Thermodynamic study of the Na-Cu-Cl-SO 4 -H 2 O system at the temperature K

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1 J. Chem. Thermodynamics 2, 32, doi:1.16/jcht Available online at on Thermodynamic study of the Na-Cu-Cl-SO 4 -H 2 O system at the temperature K Christomir Christov a Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria The molalities m of (m 1 CuCl 2 + m 2 CuSO 4 )(aq) have been investigated in saturated solutions at the temperature K by the physico-chemical analysis method. Only the crystallization of the simple salts CuCl 2.2H 2 O, and CuSO 4.5H 2 O have been established. The ternary solutions (m 1 NaCl + m 2 CuCl 2 )(aq), (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq), and (m 1 CuCl 2 + m 2 CuSO 4 )(aq) have been simulated thermodynamically at T = K using the Pitzer model. The ternary parameters of ionic interaction have been chosen on the basis of the compositions of saturated ternary solutions taking into account the unsymmetrical mixing terms. The calculated thermodynamic properties have been used for a thermodynamic study of the quaternary reciprocal system Na-Cu-Cl-SO 4 -H 2 O. A very good agreement is found between calculated and experimental solubility isotherms. c 2 Academic Press KEYWORDS: solubility diagram; thermodynamic functions; Pitzer model 1. Introduction The purpose of the present work is to study thermodynamically the quaternary reciprocal Na-Cu-Cl-SO 4 -H 2 O system on the basis of the Pitzer model. The necessary thermodynamic properties of the binary and ternary solutions have been calculated and the solubility isotherms plotted. Studies on the solubility diagrams of ternary and multicomponent solutions with the participation of sodium and copper chlorides and sulphates are of importance especially for the production of copper chloride and copper sulphate. This is why these solutions have been the subject of many experimental and thermodynamic investigations. Druzhinin and Kosyakina (1) and Schreinemakers and de Baat (2) have studied the solubilities of the quaternary solutions under consideration at T = K. However, their reported results differ substantially and the differences may be attributed to the different solid phases obtained by the authors during the investigation of the corresponding ternary subsystems. In their work on (m 1 NaCl + m 2 CuCl 2 )(aq) Druzhinin and Kosyakina (1) have established a crystallization field of the double salt NaCl.CuCl 2.2H 2 O, whereas Schreinemakers and a Current address: Department of Chemistry, University of California, San Diego, La Jolla, CA , U.S.A // $35./ c 2 Academic Press

2 286 C. Christov de Baat (2) have found only the fields of equilibrium crystallization of the corresponding simple salts NaCl and CuCl 2.2H 2 O. The results of Schreinemakers and de Baat (2) have been confirmed by Skripkin and Chernih. (3) While investigating the solubilities in (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq), Schreinemakers and de Baat (2) have obtained the crystallization of a double salt with the composition Na 2 SO 4.CuSO 4.2H 2 O. In a work on the same solutions, Druzhinin and Kosyakina (1) have reported, in addition to the above double salt, the crystallization field of solid solutions of the type Na 2 SO 4.CuSO 4.2H 2 O.nNa 2 SO 4. The data on the solid phases crystallizing in (m 1 CuCl 2 + m 2 CuSO 4 )(aq) also exhibit important differences. Schreinemakers (4) has found that the solubility isotherm contains crystallization fields of CuCl 2.2H 2 O and CuSO 4.5H 2 O. In addition to the above phases, Druzhinin and Kosyakina (1) have postulated the crystallization of two lower crystalline hydrates, namely CuSO 4.4H 2 O and CuSO 4.3H 2 O. Nevertheless, the compositions of the saturated ternary solutions are very close to those obtained by Schreinemakers. (4) The above differences in the three ternary solutions lead to significant differences in the quaternary system under consideration. According to Schreinemakers and de Baat, (2) the phase diagram contains crystallization fields of NaCl, Na 2 SO 4.1H 2 O, CuCl 