CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 35–42

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CALPHAD: Computer Coupling of Phase Diagrams andThermochemistry

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Correlation of the solubilities of alkali chlorides in mixed solvents:Polyethylene glycolþH2O and EthanolþH2O

Jorge A. Lovera a, Aldo P. Padilla a, Hector R. Galleguillos a,b,n

a Department of Chemical and Mineral Process Engineering, University of Antofagasta, Av. Angamos 601, Antofagasta, Chileb Centro de Investigacion Cientıfico y Tecnologico para la Minerıa (CICITEM), Av. Jose Miguel Carrera 1701, 41 piso, Antofagasta, Chile

a r t i c l e i n f o

Article history:

Received 18 November 2011

Received in revised form

24 March 2012

Accepted 24 March 2012Available online 8 May 2012

Keywords:

Experimental solubility

Solubility correlation

Modified Pitzer model

16/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.calphad.2012.03.002

esponding author at: Department of Chemica

asta, Avenida Angamos 601, Antofagasta, Chi

ail address: hgalleguillos@uantof.cl (H.R. Gall

a b s t r a c t

Solubility data for the LiClþPEG 4000þH2O system at 25 1C were obtained. These data, along with

other data published in the literature for the NaClþPEG 4000þH2O, KClþPEG 4000þH2O, LiClþ

C2H5OHþH2O, NaClþC2H5OHþH2O, and KClþC2H5OHþH2O ternary systems at 25 1C, were correlated

using a modified Pitzer model. The values of the solubilities calculated using the model are in good

agreement with the experimental observations. Using the model parameterization established in this

study, the yield of precipitated salt was calculated as a function of kg PEG 4000 or C2H5OH/100 kg of

saturated solution.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

One of the methods employed in crystallization to producesupersaturated solutions is termed drowning out. This separationmethod consists of adding an additional component that ismiscible with the original solution to decrease the solubility ofthe salt of interest. This crystallization technique has a number ofadvantages compared with traditional evaporation or coolingprocedures, including increased yields, operation at ambienttemperature, higher purity of crystals, selectivity and others [1].

The prediction or correlation of salt solubility data in mixedsolvents is an important tool for the design and simulation of thedrowning-out crystallization process. To carry out this type ofanalysis, several models have been proposed in the literature basedon the thermodynamics of the electrolytes. Farelo et al. [2] used thePitzer mole fraction-based thermodynamic model to represent thephase equilibrium of the NaClþKClþwaterþethanol system from(298 to 323) K with up to 20 mass% ethanol in the solvent. The resultsobtained are very good—the model reproduced the experimentalsolubility data for both salts with a standard deviation of70.023 mol/kg solvent. Zeng et al. [3] employed the extended BETmodel to predict the solubility of magnesium chloride in theHClþLiClþMgCl2þH2O system, using HCl as a salting-out agent.The solubilities predicted at (273, 293, and 313) K are in goodagreement with the experimental values, with standard deviations

ll rights reserved.

l Engineering, University of

le. Tel.: þ56 55 637344.

eguillos).

lower than 0.092 mol kg�1. Marcilla et al. [4] and Reyes et al. [5]presented a method to simultaneously correlate the equilibrium datafor all of the equilibrium regions present in ternary systems com-posed of waterþorganic solventþsalt. The NRTL model was used bythe authors to formulate the liquid-phase activity. In general, theresults are good when the salt crystallizes anhydrously, as is the caseof sodium chloride at 298 K and potassium benzylpenicillin at293 K [4]. However, the deviations obtained between the experi-mental and calculated data are higher for lithium chloride at 298 K.Because lithium chloride crystallizes in both monohydrate andanhydrous forms, there is a greater number of equilibrium zones,complicating the simultaneous correlation of the equilibrium data inall existing regions. The results improved when the Gibbs energy formonohydrated salt was considered as a fitting parameter [5].

Jimenez et al. [6] used the method of Kan et al. [7] to represent thesolid–liquid equilibrium of potassium sulfate in different waterþor-ganic solvent mixtures at (288, 308 and 318) K. Because the activitycoefficient of an electrolyte in a waterþorganic solventþsalt systemdepends simultaneously on the concentration and content of theorganic co-solvent, Kan et al. [7] defined an overall activity coefficientto quantify these effects separately. The Pitzer model of virialcoefficients was used to quantify the effect of the salt, whereas asimilar equation from the Born model was used to quantify the co-solvent effect. In general, the results show a good agreementbetween experimental and calculated values; for example, a meanabsolute deviation of 0.0063 mol �kg�1 is obtained for the potassiumsulfateþwaterþ1-propanol system.

