Published: March 11, 2011
r 2011 American Chemical Society 1793 dx.doi.org/10.1021/je100743h | J. Chem. Eng. Data 2011, 56, 1793–1797
ARTICLE
pubs.acs.org/jced
Equilibria in the Quaternary System KCl�NaCl�CaCl2�H2O
at 283.15 K
Cui Peng, Zhancheng Guo,* and Fuli Zhang
Key Laboratory of Ecological and Recycle Metallurgy, Ministry of Education, University of Science and Technology, Beijing, 100083,
China
ABSTRACT: The solubilities and physicochemical properties in the quaternary system KCl�NaCl�CaCl2�H2O at 283.15 K
have been measured with the isothermal method. The dry-salt phase diagram, water-phase diagram, and physicochemical properties
vs composition in the system were plotted according to the measured data. The system contained only the forms of single salts, and
no double salts or solid solution were found. On the basis of the extended Harvie�Weare (HW) model and the temperature
coefficients of the single-salt parameters obtained from the calorimetric data, the Pitzer parameters for KCl, NaCl, and CaCl2 and the
mixed ion-interaction parameters at 283.15 K were obtained. In addition, the average equilibrium constants of the solids at the same
temperature were obtained using a method derived from the activity coefficient model of the electrolyte solution theory. Using the
average equilibrium constants of the solids at equilibrium, the solubility predictions for the quaternary system are presented. A
comparison between the calculated and experimental results suggests that the predicted solubility data obtained with the extended
HW model agree well with the experimental data.
’ INTRODUCTION
Sintering dust arrested by electrostatic precipitators in the
sinter plant of integrated iron and steel companies has been
found enriched with potassium chloride up to 30 % to 50 % (by
weight).1,2 Water leaching was proposed to extract the potassium
chloride from the sintering dust, and the leaching solution can be
considered as a quaternary system KCl�NaCl�CaCl2�H2O
after sulfide precipitation for removing the slight amount of
dissolved heavy metal impurities.
As an alternative method to obtain a potassium chloride
product, evaporation-cooling crystallization needs solubility data
of the quaternary system KCl�NaCl�CaCl2�H2O at tempera-
tures over a wide range. However, there are only some solubility
data of this quaternary system and its ternary subsystems
KCl�NaCl�H2O, KCl�CaCl2�H2O, andNaCl�CaCl2�H2O
between (291.15 and 368.15) K,3�7 although the metastable
equilibria of the quaternary system at 288.15 K have been
experimentally measured and also calculated with the Pitzer and
extended Harvie�Weare (HW) models.8,9 Equilibria of the
quaternary system KCl�NaCl�CaCl2�H2O at 283.15 K were
investigated in this paper. Both the measured solubility data and
the predicted solubilities based on the extended HW model are
presented.
’EXPERIMENTAL SECTION
The experiments were carried out as equilibrium investiga-
tions. Samples were prepared by mixing the individual salts and
water in suitable proportions in closed plastic bottles. The bottles
were shaken in an air-bath, which was electrically heated and
carefully insulated. The air of the bath was vigorously stirred by
means of fans. The temperature was constant to within 0.1 �C.
After three or four days, the sample was passed through a glass
filter with pore size of 0.22 μm, without taking the bottle
containing the sample or the filter out of the thermostat. Small
amounts of the solution and the solid phase were immediately
weighed for analysis. One of the components was added to the
pure filtered solution, and the experiments were repeated as
before.
The compositions of both the solid phase and the liquid phase
were determined by chemical methods. The concentration of Kþ
and Naþ was determined using a flame photometer FP640 after
being diluted step by step until the concentration was at or near
the middle of the standard curve. The Kþ concentration in some
samples was also analyzed by gravimetric methods using sodium
tetraphenyl borate and compared with that obtained by FP640.
The relative error was about ( 5 %. The concentration of Cl�
was determined using an ion chromatograph (792 basic IC made
by Metrohm). The average deviation was less than ( 1 %. The
Ca2þ concentration was determined by titration with ethylene
diamine tetraacetic acid (EDTA), and the uncertainty was within
( 0.3 %. The concentration of Naþ was also evaluated by ion
balance and compared with the value measured by FP640, and
the average deviation was within 5 %. The pH value of the liquid
phase was measured with a PHS-3C precision pH meter. The
densities (F) were measured with a density bottle with a
precision of ( 0.0002 g 3 cm
�3.