2.2H 2 O, CuSO 4.5H 2 O, Na 2 SO 4, and Na 2 SO 4.CuSO 4.2H 2 O, while Druzhinin and Kosyakina (1) have established the crystallization of four more solid phases: NaCl.CuCl 2.2H 2 O, CuSO 4.4H 2 O, CuSO 4.3H 2 O, and Na 2 SO 4.CuSO 4.2H 2 O.nH 2 O. Filippov et al. (5) and Filippov and Nohrin (6) have also determined the compositions of the saturated ternary solutions and the solid phases crystallizing from them in (m 1 NaCl + m 2 CuCl 2 )(aq) and (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq) at T = K. The solubility isotherms obtained by these authors are very close to those presented by Schreinemakers (4) and Schreinemakers and de Baat. (2) Downes and Pitzer (7) have used the isopiestic method to determine the dependence of the osmotic coefficients on the concentration of the binary CuCl 2 (aq) and CuSO 4 (aq) and the ternary (m 1 NaCl + m 2 CuCl 2 )(aq), (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq), and (m 1 CuCl 2 + m 2 CuSO 4 )(aq) solutions. On the basis of the obtained dependence, the authors have also determined the binary and ternary Pitzer ion-interaction parameters. Pabalan and Pitzer (8) have simulated (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq) and plotted the theoretical solubility isotherm. The results of the calculation are in very good agreement with the experimental data of Filippov and Nohrin. (6) The authors have used ternary parameters determined by Downes and Pitzer (7) without the unsymmetrical mixing terms E θ and E θ (reference 9) (θ Na,Cu =. and ψ Na,Cu,SO4 =.11; E θ = E θ =.). Simulating the solubility isotherm of (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq), Filippov and Nohrin (6) have found the following values: θ Na,Cu =.31 and ψ Na,Cu,SO4 =.125 for the ternary parameters. These values have been calculated on the basis of the isopiestic data proposed by Downes and Pitzer. (7) Filippov et al. (5) have performed additional isopiestic determinations of the osmotic coefficients for the ternary solutions (m 1 NaCl + m 2 CuCl 2 )(aq), thus broadening considerably the concentration range of their measurements. This has permitted them to calculate ternary parameters which also describe well unsaturated and saturated ternary solutions. The values proposed are θ Na,Cu =.644 and ψ Na,Cu,Cl =.358. In calculating θ MN and ψ MNX, Filippov

3 Study of the Na-Cu-Cl-SO 4 -H 2 O system 287 TABLE 1. Experimental mass fraction solubilities w in (m 1 CuCl 2 + m 2 CuSO 4 )(aq) at T = K 1 2.w (liquid phase) 1 2.w (wet solid phase) Solid phase CuCl 2 CuSO 4 CuCl 2 CuSO CuSO 4.5H 2 O CuSO 4.5H 2 O CuSO 4.5H 2 O+ CuCl 2.2H 2 O CuCl 2.2H 2 O and Nohrin (6) and Filippov et al. (5) did not take into consideration the unsymmetrical mixing terms E θ and E θ (reference 9). The ternary (m 1 NaCl + m 2 Na 2 SO 4 )(aq), being a subsystem of the multicomponent seawater system, has also been the subject of many experimental (1) and thermodynamic (11, 12) investigations at T = K. The inconsistent literature data on the type of solubility diagram for (m 1 CuCl 2 +m 2 CuSO 4 )(aq) have prompted additional experimental solubility investigations. 2. Experimental The solubilities of (m 1 CuCl 2 + m 2 CuSO 4 )(aq) at T = K were studied by the method of isothermal decrease of supersaturation. (13, 14) Equilibrium was attained by continuous stirring for a period of 24 h. The reagents used (CuCl 2.2H 2 O and CuSO 4.5H 2 O) were of analytical grade (mass fraction >.99). The compositions of the saturated solutions and the corresponding wet solid phases were determined by titrimetric methods. The concentration of Cu 2+ was established by direct complexometric titration at ph = 5.5 to 6. (ethanoate buffer) with xylenol orange as an indicator. (13) The concentration of Cl was determined argentometrically by the Mohr method. (14, 15) The compositions of the thoroughly suction-dried solid phases were established using Schreinemakers s graphic method. (14, 15) The results obtained are presented in table 1. The experimental error is within the range ±(.1 to.3) per cent. Each experimental result represents the arithmetic mean of three parallel determinations. Only the crystallization of the simple salts CuCl 2.2H 2 O and CuSO 4.5H 2 O have been established. The compositions of the saturated ternary solutions from which the solid phases crystallize are very close to those obtained by Schreinemakers. (4) 3. Solubility calculations During the first stage of our thermodynamic analysis we simulated the solubilities of the ternary (m 1 NaCl + m 2 CuCl 2 )(aq), (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq), and

