Article pubs.acs.org/jced
Phase Diagram of the NaCl + RbCl + H2O System Dandan Gao,*,†,‡ Dongdong Li,†,§ Bin Hu,†,§ and Wu Li*,†,§ †
Key Laboratory of Comprehensive and Highly Efficient Utilization of Salt Lake Resources, Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining, 810008, P. R. China ‡ Qinghai Engineering and Technology Research Center of Comprehensive Utilization of Salt Lake Resources, Xining, 810008, P. R. China § Key Laboratory of Salt Lake Resources Chemistry of Qinghai Province, Xining, 810008, P. R. China ABSTRACT: Solubility isotherms of the ternary NaCl + RbCl + H2O system were elaborately determined at T = (273.15 and 298.15) K by an isothermal equilibrium method, and the results showed that there are only two solubility branches for the solid phase NaCl(cr) and RbCl(cr) at both temperatures. The liquid composition of invariant points at T = (263.15, 323.15, 338.15, and 348.15) K were also determined. The experimental data at T = 298.15 K were reproduced using a Pitzer−Simonson−Clegg activity model by adding a temperature independent ternary mixing parameter. Then, the solid−liquid equilibria in the ternary NaCl + RbCl + H2O system were predicted from the available binary parameters obtained in our previous study and the mixing parameter regressed at 298.15 K in this study. The model was further validated by comparing the predictions with the present data at other temperatures that were not used in parametrization. Finally, the phase diagram of the ternary NaCl + RbCl + H2O system in the temperature range from the lowest eutectic point to 373.15 K was constructed to lay the foundation for equilibria property predictions for more complex Rb-containing systems.
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INTRODUCTION
EXPERIMENTAL SECTION Chemicals and Apparatus. Chemicals used in this work are given in Table 1. Rubidium chloride (mass fraction purity > 0.9995, CAS number 7791-11-9) was purchased from Shanghai Aladdin Reagent Company, and was used without further purification. Sodium chloride (mass fraction purity > 0.9999, CAS number 7647-14-5) was purified by recrystallization once with 50% salt recovery. Doubly distilled water (electrical conductivity < 1.8 × 10−4 S·m−1) obtained from a water purification system (UPT-II-20T, Chengdu Ultrapure Technology Co., Ltd.) was used in the experiment. The impurities in the sodium chloride were analyzed by ICP emission spectrometry (Thermo Electron Corporation, ICAP 6500 DUO). In this study, solubility determination was carried out in a thermostatic water bath (Lauda 219,Germany) with a temperature standard uncertainty of 0.05 K, and the mass of samples were weighed using a Sartorius QUINTIX224-1CN balance which has a range of measurement up to 200 g with a standard uncertainty of 0.1 mg. The type of solid phase in equilibrium with solution was identified by X-ray diffractometer (X′Pert PRO, 2006 PANalytical). Solubility Determination. A 250 mL Erlenmeyer flask with rubber stopper containing saturated solution NaCl + RbCl + H2O with different ratios of NaCl and RbCl salt, was placed in a thermostatic water bath. Before the determination of
Rubidium (Rb) and its related compounds have already been widely used in many fields, especially in electronics, medication, and defense industries for their unique physical and chemical properties. Pegmatite, brines, and salt beds are the most common mineral source of Rb.1 In brines and salt beds, Rb is present as chlorides and associated with sodium (Na) and potassium (K) nearly all the time. To reveal the partition behavior of Rb during brine fractional crystallization, the phase diagram of Rb containing systems is essential. Among these systems, the ternary NaCl + RbCl + H2O system is the most basic one for studying more complex Rb-containing systems. For such a simple system, however, its complete multitemperature phase diagram has never been outlined except for an unexamined solubility isotherm at 298.15 K,2 which was later repeated in the literature3 for comparison with modeling results. In this study, the solubility isotherms of the ternary NaCl + RbCl + H2O system were determined carefully at T = (298.15 and 273.15) K. Extending our previous study,3−6 a temperature-dependent thermodynamic model for the ternary NaCl + RbCl + H2O system was developed over wide temperature and concentration ranges based on a Pitzer−Simonson−Clegg (PSC) activity model6−8 by adding a temperature independent ternary mixing parameter fitted from the solubility data at 298.15 K. To validate the model, the predicted solubility were compared with those given in the literature and in the present study at other temperatures. From the model, the phase diagram of the ternary NaCl + RbCl + H2O system over the temperature range from the lowest eutectic point to 373.15 K was constructed. © 2017 American Chemical Society
Received: October 12, 2016 Accepted: January 20, 2017 Published: February 2, 2017 1063
DOI: 10.1021/acs.jced.6b00879 J. Chem. Eng. Data 2017, 62, 1063−1067
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Table 1. Source, Purity, and CAS Number of Chemicals
a
chemical name
source
final mass fraction purity
purification method
CAS no.
