Clâ, NO3

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

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Stable Phase Equilibria of the Quaternary System Na+//Cl−, NO3−, SO42−−H2O at 353.15 K Chao Bian,† Hang Chen,†,§ Xingfu Song,*,†,‡,§ Yan Jin,† and Jianguo Yu*,† †

National Engineering Research Center for Integrated Utilization of Salt Lake Resource and ‡National Engineering Laboratory for Industrial Wastewater Treatment, East China University of Science and Technology, Shanghai 200237, China § Shanghai Institute of Pollution Control and Ecological Security, Shanghai 200092, China

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S Supporting Information *

ABSTRACT: The phase equilibria of the quaternary system Na+// Cl−, NO3−, SO42−−H2O and the subsystems Na+//Cl−, SO42−−H2O, Na+//Cl−, NO3−−H2O, Na+//NO3−, SO42−−H2O at 353.15 K were studied by the isothermal dissolution method. There are one invariant point, three univariant curves, three crystallization fields of single salt, three cocrystallization fields for two salts, and one cocrystallization field for three salts in the quaternary system. Neither double salt nor solid solution is found in the system at 353.15 K. At the invariant point of Na+//Cl−, NO3−, SO42−−H2O system, the composition of the solution is NaCl 7.00 wt %, Na2SO4 1.59 wt %, NaNO3 47.79 wt %. The order of the solubility in the mixing solution of the single salts is Na2SO4 < NaCl < NaNO3. Moreover, the solubilities of the systems at 353.15 K were calculated theoretically by using the Pitzer ion interaction model. The high ionic strength was found to be a critical factor, which influenced the calculation accuracy significantly. All data and results obtained in this paper are of great significance to the design and optimization of the fractional crystallization process of the high-saline wastewater in coal chemical industry.

1. INTRODUCTION The wastewater with high salinity discharged from various processes, such as energy industry, leather processing, textile industry, and food engineering, is becoming an important environmental problem, which limits the industrial development significantly.1 This is especially true in the coal chemical industry where the high-saline wastewater contains kinds of inorganic salts and organic contaminations.2 In the past, the high-saline wastewater in coal chemical industry was mainly treated by the method of evaporation pond in China where there were a lot of hazardous mixed salt residues. Then, with the increasingly stringent environmental regulations it was gradually replaced by the idea of zero-discharge process.3 Compared with traditional evaporation pond, the zerodischarge flowsheet not only concerns on the water treatment but also focuses more on the recycle of the dissolved inorganic salts, so that it is considered as an environmental friendly and resource-saving process. In this method, the membrane concentration technology4,5 and evaporation technique6 are usually combined to realize the water reuse,7 whereas the recycle of the inorganic salts mainly depends on the fractional crystallization process, namely, the multistep crystallization separation. Meanwhile, other operating units such as biochemical treatment, ozone oxidation, and electrocatalytic oxidation also will be involved to degrade the organic pollutants and remove the ammonia nitrogen.8−12 Although the zero-discharge flowsheet is a high-efficient method to process the high-saline wastewater, it still faces two main technical difficulties. The first one is about the separation of © XXXX American Chemical Society

the inorganic salts. It is known that high-saline wastewater in coal chemical industry has a typical inorganic composition of Na+//Cl−, NO3−, SO42−−H2O. The complicated components signify that the fractional crystallization process needs a highaccuracy engineering control to separate these salts effectively. The second one is about the organic contaminations. Because the high-saline wastewater in the coal chemical industry usually contains kinds of persistent organic pollutants, it is hard to degrade them completely even if the advanced oxidation methods are used. So the crystallized inorganic salts are easily to be contaminated by the organic pollutants.13 This paper mainly focuses on the first problem of inorganic salts separation and it is easy to understand that elaborate phase equilibrium data are the key to realize the high-accuracy fractional crystallization separation. Up to now, some solid− liquid phase equilibrium data have been reported for the saltwater system containing Na+, Cl−, NO3−, and SO42−. For example, Zhang14 investigated the solid−liquid equilibrium for the ternary system Na+//Cl−, SO42−−H2O at 313.15 K and atmospheric pressure. Zhang15 studied the stable liquid−solid phase equilibria for the quaternary system Na+//Cl−, NO3−, SO42−−H2O at 258.15, 268.15, 273.15, and 278.15 K by the isothermal dissolution method. Lin16 measured the metastable phase equilibria of the same system at 298.15 and 323.15 K by the isothermal evaporation method. It can be found that all of Received: March 14, 2018 Accepted: July 20, 2018