The Pitzer model of virial coefficients has been used widely inthe prediction and correlation of solubilities in systems thatcontain one salt (or more) in a single solvent, generally water

J.A. Lovera et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 35–4236

[8–10]. However, the original form of this model cannot beapplied successfully for mixed-solvent electrolyte solutions. Wuet al. [11] modified the Pitzer model to extend its application tothe prediction of the liquid–liquid equilibrium of polymerþsaltþwater ternary systems. These authors assumed that thenon-ionic solute (polymer) is a pseudo-solvent, and consequentlythe polymerþwater components are equivalent to a solventmixture. The application of the modified virial Pitzer equation,upon calculating the mean ionic activity coefficient of the elec-trolyte in the solvent mixture, requires a new estimation of thebinary parameters of the salt (b(0), b(1), and Cj); that is, the binaryparameters reported in the literature [12,13] cannot be usedbecause the long-range term in the original Pitzer model isreplaced by the expression of Fowler and Guggenheim [14].

The purpose of the present work is to use the method of Wuet al. to correlate the solid–liquid equilibrium of alkali chlorides(LiCl, NaCl, and KCl) at 25 1C in different mixed solvents such as(polymerþwater) and (ethanolþwater). The polymer is poly(ethylene glycol) with an average molar mass of 4000 (PEG 4000).The use of polymers as precipitant components is an importantalternative in drowning-out processes [15]. Poly(ethylene glycol) is awater-soluble polymer that can be important for the separation ofinorganic salts because it is nontoxic and non-inflammable, is aneasy-to-handle compound and is inexpensive.

The solid–liquid equilibrium data used in the correlation weretaken from the literature. Galleguillos et al. [16] reported solubi-lity data for NaCl or KCl in (ethanolþwater) mixtures at 25 1C,whereas Linke and Seidell did the same for LiCl [17]. Taboadaet al. [15] reported data on the solubility of NaCl or KCl in (PEG4000þwater) mixtures at 25 1C. In the present work, the solubi-lity of LiCl in (PEG 4000þwater) at 25 1C was measured. Thisstudy provides information about the thermodynamics of thesolid–liquid equilibrium of three alkali chlorides in mixed solvent,and this information can be useful for the design of drowning-outseparation processes.

2. Experimental procedure

2.1. Materials

Synthesis-grade samples of polyethylene glycol with an aver-age molar mass of 4000 (PEG 4000) and analytical reagent-gradeþ99% anhydrous lithium chloride were procured fromMerck and used without further purification. Salt was dried to aconstant weight in an oven at 100 1C for 48 h prior to use. Milli-Q-quality distilled water was used in all experiments.

2.2. Apparatus and procedures

The phase equilibrium study was carried out by mixing knownmasses of PEG 4000 and water with excess salt. All of thesolutions were prepared by mass using an analytical balancewith a precision of 0.07 mg (Mettler Toledo model AX204). Theresultant supersaturated solutions were contained in suitablysealed glass flasks and mechanically shaken for 48 h. All flaskswere maintained at working temperatures (2570.1 1C) in atemperature-controlled bath with a holder containing eight90-mL glass jars.

Once equilibrium was reached, the mixing was interrupted,and the solutions were allowed to decant for 60 min at a constanttemperature. The clear liquid of each equilibrium solution wascollected by syringe and filtered for subsequent determination ofthe concentration. Syringes and other apparatus used in theprocedure were maintained at a slightly elevated temperature

to avoid any tendency of salts to precipitate from the solutionsunder study because of drops in temperature.

The concentration of LiCl was determined by lithium andchloride analysis using atomic absorption spectroscopy (AAS)and the argentometric method. The AAS measurements wereperformed using a Varian model SpectrAA 220 instrument. Thesolubility values of the ternary system represent the means oftwo independent replicates. The relative standard deviation wasless than 0.43%.

