Water Activity, Solubility Determination, and Model Simulation of the

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

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Water Activity, Solubility Determination, and Model Simulation of the CaCl2−SrCl2−H2O Ternary System at 323.15 K Haijun Han,†,‡ Xiang Ji,§ Junjie Ma,† Zhifeng Xu,*,† Lijiang Guo,*,‡ Dongdong Li,‡ and Yan Yao‡ †

School of Metallurgy and Chemical Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, P. R. China Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, P. R. China § College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, P. R. China ‡

ABSTRACT: Water activities for the CaCl2−SrCl2−H2O ternary system and its sub-binary system were elaborately determined using an isopiestic vaporpressure method at 323.15 K. The solubility of the titled ternary system at 323.15 K was also determined by the isothermal equilibrium method. The Pitzer−Simonson−Clegg (PSC) model was used for correlating the determined water activity and solubility data, simulating the thermodynamic properties, and predicting the solubility isotherm of the titled system. The reliability of the determined solubility results in this work was evaluated by comparing with the solubility isotherms calculated with the PSC model. The model simulation results showed that the thermodynamic properties and solubility can be predicted with binary parameters only. The experiment and simulation results showed that the equilibrium solid phase in the CaCl2−SrCl2−H2O ternary system are pure salts, and no solid solution was found at 323.15 K.

1. INTRODUCTION The oilfield brine in the Nanyishan area, which is located in the Qaidam Basin of the Qinghai-Tibet plateau, northwest of China, is rich in potassium, strontium, lithium, and iodine resources. The concentrations of calcium and strontium ions in the Nayishan oilfield brine are very high, and this make it difficult to extract the strontium resource from the brine, since the (CaCl2·6H2O + SrCl2·6H2O)(ss) solid solution will be crystallized when water is evaporated from the oilfield brine under natural conditions. The thermodynamic properties, the equilibrium phase diagram, and their model simulation of the CaCl2−SrCl2−H2O ternary system and its sub-binary systems are of great importance for the extraction of resources from oilfield brine. The solubility results for the CaCl2−H2O system have been reported in many works in the literature,1−7 and comprehensively evaluated by Zeng8 and Li.9 The solubility data of the SrCl2−H2O binary system also have been reported in the literature.3−5,10−17 Assarsson et al.3 reported the solubility data of the ternary system CaCl2−SrCl2−H2O at 290.15 to 387.15 K, and included a relative complete phase diagram at 290.15, 333.15, and 373.15 K. From the results of Assarsson et al.,3 the solid solution (CaCl2·6H2O + SrCl2·6H2O)(ss) was completely miscible in the entire concentration range of the ternary system at 291 and 301 K. Bi et al.12 reported that the equilibrium solid phases in this ternary system at 298.15 K are pure salts (CaCl2· 6H2O(s), SrCl2·6H2O(s)) and solid solution (CaCl2·6H2O + SrCl2·6H2O)(ss). Guo et al.13 determined the thermodynamic properties for this ternary system at 298.15 K, and evaluated the solubility data reported in the literature with the PSC model, and proposed that the equilibrium solid phase in the entire concentration range of this ternary system at 298.15 K © XXXX American Chemical Society

are solid solutions rather than pure salts. According to the results detailed above, the crystallization fields of solid solution phase (CaCl2·6H2O + SrCl2·6H2O)(ss) became smaller with temperature increasing and finally disappeared at 333.15 K. When the equilibrium solid phase were pure salts, it is possible to separate the strontium chloride and calcium chloride. Thermodynamic modeling contributes to understand the reliability of the experimental solubility results. The water activities are prerequisite for the model parametrization in the ternary system. Up to now, the experimental water activities data of the ternary system CaCl2−SrCl2−H2O at 298.15 have only been reported by Guo et al.12 In our previous work, we have reported the thermodynamic properties of the subternary systems of Nanyishan oilfield brine, e.g. KCl−SrCl2−H2O, CaCl2− SrCl2−H2O and LiCl−SrCl2−H2O systems, including water activities, solid−liquid equilibrium, and model simulation. As the continuity study of our whole work, the isopiestic water activity and isothermal phase diagram on the ternary system CaCl2−SrCl2−H2O at 323.15 K are reported here. PSC model was selected to represent the properties (water activity and solubility) of the titled system.

