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Materials Science Forum
ISSN: 1662-9752, Vol. 873, pp 63-67
doi:10.4028/www.scientific.net/MSF.873.63
© 2016 Trans Tech Publications, Switzerland
Submitted: 2016-06-17
Accepted: 2016-07-01
Online: 2016-09-20
Simulation and Prediction of Solubility for the Quaternary System
Containing Lithium, Sodium, Magnesium and Chloride at 273.15 K
Xingyu JIANG1,a, Lin WANG2 and Dongchan LI3,b
1
Key Laboratory of Muddy Coast Geo-environment CGS, Tianjin Centre of China Geological Survey,
CGS Tianjin 300170, P. R. China
2
Tianjin Institute of Surveying and Mapping, Tianjin 300381, P. R. China
3
School of Marine Science and Engineering, Hebei University of Technology, Tianjin 300130,
P. R. China
a
email: jxingy@cgs.cn, bemail: dongchanli@126.com
Keywords: Predictive solubility; Thermodynamic model; Lithium chloride; Magnesium chloride.
Abstract. Solubilities of the quaternary system containing lithium, sodium, magnesium and chloride
at 273.15 K were calculated using Pitzer ion-interaction model and its extended HW model. The
values of the Pitzer single-salt parameters β(0), β(1), β(2) and Cϕ for LiCl, NaCl, and MgCl2, the mixed
ion-interaction parameters θLi,Mg, θLi,Na, θNa,Mg, ψLi,Mg,Cl, ψLi,Na,Cl and ψNa,Mg,Cl, and the Debye–Hückel
parameter Aϕ in the quaternary system at 273.15K were derived. Based on the Jänecke indexes, the
phase diagram was plotted. This study affords the necessary parameters for solubility predictions of
complicated systems and establishes a theoretical basis for the separation of these valuable minerals
from salt lake brine.
Introduction
Pitzer’s ion-interaction model and its extended HW model has elicited considerable interest in
calculating the thermodynamic properties of electrolytes in aqueous solution, such as activity
coefficient and osmotic coefficient, Gibbs energy, apparent molar heat capacities as well as enthalpies
of dilution. The models were also successfully applied to some industrial processes, such as
simulating the evaporation process of seawater, detecting the separation of minerals from brines and
predicting the component solubility in natural brines systems [1-6].
This ion-interaction model was successfully utilized for the solubility predictions of the major
seawater ions of the five-component system (Na + K + Mg + Cl + SO4 + H2O) [7-9] at 25℃ and the
ternary and quaternary subsystems of the (Na–K–Ca–Mg–H–Cl–SO4–CO2–B(OH)4–H2O) in Searles
Lake, California [10]. However salt lakes in the Qinghai-Xizang (Tibet) Plateau are famous for their
abundance of lithium, potassium, magnesium, and boron resources and also for having the highest
concentration ratio of magnesium to lithium in brine around the world with ratios of 500–800 [11].
The investigation of the thermodynamics and phase equilibria of the system is of theoretical and
practical importance to predict the actual evaporation path of mineral crystallization for the separation
and purification of the lithium-containing mixture salts effectively, so additional work has centered
on developing an ion-interaction model, which will increase the applicability to a number of diverse
geochemical systems. In the paper, the solubilities of the system containing lithium, sodium,
magnesium and chloride at 273.15 K were calculated using the Pitzer ion-interaction model, which is
essentially needed for the separation and purification of the minerals of lithium and magnesium.
Computational methods
Theoretical Considerations. The solubility of a hydrated salt in concentrated electrolyte solutions
could be calculated from thermodynamic considerations if the equilibrium constant of the hydrated
salt was known and the activity coefficients of all the electrolytes could be obtained. For a hydrated
salt MυmXυx·υOH2O, the equilibrium constant at a definite temperature for the dissolution reaction:
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans
Tech Publications, www.scientific.net. (#103412124, McMaster University, Hamilton, Canada-13/11/17,01:19:31)
64
International Conference on Materials Applications and Engineering 2016
M
υM
(1)
X υ X ⋅υ O H 2 O = υ M M ν + + υ X X ν - + υ O H 2 O
is expressed by:
(2)
ln K = υ M ln ( m M ⋅ γ M ) + υ X ln ( m X ⋅ γ X ) + υ O ln α W
where mi and γi represent the concentration (mol/kg) and activity coefficient of the hydrated ions,
respectively. The absolute values of γi for ions could not be determined, but the mean activity
coefficient γ± was defined as:
ln γ ± = (υ M ln γ M + υ X ln γ X ) / υ
(3)
where υO = υM + υX. The activity of water is related to the osmotic coefficient φ , by the equation:
(4)
ln α w = ( − M W ∑ m i ) × φ
(4
i
where Mw is the molar mass of water. These activity and osmotic coefficients were calculated from
the ion-interaction model of Pitzer.
