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. Downloaded from pubs.acs.org by UNIV OF TEXAS SW MEDICAL CTR on 10/08/18. For personal use only. 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: [email protected]. † 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. Literature Cited (1) Dortmund Data Bank, version 2008; DDBST Software and Separation Technology GmbH: Oldenburg, Germany, 2008; www.ddbst.de. 4988 Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010 (2) 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. (3) Li, J.; Polka, H.-M.; Gmehling, J. A. gE Model for Single and Mixed Solvent Electrolyte Systems. 1. Model and Results for Strong Electrolytes. Fluid Phase Equilib. 1994, 94, 89. (4) Polka, H.-M.; Li, J.; Gmehling, J. A. gE Model for Single and Mixed Solvent Electrolyte Systems. 2. Results and Comparison with Other Models. Fluid Phase Equilib. 1994, 94, 115. (5) Pinho, S. P.; Macedo, E. A. Experimental Measurement and Modeling of KBr Solubility in Water, Methanol, Ethanol and its Binary Mixed Solvents at Different Temperatures. J. Chem. Thermodyn. 2002, 34, 337. (6) Li, J.; Lin, Y.; Gmehling, J. gE Model for Single- and Mixed-Solvent Electrolyte Systems. 3. Prediction of Salt Solubilities in Aqueous Electrolyte Systems. Ind. Eng. Chem. Res. 2005, 44, 1602. (7) Huang, J.; Li, J.; Gmehling, J. Prediction of Solubilities of Salts, Osmotic Coefficients, and Vapor-Liquid Equilibria for Single and Mixed Solvent Electrolyte Systems using the LIQUAC Model. Fluid Phase Equilib. 2009, 275, 8. (8) Pinho, S. P.; Macedo, E. A. Representation of Salt Solubility in Mixed Solvents: A Comparison of Thermodynamic Models. Fluid Phase Equilib. 1996, 116, 209. (9) Kiepe, J.; Noll, O.; Gmehling, J. Modified LIQUAC and Modified LIFACsA Further Development of Electrolyte Models for the Reliable Prediction of Phase Equilibria with Strong Electrolytes. Ind. Eng. Chem. Res. 2006, 45, 2361. (10) Harner, R. E.; Sydnor, J. B.; Gilreath, E. S. Solubilities of Anhydrous Ionic Substances in Absolute Methanol. J. Chem. Eng. Data 1963, 8, 411. (11) Pavlopoulos, T.; Strehlow, H. The Solubilities of Alkali Halogenides in Methanol, Acetonitrile and Formic Acid. Z. Phys. Chem. 1954, 202, 474. (12) Emons, H.-H.; Dümke, D.; Förtsch, M. Investigation of Systems Consisting of Salts and Mixed Solvents. II The Systems Sodium Chloride Resp. Potassium Chloride, Methanol-Water and Sodium Chloride-Potassium Chloride-Methanol-Water. Wiss. Z. TH Leuna-Merseburg 1966, 8, 195. (13) Turner, W. E. S.; Bissett, C. C. The Solubilities of Alkali Haloids in Methyl, Ethyl, Propyl, and iso-Amyl Alcohols. J. Chem. Soc. London 1913, 103, 1904. (14) Simmons, J. P.; Freimuth, H.; Russel, H. The Systems Lithium Chloride-Ethyl Alcohol and Lithium Bromide-Water-Ethyl Alcohol. J. Am. Chem. Soc. 1936, 58, 1692. (15) Vlasov, Yu. G.; Antonov, P. P.; Anokhin, V. N. The System LiClLiBr-Ethanol at 25 °C. Zh. Prikl. Khim. 1975, 48, 1155. (16) Plyushchev, V. E.; Shakhno, I. V.; Komissarova, L. N.; Nadezhdina, G. V. Study of Solubility of Alkali Metal Chlorides in Some Aliphatic Alcohols. Tr. Mosk. Inst. Tonkoj Khim. Tekhnol. 1958, 7, 45. ReceiVed for reView January 5, 2010 ReVised manuscript receiVed March 15, 2010 Accepted March 24, 2010 IE100027C