4 288 C. Christov (m 1 CuCl 2 + m 2 CuSO 4 )(aq) solutions using the binary and ternary parameters determined by Downes and Pitzer. (7) Unfortunately, the calculated solubility isotherms of (m 1 NaCl + m 2 CuCl 2 )(aq) and (m 1 CuCl 2 + m 2 CuSO 4 )(aq) differed widely from those obtained experimentally most probably because the binary parameters for CuCl 2 (aq) and the ternary parameters were only valid up to concentrations considerably lower than those of the saturated solutions. The parameter θ Na,Cu takes into account the interactions of the type Na-Cu in the ternary solutions and its value should remain constant during the simulation of the chloride in (m 1 NaCl + m 2 CuCl 2 )(aq) and the sulphate in (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq). Filippov and Nohrin (6) and Filippov et al. (5) have proposed different values, which do not allow the simulation of the quaternary solutions. For this reason, we simulated again in the present investigation the ternary (m 1 NaCl+ m 2 CuCl 2 )(aq), (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq), and (m 1 CuCl 2 + m 2 CuSO 4 )(aq) solutions on the basis of the Pitzer model. The calculated thermodynamic properties were used to plot the phase diagram of the quaternary reciprocal Na-Cu-Cl-SO 4 -H 2 O system. The basic Pitzer model (9, 12) was successfully used for the solution of many theoretical and practical problems. It was shown that the ion-interaction model could be used to obtain a sufficiently exact description of the properties of saturated and unsaturated binary, (16, 17) ternary, (18, 19) and multicomponent (11, 12, 2) electrolyte solutions from which phases with a constant stoichiometric composition (simple and double salts) or solid solutions (21 23) crystallized. The systems were investigated using an approach which had already been applied to other ternary (18) and multicomponent (2, 24) solutions. This approach consists of: the determination of the Pitzer binary parameters (β (), β (1), β (2), C φ ) which take into account the interionic interactions of two ions and three ions; the determination of the Pitzer ternary parameters (θ MN and ψ MNX ) characterizing the interaction between two different ions of the same sign and the interaction between three ions, respectively; the calculation of the solubility isotherms of the three-component solutions; and the calculation of the solubility isotherm of the quaternary solutions. BINARY SOLUTIONS The ion-interaction parameters of the binary subsystems have been determined by many authors. Since the calculation of the compositions of saturated ternary and quaternary solutions was one of the main purposes of the simulation, the applicability of the binary parameters to binary solutions of high molalities up to saturation with the lowest value of the standard deviation σ of the osmotic coefficients was a very important criterion for the choice of the binary parameters. For NaCl(aq) we used the parameters of Filippov et al., (5) which were applied by the authors to the simulation of (m 1 NaCl + m 2 CuCl 2 )(aq). The values of the parameters for CuSO 4 (aq) were taken from Downes and Pitzer. (7) These parameters were utilized by Pabalan and Pitzer (8) in simulating the ternary (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq). We simulated Na 2 SO 4 (aq) using the parameters of Kim and Frederick (17) which are valid almost up to the saturated binary solution with a lower standard deviation (σ = ) than that resulting from the parameters proposed by Pitzer and Mayorga (16) (σ = ).