Pitzer Ion-interaction Model. Pitzer ion-interaction and its extended HW model were used to
calculate osmotic and activity coefficients [2,7]. These equations are as in following:
Nc
Na
∑ mi (φ − 1) = 2( − Aφ I 3/ 2 / (1 + 1.2 I 1/ 2 ) + ∑ ∑ mc ma ( Bcaφ + ZCca ) +
i
c =1 a =1
N a −1
Na
∑ ∑
+
a=1 a' = a +1
Nc
Nn
c=1
n=1 c=1
N c −1
Nc
∑ ∑
mc mc' ( Φ φcc' +
c=1 c ' = c+1
Nc
Na
a=1
c=1
a=1
Na
∑∑m m C
c
a
c=1 a =1
+ zX
(5)
c=1
a=1
c=1
c
a
F = − A [I
∑
N c −1 N c
∑ ∑ mmψ
c
c'
cc'X
(7)
c=1 c'=c+1
Nn
ca
+ ∑ mn (2λnX )
1/ 2
Nc
Na
) + 2 / 1.2 ln(1 + 1.2 I 1/ 2 )] + ∑ ∑ m c m a B ca' +
c=1 a=1
Z =
m a m a'ψ aa'M
a=1 a'=a + 1
n=1
/ (1 + 1.2 I
C MX = C Mφ X / (2 z M z X
Na
∑ ∑
n=1
Nc
Na
N a −1
(6)
Na
∑∑m m C
1/ 2
)
+ ∑ m n (2 λ nM )
Nc
c=1 a=1
φ
cc'a
Nn
ca
ln γ X = z X 2 F + ∑ mc (2 BcX + ZC cX ) + ∑ ma (2 Φ Xa + ∑ mcψ Xac ) +
Nc
a
a=1
Nc
Na
Nc
∑mψ
ma ma' ( Φ φaa' + ∑ mcψ aa'c ) + ∑ ∑ mn mc λnc
ln γ M = z M 2 F + ∑ m a (2 B M a + Z C M a ) + ∑ m c (2 Φ M c + ∑ m aψ M ca ) +
+ zM
Na
1/ 2
)
N c −1
Nc
∑ ∑
c=1 c'=c+1
m c m c' Φ 'cc' +
N a −1 N a
∑ ∑
a=1 a'=a+1
m a m a' Φ 'aa'
(8)
z i mi
i
φ
(0)
(1)
(2)
BCA
= β CA
+ β CA
exp( −α 1 I 1/ 2 ) + β CA
exp( −α 2 I 1/ 2 )
(9)
(0)
(1)
(2)
BCA = β CA
+ β CA
g (α1 I 1/ 2 ) + β CA
g (α 2 I 1/2 )
'
(1)
(2)
BCA
= [ β CA
g '(α 1 I 1/2 ) + β CA
g '(α 2 I 1/ 2 )] / I
Φ φij = θ ij + Eθ ij + I Eθ ij'
Φ ij = θ ij + Eθ ij
(10)
Φ ij' = Eθ ij'
(0)
(1)
( 2)
φ
In the above equations, β MX
and CMX
are Pitzer interaction parameters of single salts, in
,β MX
,β MX
(2)
which β MX is important to 2-2 or higher valence electrolytes; θij represents the interaction of the two
ions with the same sign; and ψ ijk represents the interaction amongthe three ions, in which the sign of
the third one is different from the first two ions;
0.378124 at 273.15 K.
Aφ
is the Debye–Hückel parameter has the value of
Materials Science Forum Vol. 873
65
Pitzer parameters. The Pitzer ion-interaction model and HW model have been successfully used in
calculating thermodynamic properties and the solubilities of electrolytes [7-9]. Using the Pitzer’s
single salt parameters, the mixing ion-interaction parameters and the solubility products of the
solid−liquid phase equilibria allows us to identify the coexisting solid phases and their compositions
at equilibrium [3,12].
Table 1 Values for the standard chemical potentials of minerals in the system at 273.15 K
Minerals
Chemical formula
ln Ksp
lithium chloride dihydrate
LiCl·2H2O
9.9121
sodium chloride
NaCl
3.4651
bischofite
MgCl2·6H2O
10.96446
The solubility equilibrium constants ln Ksp of minerals in this quaternary system containing
lithium, sodium, magnesium and chloride are listed in Table 1. Pitzer’s single salt parameters β(0), β(1),
β(2), and Cϕ LiCl, NaCl, and MgCl2, the mixed ion-interaction parameters θLi,Mg, θLi,Na, θNa,Mg,
ψLi,Mg,Cl, ψLi,Na,Cl and ψNa,Mg,Cl at 273.15 K were obtained from our work or the literature9,12. All of the
parameters used in the prediction are presented in Table 2.
Table 2 Pitzer’s parameters in the solution of the system at 273.15 K
β(0)
β(1)
Cφ
Θccˊ
Ψccˊa
Ref.
0.2173
0.0532
0.3616
–
–
–
-0.3229
0.2419
1.2942
–
–
–
-0.003516
0.004358
0.009302
–
–
–
–
–
–
-0.01204
0.02219
0.0700
–
–
–
–
–
–
This work
9
9
This work
9
9
–
–
–
–
0.001900
This work
–
–
–
–
–
–
–
–
-0.01507
-0.00892
This work
9
Species
LiCl
NaCl
MgCl2
Li+,Mg2+
Li+,Na+
Na+,Mg2+
Li+,Mg2+,Cl+
+
-
Li ,Na , Cl
Na+,Mg2+,ClResults and discussions
Based on the Pitzer ion-interaction model and the extended HW model for aqueous electrolyte
solutions, the solubilities of the quaternary system containing lithium, sodium, magnesium and
chloride at 273.15 K have been calculated. The ion concentration values are expressed by the molality
[m/(mol/ kg H2O)].
