Article pubs.acs.org/jced
Water Activity Measurements by the Isopiestic Method for the MCl−CaCl2−H2O (M = Na, K) Systems at 323.15 K Haijun Han,†,‡ Lijiang Guo,‡ Dongdong Li,‡ Ouyang Dong,‡ Yan Yao,‡ Ning Zhang,† and Dewen Zeng*,† †
College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, P. R. China Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, P. R. China
‡
ABSTRACT: In this work, the water activities of the NaCl−CaCl2− H2O and KCl−CaCl2−H2O ternary systems and of their sub-binary systems NaCl−H2O and KCl−H2O were measured using an isopiestic method at 323.15 K. The isopiestic composition line for the NaCl− CaCl2−H2O system was found to obey the Zdanovskii rule very well, whereas the KCl−CaCl2−H2O system deviated slightly. The addition of NaCl to an aqueous solution of CaCl2 decreased its water activity for all CaCl2 molalities. However, KCl was found to decrease and increase the water activity at low and high CaCl2 molality, respectively. The turning point appears at 8.0 mol·kg−1 CaCl2 solution. The Pitzer− Simonson−Clegg (PSC) model was applied to represent the water activity of the two ternary systems, and the calculated results are discussed.
1. INTRODUCTION Phase equilibria of multicomponent systems at multiple temperatures are involved in salt lake chemical industrial processes. Modeling and simulation are necessary to represent the complicated crystallization behavior of these systems and to design economical crystallization processes. To parametrize a thermodynamic model, properties are needed for multiple temperatures of a multicomponent system, especially the water activity. Until now, most studies on water activity in multicomponent systems concerning salt lakes have been limited to 273.15 K and 298.15 K.1−19 By improving the isopiestic apparatus, we have planned to measure systematically the water activity of multicomponent salt lake systems at higher temperatures. In the previous work,20 the water activity for the ternary systems NaCl(KCl)−MgCl2−H2O at 323.15 K was reported. As a continuing study in this series of work, the water activity for the ternary systems NaCl(KCl)−CaCl2−H2O at 323.15 K is reported here. The results help us understand deeply the thermodynamic properties of these systems.
and the largest relative deviation for each of three parallel samples could be controlled to lower than 0.05 %. The impurity contents in the salts were analyzed using an inductively coupled plasma (ICP) atomic emission spectrometry (Thermo Electron Corporation, ICAP 6500 DUO). 2.2. Apparatus and Procedure. The isopiestic measurement setup and procedure in this work are the same as described in our previous work20 and will not be described again here. The weight correction method for each cup of solution was similar to that described in our previous work.21
3. EXPERIMENTAL RESULTS AND DISCUSSIONS Pure CaCl2(aq), NaCl(aq), and KCl(aq) were all used as reference systems and were verified with each other to guarantee the reliability of the experimental data. The osmotic coefficients ϕ for each pure CaCl2, NaCl, and KCl aqueous solution as a function of their molalities (m) (eq 1) have been reported in our previous work20 and is used directly in this work. ϕ = p1 + p2 (m/mol ·kg −1)0.5 + p3 (m/mol ·kg −1)
2. EXPERIMENTAL SECTION 2.1. Materials. Doubly distilled water with conductance lower than (1.5·10−4) S·m−1 was used for all experimental processes. NaCl and KCl (both products of the Sinopharm Chemical Reagent Co., Ltd. G.R.) were purified by recrystallization times three, and the impurity content for each element Li, Na, (or K), Ca, and Mg in the salts was found to be less than 0.01 % in mass. CaCl2 (Aladdin Industrial Inc., purity > 0.9999 in mass fraction) was directly used to prepare stock solution without any extra purification. The maximum contents of the selected impurities (elemental Na, K, Mg, Sr, Ba, and Fe) were analyzed to be lower than 0.02 % (in mass). The CaCl2 content was determined using the precipitation method with AgNO3 (99.95 % in mass), © XXXX American Chemical Society
+ p4 (m/mol ·kg −1)1.5 + p5 (m/mol ·kg −1)2 + p6 (m/mol ·kg −1)2.5 + p7 (m/mol ·kg −1)3 + p8 (m/mol ·kg −1)3.5
(1)
The osmotic coefficient of these pure salt solutions can be calculated using eq 1 as long as the molality of any pure salt solution is known. Received: February 17, 2015 Accepted: June 16, 2015
A
DOI: 10.1021/acs.jced.5b00155 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Measured Isopiestic Molalities m and Calculated Water Activities aw for the Ternary System NaCl−CaCl2−H2O at 323.15 Ka mNaCl
mCaCl2
mNaCl
mCaCl2
no.