rubidium chloride sodium chloride nitric acid silver nitrate
Shanghai Aladdin Reagent Company China National Pharmaceutical Industry Xilong Chemical Co., Ltd. Tianjin Day Feeling Chemical Technology Development Co., Ltd.
>0.9995a >0.9998b >0.9993a >0.998a
none recrystallization none none
7791-11-9 7647-14-5 7697-37-2 7761-88-8
Stated by suppliers. bConfirmed by ICP−OES analysis.
Table 2. Solubility of the NaCl + RbCl + H2O system at T = 298.15 K Determined Experimentally in This Work (p = 0.1 MPa)a
solubility experiment, the equilibrium time was determined from one ternary point. For this point, the composition of the solution was analyzed after 3 days and 5 days, respectively. The results agreed and indicate that 3 days is enough to reach the equilibrium state. Thus, for all ternary points the equilibrium time was set to 3 days. The mixture solution in the flask were stirred with a magnetic stirrer about 3 days and then kept static for about 3 h. The supernatant liquid was taken with a syringe. A part of that supernatant liquid was injected into a weighed 15 mL quartz bottle with cover, which was evaporated to dryness at 333 K for 10 h and heated at 413 K to constant weight to determine the H2O content in the sample.9,10 Anther part of the supernatant liquid was used to determine the Cl− content by the gravimetric method of silver chloride precipitation.11 In every analyses for solution, parallel samples were taken, and the maximum relative standard uncertainty between them was less than 0.001; the relative standard uncertainty of the NaCl and RbCl content determined can be controlled within 0.005, respectively. Then the content of NaCl and RbCl in the equilibrium solution was calculated. The invariant points are determined from the phase rule, that is, the solution compositions of the invariant point do not vary when the compositions of the whole system varied, and XRD analysis.
composition of solution (100w) H2O
solid phase
48.29 44.72 41.44 40.29 37.33 34.48 34.75 34.08 33.95 28.06 22.75 15.41 15.21 10.13 4.57 0
51.71 52.55 52.42 52.49 52.92 52.93 52.74 52.86 52.94 56.59 59.93 64.46 64.56 67.70 70.80 73.48
RbCl RbCl RbCl RbCl RbCl RbCl RbCl NaCl + RbCl NaCl + RbCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl
The standard uncertainty of the measurement temperature is u(T) = 0.05 K; relative standard uncertainty of the measurement of NaCl is ur(w) = 0.003; relative standard uncertainty of the measurement of RbCl is ur(w) = 0.003; standard uncertainty of the measurement pressure is ur(p) = 0.05.
EXPERIMENTAL RESULTS The experimental solubility data of the ternary NaCl + RbCl + H2O system determined at T = (273.15 and 298.15) K are listed in Table 2 and Table 3, respectively. The results showed that there are only two solubility branches corresponding to solid phase NaCl(cr) and RbCl(cr) at both temperatures. The invariant points are 100w(NaCl) = 15.91, 100w(RbCl) = 26.46, 100w(H2O) = 57.63 at 273.15 K, and 100w(NaCl) = 13.10, 100w(RbCl) = 33.95, 100w(H2O) = 52.95 at 298.15 K, respectively. The liquid composition of invariant points at T = (263.15, 323.15, 338.15 and 348.15) K are determined and listed in Table 4.
Table 3. Solubility of the NaCl + RbCl + H2O System at T = 273.15 K Determined Experimentally in This Work (p = 0.1 MPa)a composition of solution (100w)
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THERMODYNAMIC MODELING Thermodynamic Framework. The solid−liquid phase equilibria of an electrolyte aqueous system can be determined by minimizing the total Gibbs GT energy of the whole system, which can be expressed as eq 1.
