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. 2020 Apr 21;5(17):10133–10144. doi: 10.1021/acsomega.0c00777

Solid–Liquid Phase Equilibria in the Quinary System NaCl + NaOH + Na2CO3 + Na2SO4 + H2O at 363.15 K

Jiangman Wu 1, Zhaojun Wu 1, Jinrong Liu 1,*
PMCID: PMC7203980  PMID: 32391501

Abstract

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Solid–liquid equilibria in the quinary system NaCl + NaOH + Na2CO3 + Na2SO4 + H2O at 363.15 K were measured by the wet residue method, and the equilibrium solid phases and solubilities of saturated solutions were determined experimentally. Using the experimental results, dry-salt phase diagrams and water diagrams versus composition diagrams were plotted (saturated with saturated sodium chloride, sodium hydroxide, sodium carbonate, and sodium sulfate). The experimental results show that there are a solid solution (γ-salt, mNa2SO4·nNa2CO3) and co-saturation complex salts (S3, Na2SO4·NaCl·NaOH and S1, NaOH·Na2SO4) formed in this quinary system. Based on Xu’s activity coefficient model, the solubilities of the quinary system NaCl + NaOH + Na2CO3 + Na2SO4 + H2O at 363.15 K were calculated with corresponding parameters. Comparing the experimental and calculated results, it was shown that the calculated values had a good agreement with the experimental ones.

1. Introduction

The natural soda in Inner Mongolia, with the local average atmospheric pressure of about 88.94 kPa, mainly consists of sodium carbonate (Na2CO3), sodium bicarbonate (NaHCO3), sodium sulfate (Na2SO4), and sodium chloride (NaCl).1 Therefore, the natural soda solution in Inner Mongolia can be considered a quinary system of NaOH + NaCl + Na2CO3 + Na2SO4 + H2O. Based on these components, natural soda can be used for the production of caustic soda. After natural soda is dissolved in water, the insoluble impurities can be removed through flocculation clarification. When lime milk is added, the concentration of sodium hydroxide in the caustic liquor is usually approximately 8–10%. Considering the economic efficiency and equilibrium conversion rate (the causticization rate is generally controlled at approximately 90%), a very small amount of sodium bicarbonate (NaHCO3) is retained. To obtain caustic soda products that meet quality standards, the caustic soda liquid should be concentrated, and Na2SO4, NaCl, and a small amount of Na2CO3 impurities should be removed. The evaporation method for producing caustic soda through the causticizing process generally involves three-effect evaporation. The third-effect temperature is approximately 363.15 K, at which the concentration of caustic soda is controlled at 45–48%. At the third-effect temperature, Na2SO4 and NaCl2 are removed to concentrate the diluted caustic soda liquid and remove impurities; then, the caustic soda liquid is allowed to cool to achieve separation, dehydration, and solidification to form solid caustic soda that meets the quality requirements. In the actual production process, only the third-effect temperature is controlled at 363.15 K; at this point, the evaporated liquor has reached saturation and salting out. Therefore, 363.15 K was chosen as the research temperature and 88.94 kPa was also selected as the pressure in this paper.

In the technological process of producing soda by means of vaporizing the natural solutions, the suitable amount of the evaporation of the soda solution needs to be controlled to achieve high-quality products and a high recovery percent of effective components. In addition, the order of salting out, the amount of water removed by evaporation, and the separating-out amount of the solid phase are also some very important parameters in the process design control. The phase diagram of the system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K is the important theoretical base of the determination of the parameters above.

Some studies have been carried out on the solubility of ternary and quaternary subsystems at 363.15 K.2−6 However, the solubilities of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O are scarcely reported in the literature. There are many models for correlating equilibrium data that have been used to correlate the solid–liquid equilibrium (SLE) data, such as the Pitzer model,7−12 its extended Harvie–Weare (HW)13−17 model, a modification model of the extended UNIQUAC,18,19 the extended Debye–Hückel model,20 etc. Furthermore, the predictive solubilities of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K were calculated on the basis of Xu’s extended activity coefficient model; it was constructed for the reference state of activity coefficients and literature data for single-electrolyte and mixed-electrolyte solution systems.21 Accordingly, in this paper, the experimental results and calculated results of NaOH + NaCl + Na2CO3 + Na2SO4 + H2O are presented in detail at 363.15 K.