3. Thermodynamic framework

Based on the arguments of Barata and Serrano [18] regardingthe solid–liquid equilibrium of a ternary system organic co-solvent (1)þelectrolyte (2)þwater (3), the equilibrium constantfor solubility reaction is given by

KPS ¼m22g

27 ð1Þ

where KSP is the solubility product, which is a constant thatdepends only on temperature, m2 and g7 are the molality andmean ionic activity coefficient of the electrolyte in the ternarysystem, respectively. Eq. (1) is valid for univalent salts thatcrystallize in an anhydride form. An expression for g7 is providedby the Pitzer model, which was modified by Wu et al. [11] forpolymerþelectrolyteþwater systems. For univalent salts, thisvalue is given by the following equation:

lng7 ¼�AffiffiIp

1þbffiffiIp þð1=2Þ B12r1m1þ4B22m2þ IðB012r1m1þ2B022m2Þ

�

þC112r21m2

1þ2C122r1m1m2þ2Cg222m2

2� ð2Þ

where the first term on the right-hand side is the long-rangeelectrostatic contribution (Debye–Huckel equation [14]), and thesecond term represents the short-range virial contributions. Wuet al. considered polymers as pseudo-solvents. The symbols r1 andm1 are the number of segments and the molality of the polymer,respectively. A and b are Debye–Huckel constants, and B22 and B12

are the second virial coefficients and represent the ion–ion andsegment–ion interactions, respectively. Both virial coefficients aredependent on the ionic strength, I, according to the functionalitygiven by the original Pitzer model [19]

Bij ¼ bð0Þij þ2bð1Þij

a21I

1�ð1þa1

ffiffiIpÞe�a1

ffiffiIph iþ

2bð2Þij

a22I

1�ð1þa2

ffiffiIpÞe�a2

ffiffiIph ið3Þ

where all the symbols have their usual significance [19]. In the B22

term, the parameters bð0Þ22 , bð1Þ22 and bð2Þ22 are specific to the salt andthe values a1¼2.0 and a2¼0 (bð2Þ22¼0) were used for NaCl and KCl,while the values a1¼1.4 and a2¼2.4 were used for the LiCl. Theion interaction model of Pitzer does not use the bð2Þ22 parameter for1:1 electrolytes, however its inclusion makes it possible to fitaqueous solution properties to very high concentrations [20]. Thisapproach has been used in the present work to parameterize theLiCl–H2O system. Christov [21] also used the bð2Þ22 parameter withgood results in the simulation of 2:1 electrolytes. In the B12 term,the parameters bð0Þ12 , bð1Þ12 and bð2Þ12 are specific to the interactionbetween PEG and salt (or ethanol and salt).

The values of a1 and a2 are the same as the values of thepreviously employed focus.

The symbols B012 and B022 of Eq. (2) are the derivatives of B12 andB22 with respect to I, respectively. The symbols Cg

222, C112, and C122 arethe third virial coefficients and represent the ion–ion–ion, segment–segment–ion, and segment–ion–ion interactions, respectively. For

J.A. Lovera et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 35–42 37

univalent salts the Cg222 parameter satisfies the following equation:

Cg222 ¼

3

2Cf

222 ¼ 3C222 ð4Þ

The superscript g or f in C222 denotes that the parameter isrelated to the activity coefficient or osmotic coefficient. It shouldbe noted that the interaction parameters among ions (bð0Þ22 , bð1Þ22 ,bð2Þ22 andCg

222 or Cf222) are obtained from experimental data of

binary saltþwater systems.In this work, the ionic strength I is defined as

I¼1

2

Xj

m0jz2j , m0j ¼ 1000nj=ðMnÞ, Mn¼M3n3þM1n1 ð5Þ

where zj and nj are the ionic charge and the mole number of ionicspecies j respectively. M1, M3, and M represent the molar mass ofthe polymer, water, and the mixed solvent (average values),respectively, all in g mol�1; n1, n3, and n are the mole numbersof the polymer, water, and the mixed solvent, respectively.

The constants A and b depend on the temperature and thecomposition of the solvent mixture (e.g. at 25 1C and m1¼0 thevalues are A¼1.175 kg1/2 mol�1/2, b¼1.315 kg1/2 mol�1/2), and

Table 1The physical properties of pure substances at 25 1C.