A

DOI: 10.1021/acs.jced.8b00198 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

isothermal equilibrium. In view of the complexity of the quaternary system Na +//Cl−, NO3−, SO4 2−−H2O, the equilibrium studies were divided into four parts according to the number of invariant points of the ternary systems. That is to say, the experimental points of the ternary systems were acquired by adding the second salts gradually on the basis of its binary saturation points at 353.15 K, and the quaternary samples were prepared by adding the third salt to the ternary system from low to high until the third salt was saturated at 353.15 K. A certain quantity of the salts and deionized water were mixed together in a polytetrafluoroethylene flask, and then the flask was sealed and placed in the constant temperature water bath oscillator with the constant temperature controlled at 353.15 K. The mixtures were vibrated for a specific time at a speed of 200 rpm. To ensure the sample achieved a balance, the ion concentrations of liquid phase were analyzed every 2 h. When the differences in the ion concentrations over four sequential measurements was less than 0.5%, the solid−liquid equilibrium was considered to be reached. Subsequently, the flask was standing for 24 h at 353.15 K to clarify the aqueous solution before sampling. After equilibration, a certain mass of the solution was weighed accurately and diluted with deionized water for quantitative analysis in a 100 mL volumetric flask. The density (ρ) of the liquid phase was measured by using a previously weighed 10 mL density bottle, and the standard uncertainty was 0.001 g·cm−3. The density bottle containing liquid phase was preheated at 353.15 K with a standard uncertainty of 0.05 K for 4 h. Wet residue was separated from the liquid phase by vacuum filtration using a sintered glass filter crucible, which was preheated at 353.15 K for 2 h. Similarly, a certain mass of the wet residue was weighed accurately and moved into a 100 mL volumetric flask for chemical analysis. The remainder of the solid was dried for the X-ray diffraction analysis (Rigaku D/MAX-B with a Cu target, operated with a 2θ step size of 0.02°). 2.3. Analytical Methods. There are many methods for measuring the compositions of the liquid phase and wet residue, such as chemical titration method,24,25 gravimetrical method,26,27 spectrophotometry,28 and inductively coupled plasma (ICP).29 In this paper, the chlorine ion (Cl−) was determined by titration method with standard silver nitrate solution in the presence of potassium chromate. The sulfate ion (SO42−) was measured by gravimetric method with excess barium sulfate solution based on the national standard GB/T 13025.8−2012. The content of nitrate ion (NO3−) was determined by ion chromatography (IC) and the sample concentration was previously diluted into the calibration range from 1 to 10 ppm. Three parallel samples of each equilibrated liquid phase were analyzed three times, and the average value of the three measurements was considered as the final result. The relative standard uncertainties of Cl−, SO42− and NO3− are 0.005, 0.003 and 0.025, respectively.

the existing researches mainly focused on the phase equilibrium at the relatively low temperature range from 258.15 to 323.15 K, whereas the phase equilibrium at high temperature is few. To the best of our knowledge, only Yang17 once measured the stable phase equilibria and the physical properties of Na+//Cl−, NO3−, SO42−−H2O at 373.15 K. In addition, the thermodynamic models also have been proven to be a powerful tool to investigate the phase equilibrium of saltwater systems. Pitzer18 once theoretically reproduced various thermodynamic properties of the NaCl−H2O system with temperature up to 573 K, saturation pressure up to 100 MPa, and NaCl concentration up to 6 molal. Hubert19 calculated some properties of the Na2SO4−H2O system at 298.15, 300.65, and 318.15 K reasonably by using the Pitzer model. Song20−22 regressed part of the Pitzer parameters for the system Na+//Cl−, NO3−, SO42−−H2O at 298.15 K by fitting the measured experimental data. Besides, Yan23 presented a thermodynamic model for the ternary system of NaCl− Na2SO4−H2O with electrolyte concentrations up to saturation and temperature up to 473.15 K by using the electrolyte NRTL theory. The calculated results agree well with the experiments. In general, it needs a broad temperature operating range for separating the inorganic salts in the Na+//Cl−, NO3−, SO42−− H2O system, because the flowsheet involves both the processes of cooling crystallization and evaporative crystallization. The existing equilibrium data are inadequate to meet the requirement of the high-accuracy fractional crystallization control. Especially in the high temperature range from 323.15 to 373.15 K, the phase equilibrium investigation is lacking. For this reason, the phase equilibria data of the quaternary system Na+//Cl−, NO3−, SO42−−H2O and its subsystems at 353.15 K were measured and discussed in this study. Meanwhile, the measured solubility data of the salt-water system were reproduced theoretically by the Pitzer ion interaction model.

