Ind. Eng. Chem. Res. 2010, 49, 4981–4988
4981
Solubilities of NaCl, KCl, LiCl, and LiBr in Methanol, Ethanol, Acetone, and
Mixed Solvents and Correlation Using the LIQUAC Model
Miyi Li,†,‡ Dana Constantinescu,‡ Lisheng Wang,† André Mohs,‡ and Jürgen Gmehling‡,*
Ind. Eng. Chem. Res. 2010.49:4981-4988.
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School of Chemical Engineering & EnVironment, Beijing Institute of Technology, 100081 Beijing, China,
Technische Chemie, Institut für Reine und Angewandte Chemie, Carl Von Ossietzky UniVersität Oldenburg,
D-26111, Oldenburg, Germany
The solubilities of NaCl, KCl, LiCl, and LiBr in pure methanol, ethanol, and acetone were measured over a
temperature range from 293.15 to 333.15 K. Furthermore salt solubilities in the mixed solvents (water +
methanol, water + ethanol, water + acetone, methanol + ethanol, methanol + acetone, ethanol + acetone)
were determined at 313.15 K. For a few systems solubility data are reported for the first time. In a few cases
a comparison with published data stored in the Dortmund Data Bank (DDB)1 showed disagreement. The
LIQUAC model was used to correlate the experimental data. The calculated salt solubilities are in good
agreement with the experimental results for the systems NaCl + water + methanol and KCl + water +
methanol.
2. Experimental Section
1. Introduction
The knowledge of salt solubilities in pure organic and mixed
solvent electrolyte systems is of great importance for the design
and simulation of unit operations such as crystallization,
liquid-liquid extraction, and other industrial processes.2 The
data are also required in connection with theoretical studies
concerning the liquid phase structure and its thermodynamic
properties. Accurate solubility data are also of great interest for
the development of electrolyte models. For the semiempirical
LIQUAC3,4 model, a large database was used for optimizing
the required parameters. LIQUAC can be used to correlate and
predict salt solubilities (SLE), liquid-liquid equilibria (LLE),
mean ion activity coefficients, vapor-liquid equilibria (VLE),
and osmotic coefficients for electrolyte solutions. Unfortunately,
most of the published data are only available for aqueous
systems. For pure organic or mixed solvent electrolyte systems
the number of available data is much smaller, and often the
published data show large scattering. More reliable data are
required in order to enlarge the database for fitting the required
parameters of electrolyte models.
2.1. Chemicals. Sodium chloride and potassium chloride with
purities higher than 99.7% were obtained from VWR international bvba/spr. Lithium chloride and lithium bromide with
minimum purities of 99% were supplied by Sigma-Aldrich Inc.
Prior to the measurements, the salts were dried in an oven at
433 K for 2 days. Acetone with a purity of 99.98% was supplied
by Carl Roth GmbH & Co. Ethanol and methanol with purities
greater than 99.8% were supplied by VWR. The organic solvents
were not further purified. Doubly distilled water was used for
the measurements.
2.2. Apparatus and Procedure. The apparatus used in this
work is shown in Figure 1. The experiments were carried out
in a jacketed glass cell with a volume of 140 cm3. The
temperature of the cell is controlled by circulating water from
a temperature-controlled bath. The cell was first loaded with a
small excess of salt in the chosen solvent. Then the pure organic
In this work, salt solubilities in pure organic solvents were
measured as a function of temperature. Furthermore salt
solubilities in mixtures were investigated for different solvent
compositions. Four salts (NaCl, KCl, LiCl, and LiBr) in three
organic solvents (methanol, ethanol, and acetone) and their
binary mixtures were measured over the whole solvent composition range. A well-designed procedure was implemented
to measure 7 binary systems and 12 ternary systems. Some of
the systems investigated were measured for the first time. The
data measured were used to extend the database for modeling
work. Finally, the experimental results were compared with the
results predicted by the LIQUAC model using the already
available parameters.
* To whom correspondence should be addressed. Tel.: +49-441798-3831. Fax: +49-441-798-3330. URL: http//www.uni-oldenburg.de/
tchemie. E-mail: gmehling@tech.chem.uni-oldenburg.de.
†
Beijing Institute of Technology.