5 Study of the Na-Cu-Cl-SO 4 -H 2 O system 289 TABLE 2. Pitzer binary parameters β (), β (1), β (2), and C φ at T = K where σ is the standard deviation of the osmotic coefficients Solution β () β (1) β (2) C ϕ m max mol kg 1 σ Reference NaCl(aq) Na 2 SO 4 (aq) CuCl 2 (aq) a CuSO 4 (aq) a Calculated using indices α 1 = 2 and α 2 = 1. TABLE 3. Calculated values of ln Ksp o, where Ksp o is the thermodynamic solubility product, and m(sat) is the molality of the saturated binary solutions Species ln K o sp m(sat) mol kg 1 NaCl CuCl 2.2H 2 O Na 2 SO 4.1H 2 O CuSO 4.5H 2 O Na 2 SO a Na 2 SO 4.CuSO 4.2H 2 O 9.2 a From Harvie and Weare. (11) In a previous study, (13) new parameters for CuCl 2 (aq) were proposed. A significant broadening of the molality range (m max = 5.73 mol kg 1 ) over which the parameters were applicable with a low σ value was achieved. The applicability of these parameters was demonstrated by simulating a series of ternary solutions with the participation of Cu(II) chloride. (13, 25 27) The parameter values used in the present work are presented in table 2. On the basis of the values obtained for β (), β (1), β (2), C φ, and the molality m(sat) of the saturated binary solutions, we have calculated the logarithms of the thermodynamic solubility product ln Ksp o for the crystalline hydrates (table 3). The small differences between the ln Ksp o values obtained in this paper and those reported in the literature(6, 13) are mainly due to the different m(sat) values used in the calculations. TERNARY SOLUTIONS The ternary parameters have been calculated on the basis of experimental data on the solubility. The thermodynamic model was developed on the basis of the results of Filippov et al. (5) for (m 1 NaCl + m 2 CuCl 2 )(aq), and Filippov and Nohrin (6) for

6 29 C. Christov TABLE 4. Pitzer parameters θ MN and MNX for ternary solutions at T = K System θ MN MNX NaCl-CuCl 2 -H 2 O.9.36 Na 2 SO 4 -CuSO 4 -H 2 O.9.53 NaCl-Na 2 SO 4 -H 2 O a.2.14 CuCl 2 -CuSO 4 -H 2 O.2.1 a From Pitzer. (9) (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq). For (m 1 CuCl 2 + m 2 CuSO 4 )(aq) we have used our experimental data (table 1) and the results of Schreinemakers. (4) The parameters were chosen on the basis of a minimum deviation of the logarithm of the solubility product ln Ksp o for the whole crystallization curve for each component from its value for the saturated binary solution. (19) In addition, the ln Ksp o value for the double salt Na 2SO 4.CuSO 4.2H 2 O crystallizing in (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq) had to be constant along the whole crystallization branch of the double salt. (28) The chloride and the sulphate systems with the same cations (Na and Cu) have been simulated simultaneously with a view to preserving a constant value of the θ Na,Cu parameter. Pitzer (9) and Harvie and Weare (11) have proposed the value θ Cl,SO4 =.2 for the simulation of chloro-sulphate systems with a common cation. In the present study we have simulated (m 1 CuCl 2 + m 2 CuSO 4 )(aq), assuming θ Cl,SO4 =.2 and varying the values of the ψ Cu,Cl,SO4 parameter alone. In our calculations of the ternary parameters we have included the unsymmetrical mixing terms E θ and E θ according to Pitzer. (9) The value found for ln Ksp o of the double salt Na 2SO 4.CuSO 4.2H 2 O is given in table 3, while the ternary parameters are presented in table 4. The ln Ksp o value found in this study for Na 2 SO 4.CuSO 4.2H 2 O is equal to that of Filippov and Nohrin (6) (ln Ksp o = 9.2). To calculate the standard molar Gibbs energy of reaction r G o m for the synthesis of the double salt from simple salts we have used the calculated activities of the components in their saturated binary solutions (table 3). (13, 26) Thus, for the reaction of formation of the double salt Na 2 SO 4.CuSO 4.2H 2 O: Na 2 SO 4.1H 2 O(cr) + CuSO 4.5H 2 O(cr) = Na 2 SO 4.CuSO 4.2H 2 O(cr) + 13H 2 O(l), (1) the change in the standard molar Gibbs energy is r G o m = RT [ln{a(1, 1, 2)} + 13 ln{a(,, 1)} ln{a(1,, 1)} ln{a(, 1, 5)}], (2) where a(l 1, l 2, l 3 ) is the activity of the salt l 1 A 1.l 2 A 2.l 3 A 3 in its saturated solution at T = K and ln{a(,, 1)} =, since the activity of pure water is 1 (A 1, A 2, and A 3 = H 2 O are the components in the solution). A r G o m value of.45 kj mol 1 was obtained. Using the available (reference 8) standard molar Gibbs energies of formation for the components of the synthesis reaction of the double salt from simple salts