Solvent M/(g mol�1) V/(m3 mol�1) d/(kg m�3) D

H2Oa 18.02 1.805�10�5 998.3 78.34

PEG 4000a 3750 3.12271�10�3 1201 2.206

C2H5OHb 46.07 5.862�10�5 786 24.09c

a From Wu et al. [11].b From Perry et al. [22].c From Lone et al. [23].

Table 2Solubility of LiCl �H2O(cr) in the LiClþPEG 4000þH2O

system at 25 1C.

PEG 4000 (mass%) LiCl (mass%)

0 45.85a

2.52 45.02

4.68 43.82

7.02 43.40

9.47 42.25

12.30 41.22

16.44 39.39

17.97 38.94

20.51 37.29

21.80 37.22

25.57 36.05

a Linke and Seidell [17].

Table 3Parameters at 25 1C for aqueous binary solutions.

System (1)–(2)–(3) B11�102 C111�104b

PEG–LiCl–H2O 0.70877a 0.12962a 2

PEG–NaCl–H2O 0.70877a 0.12962a 0

PEG–KCl–H2O 0.70877a 0.12962a 0

C2H5OH–LiCl–H2O �2.3288 1.7776 2

C2H5OH–NaCl–H2O �2.3288 1.7776 0

C2H5OH–KCl–H2O �2.3288 1.7776 0

a Parameters determined by Wu et al. [11].b Calculated with a1¼1.4 and a2¼2.4.

the equations for their estimation are [11]

A¼1:327757� 105

DT

ffiffiffiffiffiffiffid

DT

rð6Þ

b¼ 6:359696

ffiffiffiffiffiffiffid

DT

rð7Þ

T is the absolute temperature, and D and d are the dielectric constantand the density (in kg m�3) of the mixed solvent, respectively, andare calculated using the following empirical formulas [11]:

D¼X

i

f0iDi ð8Þ

d¼X

i

f0idi ð9Þ

where

f0i ¼niViP

i

niVið10Þ

In Eqs. (8)–(10), the sum was established only for the compo-nents of the solvent mixture; for example, PEG and water or ethanoland water. Di, di, Vi and ni are the dielectric constant, the density, themolar volume and the number of moles of pure non-ionic species i,respectively. The physical properties for PEG 4000 and water weretaken from reference [11], and those for C2H5OH were taken fromthe literature [22,23]. These values are listed in Table 1 and wereused to calculate the Debye–Huckel constants A and b.

If the salt crystallizes as a hydrate with u0 water molecules,similar expression to Eq. (1) is obtained

KPS ¼m22g

27 an0

3 ð11Þ

where a3 is the water activity. Wu et al. [11] obtained thefollowing equation for the activity coefficient of water:

lng3 ¼2AV3d

b31þb

ffiffiIp�

1

1þbffiffiIp �2lnð1þb

ffiffiIpÞ

� ��

M3

1000B11r2

1m21

�þ B12þ

nw

nSIB012

� �r1m1m2þ2 B22þ

nw

nSIB012

� �m2

2þ2C111r31m3

1

þ2C112r21m2

1m2þ2C122r1m1m22þ2Cf

222m32

ið12Þ

where V3, is the molar volume of water (in m3 mol�1). In thisequation, there are two new adjustable parameters related to thesecond (B11) and third (C111) virial coefficients of the polymersegments. The Debye–Huckel constants are determined byEqs. (6) and (7).

Since the experimental values of the osmotic and activitycoefficients are reported in the literature on a molality scale, itis necessary to convert them to a mole fraction scale. Thefollowing equations are useful for this purpose [11]:

f¼�1000lnðx3g3Þ= M3

Xion

mion

!ð13Þ

ð0Þ22 �10 bð1Þ22 �10 bð2Þ22 �10 Cf

222 �103

.4953b�13.539b 20.244b

�6.3601b

.53977 0.22024 0 3.8271

.22339 �0.22816 0 2.6470

.4953b�13.539b 20.244b

�6.3601b

.53977 0.22024 0 3.8271

.22339 �0.22816 0 2.6470

Table 4Data of binary solutions at 25 1C.

System Data type Np Nt sa Ref.

LiCl–H2O j, g 43 2 0.07 [25]

NaCl–H2O j, g 30 2 0.002 [25]

KCl–H2O j, g 28 2 0.0005 [25]

PEG4000–H2O a3 12 1 0.0002 [28]

C2H5OH–H2O g 7 2 0.008 [26]

a s¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

i

Pj½QijðexpÞ�QijðcalÞ�2=NP=Nt

q. Q stands for the thermodynamic

property; NP is the number of experimental points, and Nt denotes the number

of thermodynamic properties.