‡
Carl von Ossietzky Universität Oldenburg.
Figure 1. The apparatus applied for solubility measurements: (1) thermostatted syringe; (2) digital temperature display; (3) Pt-100 thermometer;
(4) magnetic stirring rod; (5) jacketed glass cell; (6) magnetic stirrer; (7)
temperature-controlled bath; (8) pump.
10.1021/ie100027c 2010 American Chemical Society
Published on Web 04/13/2010
4982
Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010
Table 1. Salt Solubilities (mol · kg-1) in Organic Solvents at Different Temperatures
mNaCl
mKCl
mLiCl
mLiBr
T (K)
methanol
methanol
ethanol
methanol
ethanol
acetone
methanol
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
0.241
0.238
0.235
0.231
0.225
0.219
0.217
0.212
0.209
0.0708
0.0736
0.0754
0.0780
0.0811
0.0833
0.0858
0.0888
0.0907
0.0069
0.0064
0.0061
0.0059
0.0054
0.0051
0.0050
0.0046
0.0044
10.26
10.28
10.29
10.30
10.30
10.31
10.32
10.33
10.33
5.901
5.840
5.800
5.737
5.707
5.643
5.628
5.587
5.556
0.2776
0.2556
0.2236
0.1931
0.1730
0.1509
0.1240
0.1037
16.39
16.44
16.47
16.53
16.60
16.67
16.76
16.83
16.90
solvents (methanol, ethanol, and acetone) or binary mixture with
the desired composition were added. The cell was tightly closed
during the measurement and care was taken to ensure that the
composition of the mixed solvents was not changed because of
evaporation by leaving only 3-5 mL of gas-phase in the cell.
Cell and bath temperatures were measured by precision Pt 100
thermometers with an accuracy of (0.01 K.
The binary solvent mixtures (water + methanol, water +
ethanol, water + acetone, methanol + ethanol, methanol +
acetone, and ethanol + acetone) were prepared using a balance
with an uncertainty of (0.0001 g (Sartorius A200S). The
experimental points for mixed solvents were arranged in 10%
steps by varying the salt-free mass fraction.
To avoid the formation of microcrystals and supersaturation
during the measurements, the solutions were stirred at a speed
of around 600 rpm for approximately 12 h in the case of
organic solvents or organic solvent mixtures and 6 h for
water-organic electrolyte systems. This ensured an intensive
contact between the solid and the liquid phase. After
sedimentation for 24 h in the case of the organic or mixed
organic electrolyte systems and 12 h for water-organic
electrolyte systems, three liquid samples of about 3 mL were
taken by using a syringe equipped with a 0.45 µm filter and
transferred to capped vials with a volume of 15 mL. Prior to
sampling, syringe and filter were thermostatted to a temperature 5 K above the temperature of the solution. The mass
of the empty vial (W3) and the mass of the sample together
with the vial (W1) were determined by using an electric
balance (Sartorius CP225D) with an uncertainty of (0.00001
g. The liquid samples were first dried in an oven at 353 K
for 2 days, and then at 433 K for at least 24 h. The mass of
solid together with the vial (W2) was weighed by the same
balance ((0.00001 g). The drying of the samples was
continued until a constant mass was reached. The solubility
of the salt can then be calculated by the following relation:
solubility [mol · kg-1] )
(
)
W2 - W 3
1
·
W1 - W2 Msalt
salt from the saturated solution. The solubility of each sample
was calculated by eq 1. As solubility the mean value of the
three samples was chosen. When the relative standard
deviation of one of the samples was greater than 0.5%, the
measurement was repeated, whereby the relative standard
deviation (RSD) within a set of different experimental results
was defined as
RSD % )
[
1
n-1
i
i)1
jx
]
0.5
n
∑ (x
- jx)2
100
(2)
where xi is the experimental solubility of sample i and jx is
the mean solubility of n measurements. In the case of
solubilities less than 0.1 mol · kg-1, the criterion was extended
to 3%.
3. Solubility Data
The salt solubilities measured in organic solvents are listed
in Table 1. To avoid the evaporation of acetone in the system
LiCl + acetone, a maximum temperature of 328.15 K was used.