mol·kg−1
mol·kg−1
no.
mol·kg−1
mol·kg−1
1
mCaCl2 = 0.3984
aw = 0.9814
5
mCaCl2 = 2.4684
aw = 0.8180
2
mNaCl = 0.5648 0 0.0408 0.1306 0.2198 0.3541 0.4889 0.5648 mCaCl2 = 0.6418
aw = 0.9813 0.3984 0.3709 0.3081 0.2452 0.1508 0.0556 0 aw = 0.9684
6
mNaCl = 4.7125 0 0.2568 0.8553 1.5040 2.5953 3.8724 4.7125 mCaCl2 = 3.0757
aw = 0.8191 2.4684 2.3329 2.0179 1.6778 1.1052 0.4406 0 aw = 0.7511
mNaCl = 0.9585 0 0.0660 0.2123 0.3605 0.5843 0.8183
aw = 0.9680 0.6418 0.5992 0.5009 0.4021 0.2488 0.0931
7
0 0.3211 1.0770 1.9091 3.3383 5.0574 mCaCl2 = 4.6422
3.0757 2.9165 2.5409 2.1298 1.4215 0.5755 aw = 0.5638
0.9585 mCaCl2 = 0.9267
0 aw = 0.9510
0 0.4886
4.6422 4.4379
mNaCl = 1.4556
aw = 0.9506
0 0.0958 0.3096
0.9267 0.8699 0.7305
0.5302 0.8686 1.2324
0.5915 0.3699 0.1402
1.4556 mCaCl2 = 1.6824
0 aw = 0.8931
mNaCl = 2.9406
aw = 0.8940
0 0.1742 0.5735
1.6824 1.5825 1.3532
0.9961 1.6837 2.4520 2.9406
1.1112 0.7170 0.2790 0
3
4
8
mCaCl2 = 4.9333
aw = 0.5305
9
0 0.0438 mCaCl2 = 7.4987
4.9333 4.9148 aw = 0.3189
10
0 0.0663 mCaCl2 = 8.7099
7.4987 7.4428 aw = 0.2596
0 0.0775
8.7099 8.6975
11
mCaCl2 = 10.5967
aw = 0.1937
12
0 0.0944 mCaCl2 = 11.3161
10.5967 10.5863 aw = 0.1739
0 0.1008
11.3161 11.3097
a The water activity is calculated by the equations reported in refs 22 and 23 for CaCl2 and ref 24 for NaCl. The relative standard deviation of u is uT(m) = 0.003.
The experimental water activities in the ternary systems of NaCl−CaCl2−H2O and KCl−CaCl2−H2O at 323.15 K are presented in Tables 1 and 2, respectively. In each isopiestic experimental run, the molalities (mol·kg−1) of the reference solution (the CaCl2, NaCl, or KCl pure salt solutions) and the corresponding water activity are listed in the first (and the second in some cases) line. The following data are the isopiestic molalities of other sample solution. During each isopiestic measurement run, the largest difference in molality for two parallel samples was less than 0.3 %, which stand for the total errors coming from weighing, the equilibrium time, water transportation within the isopiestic chamber, and temperature differences between the two cups. Combining the 0.1 % uncertainty associated with impurities and the 0.3 % uncertainty described above, it can be reasonably concluded that the total uncertainty for the measured molality could be less than 0.4 %, which corresponds to a greatest possible deviation in the measured water activities of ± 0.0026.