2. Experimental Section

2.1. Reagents and Instruments

All of the chemicals used in this work, primarily NaCl, Na2SO4, Na2CO3, and NaOH, were of analytical purity and mostly obtained from Tianjin Yongsheng Chemical Reagent Co., Ltd., China. Deionized water (conductivity less than 1.3 × 10–4 S·m–1, pH 6.6) was used to prepare the experimental solutions. A standard analytical balance with 0.0001 g resolution (ALC-110.4, supplied by the Sartorius AG) was employed for the determination of the sample mass. Both a 76-1-type thermostatic water bath (Jiangsu Tianyou Co., Ltd) with an uncertainty of 0.1 K and a KSA-II type thyristor DC governor (Ningbo Beilun Zhitou District Electronic Control Equipment Factory) with a 2.2 kW power were used for the equilibria measurements.

2.2. Experimental Methods

The system points were compounded as follows. For a quinary system, the system points were mixed by adding the fourth component gradually on the basis of the three salt saturation points. The equilibrium time was approximately 5 days. After equilibrium was achieved, the supernatant liquid in a balanced bottle was sampled every few hours for chemical analysis. If the relative error among the three consecutive samplings was below 0.003, equilibrium could be considered to be achieved. After reaching equilibrium, the sample solutions were allowed to rest for approximately 3 days for separation of the solid phase from the liquid phase. In addition to maintaining a constant temperature via an oil bath, the sealed bottles were filled with liquid such that the liquid contacted the top of the bottle to prevent oil from entering the bottles during sampling and affecting the experimental results. After reaching equilibrium, the sampling tubes were placed in a preheated oven to maintain the equilibrium. Samples were taken periodically for chemical analysis. When the concentrations in the solution did not change, equilibrium had been attained. After equilibrium, the liquid phase was removed and quantitatively analyzed.22 The solid phase was separated from the solution at a certain temperature. After the wet residue mixture was filtered out, one part of the solid phase was dissolved in water and analyzed by a chemical method. The other part was dried at room temperature, ground into a powder, and then analyzed by X-ray diffraction (XRD).

The total alkali content was determined by titration with standard hydrochloric acid using a methyl orange solution as the indicator.23 The NaOH content was determined by excess alkalimetry using a phenolphthalein solution as the indicator, the chlorine ion concentration was measured by silver nitrate titration, and the sulfate ion content was determined gravimetrically.24

To prove the reliability of the experimental apparatus and the method used in this study, before the formal experiment, we measured the data at one co-saturation point of one ternary system NaCl + NaOH + H2O with the experimental apparatus (Figure 1). The results (shown in Table 1) were all consistent with the data in the literature,4−6 with a relative standard uncertainty of 0.05.25−28

Figure 1.

Figure 1

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Schematic diagram of the experiment setup for phase equilibrium determinations.

Table 1. Comparison of Data of Phase Equilibria Measured and Literature Data at T = 363.15 K and P = 88.94 kPaa.

 
 fluid mass, w(B) × 100, %
    
subject Na2CO3 NaCl Na2SO4 NaOH solidc data sources
Table 2 measrd results 0 2.87 0 68.87 Cl + OH this work
lit. datab 0 2.90 0 65.00 Cl + OH b
(point 1) rel. err (%)d 0 0.01 0 0.06    
abs. errd 0 0.03 0 3.87    
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a

Standard uncertainties u are u(T) = 0.1 K, u(P) = 0.5 kPa, ur(Na2CO3) = ur(Na2SO4) = ur(NaCl) = ur(NaOH) = 0.05.

b

Data source: Stephen et al. (2).

c

Abbreviations: OH, NaOH; Cl, NaCl.

d

εr(%) = |measrd-lit.| / lit.; εa = |measrd-lit.|.