The systems with NaCl or KCl in ethanol or acetone were not
investigated, since the accuracy of the balance was not sufficient
to determine the small solubilities with the required accuracy.
A comparison of the KCl solubilities in methanol measured in
this work and those reported by Pinho and Macedo2 show good
agreement regarding the absolute solubilities and the temperature
dependence, as can be seen from Figure 2. But the solubilities
measured in this work are systematically 1.5% higher than the
(1)
where Msalt [mol · kg-1] is the molar mass of the salt.
The salt solubility measurements in pure organic solvents
were carried out over a temperature range from 293 to 333
K in 5 K steps, whereby the measurements always were
started at the highest temperature. For each experimental
point, the stirring temperature was set slightly above the
equilibrium temperature in order to avoid the formation of
microcrystals. Then the solubilities were measured at the
desired temperature after adequate sedimentation. For the
measurements of the mixed solvent electrolyte systems a
temperature of 313.15 K was chosen. For each experimental
point, three samples were taken by using the syringe equipped
with a filter, to avoid the dragging of small particles of the
Figure 2. Comparison of the KCl solubility in methanol at different
temperatures: (9) this work; (O) Pinho and Macedo;2 (4,3) further
published solubility data stored in DDB.10-12 Line represents the average
solubilities.
Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010
4983
a relative error of (1% can be assumed at high solubilities.
But the error increases with decreasing solubility. That is the
reason why the solubilities of NaCl and KCl in pure organic
solvents could not be measured.
4. Solid-Liquid Equilibria Modeling
Figure 3. Comparison of the LiCl solubility in ethanol at different
temperatures: (9) this work. The other symbols represent further published
solubility data stored in DDB.13-16
values reported by Pinho and Macedo, although the procedure
was similar to those used by Pinho and Macedo.5 On the basis
of the reproducibility of the experimental results and a comparison with the already published data, it can be concluded
that the procedure used in this work provides reliable solubilities.
Solubilities for LiCl in ethanol are shown in Figure 3. It can be
seen that a reliable description of the temperature dependence
of the solubility of LiCl in ethanol was achieved when compared
with the solubility data reported by other authors. From Figure
3 it can be seen that the available data show large scattering
and in some cases even a different temperature dependence.
Because most of the available salt solubility data in organic
solvents are quite old or questionable, an adequate evaluation
of the data is not possible. The solubilities of LiCl and LiBr in
methanol, ethanol, or acetone investigated in this work are listed
in Table 1. It can be seen, that the solubilities of LiCl and LiBr
are considerably higher than for the other alkali-metal halogenides. Even in ethanol and acetone the solubility is measurable, while for NaCl and KCl the solubility in these solvents is
too small for our measurement procedure. In general the salt
solubility in organic solvents is a lot lower than in water because
of the lower polarity and dielectric constant of the solvents.
The salt solubilities determined for mixed solvents at 313.15
K are given in Table 2. The solubilities for all the systems are
expressed on molality scale, while the solvent composition is
expressed in mass % (w %) on the salt-free basis. Since the
solubilities of NaCl and KCl in pure ethanol or acetone are very
low (<0.0001 mol/kg), the solubilities in these mixtures were
not measured. At higher salt concentrations two liquid phases
are formed in the system salt + water + acetone. Therefore
the solubilities in the system water + acetone were not
investigated in the whole composition range. For most of the
investigated systems, the well-equipped apparatus together with
an elaborate measurement procedure allowed the reliable
measurement of salt solubilities. For some of the systems, for
example, LiCl in mixed organic solvents (methanol, ethanol,
and acetone), there was no data available in the literature until
now.
The uncertainty of the measurements is mainly influenced
by the error caused by the balance, but it is also influenced by
temperature fluctuations and evaporation effects. In summary
For the calculation of the activity coefficients in electrolyte
solutions the LIQUAC model was developed that takes into
account all the interactions between ions and solvents. The
LIQUAC model was applied to calculate the VLE behavior,
osmotic coefficients, and mean ion activity coefficients for a
large number of solvents and mixed solvent electrolyte systems
reliably. Subsequently, the LIQUAC model was extended by
Li et al6 in order to predict salt solubilities in aqueous solutions
starting from tabulated standard thermodynamic properties. The
results matched very well with the experimental data, and the
deviations were less than 3%. Recently, Huang et al.7 deduced
the required equations to calculate the salt solubilities not only
in water, but also in pure organic and mixed solvent electrolyte
systems starting from tabulated standard thermodynamic properties. The results for water-methanol electrolyte systems were
in good agreement with the experimental data.