∑ GmΘ,s(T ) + ∑ (GmΘ,i(T ) + RT ln ai(T )) s
RbCl
0 2.73 6.14 7.22 9.75 12.59 12.51 13.06 13.10 15.35 17.32 20.14 20.23 22.17 24.63 26.52 a
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G T (T ) =
NaCl
i
(1)
NaCl
RbCl
H2O
solid phase
0 3.11 6.37 7.88 10.68 13.53 15.91 15.98 16.98 20.06 20.18 22.30 24.48 26.32
43.69 40.05 36.30 34.79 31.80 28.88 26.46 26.31 23.22 15.43 15.37 9.86 4.49 0
56.31 56.83 57.32 57.32 57.52 57.59 57.63 57.71 59.80 64.51 64.45 67.84 71.02 73.68
RbCl RbCl RbCl RbCl RbCl RbCl NaCl + RbCl NaCl + RbCl NaCl NaCl NaCl NaCl NaCl NaCl
a
The standard uncertainty of the measurement temperature is u(T) = 0.05 K; relative standard uncertainty of the measurement of NaCl is ur(w) = 0.003; relative standard uncertainty of the measurement of RbCl is ur(w) = 0.003; standard uncertainty of the measurement pressure is ur(p) = 0.05.
where, s stands for a solid species and i stands for an aqueous Θ species, i.e. water, simple ion, or complex. GΘm,s(T) and Gm,i (T) are the standard Gibbs energy of solid and aqueous species at temperature T, respectively. ai(T) is the activity of aqueous species i for a given aqueous composition at temperature T. R = 8.314 J·K−1·mol−1 is the gas constant. 1064
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comparison between the model-predicted polythermal phase diagram and experimental verification. Phase Diagram Simulation and Discussion. The solubility isotherm of the ternary NaCl + RbCl + H2O system at T = 298.15 K calculated without (dash line) and with (solid line) mixing parameters are presented in Figure 1. The result
Table 4. Invariant Points of the NaCl + RbCl + H2O System at Various Constant Temperatures Determined Experimentally in this Work (p = 0.1 MPa)a composition of solution (100w) index
NaCl
RbCl
H2O
solid phase
T/K
1 2b 3c 4 5 6
23.90 15.91 13.10 39.64 42.29 43.41
16.48 26.46 33.95 11.29 10.46 10.34
59.62 57.63 52.94 49.07 47.25 46.25
NaCl·2H2O + RbCl NaCl + RbCl NaCl + RbCl NaCl + RbCl NaCl + RbCl NaCl + RbCl
263.15 273.15 298.15 323.15 338.15 348.15
a
The standard uncertainty of the measurement temperature is u(T) = 0.05 K; relative standard uncertainty of the measurement of NaCl is ur(w) = 0.003; relative standard uncertainty of the measurement of RbCl is ur(w) = 0.003; standard uncertainty of the measurement pressure is ur(p) = 0.05. bThe eutectic point determined in Table 3 at 273.15 K was repeated here. cThe eutectic point determined in Table 2 at 298.15 K was repeated here.
The standard Gibbs energy of solid and aqueous species as a function of temperature was expressed as eq 2.
Figure 1. Calculated isotherms of the NaCl + RbCl + H2O system compared with experimental data at 298.15 K. red ●, experimental data of this work; ▲, experimental data in literature;2 ◇, calculated values in literature;3 −·−, calculated values without mixing parameters in this work; , calculated values with mixing parameters in this work.