2. EXPERIMENTAL SECTION 2.1. Materials and Instruments. For measuring the phase equilibrium, analytical grade sodium chloride (≥99.5%), sodium nitrate (≥99.0%), and sodium sulfate (≥99.0%) purchased from Sinopharm Chemical Reagent Co. Ltd., China were used without any further purification. The specifications of the chemical samples were listed in Table 1. Deionized water (conductivity ≤1 μS/cm) was used for the equilibrium experiments and subsequent chemical analysis. A constant temperature water bath oscillator (SW23, Julabo) with an operating range from 293.15 to 372.65 K was employed for controlling the experimental temperature. The standard uncertainty was 0.05 K. 2.2. Experimental Methods. The equilibrium investigations in this paper were performed using the method of Table 1. Chemical Sample Descriptions chemical name

source

NaCl NaNO3 Na2SO4

S1 S1 S1

a

initial mass fraction purity

purification method

final mass fraction purity

99.5% 99.0% 99.0%

none none none

99.5% 99.0% 99.0%

3. RESULTS AND DISCUSSION 3.1. The Ternary System Na+//Cl−, SO42−−H2O. The solubility and density data of the ternary system Na+//Cl−, SO42−−H2O at 353.15 K are presented in Table 2. On the basis of the experimental data, the corresponding phase diagram was plotted as shown in Figure 1. The compositions of the equilibrium liquid phase and the wet residual are all expressed in weight percentage. Points A and B represent the

analysis method titration ICb gravimetric method

a

S1: Sinopharm Chemical Reagent Co. Ltd., China. bIon chromatography. B



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Table 2. Solubility and Density Data of the Ternary System Na+//Cl−, SO42−−H2O at Temperature T = 353.15 K and Pressure P = 0.1 MPaa composition of liquid phase (w(B)b × 100) no.

NaCl

Na2SO4

H2O

1(D) 2 3 4 5 6 7 8 9 10 11(P) 12 13 14(C)

0.00 1.68 3.20 6.04 9.01 12.37 16.11 18.49 21.19 23.61 25.57 26.77 27.26 27.75

30.38 27.22 25.67 21.99 18.25 14.39 10.29 8.99 6.98 5.57 4.53 2.91 1.46 0.00

69.62 71.10 71.13 71.98 72.74 73.23 73.60 72.52 71.83 70.82 69.90 70.32 71.28 72.25

composition of wet residue (w(B)b × 100) −3

density ρ g/cm 1.2540 1.2364 1.2342 1.2221 1.2106 1.2015 1.1934 1.2014 1.2051 1.2124 1.2194 1.2137 1.2033 1.1930

NaCl

Na2SO4

H2O

equibrium solid phase

0.00 1.02 1.74 4.14 5.46 5.80 6.85 13.19 12.43 13.01 34.48 42.71 38.11 34.94

60.61 57.94 55.46 42.64 49.36 58.89 62.94 35.89 49.51 43.52 32.81 2.19 1.08 0.00

39.39 41.05 42.81 53.22 45.19 35.32 30.21 50.92 38.06 43.47 32.70 55.10 60.81 65.06

Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 + NaCl NaCl NaCl NaCl

Standard uncertainties are u(T) = 0.05 K, u(P) = 0.5 kPa, u(ρ) = 0.001 g·cm−3, ur(w(Na2SO4)) = 0.003, ur(w(NaCl)) = 0.005. bw(B) is the mass fraction of component B. a

Figure 2, the XRD patterns of phases A and B are verified to be Na2SO4 and NaCl, respectively. The XRD pattern in Figure 3

Figure 1. Solubility diagram of the ternary system Na+//Cl−, SO42−− H2O at 353.15 K: ■, liquid phase; ●, wet solid phase; P, invariant point of the ternary system; A and B, composition points of pure Na2SO4 and NaCl, respectively; APDA and BCPB, crystallization fields of Na2SO4 and NaCl, respectively.