In the LIQUAC model, the excess Gibbs energy is defined
as the sum of three contributions:
E
E
GE ) GELR + GMR
+ GSR
(3)
The first term on the right side of eq 4 represents the longrange (LR) interaction contributions caused by the Coulomb
electrostatic forces. The second term represents the middle range
(MR) interaction contributions caused by charge-dipole and
charge-induced dipole interactions. The third term takes into
account the contribution of the noncharge interactions (shortrange (SR) interactions). The UNIQUAC model has been chosen
to describe these specific interactions. The activity coefficients
in electrolyte solutions are calculated by summing up the
following three contributions:
ln γi ) ln γLR
+ ln γMR
+ ln γSR
i
i
i
(4)
where i indicates all the species in the solution.
For the solvents the pure solvent is used as standard state.
This means, that the activity coefficient of the solvent becomes
γs f 1, when xs f 1. The different contributions to the activity
coefficient can be calculated as follows:
ln γsLR )
(
2AMsdm
b3ds
)
[1 + b√I - (1 + b√I)-1 - 2 ln(1 + b√I)]
(5)
The LR term is calculated using the Debye-Hückel theory as
modified by Fowler and Guggenheim (1949). Ms is the molar
mass of solvent s (kg · mol-1), ds (kg · m-3) is the density of the
pure solvent s, and dm the density of the mixed solvents,
calculated using the following equations:
dm )
∑φ
soldsol
sol
(6)
4984
Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010
xs′Vs
φs )
the parameters between cations (c) and anions (a). B′(I) is equal
to dB(I)/dI. Mm is the mean molar mass of the mixed solvents
(kg · mol-1).
The SR term is calculated by the UNIQUAC model:
(7)
∑ x′
solVsol
sol
∑m
I ) 0.5
ionzion
2
(8)
A ) 1.327757 × 105dm0.5 /(DT)1.5
b)
{ ( )
(9)
6.35969dm0.5 /(DT)0.5
∑qxψ
i i
(10)
∑qx
Vs ) rs /
Fs ) q s /
s,ion(I)mion
-
ion
IB'sol,ion(I)]x'solmion - Ms
( )∑ ∑
Ms
Mm
∑∑
c
sol
ln γ*j MR ) (Mm)-1
∑B
k,i)
k
]}
(17)
(18)
∑qx
(19)
j,sol(I)x'sol
[ ]∑ ∑
zj2
2Mm
sol
ion
i i
(20)
ion
zj2A√I
(21)
1 + b√I
+
sol
B'sol,ion(I)x'solmion +
( )∑ ∑
zj2
2
c
∑B
j,ion(I)mion
+
ion
B'ca(I)mcma -
a
Bj,s(I ) 0)
(22)
Ms
SR
ln γ*j SR ) ln γSR
j - ln γj (B)
[Bca(I) + IB'ca(I)]mcma (13)
a
ln γSR
j (B) ) 1 -
(15)
() [
(23)
( )]
rj
rjqs
rj
rjqs
+ ln
- 5qj 1 + ln
+
rs
rs
rsqj
rsqj
qj(1 - ψj,s - ln ψs,j) (24)
The superscripted asterisk (/) indicates the unsymmetrical
convention for ions based on the mole fraction scale. The
standard state of ion j is defined as the hypothetical ideal solution
at unit molality. In this hypothetical ideal solution, mj ) m°j )
1mol · kg-1 and γj*′ ) 1. The superscripted prime (′) indicates
the molality scale. The reference state at infinite dilution for
(16)
solMsol
k k
i i
ln γ*j LR ) -
[Bsol,ion(I) +
∑ x′
∑q x ψ
where ri and qi are the van der Waals volumes and surface areas,
and ai,j represents the UNIQUAC interaction parameters,
whereby ai,j is different to aj,i. xi is the mole fraction of species
i in the solution. In these equations, the indices i and j cover all
solvents and ions.
