Isopiestic Measurements of Water Activity for the NaClâKClâMgCl

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Isopiestic Measurements of Water Activity for the NaCl−KCl−MgCl2−H2O Systems at 323.15 K Haijun Han,†,‡ Dongdong Li,‡ Lijiang Guo,‡ Yan Yao,‡ Haitang Yang,§ and Dewen Zeng*,† †

College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, China § College of Metallurgical Engineering, Hunan University of Technology, Zhuzhou, Hunan 412000, China ‡

ABSTRACT: Water activity for binary KCl−H2O, NaCl−H2O and MgCl2−H2O, as well as two ternary NaCl−MgCl2−H2O and KCl−MgCl2−H2O, systems has been measured by using an isopiestic method at 323.15 K. The isopiestic results obtained show that the isopiestic composition lines of the NaCl−MgCl2−H2O system was found to obey the Zdanovskii rule, whereas the KCl−MgCl2−H2O system was observed to deviate slightly. The experimental water activities determined were applied to regress the parameters of the Pitzer model with a good agreement. The model with new parameters is validated by comparing water activity predictions with those given in the literature and not used in the parametrization process and calculating the solubility of the NaCl−MgCl2−H2O and KCl−MgCl2−H2O systems at various temperatures with the comparison of literature values.

1. INTRODUCTION The water activity and phase equilibria for the NaCl−MgCl2−H2O and KCl−MgCl2−H2O systems are of significance in exploiting the resources of salt lakes with chloride compounds. Normally, magnesium chloride hexahydrate (MgCl2·6H2O), namely bischofite, has been manufactured in salt lake area by crystallization approach. However, high pure bischofite is very difficult to obtain due to the impurities uptake, such as NaCl and KCl.1 It is necessary to profoundly understand the phase equilibria for such complicated salt lake systems. To date, a lot of studies have been performed for the NaCl−KCl−MgCl2−H2O systems. Leimbach and Pfeiffenberg,2 Sieverts and Muller,3 and Kurnakov and Osokoreva4 determined the solubilities for the system NaCl−MgCl2−H2O and its eutectic points.5−7 References 8−12 reported the solubility isotherms and their multisaturation points in the KCl−MgCl2−H2O systems. However, there exist large discrepancies among the values reported by previous studies. Because experimental water activity for the systems NaCl−MgCl2−H2O and KCl−MgCl2−H2O is available just at 298 K,13−22 the values at elevated temperatures are necessary for evaluating the solubilities and particularly their multisaturation points by modeling. In the present investigation, water activity of systems NaCl−MgCl2−H2O and KCl−MgCl2−H2O was measured by isopiestic method at 323.15 K. Pitzer model was used to regress experimental data and the reliability of solubility data from literatures was verified.

CaCl2 (Aladdin Industrial Inc., 99.99 %) was used as a stock solution without further purification, and the content of the main impurities (elemental K, Na, Mg, Sr, Ba, and Fe) was less than 0.02 %. The CaCl2 content was determined by precipitation method with AgNO3 (99.95 %), and the largest relative deviation of the analysis for each of three parallel samples was below 0.05 %. The impurities in the salts were also analyzed by ICP Emission Spectrometry (Thermo Electron Corporation, ICAP 6500 DUO). 2.2. Apparatus. Isopiestic measurement was carried out by a new setup as described below, which has been improved upon the one used in our previous study.23 (1) A lifting device was installed into the isopiestic chamber for easy lift from the thermostat. (2) The temperature of the isopiestic chamber placed in a thermostat bath was controlled within 323.15 ± 0.01 K by using a commercial digital heating controller (Lauda Proline Command, Germany). The temperature was measured by a digital thermometer with an accuracy of ± 0.001 K, which had been calibrated by the National Institute of Metrology of China. 2.3. Procedure. Stock solutions with different YMgCl2(YMgCl2 = mMgCl2/(mMgCl2 + mMCl), (M = Na, K) were prepared by mixing pure solution of NaCl or KCl with the MgCl2 solution. Prior to the first isopiestic measurement, appropriate amounts of the stock solutions and water were added to each sample cup by using a mass buret.24 In each run, duplicate samples of the reference solution and some of the mixed solutions were used to investigate the reliability of the experimental results. After all of the sample cups were placed in the isopiestic chamber and bolted to a copper plate, the chamber was closed and slowly evacuated to degas.

