Thermodynamic study of the aqueous sodium

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The solubilities of (m1NaCl + m2CrCl3)(aq) and (m1KCl + m2CrCl3)(aq) where m denotes molality have been determined at T = 298.15K. In the sodium system, ...
J. Chem. Thermodynamics 35 (2003) 909–917 www.elsevier.com/locate/jct

Thermodynamic study of the aqueous sodium, potassium, and chromium chloride systems at the temperature 298.15 K Christomir Christov

*

Department of Chemistry, University of California, San Diego, La Jolla, CA 92093-0340, USA Received 27 August 2002; accepted 28 January 2003

Abstract The solubilities of (m1 NaCl þ m2 CrCl3 )(aq) and (m1 KCl þ m2 CrCl3 )(aq) where m denotes molality have been determined at T ¼ 298:15 K. In the sodium system, only the crystallization of the simple salts NaCl(s), and CrCl3  6H2 O(s) have been established. In the potassium system, in addition to the simple salts, a new double salt with composition 2KCl  CrCl3  H2 O also crystallizes from saturated ternary solutions. The ternary solutions have been simulated thermodynamically at T ¼ 298:15 K using the Pitzer model. The necessary thermodynamic functions (binary and ternary ion-interaction parameters, thermodynamic solubility products) have been calculated and the theoretical solubility isotherms plotted. A very good agreement is found between calculated and experimental solubility isotherms. The standard molar Gibbs energies of formation Dr G0m of solid phases crystallizing in the systems under consideration have been determined from theory. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Chromium chloride; Sodium chloride; Potassium chloride; Solubility diagram; Thermodynamic functions; Pitzer model

1. Introduction Investigations on solubilities in binary and multicomponent chromium solutions are of special practical interest especially when choosing optimum preparation conditions of chromium salts. Unfortunately, the experimental solubility data for chromium *

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chloride solutions are sparse. Olie [1] determined the binary solubility of chromium chloride hexahydrate at T ¼ 298:15 K as a function of equilibrium time. Serebrennikova et al. [2] studied the solubility in ðm1 NaCl þ m2 CrCl3 Þ(aq) at T ¼ ð293:15 and 353:15 KÞ and established the crystallization of simple salts {NaCl(s), and CrCl3  6H2 OðsÞ} only (simple eutonic type solubility isotherm). There are no solubility data in the literature on the ternary ðm1 KCl þ m2 CrCl3 Þ(aq) solutions. A comparative analysis of the ternary aqueous chloride mixtures of 1-1 and 3-1 electrolytes of the type ðm1 MCl þ m2 MeCl3 Þ(aq), and sulfate mixtures of 1-2 and 3-2 electrolytes of the type ðm1 M2 SO4 þ m2 Me2 ðSO4 Þ3 Þ(aq), where M denotes Na, or K, Me denotes Al, or Cr, or Fe, and m denotes molality, shows that sodium and potassium systems exhibit differences. From saturated ternary (m1 M2 SO4 þ m2 Me2 ðSO4 Þ3 ) (aq) aluminum and chromium sulfate solutions crystallize sodium and potassium alums {M2 SO4  Al2 ðSO4 Þ3  24H2 O} and chromium alums {M2 SO4  Cr2 ðSO4 Þ3  24H2 O}, respectively [3,4]. All three sodium chloride (m1 NaCl þ m2 MeCl3 )(aq) systems are of a simple eutonic type [2,5]. The double salt 2KCl  FeCl3  H2 O(s) crystallizes in (m1 KCl þ m2 FeCl3 Þ(aq) system [5] while the corresponding aluminum (m1 KCl þ m2 AlCl3 )(aq) system is of a simple eutonic type {KCl(s) and AlCl3  6H2 O(s) crystallization only} [6]. A double salt with 2-1-1 composition {2NH4 Cl  FeCl3  H2 O(s)} crystallizes also from saturated ternary (m1 NH4 Cl þ m2 FeCl3 ÞðaqÞ [5]. Obviously, the crystallization or the absence of it from the corresponding sodium or potassium chloride solution of a double salt and its stoichiometric composition depend on the ion radii of the cations (Mþ and Me3þ ). It is of interest to investigate (m1 KCl þ m2 CrCl3 )(aq) frðKþ Þ > rðNaþ Þ; rðFe3þ Þ > rðCr3þ Þ > rðAl3þ Þg [7] with a view to establishing the existence of the double salt 2KCl  CrCl3  H2 O(s) {analogous to 2KCl  FeCl3  H2 O(s)}. In the literature we have found no data on the thermodynamic simulation of multicomponent chromium chloride solutions. In previous studies [8,9] the Pitzer ioninteraction model has been used for the simulation of the ternary ðm1 MCl þ m2 M2 Cr2 O7 Þ(aq), and ðm1 M2 SO4 þ m2 M2 Cr2 O7 Þ(aq), and the quaternary ðm1 MCl þ m2 M2 SO4 þ m3 M2 Cr2 O7 Þ(aq) (M ¼ Na, or K) bichromate systems at T ¼ 298:15 K. The Pitzer model was also used for the thermodynamic simulation of the ternary chromate solutions ðm1 NaCl þ m2 Na2 CrO4 Þ(aq) and (m1 KCl þ m2 K2 CrO4 )(aq) [10]. It was shown that the Pitzer equations can be used to obtain an adequate description of the properties of solutions with the participation of chromate and bichromate salts. The basic Pitzer model has been successfully used for the thermodynamic simulation of the ternary [3] and quaternary [4] chromium sulfate solutions. The purpose of the present paper was a thermodynamic simulation, on the basis of the Pitzer model, of the ternary systems (m1 NaCl þ m2 CrCl3 )(aq) and (m1 KCl þ m2 CrCl3 )(aq) at T ¼ 298:15 K. The simulation was made in order to enable us to draw conclusions concerning the applicability of the Pitzer model for the simulation of multicomponent solutions with the participation of chromium chloride. 2. Experimental The initial osmotic coefficients data for CrCl3 (aq) solutions, which can be used for the determination of the Cr–Cl Pitzer binary interaction parameters, are available in