For ions j, each part of the activity coefficient is given on
the basis of the unsymmetrical convention on molality scale.
Bsol,ion(I) ) bsol,ion + csol,ion exp(-1.2I1/2 + 2dsaltI) (14)
Mm )
∑rx
[
(
ψi,j ) exp(-ai,j /T)
(12)
Bc,a(I) ) bc,a + cc,a exp(-I1/2 + dsaltI)
i
qixiψs,i
i
The MR term was originally proposed by Li et al3,4 with the
objective to represent the indirect effects between pair species.
On the basis of approximate results for the radial distribution
functions, the interactions between equally charged ions are
ignored. It is assumed that due to the interionic repulsion of
ions with the same kind of charge (positive or negative) the
interactions can be neglected, since they cannot be found in
the direct neighborhood. The middle range effects between
molecular groups are also equal to zero, because in the middle
range term only polarization effects are considered, and these
are only caused by charged particles. This leads to the following
expression for the middle range term:
∑B
∑
+
i
sol
ln γsMR )
( )]
Vs
Vs
+ ln
Fs
Fs
i
For a multicomponent mixture, D can be estimated by
solDsol
-
i i
D ) D1 + [(D2 - 1)(2D2 + 1)/2D2 - (D1 - 1)]φ2′ (11)
∑ φ′
i,s
i
qs 1 - ln
where x′s is the salt-free mole fraction of solvent s in the solvent
mixture and Vs (m3 · mol-1) is the molar volume of pure solvent
s. Subscript sol covers all the solvents in the solution. I is the
ionic strength of the solution, T is the absolute temperature,
and D is the dielectric constant for mixed solvents. For binary
mixed solvents, the Oster’s mixing rule is used:
D)
[
ln γsSR ) 1 - Vs + ln Vs - 5qs 1 -
ion
where dsalt, bsol,ion, and csol,ion are the MR interaction parameters
between the solvents (sol) and the ions. bc,a,, cc,a, and dsalt are
Table 2. Salt Solubilities (mol · kg-1) in the Mixed Solvents at 313.15 K for Different Salt-Free Mass Fractions (w′1)
water(1) + methanol(2)
water(1) + ethanol(2)
methanol(1) +
ethanol(2)
methanol(1) +
acetone(2)
ethanol(1) +
acetone(2)
mLiCl
mLiCl
mLiCl
mLiCl
11.21
13.69
15.55
17.75
19.56
5.75
6.14
6.85
7.35
7.83
8.39
8.87
9.30
9.80
1.04
1.76
2.87
3.91
4.83
5.46
6.77
8.04
8.93
0.486
0.819
1.182
1.470
2.052
2.666
3.417
4.229
5.108
water(1) + acetone(2)
w′1
mNaCl
mKCl
mLiCl
mNaCl
mKCl
mLiCl
mNaCl
mKCl
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.369
0.601
0.957
1.405
2.000
2.665
3.409
4.255
5.194
0.137
0.256
0.471
0.790
1.235
1.789
2.508
3.334
4.283
11.83
12.76
13.56
14.37
15.46
16.43
17.59
18.64
19.83
0.074
0.286
0.647
1.176
1.786
2.460
3.215
4.038
5.035
0.0295
0.121
0.336
0.672
1.122
1.685
2.346
3.170
4.150
6.94
7.91
9.77
10.98
12.57
14.25
15.89
17.05
19.23
0.0164
0.0097
0.0983
4.210
5.179
2.550
3.352
4.309
Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010
ion j is normalized, so that γ*′ f 1 when xs f 1 and I f 0. In
eq 24, the term ln γjSR is the same as in eq 18. The terms ln
γSR
j (B) and (Bj,s(I ) 0))/Ms in eq 23 represent the reference state
for ion j at infinite dilution based on the mole fraction scale.
The subscript s in eqs 22 and 24 indicates the reference solvent.