The solid-phase composition was determined by the wet residue method, and the crystalloid form could be identified by an auxiliary method; that is, the wet solid samples were dried with a filter paper and studied by powder XRD.29

3. Results and Discussion

To meet the different needs of phase diagram analysis, simplified dry-salt, sodium, and water diagrams of saturated NaCl, NaOH, Na2CO3, and Na2SO4 were constructed. The sodium curves in the diagrams are represented by blue lines, and the curves of water diagrams were plotted as red lines. The solubilities of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O components in the equilibrated solution at 363.15 K were determined and are tabulated in Table 2.

Table 2. Data of Phase Equilibria for the Quinary System NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K and 88.94 kPaa.

  liquid mass, w(B) × 100b, %
 dry-salt(liquid) mass, w(B) × 100b, %
    
no. NaOH Na2CO3d Na2SO4 NaCl H2O NaOH Na2CO3 Na2SO4 NaCl H2O mass% solidc
1 68.87 0 0 2.87 28.26 95.99 0.00 0.00 4.00 39.39 Cl + OH
2 0 9.97 0 21.09 68.94 0.00 32.09 0.00 67.90 221.96 C1 + Cl
3(D1) 0 10.04 1.26 20.96 67.74 0.00 31.12 3.91 64.97 209.98 C1 + Cl + γ
4 0 8.16 1.66 23.26 66.92 0.00 24.67 5.02 70.31 202.29 γ + Cl
5 0 7.04 1.87 23.54 67.55 0.00 21.69 5.76 72.54 208.17 γ + Cl
6 0 4.29 2.19 23.45 70.07 0.00 14.33 7.32 78.35 234.11 γ + Cl
7(D2) 0 1.22 4.75 23.75 70.28 0.00 4.10 15.98 79.91 236.47 S + γ + Cl
8 0 0 5.71 25.75 68.54 0.00 0.00 18.15 81.85 217.86 S + Cl
9 2.3 1.26 5.23 22.15 69.06 7.43 4.07 16.90 71.59 223.21 S + Cl + γ
10 5.32 1.35 5.41 18.56 69.36 17.36 4.41 17.66 60.57 226.37 S + Cl + γ
11 11.16 1.63 5.4 13.55 68.26 35.16 5.14 17.01 42.69 215.06 S + Cl + γ
12 14.79 1.77 5.12 11.26 67.06 44.90 5.37 15.54 34.18 203.58 S + Cl + γ
13(E1) 21.26 1.83 4.99 10.69 61.23 54.84 4.72 12.87 27.57 157.93 S + Cl + γ + S3
14 27.34 0 3.97 15.75 52.94 58.10 0.00 8.44 33.47 112.49 S + Cl
15 13.8 0 4.24 19.17 62.79 37.09 0.00 11.39 51.52 168.74 S + Cl
16(E2) 42.48 1.54 0.58 2.56 52.84 90.08 3.27 1.23 5.43 112.04 C + Cl + OH + S3
17(F1) 60.44 0 3.42 4.6 31.54 88.29 0.00 4.99 6.72 46.07 S + Cl + S3
18 8.04 8.06 1.31 17.84 64.75 22.81 22.87 3.72 50.61 183.69 C1 + γ + Cl
19 11.84 7.58 1.41 16.9 62.27 31.38 20.09 3.74 44.79 165.04 C1 + γ + Cl
20 19.51 7.31 1.44 13.37 58.37 46.87 17.56 3.46 32.12 140.21 C1 + γ + Cl