Figure 2. XRD pattern of phases A(Na2SO4) and B(NaCl) in the ternary system Na+//Cl−, SO42−−H2O at 353.15 K.

pure solids of Na2SO4 and NaCl, respectively. Points C and D mean the saturation points of the binary systems (NaCl−H2O) and (Na2SO4−H2O) at 353.15 K, respectively. The measured solubility of NaCl (point C) is 27.75% and the data from literature is 27.74%.30 Meanwhile, the measured solubility of Na2SO4 (point D) is 30.38%, which has a slight difference from the value of 30.41% in literature.30 As shown in Figure 1, the phase diagram includes one invariant point, two univariant curves, and three crystallization regions. Point P is the invariant point of the Na+//Cl−, SO42−−H2O system cosaturated with Na2SO4 and NaCl. The composition of the corresponding equilibrium solution is w(NaCl) = 25.57%, w(Na2SO4) = 4.53%. Along the curve CP, NaCl has priority to precipitate; however, Na2SO4 has priority along the curve DP. There are three crystallization fields corresponding to ADPA (Na2SO4), BCPB (NaCl), and an ABPA (Na2SO4 + NaCl). The crystallization field of Na2SO4 is greater than that of NaCl. The larger crystallization field indicates that the solubility of Na2SO4 in the Na+//Cl−, SO42−−H2O system is low and Na2SO4 will salt out of the solution easily with an increase of NaCl concentration. There is no double salt or solid solution in this system at 353.15 K. Moreover, the components of the equilibrium solid phases were further analyzed by x-ray diffraction (XRD). As shown in

Figure 3. XRD pattern of the invariant point P in the ternary system Na+//Cl−, SO42−−H2O at 353.15 K.

also shows that the point P is the invariant point of Na2SO4 and NaCl. In addition, Figure 4 indicates the relationship between the density and the mass fraction of NaCl in the solution. 3.2. The Ternary System Na+//Cl−, NO3−−H2O. The solubility and density data of the ternary system Na+//Cl−, NO3−H2O at 353.15 K are presented in Table 3. On the basis of the experimental data, the corresponding phase diagram was plotted as shown in Figure 5. Same as the ternary system Na+//Cl−, SO42−−H2O, the compositions of the equilibrium liquid phase and the wet residual are all expressed in weight C



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Figure 5. Solubility diagram of the ternary system Na+//Cl−, NO3−− H2O at 353.15 K: ■, liquid phase; ●, wet solid phase; Q, invariant point of the ternary system; B and E, composition points of pure NaCl and NaNO3, respectively; BCQB and EFQE, crystallization fields of NaCl and NaNO3, respectively.

Figure 4. Density of Na+//Cl−, SO42−−H2O system at 353.15 K.

percentage. Point E represents the pure solid of NaNO3 and point F is the saturation point of the binary system (NaNO3− H2O) at 353.15 K. The measured solubility of NaNO3 (point F) is 59.77% and the data from literature is 59.84%.30 As shown in Figure 5, there are one invariant point, two univariant curves, and three crystallization regions in the phase diagram of Na+//Cl−, NO3−−H2O at 353.15 K. The invariant point Q is cosaturated with NaCl and NaNO3, and the composition of the corresponding equilibrated solution is w(NaCl) = 7.02%, w(NaNO3) = 51.66%. The univariant curve CQ indicates solution in equilibrium with NaCl, and FQ indicates the solution in equilibrium with NaNO3. The three crystallization regions correspond to BCQB (NaCl), EFQE (NaNO3), and BEQB (NaCl+NaNO3). The larger crystallization field of NaCl indicates that it will salt out of the solution easily with an increase of NaNO3 concentration. There is no double salt or solid solution in this system at 353.15 K. Besides, the components of the equilibrium solid phases were further verified by XRD analysis. As shown in Figure 6, the XRD patterns of phases B and E are verified to be NaCl and NaNO3, respectively. The XRD pattern in Figure 7 presents that point Q is the invariant point of NaCl and NaNO3. Besides, with an increase of the concentration of

Figure 6. XRD pattern of phases B(NaCl) and E(NaNO3) in the ternary system Na+//Cl−, NO3−−H2O at 353.15 K.

NaNO3 the density of the solution has the tendency to increase (shown in Figure 8). 3.3. The Ternary System Na+//NO3−, SO42−−H2O. The solubility and density data of the ternary system Na+//NO3−, SO42−−H2O at 353.15 K are presented in Table 4. Also, the corresponding phase diagram was plotted. As shown in Figure 9, the phase diagram of Na+//NO3−, SO42−−H2O at 353.15 K contains one invariant point, two

Table 3. Solubility and Density Data of the Ternary System Na+//Cl−, NO3−−H2O at Temperature T = 353.15 K and Pressure P = 0.1 MPaa composition of liquid phase (w(B)b × 100) no.