2. EXPERIMENTAL SECTION 2.1. Materials. The water with a conductance of less than 1.5 × 10−4 S·m−1 was obtained by deionization and double distillation and used for all sample purifications, preparations, and dilutions in the experiment. NaCl, KCl, and MgCl2 (from Sinopharm Chemical Reagent Co. Ltd.) were purified by three recrystallizations. The impurities of salts, such as Li, Na, K, Ca, and Fe, were analyzed to be less than 0.01 %. © XXXX American Chemical Society

Received: December 2, 2014 Accepted: February 6, 2015

A

DOI: 10.1021/je501095w J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Parameters of Eq 1 for the Osmotic Coefficients of CaCl2, KCl, and NaCl Solutions parameters

CaCl2 (0−2 mol·kg−1)



NaCl (0−6.3 mol·kg−1)

KCl (0−5.7 mol·kg−1)

a b c d e f g h

0.99348 −1.24824 4.29766 −8.22391 9.56916 −6.10046 1.99931 −0.26311

−1.03457 3.21427 0.47391 −4.57273 4.53291 −2.03855 0.46777 −0.04592

−96.00309 125.83548 −26.95976 −40.21559 32.70079 −10.68154 1.68491 −0.10591

0.99957 −0.39754 0.77348 −0.81763 0.57202 −0.23342 0.05156 −0.00479

0.99826 −0.38440 0.64329 −0.64251 0.42478 −0.16678 0.03547 −0.00318

Table 2. Calculation Comparison of Water Activities, Eq 3 and Osmotic Coefficients Eq 1 for the Reference Standard Systems CaCl2−H2O and NaCl−H2O at 323.15 K m(CaCl2)

ϕCaCl2

aw(CaCl2)

−1

0.9614 0.9428 0.9207 0.9083 0.8783 0.8169 0.7683

1.1489 1.6759 2.2719 2.5904 3.3441 4.7830 5.8576

Δaw = aw(CaCl2) − aw(NaCl)

0.9504 0.9788 1.0144 1.0344 1.0837 1.1823 1.2575

0.9614 0.9426 0.9203 0.9080 0.8777 0.8160 0.7677

0.0000 0.0002 0.0004 0.0003 0.0006 0.0009 0.0006

where quantities with asterisks (*) denote the reference solutions, ν* represents the number of ions formed by the complete dissociation of one molecule of solute, m* is the isopiestic equilibrium molality of the reference solution, φ* is the osmotic coefficient of the reference solution, and Σivimi = 2mMCl + 3mMgCl2 for the MCl−MgCl2−H2O (M = Na, K) ternary systems. Water activities (aw) of the reference solutions were determined by eq 3 as ln a w =

φ = a + b(m)0.5 + c(m) + d(m)1.5 + e(m)2 + f (m)2.5 + g (m)3 + h(m)3.5

−v·M w ·m·φ 1000

(3)

where v is the number of ions for the complete dissociation of one molecule from the reference solution, that is, v = 3 for CaCl2 and v = 2 for KCl and NaCl. Mw is the molar mass of H2O, and φ is the osmotic coefficient of the reference solution. 3.2. Method Verification. To check the reliability of the procedure, isopiestic molalities for the reference solutions CaCl2−H2O and NaCl−H2O were measured at 323.15 K, and their corresponding water activities were compared, as shown in Table 2. The maximal deviation of water activity between CaCl2 and NaCl solutions is 0.0009, indicating that the isopiestic apparatus and procedure applied in this work are reliable. 3.3. Isopiestic Measurements. The experimental water activities in the ternary systems of NaCl−MgCl2−H2O and KCl−MgCl2−H2O at 325.15 K are tabulated in Tables 3 and 4, respectively. In each isopiestic experimental run, the concentration (in mol·kg−1) of the reference solution and the corresponding water activity are listed in the first line, and the following data are the isopiestic concentrations of the salts in the pure or mixed solutions. In each run of the isopiestic measurements, the largest relative concentration difference of two duplicate samples was ± 0.3 %, which can be attributed to errors in weighing, the equilibrium time, water transportation within the isopiestic chamber, and temperature differences between the two cups. Combining the uncertainty of 0.1 % from impurities with the uncertainty of 0.3 % reported above, it is reasonably evaluated that the total uncertainty of the