’RESULTS AND DISCUSSION
The experimental results for the solubilities and the relevant
physicochemical properties of the stable equilibria of the
quaternary system KCl�NaCl�CaCl2�H2O at 283.15 K are
presented in Tables 1 and 2. The solubilities of salts in the
Received: July 14, 2010
Accepted: February 25, 2011
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1794 dx.doi.org/10.1021/je100743h |J. Chem. Eng. Data 2011, 56, 1793–1797
Journal of Chemical & Engineering Data ARTICLE
equilibria are expressed as a weight percentage. The experimental
phase diagram of the system at 283.15 K was plotted, as shown in
Figure 1. The phase diagram consists of one invariant point E,
three crystallized regions of single salts KCl, NaCl, and CaCl2 3
6H2O, and three invariant solubility isotherm curves that
correspond to E1E, E2E, and E3E. This phase diagram is similar
to the metastable equilibria phase diagram of the same quatern-
ary system at 288.15 K.8
The water diagram of the system at 283.15 K is shown in
Figure 2, which presents the projection of the invariant
curves (J€anecke diagram) of this quaternary system at
283.15 K. According to the data in Table 2, the relationships
between the physicochemical properties of the solution (pH
and density) and the weight percentage of CaCl2 are
illustrated in Figure 3. As obtained in the literature,8,9
the pH and density of the equilibrium solution change
smoothly between E1 and E with the increase of calcium
chloride concentration. The pH of the solution begins to
sharply decrease when the calcium chloride concentration
increases after point E. The density of the solution gets a
maximal value at point E. The obtained special features of
point E together suggest the accuracy of the solubility
measurement.
’SOLUBILITY PREDICTIONS
Calculation of Single Salt Parameters. In this work, solubi-
lity prediction of the quaternary system at 283.15 K was done on
the basis of expressions about osmotic coefficients of the solution
and mean activity coefficients of electrolytes in the solution
proposed by Pitzer.10,11 The electrolyte parameters, including
the Pitzer single salt parameters β(0), β(1), and C(Ψ) and mixed
salt parameters θ andΨ, in those expressions were initially given
by Pitzer and Kim in 1974 and subsequently supplemented by
Harvie and Wear (HW) in 1984.12�14 However, these para-
meters for both single salt and mixed-ion interactions are all
Table 1. Quaternary System KCl�NaCl�CaCl2�H2O at 283.15 K
weight percent, solution J€anecke index, Jb (g/100 g of S)
no. KCl NaCl CaCl2, KCl CaCl2 H2O solid phase
1E1 8.71 ( 0.43 21.66 ( 1.08 0 28.68( 1.43 0 229.2( 11.4 KCl þ NaCl
2 8.05( 0.40 18.79 ( 0.93 2.77( 0.01 27.19( 1.35 9.35( 0.02 237.7( 11.8 KCl þ NaCl
3 7.89( 0.39 17.65( 0.88 4.26( 0.01 26.48( 1.32 14.30( 0.04 235.5( 11.7 KCl þ NaCl
4 7.33( 0.36 14.27( 0.71 8.30( 0.02 24.52( 1.22 27.76( 0.08 234.4( 11.7 KCl þ NaCl
5 6.91( 0.34 12.33( 0.61 10.45( 0.03 23.27( 1.16 35.20( 0.10 236.8 ( 11.8 KCl þ NaCl