21 60.38 10.04 8.22 0.87 20.49 75.94 12.63 10.34 1.09 25.77 Cl + γ + S3
22(E3) 25.09 6.32 1.5 10.53 56.56 57.76 14.55 3.45 24.24 130.20 C1 + Cl + γ + S3
23 16.42 2.57 0 10.71 70.3 55.29 8.65 0.00 36.06 236.70 C1 + Cl
24 28.46 3.15 0 9.47 58.92 69.28 7.67 0.00 23.05 143.43 C1 + Cl
25(F2) 34.21 1.69 0 4.34 59.76 85.01 4.19 0.00 10.79 148.51 C + C1 + Cl
26 36.51 1.95 0 3.64 57.9 86.72 4.63 0.00 8.65 137.53 C + Cl
27(F3) 51 2.05 0 4.01 42.94 89.38 3.59 0.00 7.03 75.25 C + OH + Cl
28 20.23 4.06 0.75 12.16 62.8 54.38 10.91 2.02 32.69 168.82 C + C1 + Cl
29 24.92 3.35 0.47 11.58 59.68 61.81 8.31 1.17 28.72 148.02 C + C1 + Cl
30(E4) 18.86 5.88 1.29 14.51 59.46 46.52 14.50 3.18 35.79 146.67 C + C1 + Cl + γ
31(F4) 81.28 0 2.58 2.33 13.81 94.30 0.00 2.99 2.70 16.02 Cl + OH + S3
32 74.98 0 2.91 3.12 18.99 92.56 0.00 3.59 3.85 23.44 Cl + S3
33 0 20.65 6.4 0 72.95 0.00 76.34 23.66 0 269.69 S + γ
34 34.18 0 2.22 0 63.6 93.91 0.00 6.09 0 174.73 S + S1
35 0 1.74 10.17 15.16 72.93 0.00 6.43 37.57 56.00 269.41 γ + S
36 0 1.71 9.32 15.96 73.01 0.00 6.34 34.53 59.13 270.51 γ + S
37 0 1.44 8.15 17.57 72.84 0.00 5.30 30.01 64.69 268.19 r + S
38 3.85 3.6 23.08 0 69.47 12.61 11.79 75.59 0 227.55 γ + S
39 8.81 2.96 19.79 0 68.44 27.92 9.38 62.71 0 216.86 γ + S
40 12.07 3.54 17.23 0 67.16 36.75 10.78 52.47 0 204.51 γ + S
41 21.89 2.29 10.22 0 65.6 63.63 6.66 29.71 0 190.69 γ + S
42(F5) 27.03 2.29 6.61 0 64.07 75.23 6.37 18.39 0 178.32 S + S1 + γ
43(F6) 41.85 0 3.13 0.71 54.31 91.60 0.00 6.85 1.55 118.87 S + S1 + S3
44 49.07 0 3.64 2.65 44.64 88.64 0.00 6.58 4.79 80.64 S + S3
45 21.88 1.1 10.15 7.51 59.36 53.84 2.71 24.98 18.48 146.06 S + S3 + Cl
46 27.62 0.75 12.74 5.88 53.01 58.78 1.59 27.11 12.51 112.81 S + S3 + Cl
47 19.05 2.05 4.45 7.71 66.74 57.28 6.16 13.38 23.18 200.66 γ + S + S3
48 20.94 2.28 5.08 5.96 65.74 61.12 6.65 14.83 17.39 191.89 γ + S + S3
49 20.88 1.87 5.37 4.99 66.89 63.06 5.65 16.22 15.07 202.02 γ + S + S3
50 22.05 2.01 5.66 4.12 66.16 65.16 5.94 16.73 12.17 195.51 γ + S + S3
51 23.04 1.89 6.27 3.07 65.73 67.23 5.52 18.29 8.96 191.80 γ + S + S3
52 24.51 2.05 5.56 1.92 65.96 72.00 6.02 16.33 5.64 193.77 γ + S + S3
53(E5) 26.12 2.22 7.09 0.73 63.84 72.23 6.14 19.61 2.02 176.55 γ + S + S3 + S1
54 48.79 0.55 0 0 50.66 98.89 1.11 0.00 0.00 102.68 C + OH
55 0 11.09 1.93 16.75 70.23 0.00 37.25 6.48 56.26 235.91 C1 + γ
56 0 16.22 2.64 12.48 68.66 0.00 51.75 8.42 39.82 219.08 C1 + γ