3. RESULTS AND DISCUSSION 3.1. Reference Solutions. CaCl2(aq), NaCl(aq), and KCl(aq) were used as isopiestic reference solutions. The osmotic coefficients φ data of CaCl2,26,27 NaCl,28 and KCl29 solutions were used to fit as a function of molality (m) by eq 1

(1)

where a, b, c, d, e, f, g, and h are empirical parameters. The obtained parameters for the CaCl2, NaCl, and KCl reference solutions are given in Table 1. The osmotic coefficients of other solutions investigated in this study were calculated by eq 2 as

v*m*φ* ∑i vm i i

aw(NaCl)

(mol·kg ) 0.9623 1.0379 1.1256 1.1734 1.2858 1.5033 0.9623

To accelerate the equilibrium process and shorten the equilibrium time, the solution concentration in each sample cup was adjusted in advance by adding water or evaporating in an oven below 333 K until the water activity of each sample was maintained at close level. The equilibrium time was set to be 2 to 7 days. When the equilibrium was reached, the sample cups were closed with the caps that were previously fixed in the capping device inside the isopiestic chamber. The chamber was then moved away from the thermostat bath, air-dried by silicone and zeolite siccative, and cleaned by a sintered glass filtering crucible. All of the capsealed cups were placed in a desiccator for 60 min and then weighed. The process for obtaining the final weight of each cup was similar to the literature.25 In the subsequent experiments, samples were roughly diluted or evaporated to another water activity level, and the same isopiestic measurement was repeated. All of the desired water activity levels of the sample cups were budgeted in advance so that the equilibrium concentration of each salt was below its solubility limit in each run of the isopiestic measurement.

φ=

ϕNaCl

−1

(mol·kg ) 0.7565 1.0496 1.3589 1.5166 1.8665 2.4897 2.9296

m(NaCl)

(2) B



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Table 3. Experimental Isopiestic Molalities, m, and Calculated Water Activities, aw, of the Ternary System NaCl−MgCl2−H2O at 323.15 Ka mNaCl −1

(mol·kg )

a

mMgCl2 −1

(mol·kg )

mNaCl −1

(mol·kg )

mMgCl2

mNaCl

−1

−1

(mol·kg )

(mol·kg )

mMgCl2 −1

(mol·kg )

mNaCl −1

(mol·kg )

mMgCl2 (mol·kg−1)

aw = 0.9617 (reference standard mCaCl2 = 0.7565)


0

1.4437


aw = 0.9614 (reference standard mNaCl = 1.1488) 0 0.7320 0.0774 0.6868 0.2463 0.5745 0.4492 0.4451 0.6864 0.2955 0.9762 0.1096 1.1488 0 aw = 0.9428 (reference standard mCaCl2 = 1.0496)

aw = 0.7677 (reference standard mNaCl = 5.8576) 0 2.7353 0.2925 2.5964 0.9753 2.2733 1.8713 1.8543 3.0378 1.3077 4.7096 0.5288 5.8576 0 aw = 0.7353 (reference standard mCaCl2 = 3.2115)

0.1530 0.4990 0.9296 1.4630 2.1557

1.3583 1.1632 0.9211 0.6298 0.2420

0 4.3759 0.1135 4.3185 0.2235 4.2662 0.4687 4.1604 aw = 0.5218 (reference standard mCaCl2 = 5.0111)

aw = 0.9426 (reference standard mNaCl = 1.6759) 0 1.0099 0.1066 0.9467 0.3440 0.8018 0.6328 0.6270 0.9794 0.4216

0

2.9896

0.3192 2.8332 1.0684 2.4905 2.0570 2.0383 3.3594 1.4462 aw = 0.6856 (reference standard mCaCl2 = 3.6289)

1.4131 0.1587 1.6759 0 aw = 0.9199 (reference standard mCaCl2 = 1.3589)