The osmotic coefficients for other solutions of mixing investigated in this study can be calculated by eq 2:
ϕ=
v*m*ϕ* ∑i vm i i
(2)
where the quantities with asterisks stand for the reference solution, ν* = 3 denotes the ion number when one CaCl2 molecule is dissociated completely, m* and ϕ* are the molality and the osmotic coefficient of the reference system at isopiestic equilibrium state, respectively, and ∑iνimi = 2mMCI + 3mCaCl2 for the MCl−CaCl2−H2O (M = Na, K) ternary systems. The water activity aw was calculated by eq 3:
ln a w = −v ·M w ·m ·ϕ
(3)
where v is the ion number when the salt is dissociated completely; that is, v = 3 for CaCl2 and v = 2 for KCl and NaCl. The variable Mw (kg·mol−1) is the molar mass of H2O. B
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Table 2. Measured Isopiestic Molalities m and Calculated Water Activities aw for the Ternary System KCl−CaCl2−H2O at 323.15 Ka mKCl no. 1
2
3
4
5
6
mol·kg
mCaCl2 −1
mol·kg
mKCl
−1
mCaCl2 −1
mol·kg−1
no.
mol·kg
7
mCaCl2 = 4.0962
aw = 0.6289
8
1.5966 0.9652 0.4224 0.2030 0.1069 0 mCaCl2 = 4.3939
3.6692 3.8557 3.9888 4.0561 4.0849 4.0962 aw = 0.5931
mCaCl2 = 0.3610
aw = 0.9832
mKCl = 0.5249 0.5249 0.4516 0.3296 0.2175 0.1216 0.0358
aw = 0.9831 0 0.0514 0.1368 0.2137 0.2794 0.3379
0 mCaCl2 = 0.6501
0.3610 aw = 0.9680
1.0371 0.4536
4.1430 4.2832
mKCl = 1.0115 1.0115 0.8641 0.6220
aw = 0.9676 0 0.0983 0.2581
9
0.2172 0.1142 0 mCaCl2 = 5.6570
4.3406 4.3639 4.3939 aw = 0.4560
0.4044 0.2231 0.0648 0 mCaCl2 = 0.8935
0.3973 0.5128 0.6123 0.6501 aw = 0.9532
10
0.5911 0.2814 0.1476 0 mCaCl2 = 6.3224
5.5813 5.6232 5.6374 5.6570 aw = 0.3978
mKCl = 1.4700 1.4700 1.2468 0.8870 0.5696
aw = 0.9527 0 0.1419 0.3681 0.5596
11
0.6652 0.3150 0.1652 0 mCaCl2 = 6.5561
6.2811 6.2943 6.3112 6.3224 aw = 0.3799
0.3110 0.0895 0 mCaCl2 = 1.4864
0.7147 0.8448 0.8935 aw = 0.9097
0.6909 0.3270 0.1713 0
6.5237 6.5331 6.5455 6.5561
mKCl = 2.7456
aw = 0.9104
2.7455 2.2957 1.5862 0.9956 0.5308
0 0.2612 0.6582 0.9780 1.2199
0.1496 0 mCaCl2 = 2.2985
1.4131 1.4864 aw = 0.8354
mKCl = 4.9059
aw = 0.8364
4.9059 4.0241 2.6834 1.6307 0.8472
0 0.4578 1.1134 1.6018 1.9470
0.2336 0 mCaCl2 = 2.7614
2.2059 2.2985 aw = 0.7865
3.3698 2.0142
1.3983 1.9786
1.0323 0.2817 0
2.3723 2.6603 2.7614
12
mCaCl2 = 7.5931
aw = 0.3136
13
0 0.1989 0.3807 0.8070 mCaCl2 = 7.7516
7.5931 7.5979 7.6064 7.6199 aw = 0.3050
0 0.2031 0.3883
7.7516 7.7578 7.7594
14
mCaCl2 = 8.8792
aw = 0.2526
15
0 0.2331 0.4468 0.9514 mCaCl2 = 10.6654
8.8792 8.9051 8.9288 8.9831 aw = 0.1918
0 0.2806 0.5389
10.6654 10.7206 10.7693
1.1524 mCaCl2 = 11.3585
10.8813 aw = 0.1732
0 0.2990 0.5742 1.2302
11.3585 11.4243 11.4743 11.6164
16
a
The water activity is calculated by the equations reported on in refs and 23 for CaCl2 and ref 25 for KCl. The relative standard deviation of u is uT(m) = 0.003. C
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concentration is abnormal and can hint at some structural changes of the solution in the mixing process. As mentioned by Pitzer26 and Rard,27 the species CaClx(H2O)y(2‑x)+ may exist in a CaCl2 solution with a high molality. The addition of KCl can decrease the water activity by combining free water molecules with K+ ions. However, it can increase the water activity by replacing the bound water molecules in the inner coordinationspheres of the Ca2+ ion with Cl− ions. The former effect is preferable to the latter in relatively dilute CaCl2 solutions and vice versa for concentrated CaCl2 solutions.
