Brazilian Journal

of Chemical ISSN 0104-6632 Printed in Brazil Engineering www.abeq.org.br/bjche

Vol. 31, No. 02, pp. 561 - 570, April - June, 2014 dx.doi.org/10.1590/0104-6632.20140312s00002760

SOLUBILITY MEASUREMENT AND SOLID-LIQUID EQUILIBRIUM MODEL FOR THE TERNARY SYSTEM MgBr2 + MgSO4 + H2O AT 288.15 K

Dan Li1*, Bo Huang2, Lingzong Meng3,4 and Qinhong Xu3

1School of Media Communications, Phone/Fax: +86-539-8766336, Linyi University, Linyi 276000, P. R. China. E-mail: [email protected] 2Linyi Institute of Product Quality Supervision, Inspection and Testing, Linyi, 276000, P. R. China. 3School of Chemistry and Chemical Engineering, Linyi University, Linyi, 276000, P. R. China. 4Tianjin Key Laboratory of Marine Resources and Chemistry, Tianjin University of Science and Technology, Tianjin, 300457, P. R. China.

(Submitted: July 12, 2013 ; Revised: August 28, 2013 ; Accepted: September 23, 2013)

Abstract - The of magnesium minerals and the refractive index of the ternary system MgBr2 + MgSO4 + H2O at 288.15 K were investigated using an isothermal dissolution method. It was found that there are two invariant points in the diagram and the solubility isotherm of this ternary system consists of three branches, corresponding to equilibrium crystallization of Epsomite (MgSO4·7H2O, Eps), hexahydrite (MgSO4·6H2O, Hex) and magnesium bromide hexahydrate (MgBr2·6H2O, Mb). Neither solid nor double salts were found. The refractive indices calculated from empirical equation are in good agreement with the experimental data. Combining the results from solubility measurements with the single-salt parameters for MgBr2 and MgSO4, and the mixed ion-interaction parameter θ , the parameter ψ at 288.15 K was Br,SO4 Mg,Br,SO4 fitted using the Pitzer theory and Harvie-Weare (HW) approach. In addition, the average equilibrium constants of the stable equilibrium solids at 288.15 K were obtained by a method using the activity product constant. A chemical model, which combined the Pitzer parameters and the average equilibrium constants, was constructed to calculate the solid + liquid equilibria in the ternary system MgBr2 + MgSO4 + H2O at 288.15 K. The model agreed well with the equilibrium solubility data for the magnesium salts. Keywords: Phase equilibrium; ; Magnesium bromide; Solubility; Pitzer model.

INTRODUCTION and mineral systems. Therefore, investigations of the thermodynamics and the phase diagram of bromine- Bromine-containing brine is widely distributed in containing systems at different are valu- the Qinghai-Tibet Plateau and the Sichuan basin of able, because this investigation provides the theoreti- China (Zheng et al., 1988; Sang et al., 2011). These cal foundation and scientific guidance for the com- brines belong mostly to the complex system Li + Na prehensive and effective exploitation of bromine + K + Mg (Ca) + Cl +SO4 + Br + borate + H2O. The resources. phase equilibria and phase diagrams are the theoreti- The phase equilibria of some three-, four- or five- cal foundations for exploiting the brine resources and component bromine-containing systems have been describing the geochemical behaviour of the brine reported (Sang et al., 2011; Cui et al., 2013; Christov,