The pure solvent is considered as a reference solvent. The
variables given in eqs 3 -24 were already defined in detail in
the paper of Li et al.3,4 On the basis of the molality scale, the
complete expression of the activity coefficient of ion j can be
obtained from
LR
ln γ*′
+ ln γ*j MR + ln γ*j SR) j ) (ln γ*
j
ln(Ms /Mm + Ms
∑m
ion)
(25)
(
(
where a are activities and γ are the activity coefficients of the
different species. Ksp is identical with the solubility product of
the salt Mv+Xv- · nH2O, since aMX · nH2O is unity. Equation 27
can be used not only for aqueous solutions but also for organic
or mixed solvent electrolyte solutions. The solubility product
can be calculated using standard thermodynamic properties of
the salt and the ions, such as the standard Gibbs energy of
formation, standard enthalpy of formation, and standard heat
capacity as mentioned by Li et al.6 The solubility product of
the salts in aqueous systems can easily be obtained from the
available standard thermodynamic properties, for example, of
the ions in aqueous solution. Unfortunately, these data are
usually not available for the ions in organic or mixed solvent
electrolyte systems. Huang et al.7 proposed a procedure to solve
this problem. By using the following equations, the solubility
product of the salt in aqueous electrolyte systems can, for
example, be transferred to mixed solvent electrolyte systems
containing water, whereby
ln Ksp(aq+org)(T) ) ln Ksp(aq)(T) - [ν+ωM(aq/aq+org) +
ν-ωX(aq/aq+org)] (28)
(
]
)
) ( )
)
[(
)
(
]
)
)
Bi,aq(I ) 0) ) bi,aq + ci,aq
Mν+Xν- · nH2O(solid) a ν+M(liquid) + ν-X(liquid) +
nH2O(liquid) (26)
aMX · nH2O
) ν+ ln(mMγ*′)
M + ν- ln(mXγ*′)
X + n ln(xH2OγH2O)
(27)
(
)
raq+org
1
1
+ ln
+
raq+org
raq
raq
qaq+org
qaq
raqqaq+org
- 5qX ln
+
5rX
raq
raq+org
raq+orgqaq
x´aqψaq,X + x´orgψorg,X
+
qX ln
ψaq,X
BX,aq(I ) 0)
(x´aqψX,aq + x´orgψX,org - ψX,aq) +
Maq
BX,aq+org(I ) 0)
+ ln(Maq /Maq+org) (30)
Maq+org
In this work, the LIQUAC model based on Huang et al7 was
used to correlate the solubility data. For the ions in the
electrolyte solutions, the unsymmetrical convention for the
activity coefficients and the molality scale were used. With the
assumption that all salts completely dissociate in the solution,
one can obtain
ν+ ν- n
aX aH2O
aM
[(
ωX(aq/aq+org) ) rX
5. Calculation of Salt Solubilities in Water-Methanol
Electrolyte Systems
ln Ksp(T) ) ln
) ( )
raq+org
1
1
+ ln
+
raq+org
raq
raq
qaq+org
qaq
raqqaq+org
- 5qM ln
+
5rM
raq
raq+org
raq+orgqaq
x´aqψaq,M + x´orgψorg,M
+
qM ln
ψaq,M
BM,aq(I ) 0)
(x´aqψM,aq + x´orgψM,org - ψM,aq) +
Maq
BM,aq+org(I ) 0)
+ ln(Maq /Maq+org) (29)
Maq+org
ωM(aq/aq+org) ) rM
ion
where Mv+Xv- · nH2O indicates the solid salt consisting of V+
cations M, V- anions X, and n water molecules in the hydrated
crystal. On the basis of eq 26, a chemical equilibrium constant
Ksp can be defined:
(
4985
(31)
Bi,aq+org(I ) 0) ) xaq
′ bi,aq + xorg
′ bi,org + xaq
′ ci,aq + xorg
′ ci,org
(32)
raq+org ) xaq
′ raq + xorg
′ rorg
(33)
qaq+org ) xaq
′ qaq + xorg
′ qorg
(34)
The electrolyte system water + methanol + NaCl and water
+ methanol + KCl were chosen to test the derived expression
by Huang et al.7 It has been shown that eqs 28-34 can be
applied successfully for the prediction of salt solubilities in the
system water + methanol.