Fig. 1. Comparison of g versus m for aqueous NaCl and aqueous KCl at 25 1C (J), the

recommended values of Hamer and Wu for NaCl [24]; (n), the recommended values of

Hamer and Wu for KCl [25]; (—), calculated from the modified Pitzer model.

Fig. 2. Comparison of g versus m for aqueous LiCl at 25 1C (J), the recommended

values of Hamer and Wu for LiCl [25]; (—), calculated from the modified

Pitzer model.

J.A. Lovera et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 35–4238

gðxÞ7 ¼ gðmÞ7 M3=Mþ0:001M3

Xion

mion

" #ð14Þ

where f and x3, are the osmotic coefficient and the mole fractionof water, respectively. It is worth noting that the activity coeffi-cients calculated with the extended Debye–Huckel equation ofFowler–Guggenheim are the rational activity coefficients, and notthe molal activity coefficients [24].

Given that the polymer is considered a pseudo-solvent, the useof the modified Pitzer equation to calculate the electrolyteactivity coefficient would be valid strictly for polymerþsaltþwater systems. However, we propose that it is also valid for anelectrolyte in a mixed solvent such as ethanolþwater.

Fig. 3. Comparison of water activity versus mass% for aqueous PEG 4000 at 25 1C

(J), experimental data [28]; (—), calculated from the modified Pitzer model.

Fig. 4. Comparison of water activity versus mole fraction for aqueous ethanol at

25 1C (J), the recommended values of Gmehling et al. [26]; (—), calculated from

the modified Pitzer model.

Table 5Cross parameters between PEG or C2H5OH and salt at 25 1C.

System (1)–(2)–(3) bð0Þ12 �10 bð1Þ12 �10 bð2Þ12 �10 C112�102 C122�102 lnKps

PEG–LiCl–H2O �2.1801 �10.226 13.522 1.8112 0.43757 11.96a

PEG–NaCl–H2O �1.9146 0.97900 0 0.28593 1.7176 3.616b

PEG–KCl–H2O �0.91185 0.091816 0 0.11009 1.3568 2.072b

C2H5OH–LiCl–H2O �1.2496 9.8611 2.6680 �0.15355 0.45256 11.96a

C2H5OH–NaCl–H2O 1.0839 �0.94622 0 �0.014932 �0.27092 3.616b

C2H5OH–KCl–H2O 0.76676 �0.37190 0 �0.011154 0.83774 2.072b

a From Monnin et al. [27].b From Pitzer [29].

Table 6Data and standard deviations (s) of fit of the ternary systems at 25 1C.

Sistema (1)–(2)–(3) Np sg a 5% PEG Np sg a 10% PEG Ref. Np swa Ref.

LiCl–PEG 4000–H2O 11 0.037 11 0.019 [31] 11 0.46 t sb

NaCl–PEG 4000–H2O 11 0.025 12 0.024 [29] 12 0.38 [15]

KCl-PEG 4000–H2O 14 0.019 16 0.024 [30] 13 0.33 [15]

LiCl–C2H5OH–H2O 10 0.55 [17]

NaCl–C2H5OH–H2O 22 0.68 [16,17]

KCl–C2H5OH–H2O 10 0.48 [16]

a sQ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPi Q iðexpÞ�QiðcalÞ� � 2

=NP

q. Q represents activity coefficient (g) or solubility in mass% (w).

b t s: this study.

Fig. 5. Comparison of mean MCl activity coefficient in the PEG 4000þMClþH2O

(M¼Li, Na, and K) ternary system at 25 1C and 5% PEG (J), the recommended

values of Morales et al. for LiCl [32]; (n), the recommended values of Morales et al.

for NaCl [30]; (&), the recommended values of Hernandez-Luis et al. for KCl [31];

(—), calculated values by simultaneous fit.

Fig. 6. Comparison of mean MCl activity coefficient in the PEG 4000þMClþH2O

(M¼Li, Na, and K) ternary system at 25 1C and 10% PEG (J), the recommended

values of Morales et al. for LiCl [32]; (n), the recommended values of Morales et al.

for NaCl [30]; (&), the recommended values of Hernandez-Luis et al. for KCl [31];

(—), calculated values by simultaneous fit.