NaCl

NaNO3

H2O

1(C) 2 3 4 5 6 7 8 9 10 11 12 13 14(Q) 15 16 17(F)

27.75 25.97 24.45 21.59 19.31 17.21 15.39 13.56 12.08 10.92 10.14 9.03 8.12 7.02 4.38 1.72 0.00

0.00 3.50 6.46 12.98 18.31 23.25 27.87 32.55 35.41 38.85 41.83 45.55 49.04 51.66 55.05 57.77 59.77

72.25 70.53 69.09 65.44 62.38 59.55 56.73 53.89 52.51 50.23 48.03 45.42 42.84 41.32 40.56 40.51 40.23

composition of wet residue (w(B)b × 100) density ρ g/cm

−3

1.1930 1.2066 1.2181 1.2484 1.2742 1.2988 1.3236 1.3493 1.3616 1.3829 1.4040 1.4293 1.4548 1.4697 1.4760 1.4751 1.4770

NaCl

NaNO3

H2O


39.04 30.82 34.08 34.32 41.92 32.82 30.49 20.40 23.43 19.43 28.01 21.73 14.31 14.77 2.33 1.21 0.00

0.00 3.33 6.07 11.06 13.33 19.08 22.86 30.03 31.04 35.07 33.47 38.81 45.99 53.59 75.70 69.10 62.13

60.96 65.85 59.85 54.61 44.75 48.10 46.65 49.58 45.53 45.50 38.52 39.46 39.70 31.64 21.97 29.69 37.87

NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl + NaNO3 NaNO3 NaNO3 NaNO3

Standard uncertainties are u(T) = 0.05 K, u(P) = 0.5 kPa, u(ρ) = 0.001 g·cm−3, ur(w(NaCl)) = 0.005, ur(w(NaNO3)) = 0.025. bw(B) is the mass fraction of component B. a

D



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Figure 7. XRD pattern of the invariant point Q in the ternary system Na+//Cl−, NO3−−H2O at 353.15 K.

Figure 9. Solubility diagram of the ternary system Na+//NO3−, SO42−−H2O at 353.15 K: ■, liquid phase; ●, wet solid phase; R, invariant point of the ternary system; E and A, composition points of pure NaNO3 and Na2SO4, respectively; EFRE and ADRA, which are the crystallization fields of NaNO3 and Na2SO4, respectively.

shown in Figure 10, the XRD pattern of phases A and F are verified to be Na2SO4 and NaNO3, respectively. Meanwhile,

Figure 8. Density of Na+//Cl−, NO3−−H2O system at 353.15 K.

univariant curves and three crystallization regions. The composition of the invariant point R in mass fraction is w(NaNO3) = 57.81% and w(Na2SO4) = 1.79%. The two univariant curves FR and AR represent the solubility curves of NaNO3 and Na2SO4, respectively. The three crystallization regions are ADRA (Na2SO4), EFRE (NaNO3), and AERA (Na2SO4 + NaNO3). Obviously, the crystallization area of Na2SO4 in this ternary system is considerably bigger than that of NaNO3. Similarly, the components of the equilibrium solid phase were further verified by XRD analysis. There is no double salt or solid solution in this system at 353.15 K. As

Figure 10. XRD pattern of phases E(NaNO3) and A(Na2SO4) in the ternary system Na+//NO3−, SO42−−H2O at 353.15 K.

the XRD pattern in Figure 11 also shows that the point R is the invariant point of Na2SO4 and NaNO3. Figure 12 illustrates the relationship between density and w(NaNO3) in the solution. With an increase of the

Table 4. Solubility and Density Data of the Ternary System Na+//NO3−, SO42−−H2O at Temperature T = 353.15 K and Pressure P = 0.1 MPaa composition of liquid phase (w(B)b × 100)

composition of wet residue (w(B)b × 100)

no.

NaNO3

Na2SO4

H2O

density ρ g/cm−3

NaNO3

Na2SO4

H2O


1(E) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16(R) 17 18(F)

0.00 4.01 7.52 14.53 20.58 26.37 30.86 37.45 41.68 44.81 46.51 48.03 50.98 51.85 56.10 57.81 58.59 59.77

30.38 26.76 24.67 18.75 14.83 11.41 8.75 7.12 5.66 4.45 3.92 3.39 2.87 2.77 1.86 1.79 1.01 0.00

69.62 69.23 67.81 66.71 64.59 62.22 60.40 55.43 52.66 50.74 49.57 48.58 46.15 45.38 42.04 40.41 40.40 40.23