GsΘor i(t ) = A(t − t ln t ) − Bt 2/2 − Ct 3/6 − Dt 4 /12 − E /2t + F − Gt
(2)
where t = (T/K)/1000, A, B, C, D, E, F, and G are temperature coefficients. Other thermodynamic quantities of a species at standard state derived from eq 2 were expressed as eq 3 to eq 5
shows that the calculated solubility isotherm without mixing parameters deviates from the experimental data determined in the present study and in the literature at 298.15 K and the simulated line reported by Hu et al.2,3 Thus, the mixing parameter WNaRbCl of the ternary system was introduced, which was determined by fitting the solubility isotherm of the ternary system at 298.15 K. After adding this mixing parameter, the isotherm was reproduced accurately. To investigate the temperature dependency of the mixing parameter WNaRbCl, the solubility isotherm at 273.15 K was predicted with constant WNaRbCl determined at 298.15 K and compared with the experimental values determined in the present study. Figure 2 shows the model predicted and experimental determined solubility isotherm at 273.15 K. The predictions are in excellent agreement with the experimental values listed in Table 3, which suggested the mixing parameter
HsΘor i(t ) = At + Bt 2/2 + Ct 3/3 + Dt 4 /4 − E /t + F (3)
SsΘor i(t )
2
3
2
= A ln t + Bt + Ct /2 + Dt /3 − E /2t + G (4)
C pΘ, s or i(t ) = A + Bt + Ct 2 + Dt 3 + E /t 2
(5)
For solid and aqueous species, these thermodynamic quantities take their conventional meaning. The activity of aqueous species ai takes an unsymmetric reference state formation and is represented using the Pitzer−Simonson−Clegg (PSC) model.7,8 The activity coefficient equations of the PSC model for a ternary mixing system can be found in the literature8 and are not repeated here. In the ternary NaCl + RbCl + H2O system, solid phases are all inherited from its sub-binary systems NaCl + H2O and RbCl + H2O and there is no new compound found. Hence, the temperature-dependent PSC equation parameters for binary system NaCl + H2O and RbCl + H2O and standard Gibbs energy of all solid phases can be taken from the previous study.4,5 There are three mixing parameters WNaRbCl, UNaRbCl, and Q1,NaRbCl in the ternary mixing equations8 for a ternary system but we found just one mixing parameter WNaRbCl = −3.0 is necessary for accurately representing the solubility isotherm of the NaCl + RbCl + H2O system at 298.15 K. Further, we found the solubility isotherm of the system at 273.15 K can be accurately predicted also with WNaRbCl = −3.0. Thus, we speculate the mixing parameter WNaRbCl is temperature independent and other mixing parameters are unnecessary at all temperatures at least in the temperature range we concentrated. The speculation finally was confirmed from the
Figure 2. Calculated isotherms of the NaCl + RbCl + H2O system compared with experimental data at T = 273.15 K. red ●, experimental data of this work; , calculated values of this work (solubility isotherm of the NaCl + RbCl + H2O system at 273.15 K). 1065
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Figure 3. Predicted polythermal phase diagram of the NaCl + RbCl + H2O system. (a) Temperature projection drawing: red ●, experimental invariant points at various temperatures determined in this work (listed in Table 4); , predicted values of this work. A, Peritectic point NaCl + NaCl·2H2O + liquid; B, peritectic point NaCl·2H2O + NaCl + RbCl + liquid; C, eutectic point ice + RbCl + liquid; D, eutectic point ice + NaCl·2H 2O + liquid; E, eutectic point ice + NaCl·2H 2O + RbCl + liquid. (b) 3D plot.
WNaRbCl may be temperature independent and other mixing parameters are unnecessary. Furthermore, the reliability of the temperature-dependent ternary model was further validated by comparing predictions with all the experimental invariant points (see Table 4) determined in this work. The excellent agreement shown in Figure 3a indicates that the model can be successfully used to predict the phase equilibria properties of the ternary systems over a wide temperature range. Finally, the phase diagram of the NaCl + RbCl + H2O system was predicted over the temperature range from 247.65 to 373.15 K. Figure 3 panels a and b show the temperature projection drawing and 3D plot, respectively. Eutectic and peritectic points, which are plotted in Figure 3a and listed in Table 5, of the system were also predicted from the present ternary model.
the present work at 298.15 K were used to regress the mixing PSC parameter WNaRbCl of the ternary system. The temperature independent nature of WNaRbCl was identified. From the obtained model, the phase diagram of the ternary NaCl + RbCl + H2O system is predicted accurately over the temperature range from the lowest eutectic point to 373.15 K.
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Corresponding Authors
*E-mail:
[email protected]. Tel: + 86 13639756374. *E-mail:
[email protected]. Tel.: + 86 13709720468. ORCID
Wu Li: 0000-0002-4254-4191 Funding
This work was financially supported by the National Natural Science Foundation of China (Grants U1407131,51404234 and 41472078).