J.A. Lovera et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 35–42 39

4. Results and discussion

4.1. Experimental results

The experimental solubilities of LiCl �H2O in the PEG 4000þLiClþH2O system

at 25 1C are presented in Table 2. The solubility is expressed as the mass% or the

grams of anhydrous lithium chloride per 100 g of saturated solution, and the

composition of PEG 4000 is expressed in the same way; i.e., mass% or grams of PEG

4000 per 100 g of saturated solution. The binary point is from the solubility data

reported by Linke and Seidell [17]. Note that the solubility of LiCl decreases as the

concentration of PEG 4000 in the ternary system is increased. It has been

hypothesized that the solid phase that crystallizes from PEG 4000þLiClþH2O

solutions is the same as the solid that precipitates from a saturated solution of LiCl

in the absence of PEG at 25 1C; that is, the solid is LiCl �H2O hydrate. This premise

is also fulfilled in C2H5OHþLiClþH2O solutions at 25 1C up to a certain alcohol

concentration (66.8% by weight) [17]. The decrease in the LiCl solubility can be

explained by the solventing out effect. The contribution of polymer molecules to

the LiClþH2O system tends to invert the dissociation equilibrium of the salt.

4.2. Correlation

The relationship between the solubility of the salt and solvent concentration is

given by Eq. (1) or (11). Solving this equation for the solubility requires knowing

J.A. Lovera et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 35–4240

KSP and the parameters of the activity coefficient model: the characteristic

coefficients of the salt (bð0Þ22 , bð1Þ22 , bð2Þ22 and Cf222) and the polymer (B11 and C111)

and the cross virial coefficients between the salt and the polymer (bð0Þ12 , bð1Þ12 , bð2Þ12 ,

C112 and C122). The parameters bð0Þ22 , bð1Þ22 , bð2Þ22 and Cf222 have different values from

those in the original Pitzer model and should be correlated.

The binary parameters for the salt have been estimated by fitting data from

the literature at 25 1C, following the same procedure as used by Wu et al. [11]. The

data for the LiCl–H2O, NaCl–H2O, and KCl–H2O systems were taken from the

recommended values of Hamer and Wu [25]. Values of the parametersbð0Þ22 , bð1Þ22 , bð2Þ22

and Cf222 are shown in Table 3. The second and third coefficients for PEG 4000 (B11

and C111) were taken from Wu et al. [11], and those for ethanol were calculated by

fitting VLE data at 25 1C of the C2H5OH–H2O system [26]. These parameters are

also shown in Table 3. The standard deviation (s) for the data type (Q), the number

of experimental points (NP) and the number of thermodynamic properties (Nt)

used in the correlation are listed in Table 4. The standard deviation values show

that the correlation of the data of binary aqueous systems is good, except for LiCl,

which has a larger standard deviation. This high standard deviation value may be

due to different factors: (a) the formation of Li–Cl ionic pair; (b) high hydration of

the lithium ion; and (c) strong variation of the dielectric constant of the

dissolution with increased concentrations. This last factor seems to be very

Fig. 8. Solubility of NaCl(cr) in the NaClþPEG 4000þH2O system at 25 1C.

(J), experimental data [15]; (—), calculated data.

Fig. 7. Solubility of LiCl �H2O(cr) in the LiClþPEG 4000þH2O system at 25 1C.

(J), experimental data (from this study); (—), calculated data.

important given that Monnin et al. [27] obtained good results in the representa-

tion of osmotic coefficients of the LiCl–H2O system, using the mean spherical

approximation model, which incorporates the variation of this property with the

concentration. It is important to note that the incorporation of the bð2Þ22 parameter

in the adjustment decreases the standard deviation from 1.03 (with bð2Þ22¼0) to

0.07 and with this value of s good results were obtained in the representation of

the solubility of LiCl in the mixed solvents studied in this work (see Figs. 7 and 10

further below).