2. EXPERIMENTAL SECTION 2.1. Materials. Strontium chloride hexahydrate (Sinopharm Chemical Reagent Co. Ltd., G. R.) was purified by twice recrystallizations. Calcium chloride (purity by mass fraction >0.9995, Aladdin Industrial Inc.) was used directly without further Received: January 2, 2018 Accepted: April 6, 2018

A

DOI: 10.1021/acs.jced.8b00003 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Reagents Prepared in this Worka reagents

source

initial mass fraction purity

purification method

final mass fraction purity

analysis method

strontium chloride hexahydrate calcium chloride ammonium carbonate silver nitrate

Sinopharm Chemical Reagent Co. Aladdin Sinopharm Chemical Reagent Co. Sinopharm Chemical Reagent Co.

>0.998 >0.9995 >0.998 >0.9995

recrystallization none none none

0.9999 0.9998 none none

ICP ICP

a

The impurity of the chemical reagents were determined, and the purity basis is mass.

purification. The final impurities were determined by ICPAES (ICAP 6500 DUO, Thermo Scientific), and the results are tabulated in Table 1. Doubly distilled water, with conductivity less than 1.2 × 10−4 S m−1, was used to prepare all samples for purifications, isopiestic determinations, phase equilibrium experiments, and chemical analysis. Silver nitrate and ammonium carbonate (Sinopharm Chemical Reagent Co. Ltd., G. R. grade) were used for chemical analysis. The characteristics of the chemical samples used in this work are listed in Table 1. 2.2. Apparatus and Procedures. The apparatus and procedures for solid−liquid phase equilibrium and isopiestic determinations were the same as in our previous work,10,18,19 and will will be mentioned here only as needed. In the solubility determinations, the compositions of solid and liquid phase were determined by analyzing the concentrations of Cl−, Ca2+, and Sr2+. The Cl− concentration was determined using the precipitation method with AgNO3 (99.95%) precipitator, as described in the literature,20 and the relative error among these parallel samples was less than 0.05%. The total contents of Ca2+ and Sr2+ were determined gravimetrically by precipitating with ammonium carbonate solution, as described in the literature,21 and the relative error among the parallel samples was less than 0.5%. The analysis method and processes of sampling are described briefly as follows. (1) A certain amount of clear equilibrium solution was removed by a pipet covered with glass cloth as a filter and transferred to a weighed (m1) 25 cm3 weighing bottle and then closed with a glass stopper at once. The bottle with the sample was quickly weighed, and the the weight (m2) of the weighing bottle and sample was recorded. m2 − m1 represents the weight of sample. To avoid crystallization from precipitating in the saturation solution during the sampling process, the temperature of ambient and the sampling devices were adjusted in advance before every sampling event, so that the temperatures were all near that of the baths. (2) The sample in the weighing bottle was carefully transferred to a weighed (m3) volumetric flask with the aid of funnel. Solution spills are not allowed in this operation process. After transfer is completed, under a rough setting capacity and weighing, the weight (m4) of the volumetric flask was recorded. The flask was sealed, shaken, and sparged. (3) A certain amount (m5, three duplicate samples for Cl−, and three duplicate samples for MCO3, M = Ca, Sr) of solution was removed by a mass buret from the volumetric flask and was used for analyzing the concentrations of Ca2+, Sr2+, and Cl− by using two precipitation methods (AgCl and MCO3, M = Ca, Sr). The weight (m6) of Ca2+, Sr2+, and Cl− were obtained from the two precipitation methods, and then the weight (m7) of water was obtained. So the concentrations of the solution were obtained. Finally the concentration of original solution can be calculated. The types of solid phases are detected by X-ray diffraction (XRD).

3. RESULTS AND DISCUSSION 3.1. Isopiestic Determination Results. CaCl2(aq) was used as reference standard solution in the isopiestic determination. The osmotic coefficients of the pure CaCl2 solutions22 were used to fit as a function of molality (m) by eq 1. Table 2. Experimental Isopiestic Molality m and Calculated Water Activities aw of the Ternary System CaCl2−SrCl2− H2O at 323.15 K and 0.1 MPaa mCaCl2 no.

mSrCl2 mol kg−1

mCaCl2 no.