57 0 24.44 4.59 3.49 67.48 0.00 75.15 14.11 10.73 207.50 C1 + γ
58 11.8 13.16 4.28 0 70.76 40.36 45.01 14.64 0.00 241.99 C1 + γ
59 21.55 5.08 2.25 0 71.12 74.62 17.59 7.79 0.00 246.26 C1 + γ
60(F7) 61.85 4.89 1.78 0 31.48 90.27 7.14 2.59 0.00 45.94 C1 + OH + γ
61(F6) 51.66 2.86 0.84 0 44.64 93.32 5.17 1.52 0.00 80.64 C1 + C + OH
62 30.11 1.65 0 4.6 63.64 82.81 4.54 0.00 12.65 175.03 C1 + Cl
63 24.67 1.58 0 7.14 66.61 73.88 4.73 0.00 21.38 199.49 C1 + Cl
64(E6) 25.1 7.52 0.94 3.62 62.82 67.51 20.23 2.53 9.74 168.96 C1 + γ + Cl + OH
65 72.99 3.42 1.45 3.78 18.36 89.40 4.19 1.78 4.63 22.49 C1 + OH + Cl
66 54.62 2.61 0.2 1.93 40.64 92.01 4.39 0.34 3.25 68.46 C + OH + Cl
67(E7) 56.77 1.21 0.21 1.32 40.49 95.40 2.03 0.35 2.22 68.04 C1 + OH + Cl + C
68 71.62 0 2.75 0 25.63 96.30 0.00 3.69 0.00 34.46 OH + S1
69(F9) 78.12 0 3.7 1.07 17.11 94.25 0.00 4.46 1.29 20.64 OH + S1 + S3
70(F10) 55.85 2.09 1.69 0 40.37 93.66 3.50 2.83 0.00 67.70 OH + γ + S1
71 36.72 0.09 1.84 1.76 59.59 90.87 0.22 4.55 4.36 147.46 OH + γ + S1
72 45.46 0.32 2.19 1.78 50.25 91.38 0.64 4.40 3.58 101.01 OH + γ + S1
73 48.32 0.66 3.44 1.62 45.96 89.42 1.22 6.36 2.99 85.05 OH + γ + S1
74(E8) 53.31 0.86 3.97 1.3 40.56 89.69 1.45 6.68 2.19 68.24 OH + S1 + γ + S3
75 81.29 1.22 4.93 1.19 11.37 91.72 1.38 5.56 1.34 12.83 OH + S1 + S3
76 79.61 1.96 6.87 0.91 10.65 89.09 2.19 7.69 1.02 11.92 OH + S1 + S3
77 77.85 2.01 7.37 0.42 12.35 88.82 2.29 8.41 0.48 14.09 OH + S1 + S3
78 63.32 1.17 3.44 1.57 30.5 91.11 1.68 4.95 2.26 43.88 OH + γ + S3
79(E9) 65.32 2.17 4.55 2.74 25.22 87.35 2.90 6.08 3.66 33.73 OH + γ + S3 + C1
80 75.75 1.98 4.57 4.17 13.53 87.60 2.29 5.29 4.82 15.65 OH + γ + C1
81 79.02 1.66 4.33 4.64 10.35 88.14 1.85 4.83 5.18 11.54 OH + γ + C1
82 82.48 1.34 4.04 4.28 7.86 89.52 1.45 4.38 4.65 8.53 OH + γ + C1
83 83.83 1.28 4.13 5.88 4.88 88.13 1.35 4.34 6.18 5.13 OH + γ + C1
84 65.86 0.43 2.57 5.06 26.08 89.09 0.58 3.48 6.85 35.28 OH + γ + C1
85 62.12 0.27 2.38 5.72 29.51 88.13 0.38 3.38 8.11 41.86 OH + γ + C1
86 55.29 0.56 0.32 1.32 42.51 96.17 0.97 0.56 2.29 73.94 C + C1 + OH
87(E10) 81.74 2.35 2.93 2.79 10.19 91.01 2.62 3.26 3.11 11.35 OH + S3 + C1 + Cl
88 80.24 2.75 3.16 1.05 12.8 92.02 3.15 3.62 1.20 14.68 Cl + OH + S3
89 17.14 10.99 0 0 71.87 60.93 39.07 0.00 0.00 255.49 C1 + C
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a