6 6.35( 0.32 10.51( 0.52 13.95( 0.04 20.61( 1.03 45.28 ( 0.13 224.5( 11.2 KCl þ NaCl
7 4.84( 0.24 6.21 ( 0.31 20.98( 0.06 15.11( 0.75 65.50( 0.19 212.2( 10.6 KCl þ NaCl
8 3.97( 0.19 4.27( 0.21 25.27( 0.07 11.85( 0.59 75.41( 0.22 198.4( 9.9 KCl þ NaCl
9 3.18( 0.16 2.50( 0.12 28.86( 0.08 9.21( 0.46 83.56( 0.25 189.5( 9.4 KCl þ NaCl
10 2.25( 0.11 0.84( 0.04 34.66( 0.10 5.96( 0.29 91.81( 0.27 164.9 ( 8.2 KCl þ NaCl
11E 1.954( 0.097 0.697( 0.034 36.99( 0.11 4.93( 0.24 93.31( 0.27 152.2( 7.6 KCl þ NaCl þ C6a
12 1.316( 0.065 0.700( 0.035 39.11( 0.11 3.20( 0.16 95.10( 0.28 143.1( 7.1 NaCl þ C6
13 0.760( 0.038 0.645( 0.032 38.73( 0.11 1.89( 0.09 96.50( 0.29 149.1 ( 7.4 NaCl þ C6
14 0.737( 0.036 0.674( 0.033 38.31( 0.11 1.86( 0.09 96.45( 0.29 151.7( 7.5 NaCl þ C6
15E2 0 0.533( 0.026 35.19 ( 0.10 0 98.51( 0.29 179.9( 8.9 NaCl þ C6
16 0.337( 0.016 0.626( 0.031 39.45( 0.12 0.83( 0.04 97.62( 0.29 147.4( 7.3 NaCl þ C6
17 2.125( 0.106 0.468( 0.023 38.62( 0.12 5.16( 0.25 93.71( 0.28 142.6( 7.1 KCl þ C6
18E3 2.051( 0.102 0 38.47 ( 0.11 5.06( 0.25 94.94( 0.28 146.7( 7.3 KCl þ C6
19 2.131( 0.106 0.314 ( 0.015 38.44( 0.11 5.21( 0.26 94.02( 0.28 144.5( 7.2 KCl þ C6
20 2.110( 0.105 0.344( 0.017 39.17( 0.12 5.07( 0.25 94.10( 0.28 140.2( 7.0 KCl þ C6
aC6, CaCl2 3 6H2O.
Table 2. pH and Density Data of the Liquid Phase in the
Quaternary System KCl�NaCl�CaCl2�H2O at 283.15 K
no. pH F/(g 3 cm
�3)
1,E1 6.68 1.2341
2 6.56 1.2385
3 6.58 1.2426
4 6.42 1.2525
5 6.25 1.2592
6 6.17 1.2732
7 5.90 1.2896
8 5.70 1.3132
9 5.61 1.3312
10 NDa 1.3900
11E 5.05 1.4289
12 4.65 1.3775
13 4.56 1.3901
14 4.56 ND
15E2 ND 1.3878
16 4.62 1.3815
17 4.61 1.4163
18E3 ND 1.4243
19 ND 1.4162
20 ND ND
aND = not detected.
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电解质溶液的平均活度系数
1795 dx.doi.org/10.1021/je100743h |J. Chem. Eng. Data 2011, 56, 1793–1797
Journal of Chemical & Engineering Data ARTICLE
obtained from standard conditions at 298 K. So it is necessary to
get the values of the parameters for the quaternary system
KCl�NaCl�CaCl2�H2O at 283.15 K first. These parameters
are not only affected by the structure of the electrolytes and
interaction of mixed ions but also influenced by temperature of
the system. It is reported that the single parameters β(0), β(1), and
C(Ψ) at any temperature T can be calculated by the following
equations when there is no remarkable temperature deviation
from 298 K.15�18
βð0ÞT ¼ βð0Þ298 þ
Z T
298
∂βð0Þ
∂T
dT ð1Þ
βð1ÞT ¼ βð1Þ298 þ
Z T
298
∂βð1Þ
∂T
dT ð2Þ
CðjÞT ¼ CðjÞ298 þ
Z T
298
∂CðjÞ
∂T
dT ð3Þ
where βT
(0), βT
(1), and CT
(j) are Pitzer single parameters at
temperature T; β298
(0) , β298
(1) , and C298
(j) are Pitzer single parameters
at 298 K; and (∂β)(0)/(∂T), (∂β)(1)/(∂T), and (∂C)(j)/(∂T),
listed in Table 3, are the partial derivatives of the single
parameters with respect to temperature T. So the Pitzer single
parameters of KCl, NaCl, and CaCl2 at 283.15 K were thus
obtained, as shown in Table 4.