1

mCaCl2 = 0.4343

aw = 0.9793

2

0.4343 0.3908 0.3055 0.2214 0.1311 0.0440 0 mCaCl2 = 1.0606

0 0.0432 0.1306 0.2173 0.3054 0.3941 0.4393 aw = 0.9419

3

1.0606 0.9631 0.7495 0.5441 0.3264 0.1096 0 mCaCl2 = 1.3401

0 0.1064 0.3212 0.5341 0.7601 0.9821 1.0949 aw = 0.9219

4

1.3401 1.2115 0.9480 0.6886 0.4128 0.1390 0 mCaCl2 = 2.0148

0 0.1338 0.4262 0.6760 0.9612 1.2454 1.3886 aw = 0.8645

2.0148 1.8224 1.4290 1.0390 0.6243

0 0.2013 0.6123 1.0200 1.4537

0.2105 0

1.8865 2.1063

mSrCl2 mol kg−1

5

mCaCl2 = 2.1411

aw = 0.8521

6

2.1411 1.9376 1.5196 1.1057 0.6644 0.2241 0 mCaCl2 = 2.7554

0 0.2140 0.6512 1.0854 1.5471 2.0080 2.2424 aw = 0.7876

7

2.7554 2.4958 1.9622 1.4310 0.8619 0.2915 0 mCaCl2 = 3.5913

0 0.2756 0.8408 1.4048 2.0007 2.6116 2.9203 aw = 0.6895

8

3.5913 3.2564 2.5662 1.8750 1.1321 0.3838 0 mCaCl2 = 4.8270

0 0.3597 1.0998 1.8408 2.6363 3.4392 3.8508 aw = 0.5425

9

4.8270 4.3978 3.4476 2.5025 mCaCl2 = 5.1959

0 0.4731 1.4473 2.4717 aw = 0.5018

5.1959 4.7266 3.7796

0 0.5067 1.5781

a

Water activity is calculated using eqs 1 and 3 with the parameters in ref 18. The uncertainty for the water activity is absolute uncertainty. m, molality, moles per kilogram of solvent (pure water in this work). The relative standard uncertainty is ur(m) = 0.003, u(T) = 0.03 K, and ur(p) = 0.01. B



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ϕ = a + b(m /mol ·kg −1)0.5 + c(m /mol ·kg −1)

Table 3. Experimental Solubility Data for the Ternary System CaCl2−SrCl2−H2O at 323.15 K and 0.1 MPaa composition of the solution (100wb) no.

CaCl2

H2O

SrCl2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0 0.96 3.58 7.44 14.27 20.71 24.54 25.05 25.57 26.89 35.35 42.12 50.08 56.18 56.41 56.86

57.94 58.01 58.27 58.60 59.05 58.83 58.41 58.53 58.51 58.37 57.88 54.94 49.00 43.01 42.93 43.14

42.06 41.03 38.15 33.96 26.68 20.46 17.05 16.42 15.92 14.74 6.77 2.94 0.95 0.81 0.66 0

+ d(m /mol ·kg −1)1.5 + e(m /mol ·kg −1)2

composition of the wet solid phase (100w) CaCl2 0.65 1.43 2.81 6.07 10.10 10.31 11.24 12.75 16.05 26.64 24.70 45.08 59.64 50.08

H2O 49.63 47.81 47.54 48.54 49.21 45.10 39.73 38.48 41.91 47.45 40.18 45.81 38.94 36.08

SrCl2 49.71 50.76 49.65 45.39 40.69 44.59 49.03 48.77 42.04 25.91 35.12 9.11 1.42 13.84

+ f (m /mol ·kg −1)2.5 + g (m /mol ·kg −1)3 solid phasec

+ h(m /mol ·kg −1)3.5

A A A A A A A A+B A+B B B B B B+C B+C C

(1)

where a, b, c, d, e, f, g, and h are empirical parameters. The parameters in eq 1 for CaCl2 were reported in our previous work.18 The osmotic coefficients of the other solutions to be determined in this study were calculated using eq 2 as

ϕ=

v*m*ϕ* ∑i vm i i

(2)

where the quantities with asterisks (∗) represent the isopiestic reference standard, v* = 3 stands for the number of ions formed by the complete dissociation of one molecule of CaCl2, m* denotes the isopiestic equilibrium molality of the reference solution, ϕ* means the osmotic coefficient of the reference solution, and ∑ivimi = 3mCaCl2 + 3mSrCl2 for the CaCl2−SrCl2−H2O ternary system. The water activities aw of the reference standards solution were calculated using eq 3:

a

The standard uncertainties u are ur(w) = 0.005, u(T) = 0.03 K, and ur(p) = 0.01. bw: mass fraction. cA, SrCl2·6H2O; B, SrCl2·2H2O; C, CaCl2·2H2O.