0 0.3598 1.2092

3.3562 3.1935 2.8186

aw = 0.9203 (reference standard mNaCl = 2.2719)


0 0.1371 0.4462 0.8302

1.2947 1.2168 1.0400 0.8227

0 3.4809 0.3732 3.3126 1.2564 2.9286 aw = 0.6161 (reference standard mCaCl2 = 4.2021)

1.2932 1.8949 2.2719

0.5567 0.2127 0

0 3.8569 0.4141 3.6761 aw = 0.5509 (reference standard mCaCl2 = 4.7530)


0

4.3218


0.4651

4.1290

2.5904 0 aw = 0.8768 (reference standard mCaCl2 = 1.8665)

0 0.1173

4.5229 4.4640

aw = 0.8776 (reference standard mNaCl = 3.3441) 0 1.7665

0.2311

4.4103

0.1877 0.6169 1.1616 1.8391


1.6665 1.4381 1.1511 0.7917



0 0.1344 0.2655



0 0.2493 0.8271 1.5758

2.3360 2.2134 1.9280 1.5614


2.5344 3.8776 4.7830

1.0911 0.4353 0

0 5.6771 0.1475 5.6126 0.2935 5.6010 aw = 0.3423 (reference standard mCaCl2 = 7.1080) 0 0.1530 0.3044

5.1763 5.1133 5.0669

5.8771 5.8213 5.8090

Water activity is calculated by the equations reported in refs 26 and 27 for CaCl2 and ref 28 for NaCl; standard uncertainty u is ur(m) = 0.003.

4. MODELING 4.1. NaCl−MgCl2−H2O System. The binary parameters of the Pitzer model for the NaCl−H2O28 and MgCl2−H2O29−31 systems were taken from the literature and shown in Table 5 and Figure 1. The ternary mixing parameters θNa,Mg and ψNaMgCl were obtained by fitting the water activities in Table 3 measured in this work and listed in Table 6. The thermodynamic solubility products ln Ksp of all salts in the NaCl−KCl−MgCl2−H2O systems at 323.15 K are also given in Table 7. With either the binary Pitzer model parameters only or the binary parameters plus the mixing parameters, the water activities, and the solubility isotherm at 323.15 K of the NaCl− MgCl2−H2O ternary system were calculated. The comparisons of the solubility isotherms (Figure 4) and the water activities (Figure 5a, b) indicate that the mixing parameters did not improve the predictions for either the water activity or the

measured salt concentration should be less than 0.4 %, corresponding to a largest possible deviation in the measured water activities of ± 0.0026. Water activities of the binary systems NaCl−H 2 O, KCl−H2O, and MgCl2−H2O determined in this study were compared with those in the literature.28−31 It can be observed from Figure 1 that the experimental results agree well with the literature values. The experimentally measured isopiestic points and equalwater activity lines of the ternary systems NaCl−MgCl2−H2O and KCl−MgCl2−H2O at 323.15 K are shown in Figures 2 and 3. All the isopiestic composition points in the NaCl− MgCl2−H2O system are found to be roughly in straight lines at the low and intermediate salt concentrations. This apparent behavior is indicative of the Zdanovskii rule. In the KCl−MgCl2− H2O system, however, the isopiestic lines positively deviate from the Zdanovskii rule line (solid lines in Figure 3). C



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Table 4. Experimental Isopiestic Molalities, m, and Calculated Water Activities, aw, of the Ternary System KCl−MgCl2−H2O at 323.15 Ka mKCl

mMgCl2 −1

−1

(mol·kg )

(mol·kg )

mMgCl2 −1

(mol·kg )

mMgCl2

mKCl

−1

−1

(mol·kg )

(mol·kg )

mKCl

−1

mMgCl2 −1

(mol·kg )

(mol·kg )

(mol·kg−1)