To facilitate comparison, the experimentally measured isopiestic results for the ternary systems MCl−CaCl2−H2O (M = Na, K) at 323.15 K are shown in Figures 1 and 2 with inserts plotted for clarification. As shown in Figure 1, each set of
4. MODELING AND COMPARISON To further compare the effects of the addition of NaCl and KCl on the water activity of CaCl2 aqueous solution, we used the Pitzer−Simonson−Clegg model28,29 (PSC) to represent their water activities as a function of salt molalities. In the framework of the model, the water activity for a ternary system taking the form MX + NX2 + H2O is expressed as the product of water activity coefficient f w and the water mole fraction xw: a w = fw x w ,
Figure 1. Experimental isopiestic lines compared with the Zdanovskii rule in the NaCl−CaCl2−H2O system at 323.15 K. The dashed lines correspond to the Zdanovskii rule and the filled circles connected by solid lines are the experimental values. The dashed lines are overlapped by the solid lines and thus invisible.
ln fw = 2Ax Ix 3/2/(1 + ρIx1/2) − xMx XBMX 1 1 exp( −αMX × exp( −αMXIx1/2) − xMx XBMX Ix1/2) 1 − x Nx XB NX exp( −αNXIx1/2) − x Nx XB NX
isopiestic composition points in the NaCl−CaCl2−H2O system are found to exist in a roughly straight line, indicating that the mixing behavior of this ternary system obeys the Zdanovskii rule. The downward slope of the isopiestic lines with increasing NaCl molality indicates that the addition of NaCl to the CaCl2 aqueous solution decreases the water activity. However, in the KCl−CaCl2−H2O system, the isopiestic composition lines positively deviate from the Zdanovskii rule (dashed lines in Figure 2). It is also observed that the isopiestic lines decrease at relatively low CaCl2 molalities and increase at high CaCl2 molality with increasing KCl molality. The turning point appears at a CaCl2 molality of 7−8 mol·kg−1(nH2O/nCa2+ = 7 to 8). The changing tendency of the lines means that the addition of KCl to the CaCl2 aqueous solution can either decrease or increase the water activity for a low and high molality, respectively. While it is easily understandable that the addition of KCl to a CaCl2 solution of low concentration decreases the water activity of the solution, the increasing of the water activity resulting from the addition of KCl to a CaCl2 solution of high
1 × exp( −αNX Ix1/2) − 2xMx N(vMN + Ixv′MN )
+ (1 − x w )(1/F ){EM(z M + z X)/(z Mz X)W1,MX + E N(z N + z X)/(z Nz X)W1,NX } + (1 − 2x w)xX × {xM(z M + z X)2 /(z Mz X)U1,MX + x N(z N + z X)2 /(z Nz X)U1,NX} + 4x w(2 − 3x w)x X × (xMV1,MX + x NV1,NX) − 2xMx NWMNX − 4xMx N(xM /vM(X) − x N/vN(X))UMNX + 4(1 − 2x w )xMx NQ 1,MNX ,
(4)
with ρ = 2150(dw/DT) . Ax and Ix are Debye−Hückel parameter and ionic strength in mole fraction, respectively. xX, xM, xN are the mole fraction of the substances which obey the relation xM + xN + xX = 1 − xw. dw, D, and T are the density of water in g·cm−3, the dielectric constant of 1/2