Calculation of Mixed-Ion Interaction Parameters. The
mixed-ion interaction parameters given by Pitzer and HW were
also obtained at 298 K. In this paper, the Pitzer mixed ion-
interaction parameters θK,Na, θK,Ca, θNa,Ca ΨK,Na,Cl, ΨK,Ca,Cl,
and ΨNa,Ca,Cl are calculated on the basis of solubility data of
binary systems of KCl�NaCl�H2O, KCl�CaCl2�H2O, and
NaCl�CaCl2�H2O at 283.15 K with resort to multiple linear
regression by the least-squares method. The results are listed in
Table 5, and a comparison between the parameters fitted in this
paper and those parameters reported at (298.15 and 288.15) K
are also shown. At the same time, the equilibrium constants of the
three salts, KCl, NaCl, and CaCl2 3 6H2O, are obtained as
presented in Table 6.
On the basis of the Pitzer equations and extendedHWmodel
and those fitted parameters of both single salt and mixed-ion
interaction and the equilibrium constants, solubilities of the
quaternary system KCl�NaCl�CaCl2�H2O at 283.15 K are
calculated. Comparison between the experimental phase dia-
gram and those calculated is shown in Figure 4. The results
in Figure 4 show that the predicted solubilities of the quatern-
ary system agree well with the experimental ones, indicating
that the parameters and the equilibrium constants are fitted
reliably.
’CONCLUSIONS
The equilibrium of the quaternary system KCl�NaCl�
CaCl2�H2O at 283.15 K was determined experimentally with
the isothermal method. The density and pH of the equilibrium
solution were also measured. On the basis of the experimental
data, the dry-salt phase diagram of the system includes one
three-salt cosaturated point, three equilibrium solubility iso-
thermal curves, and three crystallization zones of KCl, NaCl,
and CaCl2 3 6H2O. No double salts or solid solution were
found. On the basis of the Pitzer equations and extended
HW model, single salt parameters and mixed-ion interaction
parameters were fitted using multiple linear regression using
the least-squares method according to the solubility data of the
three binary systems (KCl�NaCl�H2O, KCl�CaCl2�H2O,
and NaCl�CaCl2�H2O) at 283.15 K. Solubility predictions of
the quaternary system KCl�NaCl�CaCl2�H2O at 283.15 K
have been made using the average equilibrium constants of
the solids. The results demonstrate that the Pitzer parame-
trizations based on the temperature coefficients and the
average equilibrium constants of the solids as a judgment of
the quaternary system equilibrium are reliable. The calcu-
lated solubilities with the extended HW model through the
average equilibrium constants agree well with the experi-
mental data.
Figure 1. Phase diagram of the quaternary system KCl�NaCl�CaCl2�H2O at 283.15 K.
Figure 2. Water-phase diagram of the system KCl�NaCl�CaCl2�
H2O at 283.15 K.
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1796 dx.doi.org/10.1021/je100743h |J. Chem. Eng. Data 2011, 56, 1793–1797
Journal of Chemical & Engineering Data ARTICLE
’AUTHOR INFORMATION
Corresponding Author
*Tel.: þ86 010 82375042. Fax: þ86 010 82375042. E-mail:
zcguo@metall.ustb.edu.cn.
Funding Sources
The authors would like to thank the National Natural Science
Foundation of China (No. 50974018) andMinistry of Education
(No. 108007) for the financial support.
’REFERENCES
(1) Peng, C.; Zhang, F. L.; Guo, Z. C. Separation and Recovery of
Potassium Chloride from Sintering Dust of Ironmaking Works. ISIJ Int.
2009, 49 (5), 735–742.
(2) Peng, C.; Guo, Z. C.; Zhang, F. L. Discovery of Potassium
Chloride in the Sintering Dust by Chemical and Physical Characteriza-
tion. ISIJ Int. 2008, 48 (10), 1398–1403.
(3) William, F. L. Solubilities Inorganic andMetal-organic Compounds;
a Compilation of Solubility Data from the Periodical Literature; American
Chemical Society: WA, 1965.