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the literature at T ¼ 298:15 K only [11–13]. Note that the ternary solubility data of Serebrennikova et al. [2] for (m1 NaCl þ m2 CrCl3 )(aq) are at T ¼ 293:15 K and T ¼ 353:15 K. For this reason, additional solubility experiments were performed at T ¼ 298:15 K. The solubilities of (m1 NaCl þ m2 CrCl3 )(aq) and (m1 KCl þ m2 CrCl3 )(aq) at T ¼ 298:15 K were studied by the method of isothermal decrease of supersaturation [10,14,15]. Different weight ratios of sodium or potassium chlorides and chromium chloride were used for each experiment. Crystal salts in excess of the T ¼ 298:15 K solubilities were mixed with water. The solution was heated until the solid phases were completely dissolved and then transferred to a double walled glass thermostat and cooled rapidly to the desired temperature of 298.15 K. Equilibrium was attained by continuous stirring for a period of 24 h. All the chemicals used were of analytical grade. The composition of the saturated solutions and the corresponding wet-solid phases were established by the following methods: the chromium ions were determined by iodometric titration [2,10,16,17]; the amount of chloride was found argentometrically by the Mohr method; potassium ions were determined amperometrically by titration with a solution of concentration 0.1 mol  dm3 of NafðC6 H5 Þ4 Bg [14]. The composition of the thoroughly suction-dried solid phases were established by SchreinemakersÕs graphical method [18]. The phase composition of solid phases crystallizing from saturated solutions was also studied using a SIEMENS X-ray diffractometer, type D5000 (Cu radiation), at a scanning rate of p/90 per minute [10]. The details of the X-ray diffractometry identification method have been presented in a previous study [19]. The results of the investigation on ðm1 NaCl þ m2 CrCl3 Þ(aq) and (m1 KCl þ m2 CrCl3 )(aq) at T ¼ 298:15 K are presented in tables 1 and 2 and figures 1 and 2. The experimental error of the solubility measurements is within the range (0.1 to 0.3) per cent. Each experimental result represents the arithmetical mean of three parallel determinations. For potassium solutions, the results obtained by using different analytical methods are in good agreement. Only the crystallization of the simple salts, NaCl(s) and CrCl3  6H2 O(s), have been established in the sodium system. For the potassium system, it has been established that, in addition to the simple salt, KCl(s) and CrCl3  6H2 O(s), a new double salt with composition 2KCl  CrCl3  H2 O TABLE 1 Experimentally determinated mass fraction solubilities w in (m1 NaCl þ m2 CrCl3 )(aq) at T ¼ 298:15 K 102  w(Liquid phase)