Standard uncertainties u are u(T) = 0.1 K, u(P) = 0.5 kPa, ur(Na2CO3) = ur(Na2SO4) = ur(NaCl) = ur(NaOH) = 0.05.

b

w(B) is the mass fraction of component (B).

c

Abbreviations: S, Na2SO4; OH, NaOH; Cl, NaCl; C1, Na2CO3·H2O; C, Na2CO3; γ, mNa2SO4·nNa2CO3; S3, Na2SO4·NaCl·NaOH.

d

The data in the columns are the data measured in this work.

3.1. Diagrams of Dry Salt, Water, and Sodium Chloride (Saturated with NaCl)

The solubility of the equilibrated liquid phase was expressed as the mass fraction. Based on the Jänecke dry-salt indices, the dry-salt, water, and sodium chloride (saturated with NaCl) diagrams were plotted, as shown in Figure 2.

Figure 2.

Figure 2

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Dry-salt solubility, water, and sodium chloride diagram of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K (saturated with salt NaCl).

The phase diagram of the quinary system has five crystallization fields all saturated with NaCl (Figure 1): Na2SO4 + NaCl (BD2E1F1B field), NaCl + γ (D1D2E1E3E4D1 field), Na2CO3·H2O + NaCl (CD1E4F2C field), S3 + NaCl (E1F1F4E2E3E1 field), Na2CO3 + NaCl (F3E2E3E4F2F3 field), and NaOH + NaCl (AF4E2F3A field). The crystallization field of NaOH + NaCl is the smallest and corresponds to the highest solubility in the quinary system. The NaCl + γ field is larger than the other fields, which means that it is very easily separated from the solution. There are four co-saturation points (E1, E2, E3, and E4). The complex salt S3 (Na2SO4·NaCl·NaOH) and the solid solution γ (mNa2SO4·nNa2CO3) were simultaneously found in the quinary system. Figure 3 shows the powder XRD patterns of the co-saturation points in this system.

Figure 3.

Figure 3

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X-ray diffraction photographs of the co-saturation points E1, E2, E3, and E4 of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K (saturated with salt NaCl).

E1: saturated with NaCl, γ, S3, and Na2SO4.

E2: saturated with NaCl, S3, NaOH, and Na2CO3.

E3: saturated with NaCl, γ, S3, and Na2CO3·H2O.

E4: saturated with NaCl, γ, Na2CO3, and Na2CO3·H2O.

3.2. Diagrams of Dry Salt, Water, and Sodium Hydroxide (Saturated with NaOH)

The dry-salt, water, and sodium hydroxide (saturated with NaOH) diagrams were constructed, as shown in Figure 4, on the basis of the experimental data.

Figure 4.

Figure 4

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Dry-salt solubility, water, and sodium hydroxide diagram of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K (saturated with salt NaOH).

The diagram for NaOH saturation clearly shows that the phase diagram of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K consists of six crystallization fields, five solubility curves, and four co-saturation points (E7, E8, E9, and E10). NaOH + NaCl is larger than the other crystallization fields, and the NaOH + γ crystallization field is the smallest. The powder XRD patterns of the co-saturation points (E7, E8, E9, and E10) are shown in Figure 5.

Figure 5.

Figure 5

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X-ray diffraction photographs of the co-saturation points E7, E8, E9, and E10 of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K (saturated with salt NaOH).

E7: saturated with NaOH, NaCl, Na2CO3·H2O, and Na2CO3.

E8: saturated with NaOH, γ, S1, and S3.

E9: saturated with NaOH, γ, Na2CO3·H2O, and S3.

E10: saturated with NaOH, NaCl, Na2CO3·H2O, and S3.

3.3. Diagrams of Dry Salt, Water, and Sodium Carbonate (Saturated with Na2CO3)

Figure 6 presents a diagram of dry salt, water, and sodium carbonate in this system, which is saturated with Na2CO3. The phase diagram of the quinary system consists of five crystallization fields and two co-saturation points (E6 and E7). The five crystallization fields correspond to Na2CO3·H2O + γ, Na2CO3·H2O + NaCl, Na2CO3 + NaCl, Na2CO3 + NaOH, and Na2CO3·H2O + NaOH. The crystallization field of Na2CO3 + NaCl is the smallest, while that of Na2CO3·H2O + γ is larger than the other fields. The powder XRD image at point E6 is shown in Figure 7.

Figure 6.