*To whom correspondence should be addressed

562 Dan Li, Bo Huang, Lingzong Meng and Qinhong Xu

2012a, 2012b and 2012c; Christov, 2011). The ternary predictions demonstrated that the Pitzer and HW system MgBr2 + MgSO4 + H2O has previously been model could be expanded to calculate the solubility investigated at 273.15, 298.15 and 308.15 K since of bromine minerals in complex brines accurately. the 1960s, but the solubility data and the reports of However, studies modelling the ternary system the corresponding equilibrium solid phases are not MgBr2 + MgSO4 + H2O at 288.15 K are still lacking complete. In the literature (Howard and Silcock, in the literature. 1979), both MgSO4·7H2O and MgSO4·6H2O occur at In this study, the and the relevant re- 273.15 K, but no invariant points saturated with fractive indices of the ternary system MgBr2 + MgSO4·7H2O + MgSO4·6H2O have been reported yet. MgSO4 + H2O at 288.15 K were determined. Addi- More complicatedly, at 298.15 K, there are five crys- tionally, a chemical model incorporating Pitzer theory tallisation fields, corresponding to MgSO4·7H2O, and the HW approach was constructed to calculate MgSO4·6H2O, MgSO4·5H2O, MgSO4·H2O and the solid + liquid equilibrium in the ternary system. MgBr2·6H2O, but there is only one invariant point saturated with MgBr2·6H2O + MgSO4·H2O. At 308.15 K, there are only two crystallisation fields EXPERIMENTAL SECTION (MgBr2·6H2O and MgSO4·7H2O). All the data for the system MgBr2 + MgSO4 + H2O system at 273.15, Apparatus and Reagents 298.15 and 308.15 K need to be investigated again. Recently, we reported a detailed study on the system A thermostatic shaker (model THZ-82, Jintan at 323.15 K (Meng et al., 2013). It was found that Yitong Electronics Co., Ltd., China) was used to pre- there are four crystallisation fields MgSO4·6H2O, pare the in its equilibrium state. The tem- MgSO4·4H2O, MgSO4·H2O and MgBr2·6H2O. As it perature in the thermostatic bath was maintained at a is known, the in the Qinghai-Tibet constant temperature of (288.15 ± 0.1) K, and the de- Plateau in summer is nearly 288.15 K, but the ter- tailed experimental procedures were described previ- nary system at 288.15 K has not been reported in the ously (Meng et al., 2011). The solid phase minerals literature to date. were determined using Schreinemaker’s method (Song, Computer models, which can predict the behav- 1991) and an X-ray diffractometer (D8 Advance, iour of solutions and solid + liquid equilibria with Bruker Ltd., Germany). All the analytical grade chemi- close to experimental accuracy, have wide applica- cals, which were obtained from the Chengdu Aike bility. The current theory for aqueous solutions of Chemical Reagent Plant or the Shanghai Xinbao Fine electrolytes is reliable for calculating the solubilities Chemical Plant, were recrystallised before use, includ- of a salt-water system. There are also studies that ing magnesium bromide hexahydrate (MgBr2·6H2O, embrace currently available theories of electrolyte with mass fraction 0.98) and epsomite (MgSO4·7H2O, solution chemistry to simulate the physicochemical 0.99). Doubly deionised water (DDW) with a processes of solutes, and these studies are able to conductivity of less than 1.2×10-4 S·m-1 at 298.15 K predict thermodynamic behaviour. These widely was used to prepare the series of artificial, synthe- used models are important for studying the geo- sised brines and for the chemical analysis. chemistry of natural waters and mineral deposits, as well as for solving environmental problems and op- Experimental Methods timising industrial processes (Christov, 2012a). Pitzer and co-workers developed an ion-interaction The isothermal dissolution method was used in model and published a series of papers (Pitzer 1973; this study. A series of artificially synthesised brines Pitzer 1992), which gave a set of expressions for the were mixed from the appropriate quantities of salts osmotic coefficients of a solution and the mean ac- and DDW, which were calculated according to the tivity coefficients of electrolytes in solution. Single composition at phase equilibrium, and then were ion activity coefficients, which are more convenient loaded into clean polyethylene bottles and capped to use in solubility calculations, are given in the tightly. The bottles were placed in a thermostatic Harvie and Weare modelling approach (Harvie and rotary shaker, which was maintained at a constant Weare, 1980; Harvie et al, 1984). On the basis of the temperature of (288.15 ± 0.1) K and a rotation speed of Pitzer approach and its extension the Harvie-Weare 120 rpm to accelerate equilibration of the complexes. (HW) model (denoted hereafter as the Pitzer and HW The rotary system rested for 2 h before sampling, model), the solubilities of the systems containing and a 1.0 mL sample of the clarified solution was bromine were predicted (Meng, 2013; Christov, taken from each polyethylene bottle with a pipette at 2012a, 2012b and 2012c; Christov, 2011), and these regular intervals and then used for a refractive index