6. Results and Discussion
All parameters required for the calculations were taken from
Huang et al.7 Additionally new parameters for LiCl and LiBr
were fitted using vapor-liquid equilibria (VLE), osmotic
coefficients, solid-liquid equilibria (SLE), and mean ion activity
coefficients stored in the Dortmund Data Bank. The parameters
used for the calculation are listed in Table 3 or were taken from
ref 7. The salt solubilities of NaCl and KCl in the mixed solvents
at 313.15 K were predicted with the existing parameters. The
calculated results are shown in Figures 4-5 together with the
experimental solubilities of this work and data published by
other authors stored in the DDB. From the figures it can be
seen that the measured salt solubilities in the mixed solvents
are in good agreement with the data of Pinho and Macedo8 and
that the LIQUAC model is able to describe the salt solubilities
Table 3. The Correlated MR and SR Parameters of the Model in
This Work
i
+
Li
Li+
BrBrLi+
Li+
j
bij
cij
aij
aji
dij
H2O
MeOH
H2O
MeOH
ClBr-
-0.25121
-0.27605
0.04002
-0.02844
0.32999
0.40366
0.01648
0.11215
-0.03810
-0.05433
-0.30497
0.52021
-927.39
-1075.56
4179.03
27.59
-887.60
-70.18
-4469.29
-5151.06
1078.11
1101.21
-4297.14
-6532.19
0.15343
0.13686
4986
Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010
Figure 4. NaCl solubility in the system methanol + water at different saltfree mole fractions: (9) this work at 313.15 K; (s) LIQUAC model at
313.15 K; (O) Pinho and Macedo8 at 298.15 K; ( · · · ) LIQUAC model at
298.15 K; (4) Pinho and Macedo8 at 323.15 K; (---) LIQUAC model at
323.15 K.
Figure 5. KCl solubility in the system methanol + water binary solvent
mixture at different salt-free mole fractions: (9) this work at 313.15 K;
(s) LIQUAC model at 313.15 K; (O) Pinho and Macedo8 at 298.15 K;
( · · · ) LIQUAC model at 298.15 K; (4) Pinho and Macedo8 at 323.15 K;
(---) LIQUAC model at 323.15 K.
in those electrolyte systems reliably. As expected, with the
increasing mole fraction of methanol, the salt solubility strongly
decreases. Since the parameters for systems with ethanol and
acetone were not given by Huang et al.,7 they were not included
in this correlation.
Additionally two salts (LiCl, LiBr) were investigated to check
the capability of the LIQUAC model in describing the SLE
behavior. New parameters were correlated using osmotic
coefficients (φ), mean activity coefficients (γ(), vapor-liquid
equilibria, and salt solubilities. The parameters were determined
by minimization of the following objective function using the
Simplex-Nelder-Mead method:
F(aij, aji, bij, cij) )
∑ ∑w
Q
np
nt
(
)
Qexp - Qcalc
100
Qexp
2
) min
(35)
Figure 6. Molal osmotic coefficients for aqueous electrolyte systems: (0)
LiCl + water system at 298.15 K from DDB;1 (s) LIQUAC model at
298.15 K; (O) LiBr + water system at 298.15 K from DDB;1 ( · · · ) LIQUAC
model at 298.15 K.
Figure 7. Experimental and calculated system pressures of aqueous binary
systems: (0) LiCl + water at 298.15 K from DDB;1 (s) LIQUAC model
at 298.15 K; (O) LiCl + water at 323.15 K from DDB;1 ( · · · ), LIQUAC
model at 323.15 K; (4) LiBr + water at 323.15 K from DDB;1 (---)
LIQUAC model at 323.15 K.
where Q represents the respective value of φ,γ(, T, P, and m,
and wQ is a weighting factor for Q; np and nt refer to the number
of data points and data types, respectively. The subscripts “exp”
and “calc” refer to experimental and calculated values. The
experimental data were taken from the DDB.
In this study, the polar organic solvent methanol was
investigated since the system methanol-water-salt is homogeneous. The new fitted parameters are listed in Table 3. The
van der Waals volumes and surface areas for the ions were taken
directly from Kiepe,9 and the short-range interaction parameters,
the volume, and surface area parameters for the solvents are
from the already published parameters of the UNIQUAC model.