7 Study of the Na-Cu-Cl-SO 4 -H 2 O system CuCl 2.2H 2 O 5. m 2 /(mol kg 1 ) NaCl m 1 /(mol kg 1 ) FIGURE 1. Molality m 2 as a function of molality m 1 in (m 1 NaCl + m 2 CuCl 2 )(aq) at T = K., experimental data of Filippov et al.; (5), calculated values. {reaction (1)} and the calculated r G o m value, we have determined the standard molar Gibbs energy of formation f G o m of Na 2SO 4.CuSO 4.2H 2 O(cr). The value ( f G o m = kj mol 1 ) obtained in this work is very close to that calculated by Pabalan and Pitzer (8) ( f G o m = kj mol 1 ). The solubility isotherms of the ternary solutions at T = K were calculated on the basis of the thermodynamic properties obtained. A method described in previous works (13, 19) has been used. The calculated and experimental solubility isotherms are presented in figures 1 to 3. The calculated values agree very well with the experimental results obtained in this study and those in the literature. In addition, for (m 1 NaCl + m 2 CuCl 2 )(aq) and (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq) there is very good agreement between the solubility isotherms calculated in this work and those calculated by Filippov and Nohrin, (6) Filippov et al., (5) and Pabalan and Pitzer. (8) QUATERNARY SYSTEM The calculated binary and ternary ion-interaction parameters and the thermodynamic solubility products have been used to draw the theoretical solubility diagram of the quaternary Na-Cu-Cl-SO 4 -H 2 O system at T = K. The values of the ternary parameters for (m 1 NaCl + m 2 Na 2 SO 4 )(aq) (table 4) have been taken from Pitzer. (9) These parameters were used by Harvie and Weare (11) in their

8 292 C. Christov 1.6 CuSO 4.5H 2 O 1.4 m 2 /(mol kg 1 ) Na 2 SO 4.CuSO 4.2H 2 O.4.2 Na 2 SO 4.1H 2 O m 1 /(mol kg 1 ) FIGURE 2. Molality m 2 as a function of molality m 1 in (m 1 Na 2 SO 4 + m 2 CuSO 4 )(aq) at T = K., experimental data of Filippov and Nohrin; (6), calculated values. simulation of the multicomponent seawater system. Table 3 also shows the value of ln Ksp o for anhydrous sodium sulphate calculated on the basis of the data on the chemical potentials of Na 2 SO 4 and sodium and sulphate ions presented by Harvie and Weare. (11) The composition of the quaternary invariant points was calculated as that at which the chemical potential of three solid phases was constant. The results obtained are given in figure 4 as a horizontal anhydrous projection of the solubility diagram, presented as a quadrangular prism. (2, 24) Table 5 shows the molality of the calculated and experimentally determined (2) invariant points. The chloride concentration can be obtained from the charge balance. A good agreement has been achieved between the predicted and experimental values. The results obtained allow conclusions to be made on the applicability of (1) the approach used (on the basis of data concerning the compositions of the ternary solutions) for choosing the ternary parameters of the systems under consideration, and (2) the calculated and utilized thermodynamic properties (binary and ternary parameters of ionic interaction, thermodynamic solubility products) for a sufficiently exact description of the properties of the ternary and quaternary systems investigated. A relatively large difference between the calculated and experimental values is observed for the compositions of eutonic solutions from which (1) halite, thenardite, and Na 2 SO 4.CuSO 4.2H 2 O, and (2) thenardite, mirabilite, and Na 2 SO 4.CuSO 4.2H 2 O crystallize simultaneously. In addition to possible experimental error, a probable reason for these differences may be the ln Ksp o value for Na 2SO 4 (ln Ksp o =.662) used in this work.