According to the calculated data, the phase diagram, water-diagram and water activity diagram of
the system at 273.15 K is shown in Figure 1. Phase diagram consists of two invariant points, saturated
with salts NaCl + MgCl2·6H2O + LiCl·MgCl2·7H2O, NaCl +LiCl·MgCl2·7H2O + LiCl·2H2O; and
four crystallization zones corresponding to sodium chloride (NaCl), lithium chloride dihydrate
(LiCl·2H2O), lithium carnallite (LiCl·MgCl2·7H2O), and bischofite (MgCl2·6H2O), and the
crystallization area of sodium chloride is the largest, while the crystallization area of lithium carnallite
is the smallest in the system. It can be further found that the water content and water activity of the
equilibrium solution in Figures 2 and 3 are change regularly with the change of lithium chloride
Jänecke index, and have singularity changes at the invariant points and achieve minimum value at the
invariant point E cosaturated with sodium chloridem, lithium carnallite and lithium chloride in the
system.
66
International Conference on Materials Applications and Engineering 2016
NaCl
100
NaCl
80
J(NaCl)
1.5
J(NaCl)
1.2
60
40
NaCl
20
NaCl
0.9
E F
0
0
20
MgCl2
40
60
J (LiCl)
A
80
100
LiCl
B
0.6
E F
0.3
Lic
MgCl 2 •6H 2 O
0.0
0
20
40
60
C
J(LiCl)
MgCl2
LiCl •2H 2O
D
80
100
LiCl
Fig. 1 Phase diagram of the quaternary system containing lithium, sodium, magnesium and chloride at 273.15 K.
Lic, LiCl·MgCl2·7H2O.
200
A
J(H2O)
180
160
140
E
F
C
D
B
80
100
120
0
20
40
60
J(LiCl)
Fig. 2 Water content diagram of the quaternary system containing lithium, sodium, magnesium and chloride at
273.15 K
0.4
A
aw
0.3
0.2
0.1
E
F
C D
B
80
100
0.0
0
20
40
60
J(LiCl)
Fig. 3 Water activity diagram of the quaternary system containing lithium, sodium, magnesium and chloride at
273.15 K
Conclusion
Pitzer single-salt parameters, mixed ion-interaction parameters, and solubility product of the
minerals in the quaternary system containing lithium, sodium, magnesium and chloride at 273.15 K
were fitted, and the solubilities of the system were calculated using Pitzer ion-interaction model and
the extended HW model for aqueous electrolyte solutions. Neither crystallization zones disappeared
nor new crystallization region was produced in this quaternary system. The results demonstrate that
Materials Science Forum Vol. 873
67
these parameters and constants calculated through the Pitzer equation are reliable in the quaternary
system, and the results could provide a theoretical basis for exaction of lithium salts from salt lake
brine resources.
Acknowledgements
These research financially supported by the Program of the National Natural Science Foundation
of China (No. 21406048), applied basic research plan of Hebei Province (No.13963103D), and the
Natural Science Foundation of Tianjin (No. 15JCQNJC06100) are greatly acknowledged.
References
[1] K.S. Pitzer: J. Phys. Chem. Vol. 77 (1973), p. 268
[2] K.S. Pitzer: Activity coefficients in electrolyte solutions (CRC Publications, Boca Raton 1991).
[3] P.S. Song and Y. Yao: Calphad Vol. 25 (2001), p. 329
[4] X.Y. Zheng, Y. Tang and Y. Xu: Salt Lakes of Tibet (Chinese Science and Technology Press,
Beijing 1988).
[5] X.Y. Zheng, M. G. Zhang, Y. Xu and B.X. Li: Salt Lakes in China (Chinese Science Press, Beijing
2002).
[6] J.E. Teeple: The industrial development of seales Lake brines: with equilibrium data (The
Chemical Catalog Company, New York 1929).
[7] C.E. Harvie and J.H. Weare: Geochim. Cosmochim. Acta Vol. 44 (1980), p. 981
[8] C.E. Harvie, H.P. Eugster and J.H. Weare: Geochim. Cosmochim. Acta Vol. 46 (1982), p. 1603
[9] C.E. Harvie, N. Møller and J.H. Weare: Geochim. Cosmochim. Acta Vol. 48 (1984), p. 723
[10] A.R. Felmy and J.H. Weare: Geochim.Cosmochim. Acta Vol. 50 (1986), p. 2771
[11] M.P. Zheng, J. Xiang, X.J. Wei and Y. Zheng: Saline lakes on the Qinghai-Tibet Plateau
(Beijing Science and Technology Press, Beijing 1989).
[12] P.S. Song and Y. Yao: Calphad Vol. 27 (2003), p. 343
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