102  w(Wet-solid phase)

NaCl

CrCl3

NaCl

CrCl3

26.5 23.0 17.0 9.99 1.99 1.51 0.80 0

0 4.11 10.9 19.9 35.0 37.1 40.8 41.6

88.6 84.2 85.1 79.0 81.3 76.5 49.4 0

0 0.85 2.30 4.85 6.26 8.80 38.3 40.2

Solid phase

NaCl NaCl NaCl NaCl NaCl NaCl NaCl þ CrCl3  6H2 O CrCl3  6H2 O

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TABLE 2 Experimentally determinated mass fraction solubilities w in (m1 KCl þ m2 CrCl3 )(aq) at T ¼ 298:15 K 102  w(Liquid phase)

102  w(Wet-solid phase)

KCl

CrCl3

KCl

CrCl3

26.2 25.2 20.7 18.1 14.8 10.7 9.45 8.08 4.85 2.53 1.53 1.01 0

0 0.91 3.93 8.35 12.0 15.3 18.1 19.3 26.6 35.8 38.3 39.9 41.6

90.8 87.9 94.5 70.6 89.6 87.0 79.2 77.7 70.5 64.3 37.2 31.4 0

0 0.12 0.54 2.01 1.25 2.79 4.09 5.95 6.88 25.1 46.2 46.8 40.2

Solid phase

KCl KCl KCl KCl KCl KCl KCl KCl KCl KCl þ 2KCl  CrCl3  H2 O 2KCl  CrCl3  H2 O 2KCl  CrCl3  H2 O CrCl3  6H2 O

FIGURE 1. Solubilities m(sat) in (m1 NaCl þ m2 CrCl3 )(aq) at T ¼ 298:15 K: , present experimental data (table 1); –––, calculated values.

(2-1-1) also crystallizes from saturated ternary solutions. The existence of 2MCl  MeCl3  H2 O double salts depends on the occurrence of closest packing in their crystal structure. The differences established between the corresponding (m1 MCl þ m2 MeCl3 )(aq) systems show that the small ion radii of the univalent sodium frðNaþ Þg, and aluminum frðAl3þ Þg metal ions do not allow an arrangement close to the most dense one. For this reason, no double salts are formed from ðm1 NaCl þ m2 MeCl3 Þ(aq) and (m1 MCl þ m2 AlCl3 )(aq). The larger ionic radius of potassium frðKþ Þg, ferric frðFe3þ Þg, and chromium frðCr3þ )} cations is the reason for the crystallization of 2KCl  FeCl3  H2 O and 2KCl  CrCl3  H2 O double salts.

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FIGURE 2. Solubilities m(sat) in (m1 KCl þ m2 CrCl3 )(aq) at T ¼ 298:15 K: , present experimental data (table 2); –––, calculated values.

In the literature there is a disagreement with respect to the concentration of the saturated binary solution CrCl3 (aq). According to the data of Serebrennikova et al. [2] the solubility of chromium chloride hexahydrate increases with temperature from a mass fraction of 0.407 at T ¼ 293:15 K to a mass fraction of 0.543 at T ¼ 353:15 K. According to the results of Olie [1] the concentration of the saturated CrCl3 (aq) binary solution depends on the equilibrium time and varied at T ¼ 298:15 K between a mass fraction of 0.408 and 0.4355. In the present work a mass fraction chromium chloride hexahydrate solubility of 0.416 (tables 1 and 2) has been established.

3. Calculation of the solubility The solutions (m1 NaCl þ m2 CrCl3 )(aq) and (m1 KCl þ m2 CrCl3 )(aq) at T ¼ 298:15 K have been simulated using the Pitzer model [20,21] at T ¼ 298:15 K with the aim of calculating the solubility isotherms and determining the thermodynamic characteristics of the salts crystallizing from the saturated aqueous solutions. The Pitzer model allows the determination of the activity coefficients in saturated and unsaturated electrolyte solutions with an accuracy of (2 to 6) per cent [6,8,21]. The simulation has been performed as follows: determination of the Pitzer binary parameters bð0Þ ; bð1Þ , and C / taking into account the ionic interactions of two ions and three ions; determination of the Pitzer ternary parameters fh(MN) and w(MNX)} characterizing the interaction between two different ions of the same sign (MN) and the interaction between three ions (MNX, MMX, and NNX), respectively; and calculation of the solubility isotherms of the three-component solutions. The same scheme has been used to simulate other ternary [3,10,14,15] and multicomponent