Fig. 1 shows the results for NaCl and KCl, observing a good agreement between

the activity coefficients for NaCl and KCl recommended by Hamer and Wu [25]

and those obtained with the model. Fig. 2 shows the LiCl results. It can be

observed that the variation of the activity coefficient with the molality is very

different from the behavior presented by NaCl and KCl. The LiCl presents a high

level of solubility and unusually high values of the activity coefficients. The

activity coefficient presents an abrupt increase with the increase of concentration,

beginning at 5 m. For example, at molalities of 5, 10, and 19, the values of the

activity coefficient are 2.0, 9.6, and 57.0, respectively. Owing to this behavior, it

was necessary to incorporate a new parameter in the adjustment of this

electrolyte to reach an acceptable deviation. Fig. 2 shows a satisfactory agreement

Fig. 9. Solubility of KCl(cr) in the KClþPEG 4000þH2O system at 25 1C.

(J), experimental data [15]; (—), calculated data.

Fig. 10. Solubility of LiCl �H2O(cr) in the LiClþC2H5OHþH2O system at 25 1C.

(J), experimental data [17]; (—), calculated data.

J.A. Lovera et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 35–42 41

between the activity coefficients for LiCl recommended by Hamer and Wu [25]

and those obtained with the model. Figs. 3 and 4 show the activity of water for the

PEG 4000þwater and ethanolþwater systems, respectively. The figures maintain

the same units of concentration derived from the experimental information

[26,28]. It can be observed that both systems show a good agreement between

the experimental information and the values calculated with the model. It was

also observed that both systems are far behaving as the ideal solution, with the

increased concentration of PEG 4000 or ethanol.

The solubility product, KSP, for LiCl �H2O was obtained from Monnin et al. [27],

and those for NaCl and KCl were determined from the standard-state chemical

potentials reported by Pitzer [29]. These values are shown in Table 5.

Then, the unknowns in Eqs. (1) or (11) are reduced to the solubility of the salt,

m2, and the salt-polymer cross parametersbð0Þ12 , bð1Þ12 , bð2Þ12 , C112, and C122. In solving

the equation for the solid–liquid equilibrium, the information from the solubility

and the activity coefficient of salt g7 in the ternary system PEG 4000þsaltþwater

[30–32] have been fitted simultaneously using the least squares criteria to find the

unknown parameters. The function to minimize is

SCE¼Xk ¼ 1

w2kðexpÞ�w2kðcalÞ

w2kðexpÞ

� �2

þXk ¼ 1

g2kðexpÞ�g2kðcalÞ

g2kðexpÞ

� �2

ð15Þ

Fig. 12. Solubility of KCl(cr) in the KClþC2H5OHþH2O system at 25 1C.

(J), experimental data [16]; (—), calculated data.

Fig. 11. Solubility of NaCl(cr) in the NaClþC2H5OHþH2O system at 25 1C.

(J), experimental data [16]; (m) experimental data [17]; (—), calculated data.

where SCE represents the sum of squared random errors and w2 is the solubility of

the salt in the solvent mixture expressed as the mass% of salt. The sum includes all

experimental data. The problem of minimizing the SCE function is solved using the

Newton–Raphson numeric algorithm.

Once the optimal parameters were found, w2 was calculated by trial and error

for different values of w1 (mass% of organic component), thus generating a smooth

curve of isothermal solubility. The solubility data employed in correlating the

different systems were obtained from the literature [15–17] along with those

shown in Table 2. The results of the estimated parameters (bð0Þ12 , bð1Þ12 , bð2Þ12 , C112, and

C122) are shown in Table 5, while the standard deviations in the correlation of

activity coefficients and solubility are reported in Table 6. Figs. 5 and 6 show the

results of the correlation of activity coefficients for different compositions of PEG

4000, indicating a good agreement between the values reported in the literature

[30–32] and those calculated in this work. However, for ionic strengths higher

than 2 mol kg�1, the quality of the data fit decreases. These differences are mainly

due to the solubility data used in the simultaneous fit. Taboada et al. [15] reported

that the saturated solutions of NaCl and KCl reached concentrations of PEG 4000 of

53% and 49%, respectively. However, the B11 and C111 parameters obtained from

binary solutions reach a concentration of PEG of 38% [11]. Despite these

Fig. 13. Amount of NaCl precipitated versus kg pseudo-solvent/100 kg saturated

solution at 25 1C.

Fig. 14. Amount of KCl precipitated versus kg pseudo-solvent/100 kg saturated

solution at 25 1C.

J.A. Lovera et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 35–4242

differences, the activity coefficients contributed significantly to achieve a good

correlation of solubility data.