Brazilian Journal of Chemical Engineering

Solubility Measurement and Solid-Liquid Equilibrium Model for the Ternary System MgBr2 + MgSO4 + H2O AT 288.15 K 563 measurement. If the difference between two refrac- in the stable equilibrium solutions and the wet resi- tive index measurements was within ± 0.0002, then due are expressed as mass percentage. Based on the the equilibrium state was achieved. Otherwise, the experimental data (Table 1), the stable phase dia- solution was rotated continually until the equilibrium gram of the system at 288.15 K was plotted, as state was achieved. Generally, it took approximately shown in Figure 1. 20 days to reach the equilibrium state. Twice, at different times, a sample of approximately 5.0 mL Table 1: Solubility data of the ternary system was taken, weighed and diluted to a final volume of MgBr2 + MgSO4 + H2O at 288.15 K. 250 mL using a volumetric flask filled with DDW. Then, a quantitative analysis was performed. If the No. Liquid phase, Wet residue, Equilibrium difference between the of the two 102wa 102w solid phaseb liquid phases was within ± 0.3% in mass fraction, MgBr2 MgSO4 MgBr2 MgSO4 1, A 0.00 24.60 —c — Eps then the solubility of this equilibrium point, which 2 4.37 20.10 1.82 36.34 Eps was the average of the experimental data, was ob- 3 7.38 17.22 3.31 35.75 Eps tained. Meanwhile, some of the wet residue was 4 10.15 14.99 4.51 35.14 Eps separated from the solution, and one portion of the 5 13.34 12.19 5.78 34.31 Eps wet residue was weighed and dissolved to a final 6 17.59 9.67 7.32 32.81 Eps 7 21.62 7.24 8.85 32.24 Eps volume of 250 mL using a volumetric flask filled 8 24.06 6.06 10.77 30.3 Eps with DDW for chemical analysis by Schreinemaker's 9 27.51 4.43 12.46 29.45 Eps wet residue method (Song, 1991) (i.e., the solid 10 29.50 3.83 13.58 28.55 Eps phase mineral point lies on the extension of the line 11 32.82 2.69 15.08 27.95 Eps 12 35.71 2.55 16.43 28.09 Eps on the phase diagram through the composition points 13 38.25 2.31 18.13 27.33 Eps of the liquid phase and the wet residue). Another 14 39.61 2.14 18.69 26.70 Eps portion was dried, ground into powder and analysed 15, E 43.33 1.87 20.47 27.40 Eps + Hex by X-ray diffraction. The solid phase could then be 16 44.52 1.72 22.34 27.21 Hex identified. 17 45.60 1.57 27.67 21.34 Hex 18 46.89 1.29 28.05 21.76 Hex 19, F 49.10 1.03 28.41 24.12 Hex + Mb Analytical Methods 20, B 49.70 0.00 — — Mb a b w, mass percentage; Eps, MgSO4·7H2O; Hex, MgSO4·6H2O; Mb, c The concentrations of the liquid phases and the MgBr2·6H2O; —, means not detected. wet residues were analysed with chemical analytical methods. The of Mg2+ was determined Table 2: Experimental and calculated refractive with a precision of within ± 0.3% in mass fraction by index data of the ternary system at 288.15 K. titration with an EDTA standard solution in the pres- - No. Exp. value Calc. value Relative ence of the indicator Eriochrome Black-T. The Br a concentration was measured by titration with a stan- error/% 1, A 1.3792 1.3777 0.11 dard solution of Hg(NO3)2 using a mixed indicator of 2 1.3824 1.3798 0.19 diphenylcarbazone and bromophenol blue (precision: 3 1.3852 1.3817 0.25 2- ± 0.3%) (Zhai et al., 1988). The SO4 concentration 4 1.3862 1.3842 0.14 was calculated by subtraction via charge balance. An 5 1.3881 1.3867 0.10 6 1.3905 1.3922 -0.12 Abbe refractometer (model WZS-1) was used to 7 1.3951 1.3974 -0.17 measure the refractive index (nD) with an uncertainty 8 1.3979 1.4011 -0.23 of ± 0.0001. Through control with a thermostat, all 9 1.4034 1.4064 -0.22 measurements were conducted at the desired tem- 10 1.4068 1.4102 -0.24 perature of (288.15 ± 0.1) K. 11 1.4122 1.4161 -0.28 12 1.4199 1.4229 -0.21 13 1.4273 1.4287 -0.1 14 1.4309 1.4317 -0.06 RESULTS AND DISCUSSION 15, E 1.4428 1.4404 0.16 16 1.4465 1.4431 0.23 17 1.4508 1.4475 0.23 Solubility and Refractive Index Data 18 1.4542 1.4502 0.27 19, F 1.4593 1.4554 0.27 The solubility and the refractive index data of the 20, B 1.4549 1.4549 0.00 system MgBr2 + MgSO4 + H2O at 288.15 K are pre- a Relative error = (experiment value - calculated value)/ experiment sented in Tables 1 and 2. The mineral concentrations value.