Figure 6

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Dry-salt solubility, water, and sodium carbonate diagram of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K (saturated with salt Na2CO3).

Figure 7.

Figure 7

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X-ray diffraction photograph of the co-saturation point E6 of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K (saturated with salt Na2CO3).

E6: saturated with NaCl, γ, Na2CO3·H2O, and NaOH.

3.4. Diagrams of Dry Salt, Water, and Sodium Sulfate (Saturated with Na2SO4)

The powder XRD image at point E5 is shown in Figure 7. Figure 8 presents a diagram of dry salt, water, and sodium sulfate in this system, which is saturated with Na2SO4. The phase diagram of the quinary system consists of four crystallization fields and two co-saturation points (E5 and E6). The four crystallization fields correspond to Na2SO4 + γ, Na2SO4 + S1 (NaOH·Na2SO4), Na2SO4 + S3 (Na2SO4·NaCl·NaOH), and Na2SO4 + NaCl.

Figure 8.

Figure 8

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Dry-salt solubility, water, and sodium sulfate diagram of the quinary system NaOH + NaCl + Na2CO3 + Na2SO4 + H2O at 363.15 K (saturated with salt Na2SO4).

E5: saturated with γ, Na2SO4, S1, and S3.

4. Solubility Predictions

Xu et al.21,30−32 proposed a new hypothesis for the reference state of activity coefficients for solubility prediction, considering the solute in the salt-water system as molecules. In addition, they also put forward a new assumption for the standard state, as follows. When the concentration of the solute is close to solubility, activity ai (= miγi) is close to 1. On the basis of the Pitzer ion-interaction model, they deduced a new model formula as follows.

4. 1
4. 2
4. 3
4. 4

where mj is the molality of solute j, and Ei, Fi,j, and Gi,j are the interaction parameters at a particular temperature.

The standard state used in the model is proposed to facilitate the calculation of SLE. Therefore, it only makes sense for SLE, and the standard state is not physically meaningful for other cases.

The software 1stOpt 6.0 (7D-Soft High Technology, Inc.) was used to correlate the model parameters. And the optimization algorithm was the Universal Global Algorithm, which set the convergence index as 1 × 10–15, the maximum number of iterations as 5000, and the output control as 50 in real time.

The solubilities of the quinary system NaOH + Na2CO3 + Na2SO4 + NaCl + H2O at 363.15 K were calculated. A comparison between the calculated phase diagrams and the predicted phase diagrams is shown in Figure 9.

Figure 9.

Figure 9

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Correlation of experimental SLE data for NaOH–Na2CO3–Na2SO4–NaCl–H2O: (a) saturated with NaCl; (b) saturated with Na2SO4; (c) saturated with Na2CO3; and (d) saturated with NaOH.

For the sake of simplicity, water-salt parameters for electrolyte solutions were shared in single-salt systems and mixed-salt systems. The predicted solubilities were in good agreement with the experimental data, which confirms that the obtained mixed-salt parameters21 are reliable for predicting the solubilities of the NaOH + Na2CO3 + Na2SO4 + NaCl + H2O system.

5. Conclusions

For determining the suitable amount of evaporation for producing sodium hydroxide by means of vaporizing the natural soda solutions in Inner Mongolia, the phase equilibria for the quinary system NaOH–Na2CO3–Na2SO4–NaCl–H2O at 363.15 K were studied in this paper. According to the measured solubility data and the literature solubility data, dry-salt phase diagrams and water diagrams versus composition diagrams were plotted (saturated with saturated NaCl, NaOH, Na2CO3, and Na2SO4, respectively). Also, analyses and discussions are made on the construction of these phase diagrams.

This study lays a foundation for the analysis and calculation of the diagram for the vaporizing process for the quinary system NaOH–Na2CO3–Na2SO4–NaCl–H2O at 363.15 K. Using the corresponding parameters, which were fitted with Xu’s activity coefficient model, the solubility data of this quinary system were calculated. The results show a satisfactory agreement with those measured.

Acknowledgments

This work was supported by the Scientific Foundation for the High Education Institutes, Inner Mongolia (grant no. NJZY17094).

The authors declare no competing financial interest.

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