9 Study of the Na-Cu-Cl-SO 4 -H 2 O system m 2 /(mol kg 1 ) CuSO 4.5H 2 O.4.2 CuCl 2.2H 2 O m 1 /(mol kg 1 ) FIGURE 3. Molality m 2 as a function of molality m 1 in (m 1 CuCl 2 + m 2 CuSO 4 )(aq) at T = K., Experimental data of Screinemakers; (4), Experimental data of Druzhinin and Kosyakina; (1), this work;, calculated values. TABLE 5. Experimental and calculated compositions of invariant points for the quaternary reciprocal system Na-Cu-Cl-SO 4 -H 2 O at T = K. Experimental values are from Schreinemakers and de Baat (2) m Na mol kg 1 m Cu mol kg 1 m SO4 mol kg 1 Solid phases Calculated CuCl 2.2H 2 O + CuSO 4.5H 2 O+ Experimental Na 2 SO 4.CuSO 4.2H 2 O Calculated CuCl 2.2H 2 O + NaCl+ Experimental Na 2 SO 4.CuSO 4.2H 2 O Calculated NaCl + Na 2 SO 4 + Experimental Na 2 SO 4.CuSO 4.2H 2 O Calculated Na 2 SO 4 + Na 2 SO 4.1H 2 O+ Experimental Na 2 SO 4.CuSO 4.2H 2 O

10 294 C. Christov CuCl 2 CuSO F 8 E D A C B NaCl Na 2 SO 4 FIGURE 4. Solubilities in the quaternary reciprocal system Na-Cu-Cl-SO 4 -H 2 O at T = K. The values are plotted in terms of the Janecke indices of the ions. Experimental data:, ternary invariant points {for (m 1 NaCl + m 2 Na 2 SO 4 )(aq), data of Linke (1) };, quaternary univariant points (Schreinemakers and de Baat (2) );, quaternary invariant points (Schreinemakers and de Baat (2) ). The curves represent values predicted using parameters (tables 2, 3, and 4) derived from binary and ternary solutions. The stability fields of the solid phases are labeled as: A, NaCl; B, Na 2 SO 4 ; C, Na 2 SO 4.1H 2 O; D, Na 2 SO 4.CuSO 4.2H 2 O; E, CuSO 4.5H 2 O; and F, CuCl 2.2H 2 O. In fact, as was mentioned above, this value is recalculated from the data on chemical potentials presented by Robie (29) and used by Harvie and Weare (11) in a simulation of a seawater system. However, in their fundamental study the latter authors have pointed out that, with respect to the chemical potentials (i.e. ln Ksp o ) of the solid phases, small deviations were also possible.these deviations are within the framework of the ion-interaction model accuracy. For instance, in his simulation Wood (3) has used a somewhat lower value (ln Ksp o =.691). According to the fg o m data presented by Pabalan and Pitzer,(12) ln Ksp o is equal to.72. On the basis of the chemical potential values proposed by Wagman, (31) we have calculated an even lower value (ln Ksp o =.734). However, in the present study we have used the ternary parameters θ Cl,SO4 and ψ Na,Cl,SO4, applied by Harvie and Weare (11) to the simulation of (m 1 NaCl + m 2 Na 2 SO 4 )(aq). For this reason, it