0

4.5229

aw = 0.9564 (reference standard mKCl = 1.3574) 0 0.8108 0.0742 0.7683 0.2677 0.6569 0.5276 0.5044 0.8150 0.3337 1.1657 0.1247 1.3574 0 aw = 0.9546 (reference standard mCaCl2 = 0.8683)

aw = 0.8322 (reference standard mKCl = 5.0299) 0 2.1962 0.2042 2.1161 0.7698 1.8888 1.6097 1.5390 2.6602 1.0894 4.0967 0.4381 5.0299 0 aw = 0.7903 (reference standard mCaCl2 = 2.7319)

aw = 0.8911 (reference standard mKCl = 3.3148) 0 1.6259

0.1138

4.4897

0.1504 0.5597 1.1449 1.8436


aw = 0.9546 (reference standard mKCl = 1.4127) 0 0.8374 0.0767 0.7944 0.2772 0.6802 0.5471 0.5231 0.8457 0.3463

0

2.5519

0.2380 2.4662 0.9047 2.2198 1.9136 1.8295 3.2098 1.3144 aw = 0.6492 (reference standard mCaCl2 = 3.9291)



aw = 0.9485 (reference standard mKCl = 1.6003) 0 0.9269 0.0850 0.8802

0

0.3090 0.6114 0.9494 1.3592 1.6003

a

mKCl



aw = 0.8808 (reference standard mKCl = 3.6152) 0 1.7329 0.1605 1.6636

0

0.5992 1.2309 1.9913


1.4702 1.1769 0.8155


4.2647

0.4029 4.1751 aw = 0.5431 (reference standard mCaCl2 = 4.8274)

0.7582 0.5845 0.3888 0.1454 0

1.5583 1.3734 1.0946 0.7550


5.4168

0.1365 5.3875 aw = 0.3666 (reference standard mCaCl2 = 6.7332)

0

5.8771

aw = 0.8493 (reference standard mKCl = 4.5316) 0 2.0398 0.1894 1.9626 0.7113 1.7453 1.4791 1.4141 2.4284 0.9945 3.7089 0.3967 4.5316 0

0 3.3760 0.1101 4.3432 0.2282 4.3095 0.4127 4.2759 aw = 0.5226 (reference standard mCaCl2 = 5.0111)

Water activity is calculated by the equations reported in refs 26 and 27 for CaCl2 and ref 29 for KCl; standard uncertainty u is ur(m) = 0.003.

Table 5. Pitzer Parameters for Binary Systems at 323.15 K solute

β0MX

β1MX

β2MX

C0MX

references

MgCl2 NaCl KCl

0.33703 0.0892 0.05935

1.79758 0.2967 0.24942

0.0 0.0 0.0

0.00403 −0.0004 −0.00200

29 28 29

Table 7. Values of the Logarithm of the Thermodynamic Solubility Product ln K°sp at 323.15 K in This Work

solubility isotherm. Thus, the binary parameters are sufficient to represent the properties of the ternary system. It seems that ion interactions between cations Na+ and Mg2+ in the NaCl− MgCl2−H2O system are quite weak in the context of the Pitzer model.

salt composition

ln Ksp °

NaCl KCl MgCl2·6H2O KCl·MgCl2·6H2O

3.7367 2.5497 9.8650 10.0912

As shown in Figure 4, the predicted solubility isotherm is consistent with most literature data3,4,6,7 and, notably, exactly agrees with the recommended values given in the solubility

Table 6. Pitzer Mixture Parameters for the MCl−MgCl2−H2O, where M = Na, K, System at 323.15 K

a

i

j

k

θij

ψijk

data for parametrization

σ (binary parameters)a

σ (mixing parameters)a

Na K K

Mg Mg Mg

Cl Cl Cl

0.008 −0.041 0.083

−0.002 −0.011 −0.043

aw in Table 3 aw in Table 4 aw in Table 4 and solubility data in refs 8, 9, 11, and 12

