electrolyte solutions in equilibrium state. Using the correlation equation of the Pizter parameters as functions of temperature in the literature, the single salt parameters, mixed salt parameters and standard chemical potentials of bromide solid phases in the (NaBr + MgBr2 + CaBr2 + H2O) system and its two subsystems at 298.15 K were calculated and are listed in Tables 5−7, respectively. In the F



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Table 8. Comparison of Calculated and Experimental Invariant Points of the (NaBr + MgBr2 + CaBr2+ H2O) System and Its Two Ternary Subsystems at 298.15 Ka composition of liquid phase 100·w(B) no.

cal/exp values

w(NaBr)

w(MgBr2)

w(CaBr2)

point E1

experimental

point E2

calculated experimental

point E3


point E4


point E5


3.26 3.52 1.70 7.23 7.16 3.18 0.75 0.76 0.69 8.03 8.61 10.32 0.00 0.00 0.00 0.59 0.53

48.30 47.95 49.14 42.35 42.76 46.24 0.00 0.00 0.00 0.00 0.00 0.00 4.96 5.92 4.75 5.89 4.75

0.00 0.00 0.00 0.00 0.00 0.00 59.40 59.34 59.81 45.30 44.60 43.64 55.71 54.37 55.69 54.16 55.15

point F1

calculated experimental calculated

equilibrium solids

source

MB6 + NB

4 in this work

NB2 + NB

4 in this work

CB6 + NB

4 in this work

NB2 + NB

4 in this work

MB6 + CB6

14 in this work

MB6 + CB6 + NB

in this work

Abbreviations: NB = NaBr, NB2 = NaBr·2H2O, MB6 = MgBr2·6H2O, CB = CaBr2·6H2O.

a

ORCID

experimental and calculated phase diagrams of the three systems at 298.15 K were plotted in Figures 10, 11, and 12. Figures 10−12 show good agreement between calculated and experimental phase diagrams of the quaternary system and two ternary subsystems at 298.15 K. The compositions of all invariant points are listed in Table 8. Apparently, the calculated points A, B, C, E3, and F1 are close to experimental results, but the calculated results at points E1, E2, E4, and E5 have certain deviations from the experimental values.

Rui-Zhi Cui: 0000-0001-6861-8227 Shi-Hua Sang: 0000-0002-5948-3882 Wu Li: 0000-0002-3512-7461 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The project was supported by the National Natural Science Foundation of China (Grants 41472078 and 41273032).

5. CONCLUSIONS The stable solid−liquid equilibria of the (NaBr + MgBr2 + CaBr2 + H2O) system and its two subsystems (NaBr + MgBr2 + H2O) and (NaBr + CaBr2 + H2O) were investigated at 298.15 K by the method of isothermal dissolution. The results indicate that three systems are all of the hydrate II type without solid solution or double salt formed. The results of the two ternary subsystems are in accordance with previous experimental results. Both phase diagrams consist of two invariant points, three dissolution equilibrium curves, and three fields of crystallization. The solids are NaBr, NaBr·2H2O, and MgBr2·6H2O in the (NaBr + MgBr2 + H2O) system and are NaBr·2H2O, MgBr2·6H2O, and CaBr2·6H2O in the (NaBr + CaBr2 + H2O) system. The phase diagram of the quaternary system at 298.15 K contains only one invariant point, but has four dissolution equilibrium curves and four crystallization fields, which is different from the phase diagram topology of most quaternary salt-water systems. No new salt was found in this quaternary system. The crystallization field of NaBr·2H2O is adjacent to only one quaternary dissolution equilibrium curve. The solubilities of salts in the quaternary system and its two ternary subsystems at 298.15 K were calculated by Pitzer equation. The results show that the calculated results are in good agreement with the experimental data.

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REFERENCES

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CaBr2−H2O systems to high concentration and temperature. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2011, 35 (1), 42−53. (9) Hu, J. X.; Sang, S. H.; Liu, Q. Z. Solid-liquid equilibria in the ternary systems KBr−CaBr2−H2O and NaBr−CaBr2−H2O at 348 K. J. Chem. Eng. Data 2015, 60 (4), 993−998. (10) Zdanovskii, A.; Soloveva, E.; Liahovskaia, E.; Shestakov, N.; Shleimovich, P.; Abutkova, L.; Chermnih, L.; Kulikova, T. Experimentalnie dannie po rastvorimosti mnogokomponentnih vodnosolevih system; Khimiizdat: St. Petersburg, 2003; Vols. , I-2. (11) Christov, C. Study of bromide salts solubility in the (m1KBr + m2CaBr2)(aq) system at 323.15 K. Thermodynamic model of solution behaviour and (solid + liquid) equilibria in the ternaries (m1KBr + m2CaBr2)(aq), and (m1MgBr2 + m2CaBr2)(aq), and in the quinary (Na + K + Mg + Ca + Br + H2O) systems to high concentration and temperature. J. Chem. Thermodyn. 2012, 55 (12), 7−22. (12) Hu, J. X.; Sang, S. H.; Zhang, T. T.; Wang, D. Solid−liquid equilibria in the systems CaBr2−MgBr2−H2O and NaBr−KBr−SrBr2 at 348 K. J. Chem. Eng. Data 2015, 60 (11), 3087−3092. (13) Hu, J. X. Studies on phase equilibria and theoretical calculations of related subsystem in quinary system Na+, K+, Mg2+, Ca2+// Br−− H2O at 348 K. Master Thesis, Chengdu University of Technology, Chengdu, SiChuan, China, 2015. (14) Cui, R. Z.; Wang, Z. C.; Xu, J. S.; Sang, S. H. Measurements and calculations of solid-liquid equilibria in the quaternary system KBr−CaBr2−MgBr2−H2O at (298 and 323) K. Fluid Phase Equilib. 2017, 450, 140−148. (15) Pitzer, K. S. Activity coefficients in electrolyte solutions; CRC Press, 1991. (16) Christov, C. An isopiestic study of aqueous NaBr and KBr at 50°C: Chemical equilibrium model of solution behavior and solubility in the NaBr−H2O, KBr−H2O and Na−K−Br−H2O systems to high concentration and temperature. Geochim. Cosmochim. Acta 2007, 71 (14), 3557−3569. (17) Christov, C. Isopiestic investigation of the osmotic coefficients of MgBr2(aq) and study of bromide salts solubility in the (m1KBr + m2MgBr2)(aq) system at 323.15 K. Thermodynamic model of solution behaviour and (solid + liquid) equilibria in the MgBr2(aq), and (m1KBr + m2MgBr2)(aq) systems to high concentration and temperature. J. Chem. Thermodyn. 2011, 43 (3), 344−353. (18) Greenberg, J. P.; Moller, N. The prediction of mineral solubilities in natural water: A chemical equilibrium model for the Na−K−Ca−Cl−SO4−H2O system to high concentration from 0 to 250°C. Geochim. Cosmochim. Acta 1989, 53 (10), 2503−2518.

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NaBr + MgBr2 + CaBr2 + H2O - American Chemical Society

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