Brazilian Journal of Chemical Engineering Vol. 31, No. 02, pp. 561 - 570, April - June, 2014

564 Dan Li, Bo Huang, Lingzong Meng and Qinhong Xu

100 1.48

1.46 F 80 B 1.44 E 2

10 60 D × n )

4 1.42

MgSO 40 ( 1.40 w A Eps 20 1.38 Hex A Mb F 1.36 0 0 102030405060 0 20406080100E B 2 H O 2 w( MgBr2) ×10 2 w( MgBr 2) ×10 Figure 2: Refractive index data versus composition of

Figure 1: Stable phase diagram of the ternary system the ternary system MgBr2 + MgSO4 + H2O at 288.15 K. ▲, experimental data; —, experimental curve. MgBr2 + MgSO4 + H2O at 288.15 K; ●, experimental solubility data; —, experimental stable isotherm curve. Comparison of the Ternary System at Different Temperatures The stable phase diagram of the system at 288.15 K consists of three stable crystallisation fields corre- The comparison of the solubility data for the ter- sponding to Epsomite (MgSO4·7H2O, Eps), hexahy- nary system MgBr2 + MgSO4 + H2O at 273.15, drite (MgSO4·6H2O, Hex) and magnesium bromide 298.15, 308.15 K (Howard and Silcock, 1979), hexahydrate (MgBr2·6H2O, Mb). Points E and F are 323.15 K (Meng et al., 2013) and 288.15 K (this the invariant points, which are saturated with Eps + study) is shown in Figure 3. The patterns for the Hex and Hex + Mb. Curves AE, EF and FB are the solubility curves at different temperatures are simi- univariant curves, which are saturated with a single lar. The areas of the crystallised regions of magne- salt (Eps, Hex or, Mb). The Eps crystallisation area sium bromide and magnesium sulphate decrease as is relatively large; whereas, the Hex crystallisation the temperature increases, and these decreases indi- area is relatively small. The smallest crystallisation cate that the solubilities are positively correlated area is that of Mb. These results indicate that magne- with temperature. The crystallisation zone for hy- sium sulphate is relatively easy to saturate and that drated magnesium bromide was considerably smaller magnesium bromide has a high solubility. Neither than that for hydrated magnesium sulphate. With this solid solutions nor double salts were found. Because information, the of magnesium bromide and it is known that the phase diagram of the MgCl2 + magnesium sulphate salts can be separated and puri- MgSO4 + H2O system at 288.15 K (Howard and fied. There is one crystallisation field for hydrated Silcock, 1979) also consists of crystallisation fields magnesium bromide; whereas, there are many crys- corresponding to Eps, Hex and MgCl2·6H2O (Bis), it tallisation fields for hydrated magnesium sulphate. is shown that magnesium bromide reacts with mag- Moreover, it is worthwhile to note that the crystalli- nesium sulphate in solution similarly to magnesium sation fields corresponding to hydrated magnesium chloride. sulphate differ greatly with temperature. Hydrated Using the refractive index data shown in Table 2, magnesium sulphate MgSO4·7H2O occurs when the the relationships of the solutions’ refractive index to temperatures are in the lower range (273.15, 288.15, the concentration of magnesium bromide were plot- 298.15 and 308.15 K); MgSO4·6H2O occurs at all ted in Figure 2. It is seen that the refractive indices of five temperatures; whereas MgSO4·4H2O and the solutions increase with the increase in magne- MgSO4·H2O occur at relatively higher temperatures sium bromide concentration, reach their maximum (308.15, 323.15 K). The crystallisation water for the values at invariant point F (Hex + Mb), and then hydrated magnesium sulphate decreases as the tem- decrease. Using the diagram (Figure 2), the refrac- perature increases. It shows that the water sorption tive index could be used to roughly estimate the decreases as the temperature increases and the sta- magnesium bromide concentration in the ternary bility field of different hydrates depends on tem- system. perature. This crystallisation information for the