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solutions [4,8,9,22] from which phases with a constant stoichiometric composition (simple or double salts) crystallize. The parameters of ionic interaction of the binary subsystems have been determined by many authors [22–24]. Since the calculation of the compositions of saturated ternary solutions was one of the main purposes of the simulation, the applicability of the binary parameters to high molality binary solutions up to saturation at the lowest value of the standard deviation r was a very important criterion for the choice of the binary parameters. The values of the Pitzer parameters for NaCl(aq) and KCl(aq) were taken from Harvie et al. [22]. Their applicability has been demonstrated by simulation of ternary and multicomponent solutions of various types [6,8,9,22]. The data on the dependence of osmotic coefficients / on molalities of binary CrCl3 (aq) fmðsatÞ ¼ 4:5 mol  kg1 g solutions are reported by Smith [11] fmðmaxÞ ¼ 1:4 mol  kg1 g, Robinson and Stokes [12] fmðmaxÞ ¼ 1:2 mol  kg1 g and by Mikulin [13]. The osmotic coefficient values of Mikulin are the same as those of Robinson and Stokes [12]. On the basis of the thermodynamic data recommended by Robinson and Stokes [12], Pitzer and Mayorga [23], and Kim and Frederick [24] we have calculated the binary parameters for CrCl3 (aq) fmðmaxÞ ¼ 1:2 mol  kg1 ; r ¼ 0:005, and mðmaxÞ ¼ 1:2 mol  kg1 ; r ¼ 0:0033, respectively} (see table 3). In order to enlarge the molality range of applicability, we have simulated again CrCl3 (aq), using data from Smith [11], and Robinson and Stokes [12]. The calculated values of the binary parameter presented in table 3 are valid upto the higher CrCl3 (aq) molality at a lower r value than those given by Pitzer and Mayorga [23]. The values of the binary interaction parameters calculated in this study are close to those presented by Pitzer and Mayorga [23]. The bð0Þ , and bð1Þ CrCl3 (aq) parameters are also close to the parameters presented in the literature for other 3-1 chlorides {see Christov [6] for AlCl3 (aq), and Kim and Frederick [24] for LaCl3 (aq), YCl3 (aq), and ScCl3 (aq)}. Using the parameters for CrCl3 (aq) the concentration dependence of the osmotic coefficients up to saturation of the solutions was calculated. The results obtained are presented, together with the experimental data available in literature, in figure 3. The results of the calculations are in very good agreement with TABLE 3 Pitzer binary parameters bð0Þ ; bð1Þ , and C / at T ¼ 298:15 K, molality m of the solution, and standard deviation (r) of the osmotic coefficients Solution

bð0Þ

bð1Þ

C/

m(max)

r

(mol  kg1 ) NaCl(aq)a KCl(aq)a CrCl3 ðaqÞb CrCl3 ðaqÞc CrCl3 ðaqÞd a

From reference [22]. From reference [24]. c From reference [23]. d This study. b

0.0765 0.04835 0.69081 0.7364 0.72234

0.2664 0.2122 2.7849 5.2553 5.5989

0.00127 )0.00084 )0.04390 )0.0451 )0.04141

1.2 1.2 1.4

0.003 0.005 0.003

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FIGURE 3. Osmotic coefficient ð/Þ of CrCl3 at T ¼ 298:15 K against molality m of CrCl3 (aq): , experimental data from reference [12]; D, experimental data from reference [11]; –––, calculated values using the parameters determined in this study (table 3).