The overall results for the salts (LiCl, LiBr) in water,
methanol, and water + methanol calculated by the LIQUAC
model are shown in Figures 6-9. As can be seen for both salts
good agreement of the correlations with the experimental data
is observed. Not only is the osmotic coefficient in the mixed
solution reliably described up to high molalities (up to about
Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010
4987
The quality of the correlations by using the LIQUAC model
can be judged by calculating the average absolute relative
deviation (AARD):
1
AARD )
Ndata
Figure 8. Experimental and calculated system pressures of the binary
systems: (0) LiBr + methanol at 298.15 K from DDB;1 (s) LIQUAC model
at 298.15 K; (O) LiCl + methanol at 298.15 K from DDB;1 ( · · · ) LIQUAC
model at 298.15 K.
Ndata
∑
i)1
|
Qcalc
- Qexp
i
i
Qexp
i
100
|
(36)
Table 4 summarizes the AARD values obtained in this work
by using the LIQUAC model. As shown in the table the results
obtained for the aqueous systems are better than for mixed
solvents and pure organic electrolyte systems. Since the available
standard thermodynamic properties of LiCl or/and of the
corresponding monohydrate seemed to be questionable, the
solubility product at 298.15 and 313.15 K was fitted additionally.
The solubility products obtained at the two temperatures are
listed in Table 4.
In Figure 9, the solubilities of LiCl in the system water +
methanol are shown for two different temperatures. In this
diagram, the solubility of LiCl monohydrate is also shown.
The intersection points of the two curves that describe the
solubility of both salts (anhydrous and monohydrate) are at
xwater ) 0.405 for a temperature of T ) 298.15 K and xwater
) 0.490 at T ) 313.15, respectively. It can be seen that the
calculated results represent well the phase equilibrium
behavior of LiCl in the mixed solvent system, and even the
univariant point of phase transition is in good agreement with
the experimental values.
The results above show that the LIQUAC model has the
capability to predict salt solubilities, osmotic coefficients,
mean ion activity coefficients, and the vapor-liquid equilibrium behavior in aqueous, methanol, and water + methanol
solvent electrolyte systems. The calculated results are in
excellent agreement with the observed experimental values
and offer new perspectives for further application of the
model in describing thermodynamic properties in mixed
solvent electrolyte systems.
7. Conclusion
Figure 9. LiCl solubility in the system water + methanol at different saltfree mole fractions: (0) this work at 313.15 K; (s) LIQUAC model at
313.15 K; (O) data set in DDB1 at 298.15 K; ( · · · ) LIQUAC model at 298.15
K.
Table 4. AARD and Solubility Product Estimated in the Correlation
AARD (%)
ln Ksp
osmotic
system
coefficient (φ) solubility pressure 298.15 K 313.15 K
LiCl + H2O
LiBr + H2O
LiCl · H2O(aq)
LiCl(aq)
LiCl + H2O +
methanol
NaCl + H2O +
methanol
KCl + H2O +
methanol
2.0
2.3
2.6
3.6
-12.06
-15.50
-11.78
-15.10
1.5
2.6
5.1
20 mol/kg) but also the VLE behavior in aqueous and mixed
solvents (Figures 7 and 8) is described correctly. The model is
even capable of predicting the conversion point between LiCl
and the monohydrate in aqueous methanol solutions and the
temperature dependence (Figure 9).
Salt solubility measurements for four salts (NaCl, KCl, LiCl,
and LiBr) in pure organic and mixed solvents were carried out
by using a static method. Reliable and reproducible experimental
data were obtained for the entire composition and temperature
range. For a few systems no data are available in literature.
The experimental data were correlated with the LIQUAC
model. The results show that the LIQUAC model is able to
describe osmotic coefficients, mean activity coefficients of the
salts, salt solubilities, and the VLE behavior in aqueous, organic,
and water + organic solvent electrolyte systems.
The main focus of this work was to measure and correlate
the salt solubilities in the system water-methanol.
Acknowledgment
The authors thank the Deutsche Forschungsgemeinschaft for
financial support of the ongoing research project. We also thank
the DDBST GmbH (Oldenburg, Germany) for providing the
latest version of the Dortmund Data Bank for the model
comparison.
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Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010
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ReceiVed for reView January 5, 2010
ReVised manuscript receiVed March 15, 2010
Accepted March 24, 2010
IE100027C