Figure 2. Experimental isopiestic lines compared with the Zdanovskii rule for the KCl−CaCl2−H2O system at 323.15 K. The dashed lines correspond to the Zdanovskii rule and the filled circles connected by solid lines are the experimental values. D
DOI: 10.1021/acs.jced.5b00155 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 3. PSC Model Parameters of Binary Systems at 323.15 K solute
αMX
BMX
α1MX
B1MX
W1,MX
U1,MX
V1,MX
source
CaCl2 NaCl KCl
13 13 13
873.1586 14.1714 5.3847
2.0 0 0
−548.0129 0 0
−40.0831 −6.7190 −2.7595
25.9625 −5.8725 −1.3749
14.7228 1.1035 0
30 this work this work
Table 4. PSC Mixing Model Parameters of the MCl−CaCl2−H2O (M = Na, K) Systems at 323.15 K
a
i
j
k
Wijk
Q1,ijk
Uijk
data for parametrization
σa
Na K
Ca Ca
Cl Cl
22.766 −9.900
−15.598 −1.944
0 0
aw in Table 1 aw in Table 2
0.0019 0.0028
σ = (1/n∑ni=1(aw(exp) − aw (calc))2)1/2
5. CONCLUSIONS In this work, the water activities for the NaCl−CaCl2−H2O and KCl−CaCl2−H2O ternary systems were measured at 323.15 K using an isopiestic method. The measured data exhibit some interesting features. The isopiestic composition lines in the NaCl−CaCl2−H2O system were found to obey the Zdanovskii rule over the entire molalities range, whereas the KCl−CaCl2− H2O system shows positive deviations from this rule. The addition of NaCl to a CaCl2 aqueous solution decreases its water activity for all CaCl2 molalities. However, KCl decreases and increases the water activity at low and high CaCl2 molalities, respectively.
the solvent water, and thermodynamic temperature, respectively. For a binary system the variables BMX, B1MX, W1,MX, U1,MX, V1,MX, αMX and α1MX are needed, and for ternary system the extra mixing parameters WMNX, Q1,MNX and UMNX must be included in eq 4. The binary model parameters for NaCl−H2O and KCl−H2O were evaluated by simulating the osmotic coefficients reported in the literature.24,25 The values of the binary model parameters are shown in Table 3. The binary model parameters for CaCl2−H2O were the same as those used in a previous work.30 The mixing parameters for each ternary system were obtained by fitting the water activity measured in this work (Tables 1 and 2) and listed in Table 4. By applying the model parameters shown in Tables 3 and 4, we calculated the water activity for a CaCl2 aqueous solution at various molalities when dried NaCl or KCl salts were added into the solutions. Selected calculated results are shown in Figure 3.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Funding
This work was financially supported by National Nature Science Foundation of China under Contract Nos. 21406253 and 21303239. Chinese Academy of Sciences is also acknowledged for its support for D. Zeng through the 100 Top Talents Project. Notes
The authors declare no competing financial interest.
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REFERENCES
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Figure 3. Water activity calculated using the PSC model when NaCl and KCl were added to various molalities of CaCl2 aqueous solutions at 323.15 K. The dashed lines represent the NaCl−CaCl2−H2O system and the solid lines represent the KCl−CaCl2−H2O system.
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DOI: 10.1021/acs.jced.5b00155 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