1.2540 1.2511 1.2600 1.2592 1.2712 1.2864 1.2982 1.3410 1.3645 1.3807 1.3910 1.3997 1.4227 1.4302 1.4622 1.4789 1.4773 1.4770

0.00 2.55 4.90 10.46 9.30 11.15 16.54 22.93 22.81 21.83 16.07 30.80 41.46 18.45 38.83 36.95 62.89 69.79

38.35 52.91 48.07 37.79 59.99 62.51 50.99 40.73 47.86 52.58 66.39 38.78 22.09 65.55 32.08 42.86 0.86 0.00

61.65 44.55 47.03 51.75 30.71 26.34 32.47 36.34 29.33 25.60 17.54 30.42 36.45 16.00 29.09 20.19 36.26 30.21

Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 Na2SO4 + NaNO3 NaNO3 NaNO3

Standard uncertainties are u(T) = 0.05 K, u(P) = 0.5 kPa, u(ρ) = 0.001 g·cm−3, ur(w(NaNO3)) = 0.025, ur(w(Na2SO4)) = 0.003. bw(B) is the mass fraction of component B. a

E



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J(Cl 22 −) = 100 ×

n(Cl 22 −) [n(Cl 22 −)

+ n((NO3)22 − ) + n(SO24 −)] (1)

J((NO3)22 − )

= 100 ×

n((NO3)22 − ) [n(Cl 22 −) + n((NO3)22 − ) + n(SO24 −)] (2)

Figure 11. XRD pattern of the invariant point R in the ternary system Na+//NO3−, SO42−−H2O at 353.15 K.

J(SO42 −) = 100 ×

[n(Cl 22 −) +

n(SO42 −) n((NO3)22 − )

+ n(SO42 −)] (3)

J(H 2O) = 100 ×

n(H 2O) [n(Cl 22 −)

+ n((NO3)22 − ) + n(SO24 −)] (4)

where n represents the amount of every kind of ion or H2O in 100 g of solution, mol. According to the Jänecke indexes in Table 5, the dry salt phase diagram and water content diagram of the system Na+// Cl−, NO3−, SO42−−H2O at 353.15 K were plotted in Figure 13 Figure 12. Density of Na+//NO3−, SO42−−H2O system at 353.15 K.

concentration of NaNO3, the density has the tendency to increase and then it declines slightly afterward. 3.4. The Quaternary System Na+//Cl−, NO3−, SO42−− H2O. The solubility (mass fraction) and density data of the quaternary system Na+//Cl−, NO3−, SO42−−H2O at 353.15 K were measured and tabulated as shown in Table 5. The dry salt phase diagram and the water content diagram are combined to describe the phase equilibrium of this system. The Jänecke indexes31 of the components were calculated previously as

Figure 13. Dry salt phase diagram of the quaternary system Na+// Cl−, NO3−, SO42−−H2O at 353.15 K.

Table 5. Solubility and Density Data of the Quaternary System Na+//Cl−, NO3−, SO42−−H2O at Temperature T = 353.15 K and Pressure P = 0.1 MPaa Jänecke index of dry salt J(Cl22−)+J((NO3)22−)+J(SO42−)=100 mol

composition of liquid phase (w(B)b•100) no.

NaCl

NaNO3

Na2SO4

H2O

density ρ g/cm−3

2Cl−

2NO3−

SO42−

H2O

solid phase

1(P) 2 3 4 5 6 7 8 9(S) 10 11 12(R) 13 14 15 16 17(Q)

25.57 21.32 17.18 13.87 11.33 9.18 7.54 7.23 7.00 4.49 2.67 0.00 7.19 7.16 7.22 7.29 7.02

0.00 12.49 22.73 31.27 37.55 43.39 47.22 51.92 47.79 48.46 49.73 57.18 52.54 49.04 47.53 49.15 51.66

4.53 3.58 2.86 2.45 2.05 1.80 1.52 1.62 1.59 1.59 1.73 1.79 1.64 1.61 1.62 0.94 0.00

69.9 62.61 57.23 52.41 49.07 45.63 43.72 39.23 43.62 45.46 45.87 41.03 38.63 42.19 43.63 42.62 41.32

1.2194 1.2795 1.3252 1.3682 1.3984 1.4308 1.4486 1.4949 1.4494 1.4295 1.4247 1.4724 1.5012 1.4642 1.4495 1.4585 1.4697

87.28 64.89 48.86 37.10 29.17 22.67 18.27 16.33 17.00 11.48 6.97 0.00 16.10 16.96 17.51 17.42 16.50