Brazilian Journal of Chemical Engineering

Solubility Measurement and Solid-Liquid Equilibrium Model for the Ternary System MgBr2 + MgSO4 + H2O AT 288.15 K 565 various minerals at different temperatures is impor- where n0 = 1.333390, the refractive index of water at tant for the recovery of hydrated magnesium sul- 288.15 K. Bi is the coefficients of each possible phate. Because of the lack of invariant points and of component i in the system. Wi is the salt of i in the some crystallisation fields in the system at 273.15, solution in mass fraction. For the calculation of the 298.15 and 308.15 K, the differences between the dia- refractive index of MgBr2 and MgSO4, coefficients Bi grams at the five temperatures were not developed were set to be 0.001725, 0.001328, respectively. The further. calculated results and experimental values are pre- sented for comparison in Table 2, and the maximum 40 relative deviations for all of the calculated results are 273.15 K less than 0.28%. The reasons for the relative errors in A 288.15 K the data in Table 2 are multifarious and include the 30 298.15 K error in the solubility data caused by temperature 2

10 308.15 K deviations, the uncertainty in the concentration, and ×

) the uncertainty in the measurements of refractive 4 323.15 K 20 index. The calculated values agree well with the experimental data, and this agreement shows that the MgSO

( coefficients Bi obtained in this work are reliable and w can be used for more complicated systems contain- 10 ing MgBr2 and MgSO4 at 288.15 K.

0 0 102030405060B SOLUBILITY PREDICTION H O 2 2 w( MgBr 2) ×10 Figure 3: Comparison of the phase diagrams of the Ion-Interaction Model ternary system MgBr2 + MgSO4 + H2O at different temperatures; ○, 273.15 K [11];▲, 288.15 K [11]; , The Pitzer theory and HW approach, which in- 298.15 K; ●, 308.15 K [11]; , 323.15 K. corporate concentration dependent equations show- ing the specific interactions of the solutes (Pitzer Empirical Equation for the Refractive Index 1973; Pitzer 1992; Harvie and Weare, 1980; Harvie et al, 1984), were used for the aqueous solutions in Song and Du (Song and Du, 1986) have given an this study. Additional work has centred on develop- expression, which has been widely used in brine ing variable temperature models below 298.15 K, systems, for the refractive index and solubility data. which have increased applicability to a number of The following empirical equation was used to cal- diverse geochemical systems (Spencer et al., 1990; culate the refractive index: Marion and Farren, 1999). The following equations, which are described in the literature (Pitzer 1992), are the main expressions related to the solubility lnnn / =∑ B × W (1) ()0 ii calculation of this model.

Ø3/2 1/2 Ø ()(ø1−= 2/∑∑∑mAIicacaca )[ −/1 ( + bI )+ mmBZC ( + ) i ca (2) ØØ +∑∑mmcc''()()]Φ+ cc ∑ m a Ψ cca '+ ∑∑ mm aa '' Φ+ aa ∑ m c Ψ caa ' cc<<' a' aa c

2 lnγ+M = zFM∑∑∑ m a() 2 B Ma ++Φ+Ψ ZC Ma m c( 2 Mc m a Mca ) aca (3) +∑∑mmaa''Ψ+ Maa z M ∑∑ mmC caca a

Brazilian Journal of Chemical Engineering Vol. 31, No. 02, pp. 561 - 570, April - June, 2014