ln a w = −vM w mϕ

(3)

where v stands for the number of ions assumed to be created when a salt dissociates completely, i.e., v = 3 for CaCl2 and SrCl2. Mw (kg·mol−1) represents the molar mass of H2O and ϕ stands for the osmotic coefficient of the CaCl2(aq) reference solution. The experimental determined isopiestic water activities results for the ternary system CaCl2−SrCl2−H2O at 323.15 K are listed in Table 2. In each run of the isopiestic experimental determination, the data in the first line represent the molality (mol·kg−1) of the reference standard solution (the CaCl2 solution) and the corresponding water activity. The following results stand for the isopiestic molalities of the salts in the pure or mixed solutions. During each run of the isopiestic determination, the maximum relative molality deviation between two parallel samples was about ±0.3%, which can be attributed to

Figure 1. Experimental equal water activity lines for the CaCl2−SrCl2− H2O system at 323.15 K.

Figure 2. Isothermal solubility curve for the system CaCl2−SrCl2−H2O at 323.15 K. All experimental data are in this work: blue ●, saturated solution composition determined in this work; ○, wet solid phase composition; red ■, CaCl2·6H2O; aqua ▲, CaCl2·2H2O; red □, SrCl2·6H2O; red ★, SrCl2·2H2O. C



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Figure 3. Solid phase XRD diagram corresponding to cosaturated points (SrCl2·6H2O(s) + SrCl2·2H2O(s)) and (SrCl2·2H2O(s) + CaCl2·2H2O(s)).

Table 4. PSC Model Parameters for Binary Systems at 323.15 K

a

solute

αMX

BMX

α1MX

B1MX

W1,MX

U1,MX

V1,MX

sources

σc

CaCl2a SrCl2b

13 13

−313.9219 164.9280

2.0 2.0

30.8408 0

0 8.1823

25.3650 47.3081

−24.4857 −41.4599

ref 22 ref 10

0.0055 0.0033

Parameters obtained from ref 22. bParameters obtained from ref 10. cCalculated as σ=

1 n

n

∑ (a w(exp) − a w(calc))2 i=1

two invariant points in this ternary system, namely (SrCl2· 6H2O(s) + SrCl2·2H2O(s)) and (SrCl2·2H2O(s) + CaCl2·2H2O(s)) invariant point, which are identified by Schreinemaker’s method24 combined with X-ray diffraction (XRD). The XRD diagram corresponding experimental points no. 8 and 14 are shown in Figure 3. The solid phases in equilibrium with the saturated solution are SrCl2·6H2O(s), SrCl2·2H2O(s), and CaCl2· 2H2O(s), respectively. Unlike the solubility phase diagram at 298.15 K13 and 323.15 K3, the solid solution (CaCl2·6H2O + SrCl2·6H2O)(ss) was not found in this system at 323.15 K. It is possible to analyze the reasons that the solid solution is not found. Even if the solid solution is formed, its phase region is very narrow, as seen in the literature,3 and difficult to detect; the errors in the analytical process and analytical method may also cause the formed solid solution to be neglected. It is also possible that there are some unknown causes, leaving us to continue to study in a follow-up work.

Figure 4. Experimental water activities for the SrCl2−H2O system at 323.15 K compared with the literature. All symbols represent experimental data: ■, experimental values in this work; ●, experimental values in ref 10. The solid line represents model calculated data from the ref 10.

4. MODELING The PSC model is chosen to correlate the determined water activity and solubility data, to evaluate the reliability of the determined solubility and water activity data, and to judge the type of solid phase. Generally, the PSC model is sufficient to represent the properties of the binary systems CaCl2−H2O7,13,18 and SrCl2−H2O10,11,13 as in our previous work. The binary parameters of the SrCl2−H2O system at 323.15 K also have been reported in the literature,10 and the values are tabulated in Table 4 and Figure 4, which was used directly in this work. To get the better binary parameters for the binary system CaCl2−H2O with low and high concentration at 323.15 K, we get them by refitting the data in the literature22 and the results are listed in Table 4 and shown in Figure 5. In our previous work13 on model simulation for the CaCl2− SrCl2−H2O ternary system at 298.15 K, the thermodynamic properties and solubility were successfully predicted with binary parameters only. We predicted the water activity of this ternary system at 323.15 K with binary parameters only, and the predicted equal water activity are consistent with the experimental