0.00 26.14 44.45 57.51 66.48 73.67 78.69 80.65 79.82 85.18 89.31 96.39 80.88 79.90 79.26 80.74 83.50

12.72 8.97 6.69 5.39 4.34 3.66 3.03 3.01 3.18 3.34 3.72 3.61 3.02 3.14 3.23 1.85 0.00

1547.57 1236.12 1055.72 909.27 819.56 730.87 687.33 574.88 687.26 753.77 777.09 652.46 560.98 648.41 686.32 660.43 630.02

Na2SO4 + NaCl Na2SO4 + NaCl Na2SO4 + NaCl Na2SO4 + NaCl Na2SO4 + NaCl Na2SO4 + NaCl Na2SO4 + NaCl Na2SO4 + NaCl Na2SO4 + NaCl + NaNO3 Na2SO4 + NaNO3 Na2SO4 + NaNO3 Na2SO4 + NaNO3 NaCl + NaNO3 NaCl + NaNO3 NaCl + NaNO3 NaCl + NaNO3 NaCl + NaNO3

Standard uncertainties are u(T) = 0.05 K, u(P) = 0.5 kPa, u(ρ) = 0.001 g·cm−3, ur(w(NaCl)) = 0.005, ur(w(NaNO3)) = 0.025, ur(w(Na2SO4)) = 0.003. bw(B) is the mass fraction of component B. a

F



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and Figure 14, respectively. As shown in Figure 13, the quaternary system is characterized by three ternary invariant

K 2 = mNO−3 × rNO−3 × mNa+ × rNa+

(6)

2 2 + × r K3 = mSO24− × rSO24− × mNa Na +

(7)

In this paper, the solubility products at 353.15 K were calculated by two steps. The solubility products at 298.15 K were acquired first by using the chemical potentials of equilibrium species reported in literatures. The chemical potential at standard state and the standard enthalpy of formation for ions Na+, Cl−, NO3−, SO42− were obtained from Shock.33 For the solids NaCl, NaNO3 and Na2SO4, the data were taken from Wagman.34 All the data are listed in the Supporting Information (Table S1). Then, the solubility products of NaCl, NaNO3, and Na2SO4 at 298.15 K can be calculated by eq 8.

Figure 14. Water content diagram of the quaternary system Na+// Cl−, NO3−, SO42−−H2O at 353.15 K.

points (P, Q, and R), one quaternary invariant point (S), three univariant curves (PS, QS, and RS), and three crystallization fields. Points P, Q, and R are the invariant points of the ternary systems Na+//Cl−, SO42−−H2O, Na+//Cl−, NO3−−H2O, Na+//NO3−, SO42−−H2O at 353.15 K, respectively. The invariant point S is cosaturated with NaCl, Na2SO4, and NaNO3, and the mass fraction composition of the corresponding solution is w(Na2SO4) = 1.59%, w(NaCl) = 7.00%, and w(NaNO3) = 47.79%. The three univariant curves PS, QS, and RS are cosaturated with two salts, respectively. Specifically, PS is cosaturated with NaCl and Na2SO4, QS is cosaturated with NaCl and NaNO3, and RS is cosaturated with Na2SO4 and NaNO3. There are three crystallization fields corresponding to Na2SO4 (ARSPA), NaCl (BPSQB), and NaNO3 (EQSRE). Apparently, the crystallization field of Na2SO4 is the biggest and that of NaNO3 is the smallest. The results indicate that the order of the solubilities is Na2SO4 < NaCl < NaNO3. In other words, it is easiest for Na2SO4 to crystallize from the mixing solution. There is no double salt or solid solution in this quaternary system at 353.15 K. The XRD pattern shown in Figure 15 also determines that point S is the invariant point of NaCl, Na2SO4, and NaNO3.

ln K 0 =

μs0 RT

(vMμM0 + vXμ X0 )

−

where K0 is the solubility product at 298.15 K; μ is the standard-state chemical potential, J·mol−1; v is the stoichiometric number; S, M, X represent the solid, cation, and anion, respectively; R is the universal gas constant, 8.3145 J·mol−1· K−1; T represents the absolute temperature in Kelvin. On the basis of K0 calculated above, using the molar reaction enthalpy ΔH0r of the solids calculated by the molar formation enthalpy of species, the solubility product at different temperatures KT can be calculated according to Van’t Hoff equation 0