11 Study of the Na-Cu-Cl-SO 4 -H 2 O system 295 would not be correct to vary the ln K o sp value for Na 2SO 4 crystallizing in the above ternary solution. This work was supported by the Bulgarian Ministry of Science and Education, Project X Part of the experimental investigations was also supported by the German Ministry of Education, Research and Technology. REFERENCES 1. Druzhinin, I.; Kosyakina, O. Russ. J. Inorg. Chem. 1961, 6, Schreinemakers, F.; de Baat, W. Gedenboek J.M. van Bemmelen, Helder 191, Skripkin, M.; Chernih, L. Russ. J. Inorg. Chem. 1994, 39, Schreinemakers, F. Z. Physik. Chem. 191, 68, Filippov, V.; Charykov, N.; Fedorov, Y. Russ. J. Inorg. Chem. 1986, 31, Filippov, V.; Nokhrin, V. Russ. J. Inorg. Chem. 1985, 3, Downes, C.; Pitzer, K. J. Solution Chem. 1976, 5, Pabalan, R.; Pitzer, K. Mineral solubilities in electrolyte solutions. Activity Coefficients in Electrolyte Solutions: 2nd edition. Pitzer, K.: editor. CRC Press: 1991, Chap. 7, pp Pitzer, K. J. Solution Chem. 1975, 4, Linke, W. Solubilities of Inorganic and Metal Organic Compounds, Vols 1 and 2: 4th edition. American Chemical Society: Washington, D.C Harvie, C.; Weare, J. Geochim. Cosmochim. Acta 198, 44, Pabalan, R.; Pitzer, K. Geochim. Cosmochim. Acta 1987, 51, Christov, C. J. Chem. Thermodynamics 1994, 26, Christov, C. J. Chem. Thermodynamics 1995, 27, Balarew, C.; Christov, C.; Valuashko, V.; Petrenko, S. J. Solution Chem. 1993, 22, Pitzer, K.; Mayorga, G. J. Phys. Chem. 1973, 77, Kim, H.; Frederick, J. J. Chem. Eng. Data 1988, 33, Christov, C. J. Chem. Thermodynamics 1995, 27, Christov, C. CALPHAD 1996, 2, Christov, C. CALPHAD 1998, 22, Christov, C.; Peternko, S.; Balarew, C.; Valuashko, V. J. Solution Chem. 1994, 23, Christov, C. Coll. Czech. Chem. Commun. 1996, 61, Christov, C. J. Chem. Thermodynamics 1996, 28, Christov, C.; Peternko, S.; Balarew, C.; Valuashko, V. Monatsh. Chemie 1994, 125, Christov, C. Coll. Czech. Chem. Commun. 1996, 61, Christov, C.; Petrenko, S. Z. Physik. Chem. 1996, 194, Christov, C. J. Chem. Thermodynamics 1999, 31, Christov, C.; Balarew, C. J. Solution Chem. 1995, 24, Robie, R.; Hemmingway, B.; Fisher, J. Thermodynamic properties of minerals and related substances at K and 1 bar pressure and at high temperatures. U.S. Geol. Survey. Bull. 1998, 456 pp. 3. Wood, J. Geochim. Cosmochim. Acta 1975, 39, Wagman, D.; Evans, W.; Parker, V.; Schumm, R.; Halow, I.; Bayler, S.; Churney, K.; Nutall, R. The NBC tables of chemical thermodynamic properties. Selected values for inorganic and C 1 and C 2 organic substances in SI Units. J. Phys. Chem. Ref. Data 1982, 11, Suppl. 2, 392 pp. WA98/65 (Received 23 December 1998; in final form 23 June 1999)