the errors from weighing, water transportation within the isopiestic chamber, equilibrium time, and temperature differences between two cups, accordingly, the maximum deviation of determined water activities should be less than 0.005. 3.2. Solubility Determination Results. The determined isothermal solubility data for the CaCl2−SrCl2−H2O ternary system at T = 323.15 K are presented in Table 3, including the compositions of liquid phase and solid phase, the corresponding solid phase kind. 3.3. Discussions. The experimentally determined isopiestic water activities data for the ternary system CaCl2−SrCl2−H2O at 323.15 K are shown in Figure 1. Similar to the water activities results for the ternary system at 298.15 K in our previous work,13 the determined isopiestic composition lines at constant water activity at 323.15 K were found to be approximately straightly lines, as shown in Figure 1. This indicates that the interaction between the two salts (CaCl2 and SrCl2) in the mixture solution is not obvious. The determined solubility data for the CaCl2−SrCl2−H2O ternary system at 323.15 K are shown in Figure 2. There are D



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determined in advance. By calculating the activities of ions and water on the solubility points of each binary system using PSC model and the binary parameters in Table 4, the solubility products ln Kosp were obtained, as shown in Table 6. Then, the Table 6. Solubility Product Parameters ln Kosp at 323.15 K

Figure 5. Calculated water activities for the CaCl2−H2O system at 323.15 K compared with literature data. The solid line represents the model calculated data from ref 22; the dashed line represents model calculated data from ref 23.

substance

ln Kosp

sources

CaCl2·2H2O SrCl2·6H2O SrCl2·2H2O

5.01 −6.78 −3.80

refs 2 and 3 ref 10 refs 3 and 17

solubility isotherms for the ternary system CaCl2−SrCl2−H2O at 323.15 K with binary parameters only were predicted, and the predicted results are showed in Figure 6. The predicted solubility isotherms for the CaCl2·2H2O (red solid line), SrCl2· 2H2O (green solid line) and SrCl2·6H2O (blue dash line) are consistent with the corresponding experiment determined results. The predicted results of equal water activity and solubility isotherms indicate that the Pitzer-Simonson-Clegg model can present the thermodynamic properties and predict the solubility isotherms for the ternary system CaCl2−SrCl2−H2O at 323.15 K with binary parameters only.

results tabulated in Table 5, the average deviation between calculated and experimental determined results is 0.0037. This indicates that the water activity in this ternary system at 323.15 K can be predicted with binary parameters only. We also try to predict the solubility isotherm of the ternary system CaCl2−SrCl2−H2O at 323.15 K. The solubility products based on the mole fraction for each solid phase should be

Table 5. Comparison of Experimental and Predicted Water Activities for the Ternary System CaCl2−SrCl2−H2O at 323.15 K mCaCl2

mCaCl2

mSrCl2 mol kg

0.4343 0.3908 0.3055 0.2214 0.1311 0.0440 0 1.0606 0.9631 0.7495 0.5441 0.3264 0.1096 0 1.3401 1.2115 0.9480 0.6886 0.4128 0.1390 0 2.0148 1.8224 1.4290 1.0390 0.6243 0.2105 0 2.1411

−1

0 0.0432 0.1306 0.2173 0.3054 0.3941 0.4393 0 0.1064 0.3212 0.5341 0.7601 0.9821 1.0949 0 0.1338 0.4262 0.6760 0.9612 1.2454 1.3886 0 0.2013 0.6123 1.0200 1.4537 1.8865 2.1063 0

aw(exp)

b

0.9793 0.9793 0.9793 0.9793 0.9793 0.9793 0.9793 0.9419 0.9419 0.9419 0.9419 0.9419 0.9419 0.9419 0.9219 0.9219 0.9219 0.9219 0.9219 0.9219 0.9219 0.8645 0.8645 0.8645 0.8645 0.8645 0.8645 0.8645 0.8521

aw(calc) 0.9832 0.9833 0.9822 0.9811 0.9803 0.9794 0.9791 0.9449 0.9444 0.9441 0.9435 0.9428 0.9425 0.9422 0.9221 0.9220 0.9207 0.9220 0.9221 0.9222 0.9223 0.8561 0.8569 0.8585 0.8599 0.8618 0.8637 0.8645 0.8479

a

deviation

c

mSrCl2 mol kg

−0.0039 −0.0040 −0.0029 −0.0018 −0.0010 −0.0001 0.0002 −0.0030 −0.0025 −0.0022 −0.0016 −0.0009 −0.0006 −0.0003 −0.0002 −0.0001 0.0012 −0.0001 −0.0002 −0.0003 −0.0004 0.0084 0.0076 0.0060 0.0046 0.0027 0.0008 0 0.0042