ΔHr0 ijj 1 1 yz jj − zzz j R kT T0 z{

ln KT = ln K 0 −

(9)

where T is in Kelvin. The solubility products of NaCl, NaNO3, and Na2SO4 at 298.15 and 353.15 K were calculated and listed in the Supporting Information (Table S2). For aqueous mixed electrolytes, the closure of Pitzer model still requires the binary cation−anion interaction parameters β(0), β(1), and Cϕ for single electrolytes, additional binary ion− ion interaction parameters θ for pairs of ions of like sign and ternary ion−ion-ion interaction parameters ψ for triplets of ions (two of like sign and one of the opposite sign).35 Because of the diversity of the hybrid system, the reported mixing parameters36 cannot meet the needs of the actual calculation. A kind of approximate calculation method is to employ the assumption of θ = ψ = 0.37 Then, the corresponding activity coefficients of the electrolytes in the multicomponent watersalt system can be calculated as 2 ln γM = Z M F+

∑ ma[2BMa + ZCMa] a

Figure 15. XRD pattern of the invariant point S in the quaternary system Na+//Cl−, NO3−, SO42−−H2O at 353.15 K.

+ |ZM| ∑ ∑ mc maCca c

ln γX = Z X2F +

3.5. Model Application. Pitzer ion interaction model has been extensively used for modeling thermodynamic properties of aqueous electrolyte systems with ionic strength up to 6−10 molal.32 In this section, the measured equilibrium data were reproduced by using the Pitzer theory with existing model parameters. For the theoretical calculation, the thermodynamic solubility products (K1 for NaCl, K2 for NaNO3, and K3 for Na2SO4) should be first known. K1 = mCl− × rCl− × mNa+ × rNa+

(8)

RT

(10)

a

∑ mc[2Bc X + ZCc X ] c

+ |Z M| ∑ ∑ mc maCca c

a

(11)

where γ is the activity coefficient; Z is the charge number; m is the molality, mol·kg−1; M, X represent cation and anion, respectively; a and c represent the anions and cations, respectively. Other parameters in the above equations were calculated as follows:

(5) G


Journal of Chemical & Engineering Data ÄÅ ÉÑ Å I1/2 Ñ 2 1/2 Ñ ϕÅ Å ÑÑ Å F = −A ÅÅ + ln(1 + bI ) ÑÑ ÅÅÇ 1 + bI1/2 ÑÑÖ b ′ + ∑ ∑ mc maBca c

a

Bca = βca(0) +

′ = Bca

Cca = Z=

2βca(1)

(12)

1/2

[1 − (1 + αI1/2)e−αI ]

2

Ä ÉÑ 2βca(1) ÅÅÅ 1/2 Ñ ÅÅ−1 + ijj1 + αI1/2 + 1 α 2 Iyzze−αI ÑÑÑ j z ÑÑ 2 { α 2I 2 ÅÅÅÇ ÑÖ k αI

(13)

(14)

Ccaϕ 2 |ZcZa|1/2

(15)

∑ mi|Zi| i

1 i 2πNAd w yz zz A = jjjj 3 k 1000 z{

1/2

ϕ

Article

2 jij e zyz jj zz k DkT {

(16) 3/2

(17)

In eq 12, I represents the ionic strength of the solution. Aϕ is a function of temperature, density, and dielectric constant of water, which can be expressed as eq 17. The value of the empirical parameter b is taken as 1.2 (kg·mol)−1/2. B, B′ represent the second virial coefficients, and they are defined in eq 13 and eq 14, respectively. The value of the empirical parameter α is assigned to be 2.0 (kg·mol)−1/2. C is the third virial coefficient and it is defined in eq 15. Z is the charge number and it can be calculated by eq 16. The Pitzer’s parameters β(0), β(1), and Cϕ listed in the Supporting Information (Table S3) were referenced from Aspen Plus database. On the basis of the calculated solubility productions (K1, K2, and K3) and the Pitzer model parameters, the solubility data of the quaternary system Na+//Cl−, NO3−, SO42−−H2O and its subsystems at 353.15 K were calculated in Matlab 2016, and the results were compared with the experimental data in Figure 16 and 17. For the binary systems NaCl−H2O, Na2SO4−H2O, and NaNO3−H2O, the modeling solubility data are w(NaCl) = 27.63%, w(Na2SO4) = 30.07%, and w(NaNO3) = 59.76%, respectively, which agree well with the experimental data within the error of 0.5%. Nevertheless, there are some differences between the calculated results and the experimental values near the invariant points in the ternary systems. On the basis of the information given in Table 6, the ionic strength is recognized to be the main reason for the difference. That is to say, with the increase of the ionic strength in the system the existing model parameters for the calculation gradually go beyond the range of application (

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