(4) Assarsson, G. O. Equlibria in Aqueous System Containing Kþ,
Naþ, Ca2þ, Mg2þ and Cl�. II: The Quaternary System CaCl2-KCl-
NaCl-H2O. J. Am. Chem. Soc. 1950, 72, 1437–1441.
(5) Assarsson, G. O. Equlibria in Aqueous System Containing Kþ,
Naþ, Ca2þ, Mg2þ and Cl�. I: The Ternary System CaCl2-KCl-H2O. J.
Am. Chem. Soc. 1950, 72, 1433–1436.
Figure 3. Relationship between physicochemical properties and weight percent of CaCl2 in the equilibrium quaternary system: (a) pH and (b) density.
Table 3. Temperature Coefficients of Pitzer Single Electro-
lyte Ion-Interaction Parameters
species (∂β)(0)/(∂T) 3 10
4 (∂β)(1)/(∂T) 3 10
4 (∂C)(j)/(∂T) 3 10
5
KCl 5.794 10.71 �5.095
NaCl 7.159 7.005 �10.54
CaCl2 �1.725 39.0 -
Table 4. Pitzer Single Electrolyte Ion-Interaction Parameters
at 283.15 K
species β(0) β(1) C(j)
KCl 0.037919 0.207345 0.000324
NaCl 0.066482 0.241322 0.002641
CaCl2 0.328378 1.32562 �0.00174
Table 5. Pitzer Mixed Ion-Interaction Parameters of the
Quaternary System
T (K) θK,Na θK,Ca θNa,Ca ref.
283.15 �4.33 3 10�3 7.025 3 10�3 5.460 3 10�2 this work
288.15 �4.661 3 10�2 6.865 3 10�2 5.000 3 10�2 3
298.15 �1.200 3 10�2 3.200 3 10�2 7.000 3 10�2 4
T (K) ΨK,Na,Cl ΨK,Ca,Cl ΨNa,Ca,Cl ref.
283.15 �2.241 3 10�3 �2.025 3 10�2 �2.628 3 10�4 this work
288.15 �3.668 3 10�3 �1.271 3 10�3 �1.271 3 10�3 3
298.15 �1.800 3 10�3 �2.500 3 10�2 1.400 3 10�2 4
Table 6. Average Equilibrium Constants of Salts of the
Quaternary System at 283.15 K
species KCl NaCl CaCl2 3 6H2O
Kaver. 6.260 2.626E1 2.879E3
Figure 4. Comparison of experimental and calculated solubilities for the equilibrium phase diagram of the quaternary system at 283.15 K: b,
experimental; O, calculated; C6, CaCl2 3 6H2O.
1797 dx.doi.org/10.1021/je100743h |J. Chem. Eng. Data 2011, 56, 1793–1797
Journal of Chemical & Engineering Data ARTICLE
(6) Mayer, T. A.; Prutton, C. F.; Lightfoot, C. W. Equilibria in
Saturated Salt Solutions: V. The Quinary CaCl2-MgCl2-KCl-NaCl-H2O
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MgCl2-KCl-H2O at 35�. J. Am. Chem. Soc. 1946, 68 (6), 1001–1002.
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Activity and Osmotic Coefficients for Mixed Electrolytes. J. Am. Chem.
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(13) Harvie, C. E.; Weare, J. H. The Prediction of Mineral Solubi-
lities in Natural Waters: The Na-K-Ca-H-Cl-SO4-OH-HCO3-CO3-
H2O System to High Ionic Strengths at 25 �C. Geochim. Cosmochim.
Acta 1984, 48, 723–751.
(14) Silvester, L. F.; Pitzer, K. S. Thermodynamics of Electrolytes. X.
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Solution Chem. 1978, 7 (5), 327–337.
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Its Applications; Tianjin University Press: Tianjin, 2002.
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worths: London, 1965.
(18) Marion, G. M.; Farren, R. E. Mineral Solubilities in the Na-K-
Mg-Ca-Cl-SO4-H2O System: A Re-evaluation of the Sulfate Chemistry
in the Spencer-Moller-Weare model. Geochim. Cosmochim. Acta 1999,
63 (9), 1305–1318.