0.0022 0.0038

0.0021 0.0018 0.0035

σ = ((1/n)Σni=1(aw(exp) − aw(cal))2)1/2 D



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Figure 4. Comparison of the experimental solubility isotherm with the prediction by the Pitzer model for the NaCl−MgCl2−H2O system at 323.15 K. All symbols are experimental data: ■, NaCl from ref 5; ●, NaCl from ref 6; ⬢, NaCl from ref 4; ★, NaCl from ref 7; ◧, MgCl2· 6H2O + NaCl from ref 5; ◐, MgCl2·6H2O + NaCl from ref 6; ◭, MgCl2·6H2O + NaCl from ref 2; black−white ⬡, MgCl2·6H2O + NaCl from ref 4; black−white ◇, MgCl2·6H2O + NaCl from ref 3; black−white ☆, MgCl2·6H2O + NaCl from ref 7; □, MgCl2·6H2O from ref 5; ○, MgCl2·6H2O from ref 6; ⬡, MgCl2·6H2O from ref 4; ☆, MgCl2·6H2O from ref 7. All lines are the solubility isotherms predicted by the Pitzer model: ----, using only the binary parameters at 323.15 K; , using both the binary parameters and the mixture parameters at 323.15 K. Figure 1. Experimental water activities for the NaCl−H2O, KCl−H2O, and MgCl2−H2O systems at 323.15 K compared with the literature. All symbols represent experimental data in this work. All lines represent literature data: the solid lines in panels a, b, and c are from refs 28 and 29; the dashed line in panel c is from ref 30; the dotted line in panel c is from ref 31.

Figure 5. Deviation of water activity in the ternary system of NaCl− MgCl2−H2O calculated by the Pitzer model from experimental values at 323.15 K, Δaw = aw(exp) − aw(cal).

Figure 2. Experimental isopiestic lines in the NaCl−MgCl2−H2O system at 323.15 K.

Figure 6. Comparison of experimental solubility isotherms and the calculated by the Pitzer model for the KCl−MgCl2−H2O system at 323.15 K. All symbols are experimental data: ▲, KCl from ref 8; ●, KCl from ref 9; ■, KCl from ref 10; ◆, KCl from ref 12; ⊕, KCl· MgCl2·6H2O from ref 9; ⊞, KCl·MgCl2·6H2O from ref 10; ◐, KCl + KCl·MgCl2·6H2O from ref 9; ◧, KCl + KCl·MgCl2·6H2O from ref 10; black−white ☆, KCl + KCl·MgCl2·6H2O from ref 11; black−white ◇, KCl + KCl·MgCl2·6H2O from ref 12; ◑, MgCl2 + KCl·MgCl2·6H2O from ref 9; ◨, MgCl2 + KCl·MgCl2·6H2O from ref 10; white−black ☆, MgCl2 + KCl·MgCl2·6H2O from ref 11; white−black ◇, MgCl2 + KCl·MgCl2·6H2O from ref 12; ○, MgCl2·6H2O from ref 9; □, MgCl2· 6H2O from ref 10; ◇, MgCl2·6H2O from ref 12. All lines are solubility isotherms predicted by the Pitzer model: dash lines, with binary parameters only; dotted lines, with binary parameters and mixing parameters fitted to experimental water activities in the ternary system; solid lines, with binary parameters and ternary parameters obtained by fitting to experimental water activities in this work and solubility data in refs 8, 9, 11, and 12.

Figure 3. Experimental isopiestic lines compared with the values predicted by the Zdanovskii rule in the KCl−MgCl2−H2O system at 323.15 K. Solid lines, Zdanovskii rule; filled circles connected by dash line, experimental values.

handbook.6 However, the values largely deviate from the solubility values reported by Yang.5 4.2. KCl−MgCl2−H2O System. Unlike the ternary NaCl− MgCl2−H2O system, it seems that using binary parameters only E



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system was found to obey the Zdanovskii rule, whereas the KCl−MgCl2−H2O system showed positive deviations from this rule. The Pitzer model was used to predict and correlate the thermodynamic properties of these systems. The Pitzer model using binary parameters only was shown to sufficiently represent the solubility isotherms of the NaCl−MgCl2−H2O ternary system. However, the mixing Pitzer model parameters θK,Mg and ψKMgCl are necessary to model the KCl−MgCl2−H2O ternary system. In the framework of the Pitzer model, ion interactions involving in like-ions are stronger in the KCl− MgCl2−H2O ternary system than in the NaCl−MgCl2−H2O ternary system. Based on the simulation results, experimental results of the solubility isotherms of the two ternary systems were evaluated.

■

AUTHOR INFORMATION

Corresponding Author

* E-mail: [email protected]. Notes

The authors declare no competing financial interest.