−1

1.9376 1.5196 1.1057 0.6644 0.2241 0 2.7554 2.4958 1.9622 1.4310 0.8619 0.2915 0 3.5913 3.2564 2.5662 1.8750 1.1321 0.3838 0 4.8270 4.3978 3.4476 2.5025 5.1959 4.7266 3.7796 σc

0.2140 0.6512 1.0854 1.5471 2.0080 2.2424 0 0.2756 0.8408 1.4048 2.0007 2.6116 2.9203 0 0.3597 1.0998 1.8408 2.6363 3.4392 3.8508 0 0.4731 1.4473 2.4717 0 0.5067 1.5781

aw(exp)b

aw(calc)a

deviationc

0.8521 0.8521 0.8521 0.8521 0.8521 0.8521 0.7876 0.7876 0.7876 0.7876 0.7876 0.7876 0.7876 0.6895 0.6895 0.6895 0.6895 0.6895 0.6895 0.6895 0.5425 0.5425 0.5425 0.5425 0.5018 0.5018 0.5018

0.8438 0.8450 0.8469 0.8489 0.8511 0.8521 0.7798 0.7834 0.7860 0.7855 0.7862 0.7854 0.7865 0.6842 0.6857 0.6845 0.6827 0.6851 0.6886 0.6905 0.5379 0.5387 0.5436 0.5502 0.5008 0.5025 0.5024

0.0083 0.0071 0.0052 0.0032 0.0010 0 0.0078 0.0042 0.0016 0.0021 0.0014 0.0022 0.0011 0.0053 0.0038 0.0050 0.0068 0.0044 0.0009 −0.0010 0.0046 0.0038 −0.0011 −0.0077 0.0010 −0.0007 −0.0006 0.0037

a aw(exp), water activities determined in this work. baw(calc), water activities calculated by PSC model with binary parameters only. cdev = aw(exp) − aw(calc);

σ=

E

1 n

n

∑ (a w(exp) − a w(calc))2 i=1



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Figure 6. Solubility isotherm comparison of experimental and predicted by the PSC model of the system CaCl2−SrCl2−H2O at 323.15 K. All symbols are experimental data of this work and literature.3 All lines are predicted solubility isotherms by PSC model with binary parameters only in this work.

5. CONCLUSIONS The equal water activities on the ternary system CaCl2−SrCl2− H2O and its sub-binary systems have been determined at 323.15 K. The isopiestic composition lines for the CaCl2− SrCl2−H2O system at 323.15 K at constant water activity were found to be approximately straightly lines, which indicate that the interaction between the two salts (CaCl2 and SrCl2) in the mixture solution is not obvious. The solubility of the ternary system CaCl2−SrCl2−H2O was determined by isothermal equilibrium method at 323.15 K. Pitzer−Simonson−Clegg (PSC) model was used for correlating the determined water activity and solubility data. It is found that the PSC model can present the thermodynamic properties and predict the solubility isotherms for this ternary system at 323.15 K with binary parameters only. The predicted solubility isotherm by PSC model with only binary parameters satisfactorily agree with the experimental determined results in this work, and the equilibrated solid phases were CaCl2·2H2O, SrCl2·2H2O, and SrCl2·6H2O. Analysis of the phase diagrams from the literature and from this work, shows the existence of a solid solution and the undiscovered reasons remain in the subsequent work.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Haijun Han: 0000-0003-1345-6544 Lijiang Guo: 0000-0002-1018-4646 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully thank the National Natural Science Foundation of China (Grants 21406253 and 21303239) for financial support of this work.

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REFERENCES

(1) Lightfoot, W. J.; Prutton, C. F. Equilibria in Saturated Solution. 1. the Ternary System CaCl2−MgCl−H2O, CaCl2−KCl−H2O, and MgCl2−KCl−H2O at 35 °C. J. Am. Chem. Soc. 1946, 68, 1001−1002. (2) Lightfoot, W. J.; Prutton, C. F. Equilibria in Saturated Solution. 2. the Ternary System CaCl2−MgCl2−H2O, CaCl2−KCl−H2O, and MgCl2−KCl−H2O at 75 °C. J. Am. Chem. Soc. 1947, 69, 2098−2100. F


Water Activity, Solubility Determination, and Model Simulation of the

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