Figs. 7–12 show results of the solubility calculations. These results indicate a good

agreement with the experimental data at 25 1C. The validity of this model has been

demonstrated for univalent salts and two mixed solvents, PEG 4000þH2O and

C2H5OHþH2O; however, the method can be extended to other types of electrolytes

to determine salt–solvent parameters based on solubility data.

The objective function used to find the cross virial coefficients between salt

and polymer was efficient because it allowed the use of electrolyte activity

coefficients between 0 and 10% PEG [30–32]. For higher concentrations of PEG,

satisfactory results were not obtained. In contrast, the determination of the cross

virial coefficients with only experimental values of activity and osmotic coeffi-

cients and their subsequent use in the estimation of solubilities was not

successful. This lack of success probably occurred because the thermodynamic

property data for the binary and ternary systems have different concentrations

ranges for the salt and the polymer. However, when the mixed solvent is

waterþethanol, only the solubility of salt in the objective function is considered

(Eq. (15)) because this information was sufficient to obtain good results.

With the parameterization of the ternary systems LiClþPEG 4000þH2O,

NaClþPEG 4000þH2O and KClþPEG 4000þH2O, it is possible to determine the

percentage of salt precipitated by the addition of PEG 4000 to a saturated solution

saltþwater. For 100 kg of saturated salt solution in water, the yield Z can be

written in terms of the concentrations of the mother liquor (w1 and w2 in mass%)

and the kilograms of pseudo-solvent (PS) added

Z¼ 1�w2

w1�

PS

w02

!� 100 ð16Þ

with the restriction

100

w1¼

PS=100þw02=q�1

ðPS=100Þð1�w2=qÞð17Þ

where w02 is the solubility of the salt in pure water in mass% and q is the ratio of the

molar masses of anhydrous salt and hydrated salt, expressed as a percentage. If the salt

crystallizes as an anhydrous salt, the q value is 100. In Eqs. (16) and (17), w1 and w2 are

related by the equilibrium equation (Eq. (1)). Recovery curves are calculated by solving

these equations for Z in terms of PS, which are shown in Figs. 13 and 14 for NaCl and

KCl, respectively. For the parameterization of the ternary systems LiClþC2H5OHþH2O,

NaClþC2H5OHþH2O and KClþC2H5OHþH2O, a similar procedure was performed,

and the results are also shown in Figs. 13 and 14 for NaCl and KCl, respectively. It can

be easily inferred that the harvesting of crystals of NaCl and KCl is maximized by using

ethanol instead of PEG 4000 as a precipitant.

However, the addition of PEG or C2H5OH to a saturated solution of LiClþH2O

does not induce crystallization, at least in the range of solubilities studied for the

LiClþPEG 4000þH2O and LiClþC2H5OHþH2O systems at 25 1C. This lack of

crystallization is the result of the solubility curve being above the line that

describes the mixing point between pure PEG 4000, or pure C2H5OH, and the

saturated solution of LiCl in water.

5. Conclusions

This work reports solubility measurements of LiCl in solutionsof PEG 4000þwater at 25 1C. The solubility of LiCl in the ternarymixture decreases with increasing concentration of the polymer,in the range from 0 to 25.6 mass%. The velocity with which thesolubility diminishes is practically constant and moderately low.

The Pitzer model modified by Wu et al. [11] has beensuccessfully applied to the correlation of the solid–liquid equili-brium of the LiClþPEG 4000þH2O, NaClþPEG 4000þH2O, andKClþPEG 4000þH2O systems at 25 1C. The goodness of fit of themodel has also been satisfactorily proven in the correlations ofthe solubilities of the three chlorides in the C2H5OHþH2O mixedsolvent.

With the parameterization of the systems studied in this work,the yield was determined based on the amount of PEG 4000 orC2H5OH added to a saturated aqueous solution of NaCl or KCl. The

results show that the yield of pure NaCl or pure KCl is higherwhen adding C2H5OH instead of PEG 4000.

Acknowledgments

The authors thank CONICYT-Chile for the support providedthrough Fondecyt Project no. 1070909 and CICITEM (ProjectR10C1004).

Appendix A. Supporting information

Supplementary data associated with this article can be found inthe online version at http://dx.doi.org/10.1016/j.calphad.2012.03.002.

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