Figure 7. Deviation of water activity in the ternary system of KCl−MgCl2−H2O calculated by the Pitzer model from experimental values at 323.15 K, Δaw = aw(exp) − aw(cal).

Funding

The authors gratefully thank the National Natural Science Foundation of China (Grants 21406253 and 21303239), the 100 Top Talents Project (Dewen Zeng), and Nature Science Foundation of Qinghai (Grant 2013-Z-927Q) for financial support of this work.

Table 8. Comparison of the Eutectic Points of the KCl−MgCl2−H2O Ternary System at 323.15 K solid phases

KCl

MgCl2

■

references

solution composition (mol·kg−1) KCl + KCl·MgCl2·6H2O

KCl·MgCl2·6H2O + MgCl2·6H2O

0.893 0.827 0.889 1.345 0.829 0.043 0.066 0.043 0.536 0.054

4.335 4.414 4.338 3.468 4.462 6.228 6.212 6.188 4.690 6.212

REFERENCES

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9 11 12 10 this work 9 11 12 10 this work

in the Pitzer model is insufficient to represent the properties of this ternary system. The predicted solubility isotherms (dashed lines in Figure 6) deviate remarkably from the experimental data.8−12 Meanwhile, the calculated water activities of the ternary system also deviate from our experimental values, as shown in Figure 7a. The mixing Pitzer model parameters θK,Mg and ψKMgCl were obtained by regressing both experimental water activities determined in this work and solubility data from refs 8, 9, 11 and12, and listed in Table 6. The water activities (Figure 7b, c) and solubility isotherms (solid lines in Figure 6) predicted by the Pitzer model with the binary and mixing parameters agree well with the experimental values. Finally, the eutectic points of the values predicted by modeling were compared with the experimental values8−12 in Table 8.

5. CONCLUSIONS We elaborately measured the water activities of the NaCl− MgCl2−H2O and KCl−MgCl2−H2O ternary systems and their sub-binary systems at 323.15 K using an isopiestic method. The isopiestic composition line in the NaCl−MgCl2−H2O F



Article

Temperatures for Mixtures in the System Na−K−Mg−Cl−SO4− OH−H2O. Geochim. Cosmochim. Acta 1987, 51, 2429−2443. (30) Balarew, C.; Tepavitcharova, S.; Rabadjieva, D.; Voigt, W. Solubility and Crystallization in the System MgCl2−MgSO4−H2O at 50 and 75 °C. J. Solution Chem. 2001, 30, 815−823. (31) Christov, C. Isopiestic Determination of the Osmotic Coefficients of an Aqueous MgCl2 + CaCl2 Mixed Solution at (25 and 50) °C. Chemical Equilibrium Model of Solution Behavior and Solubility in the MgCl2 + H2O and MgCl2 + CaCl2 + H2O Systems to High Concentration at (25 and 50) °C. J. Chem. Eng. Data 2009, 54, 627−635.