Table 5. Invariant Points in the Polythermal Phase Diagram of the NaCl + RbCl + H2O System Determined from the Thermodynamic Model
Notes
The authors declare no competing financial interest.
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composition of solution (100w) pointa
NaCl
RbCl
H2O
A B
26.25 16.79
0 23.91
73.75 59.30
C D E
0 23.11 15.99
39.59 0 22.41
60.41 76.89 61.60
a
AUTHOR INFORMATION
phase NaCl·2H2O + NaCl + L NaCl·2H2O + NaCl + RbCl + L ice + RbCl + L ice + NaCl·2H2O + L ice + NaCl·2H2O + RbCl + L
T/K
REFERENCES
(1) Suzette, M. K. Mineral Commodity Summaries (USGS) 2016; U.S. Geological Survey: VA, 2016. (2) Zdanovskii, A. B.; Solov’eva, E. F.; Lyakhovskaya, E. I. Handbook of Experimental Data on Solubility of Multicomponent Water-Salt Systems, 2nd ed.; Khimia: Leningrad, 1973; Vol. 1, Book 2. (3) Hu, B.; Song, P. S.; Li, Y. H.; Li, W. Solubility prediction in the ternary systems NaCl−RbCl−H2O, KCl−CsCl−H2O and KBr− CsBr−H2O at 25 °C using the ion-interaction model. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2015, 31, 541−544. (4) Gao, D. D.; Li, D. D.; Li, Wu. Solubility of RbCl and CsCl in pure water at subzero temperatures, heat capacity of RbCl(aq) and CsCl(aq) at T = 298.15 K, and thermodynamic modeling of RbCl + H2O and CsCl + H2O systems. J. Chem. Thermodyn. 2017, 104, 201− 211. (5) Li, D. D.; Zeng, D. W.; Yin, X.; Han, H. J.; Guo, L. J.; Yao, Y. Phase diagrams and thermochemical modeling of salt lake brine systems. II. NaCl + H2O, KCl + H2O, MgCl2 + H2O and CaCl2 + H2O systems. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2016, 53, 78−89. (6) Li, D. D.; Zeng, D. W.; Han, H. J.; Guo, L. J.; Yin, X.; Yao, Y. Phase diagrams and thermochemical modeling of salt lake brine systems. I. LiCl + H2O system. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2015, 51, 1−12.
273.25 266.75 257.75 252.25 247.65
As shown in Figure 3a.
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CONCLUSIONS The solubility isotherms of the ternary NaCl + RbCl + H2O system at T = (273.15 and 298.15) K were determined using the isothermal method in this study. It was found that there are only two solubility branches corresponding to NaCl(cr) and RbCl(cr) at both temperatures. The invariant points are 100w(NaCl) = 15.91, 100w(RbCl) = 26.46, and 100w(H2O) = 57.63 at 273.15 K; and 100w(NaCl) = 13.10, 100w(RbCl) = 33.95, and 100w(H2O) = 52.95 at 298.15 K, respectively. To develop a temperature dependent thermodynamic model for the NaCl + RbCl + H2O system, solubility data determined in 1066
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(7) Clegg, S. L.; Pitzer, K. S. Thermodynamics of multicomponent, miscible, ionic solutions: generalized equations. J. Phys. Chem. 1992, 96, 3513−3520. (8) Clegg, S. L.; Pitzer, K. S.; Brimblecombe, P. Thermodynamics of multicomponent, miscible, ionic solutions.2. mixtures including unsymmetrical electrolytes. J. Phys. Chem. 1992, 96, 9470−9479. (9) Rimbach, E. On dissolubility and decomposability of double-salts in water. II. Ber. Dtsch. Chem. Ges. 1902, 35, 1298−1309. (10) Pinho, S. P.; Macedo, E. A. Solubility of NaCl, NaBr, and KCl in water, methanol, ethanol, and their mixed solvents. J. Chem. Eng. Data 2005, 50, 29−32. (11) Vogel, A. I.; Mendham, J. Vogel’s Textbook of Quantitative Chemical Analysis; Wiley: New York, 2000.
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