the experimental data. On the basis of bð0Þ ; bð1Þ , and C / and the molality m(sat) of the saturated binary solutions the logarithm of the thermodynamic solubility product 0 0 ln Ksp for the solid phases was calculated (table 4). On the basis of ln Ksp values and using initial thermodynamic data of aqueous species [25,26] we calculated the standard molar Gibbs energy of formation Df G0m of simple salts crystallizing from saturated binary solutions (table 4). The Df G0m values obtained for halite and sylvite are compared with those presented in the literature [25]. The differences are within the error of the ion-interaction model. The ternary parameters have been calculated by using experimental solubility data obtained in this study (tables 1 and 2). The choice of the parameters is based TABLE 4 0 Thermodynamic properties of solid phases: thermodynamic solubility product, ln Ksp , standard molar Gibbs energy of synthesis reaction Dr G0m , and standard molar Gibbs energies of formation Df G0m at T ¼ 298:15 K and p0 ¼ 101325 Paa Species

m(sat)a

0 ln Ksp

(mol  kg1 ) H2 O Cl (aq) Naþ (aq) Kþ (aq) Cr3þ (aq) NaCl(cr) KCl(cr) CrCl3  6H2 O(cr) 2KCl  CrCl3  H2 O(cr) a

6.16 4.76 4.5

3.63 2.06 13.6 19.0

m(sat) is the molality of the saturated binary solutions. b From reference [26].

Dr G0m

Df G0m /(kJ  mol1 )

(kJ  mol1 )

Calc.

3.18

)384.13 )409.39 )1998.2 )1628.2

Reference [24] )237.129 )131.228 )261.905 )283.27 )215.476b )384.138 )409.14

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0 on the minimum deviation of the logarithm of the solubility product (ln Ksp ) for the whole crystallization curve of each component from its value for the saturated binary 0 solution [8–10]. In addition, the ln Ksp value for the double salt, 2KCl  CrCl3  H2 O, crystallizing in the ternary (m1 KCl þ m2 CrCl3 )(aq) solutions has to be constant along the whole crystallization branch of the double salts [14,15]. In calculating the ternary parameters, the unsymmetrical mixing terms E h and E h0 , were included according to reference [21]. In a previous study [3], the solutions (m1 Na2 SO4 þ m2 Cr2 ðSO4 Þ3 )(aq) and (m1 K2 SO4 þ m2 Cr2 ðSO4 Þ3 )(aq) have been simulated at T ¼ 298:15 K and the value h(Na,Cr) ¼ h(K,Cr) ¼ )0.07 was proposed. The h(Na,Cr) binary mixing parameter was tested also through solubility calculations in quaternary ðm1 Na2 SO4 þ m2 ðNH4 Þ2 SO4 þ m3 Cr2 ðSO4 Þ3 Þ(aq) [4]. Since the parameters h(Na,Cr), and h(K,Cr) take into account only the ionic interactions of the type Na–Cr, and K–Cr in ternary solutions, their values had to be constant for the chloride, and sulfate solutions. We have varied only the value of w(Na,Cr,Cl) and w(K,Cr,Cl) parameters and have obtained the best agreement with the experimental data at h(Na,Cr) ¼ )0.07 and w(Na,Cr,Cl) ¼ 0.01 for (m1 NaCl þ m2 CrCl3 )(aq), and h(K,Cr) ¼ )0.07 and w(K,Cr,Cl) ¼ )0.01 for ðm1 KCl þ 0 m2 CrCl3 Þ(aq). The value found for ln Ksp of the double salt is given in table 4. The solubility isotherms of the ternary solutions at T ¼ 298:15 K are calculated on the basis of the thermodynamic functions obtained. A method described in previous papers [8–10] has been used. The calculated and the experimental solubility isotherms are presented in figures 1 and 2. The agreement between the model predictions and experiments is good. The largest difference between the model and experiments occurs for the 2KCl  CrCl3  H2 O saturated solutions for which the model predicts a chromium chloride concentration that is about 5 per cent lower than the experimental value (see figure 2). The good agreement permits conclusion about the applicability of the thermodynamic approach used to obtain an adequate description of the properties of binary and ternary chromium chloride solutions. The good agreement between the model and experimental ternary solubilities indicates that the solution model bð0Þ , bð1Þ , and C / binary Cr–Cl parameters can be extrapolated from 1.4 mol  kg1 (upper osmotic coefficient data point of Smith [11]) to predict solubilities up to 4.5 mol  kg1 . In order to calculate the thermodynamic characteristics of the double salt crystallizing in the solutions, we have applied the scheme, used successfully in references [3,4,15]. The theoretical basis of the calculation method has been presented in a previous paper [15]. To calculate the standard molar Gibbs energy of reaction Dr G0m of the synthesis of the double salt from simple salts we have used the calculated activities of the components in their saturated binary solutions (table 4). Thus, for the synthesis reaction of the double salt 2KCl CrCl3  H2 O,