(11) Uhlig, J. The Solubility Diagram of Potassium Chloride, Magnesium Chloride and Water at 50 °C. Centr. Min. Geol. 1913, 417−422. (12) Kurnakov, N. S.; Osokoreva, N. A. Caliche 1932, 2, 27. Cited by Zdanovskii, A. B.; Solov’eva, E. F.; Lyakhovskaya, E. I. Handbook of Experimental Data on Solubility of Multicomponent Water-Salt Systems, Vol. 1: Three-Component Systems Book 2, 2nd ed.; Khimia: Leningrad, 1973; p 649. (13) Wu, Y.; Rush, R. M.; Scatchard, G. Osmotic and Activity Coefficients for Binary Mixtures of Sodium Chlorides, Sodium Sulfate, Magnesium Sulfate, and Magnesium Chloride in Water at 25 °C. I. Isopiestic Measurements on the Four Systems with Common Ions. J. Phys. Chem. 1968, 72, 4048−4053. (14) Platford, R. F. Isopiestic Measurements on the System WaterSodium Chloride-Magnesium Chloride at 25 °C. J. Phys. Chem. 1968, 72, 4053−4057. (15) An, D.; Teng, T.; Sangster, J. M. Vapour Pressures of CaCl2− NaCl−H2O and MgCl2−NaCl−H2O at 25 °C. Prediction of the Water Activity of Supersaturated NaCl Solutions. Can. J. Chem. 1978, 56, 1853−1855. (16) Rard, J. A.; Miller, D. G. Isopiestic Determination of the Osmotic and Activity Coefficients of Aqueous Mixtures of NaCl and MgCl2 at 25 °C. J. Chem. Eng. Data 1987, 32, 85−92. (17) Robinson, R. A.; Stokes, R. H. A Thermodynamic Study of Bivalent Metal Halides in Aqueous Solution. Part XV. Double Chlorides of Uni- and Bivalent Metals. Trans. Faraday Soc. 1945, 41, 752−756. (18) Kirginstev, A. N.; Lukyanov, A. V. Isopiestic Investigation of Ternary Solutions. 7. Ternary Solutions LiCl−CsCl−H2O, KCl− CsCl−H2O, RbCl−CsCl−H2O, KCl−CaCl2−H2O and KCl−MgCl2− H2O. Russ. J. Phys. Chem. 1966, 40, 1280−1284. (19) Padova, J.; Saad, D. Thermodynamics of Mixed Electrolyte Solutions. VIII. An Isopiestic Study of the Ternary System KCl− MgCl2−H2O at 25 °C. J. Solution Chem. 1977, 6, 57−71. (20) Kuschel, F.; Seidel, J. Osmotic and Activity Coefficients of Aqueous K2SO4−MgSO4 and KCl−MgCl2 at 25 °C. J. Chem. Eng. Data 1985, 30, 440−445. (21) Miladinovic, J.; Ninkovic, R.; Todorovic, M. Osmotic and Activity Coefficients of {yKCl + (1 − y)MgCl2}(aq) at T = 298.15 K. J. Solution Chem. 2007, 36, 1401−1409. (22) Fanghänel, T.; Grjotheim, K.; Haugsdal, B.; Voigt, W. Thermodynamics of Aqueous Reciprocal Salt Systems. V. Isopiestic Determination of Osmotic and Activity Coefficients of the System Mg2+, K+/Cl−, Br−//H2O at 100.3 °C. Acta Chem. Scand. 1991, 45, 30−36. (23) Yin, S. T.; Yao, Y.; Li, B.; Tian, H. B. Isopiestic Studies of Aqueous MgB4O7 and MgSO4 + MgB4O7 at 298.15 K and Representation with Pitzer’s Ion-Interaction Model. J. Solution Chem. 2007, 36, 1745−1761. (24) Li, H.; Dong, O. Y.; Yao, Y.; Wang, H. Y.; Zeng, D. W. The Mass Titration Analytical Method and Its Application. J. Salt Lake Res. 2011, 19, 31−36. (25) Yang, H. T.; Zeng, D. W.; Voigt, W.; Hefter, G.; Liu, S. J.; Chen, Q. Y. Isopiestic Measurements on Aqueous Solutions of Heavy Metal Sulfates: MSO4 + H2O (M = Mn, Co, Ni, Cu, Zn). 1. T = 323.15 K. J. Chem. Eng. Data 2014, 59, 97−102. (26) Gruszkiewicz, M. S.; Simonson, J. M. Vapor Pressures and Isopiestic Molalities of Concentrated CaCl2(aq), CaBr2(aq), and NaCl(aq) to T = 523 K. J. Chem. Thermodyn. 2005, 37, 906−930. (27) Zeng, D. W.; Zhou, H. Y.; Voigt, W. Thermodynamic Consistency of the Solubility and Vapor Pressure of a Binary Saturated Salt + Water System. II. CaCl2 + H2O. Fluid Phase Equilib. 2007, 253, 1−11. (28) Pitzer, K. S.; Christopher Peiper, J.; Busey, R. H. Thermodynamic Properties of Aqueous Sodium Chloride Solutions. J. Phys. Chem. Ref. Data 1984, 13, 1−102. (29) Pabalan, R. T.; Pitzer, K. S. Thermodynamics of Concentrated Electrolyte Mixtures and the Prediction of Mineral Solubilities to High G


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