2KClðcrÞ þ CrCl3  6H2 OðcrÞ ¼ 2KCl  CrCl3  H2 OðcrÞ þ 5H2 OðlÞ;

ð1Þ

the change of the standard molar Gibbs energy is Dr G0m ¼ RT ½lnfað2; 1; 1Þg þ 5  lnfað0; 0; 1Þg  2  lnfað1; 0; 0Þg  lnfað0; 1; 6Þg ; ð2Þ

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where aðl1 ; l2 ; l3 ) is the activity of the salt l1 A1  l2 A2  l3 A3 in its saturated solution at T ¼ 298:15 K and lnfað0; 0; 1Þg ¼ 0, since the activity of pure water is 1 (A1 ; A2 , and A3 ¼ H2 O are the components in the solution). Using the calculated standard molar Gibbs energies of formation for the components of the synthesis reaction (1) (table 4) and the calculated Dr G0m value, the standard molar Gibbs energy of formation Df G0m of the double salt have been calculated. The Dr G0m and Df G0m values obtained are given in table 4. Acknowledgements This work was supported in part by the German Ministry of Education, Research and Technology. The author is grateful to Dr. St. Fischer for helpful comments on X-ray data. I wish to thank Dr. S. Velikova and K. Ivanova for help in the chemical analysis. References [1] J.Z. Olie, Annorg. Chem. 51 (1906) 29; in: W. Linke, Solubilities of Inorganic and Metal Organic Compounds, vol. 1, fourth edition, American Chemical Society, Washington, DC, 1958. [2] M. Serebrennikova, M. Volinko, E. Lobazevich, Russ. J. Appl. Chem. 32 (1959) 291–295. [3] C. Christov, CALPHAD 26 (2002) 85–94. [4] C. Christov, CALPHAD 26 (2002) 341–352. [5] W. Linke, Solubilities of Inorganic and Metal Organic Compounds, vol. 1, fourth ed., American Chemical Society, Washington, DC, 1958. [6] C. Christov, CALPHAD 25 (2001) 445–454. [7] R.D. Shannon, Acta Crystallogr. A 32 (1976) 751–756. [8] C. Christov, CALPHAD 22 (1998) 449–457. [9] C. Christov, CALPHAD 25 (2001) 11–17. [10] C. Christov, K. Ivanova, S. Velikova, S. Tanev, J. Chem. Thermodyn. 34 (2002) 987–994. [11] N.G. Smith, J. Am. Chem. Soc. 69 (1947) 91–93. [12] R. Robinson, R. Stokes, Trans. Faraday Soc. 45 (1949) 612–624. [13] G. Mikulin, Voprossy Fizicheskoi Khimii Electrolitov, Izd. Khimya, 1968. [14] C. Christov, J. Chem. Thermodyn. 26 (1994) 1071–1080. [15] D. Barkov, C. Christov, T. Ojkova, J. Chem. Thermodyn. 33 (2001) 1073–1080. [16] S. Shapiro, M. Shapiro, in: Analiticheskaya Khimiya, Vysshaya shkola, Moscow, 1971, 342 p. [17] C. Christov, S. Velikova, K. Ivanova, S. Tanev, Collect. Czech. Chem. Commun. 64 (1999) 595–599. [18] F. Schreinemakers, Z. Phys. Chem. 11 (1893) 75–109. [19] D. Barkov, C. Christov, T. Ojkova, J. Chem. Thermodyn., in press. [20] K. Pitzer, J. Phys. Chem. 77 (1973) 268–277. [21] K. Pitzer, J. Solution Chem. 4 (1975) 249–265. [22] C. Harvie, N. Moller, J. Weare, Geochim. Cosmochim. Acta 48 (1984) 723–751. [23] K. Pitzer, G. Mayorga, J. Phys. Chem. 77 (1973) 2300–2308. [24] H.T. Kim, J. Frederick, J. Chem. Eng. Data 33 (1988) 177–184. [25] D. Wagman, W. Evans, V. Parker, R. Schumm, I. Halow, S. Bailey, K. Churney, R. Nuttall, J. Phys. Chem. Ref. Data 11 (Suppl. 2) (1982). [26] R. Freier, Aqueous Solutions: Data for Inorganic and Organic Compounds, Verlag, Berlin, 1975.

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