566 Dan Li, Bo Huang, Lingzong Meng and Qinhong Xu

2 lnγ=X zFX +∑∑∑ m c() 2 B cX + ZC cX+ m a( 2 Φ Xa + m c Ψ cXa ) cac (4) +∑∑mmcc'Ψ+ ccX' z X ∑∑ mmC caca c

In expressions (2) to (4), M, C and C′ represent the same sign, and ψcc′ a represents the interactions cations, X, A and A′ represent anions, and NC and NA among the three ions, in which the sign of the third refer to the number of cations and anions, respec- ion is different from the first two ions. By combining tively. Additionally, mi and γi represent the concen- −1 the Pitzer parameters and the equilibrium constants tration (mol·kg ) and the of the of single salts, a chemical model could be con- ions, respectively, Zi refers to the valence of the ions, structed to calculate the solid + liquid equilibrium in and ø refers to the permeability coefficient. The the ternary MgBr2 + MgSO4 + H2O system at 288.15 other symbols in Eqs. (3) to (5), for example, F, C, K from Eqs. (2)-(8). Z, AØ, Ψ, Φ, BØ, and B, are all described in the refer- ences (Harvie and Weare, 1980; Harvie et al, 1984). Model Parameterization -For a hydrated salt, MXּ HO, the solubil υυυMX02 The Debye–Hückel parameter Aø = 0.385646 at ity (Ksp) for the dissolution reaction at a definite temperature and pressure is 288.15 K was obtained from the literature (Spencer expressed as follows: et al., 1990). The Pitzer binary parameters for MgBr2, and the mixing parameters θ were cal- Br,SO4 MX⋅υHXOM =υZZMX+ +υ − culated from the temperature-dependent equations υυM X 0 2 MX (5) presented in the literature (Christov, 2011; Christov, +υ0H2O 2012b). The Pitzer binary parameters for MgSO4 can be gotten from the literature (Spencer et al., 1990;

Marion and Farren, 1999), but the parameter β(2) for lnKmlnm sp=υ ln(( γ))n +υ γ +υ l α (6) MMMXXX0w MgSO4 is not mentioned in the literature (Spencer et al., 1990). Therefore, the parameters for MgSO4 The activity of water is related to the osmotic co- used in this study were calculated using the literature efficient ø, by the equation (Marion and Farren, 1999). The solubility data for the ternary system MgBr2 + MgSO4 + H2O in this study were used to fit the mixing parameters lnα=−wW øM ∑mi (7) Ψ via a multiple linear regression procedure. Mg,, Br SO4 -1 where Mw is the molar mass of water (kg·mol ), and All the parameters used in the prediction are pre- the sum covers all the solute species. The activity sented in Table 3. According to the parameters and coefficients γi, and the osmotic coefficients ø can be the measured solubilities of the ternary system in this calculated using the Pitzer and HW model. work, the equilibrium constants of the minerals in the ternary system at 288.15 K were fitted for each 1 stable solution by a method using the activity prod- γγ×γ= (ννννMXMX )()+ (8) uct constant. For MgBr2·6H2O at 288.15 K, the ± MX lnKsp is 11.6742, which is very close to the data in the literature (Christov, 2011; Meng, 2013). For The mean activity coefficients γ±, which are a MgSO4·7H2O, the lnKsp calculated using the pure function of the activity coefficients γM and γX in electrolyte parameters and the solubility data in our Equation (8), can also be calculated using the Pitzer study is -4.7194, which is very close to the data in theory and HW approach. the literature (Marion and Farren, 1999), but the According to the Pitzer theory and HW approach, lnKsp for magnesium sulfate hydrate at the other the activity and osmotic coefficients are parametric points in the solubility isotherm are very different. (0) (1) (2) Ø (0) (1) functions of β , β , β , C , θcc′ and ψcc′a; β , β , The main reason may be that the parameters for (2) Ø β , and C are the parameters of a single salt; θcc′ MgBr2 and MgSO4 do not match. Another reason represents the interaction between the two ions with may be the deviation caused by the parameter fitting.

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Solubility Measurement and Solid-Liquid Equilibrium Model for the Ternary System MgBr2 + MgSO4 + H2O AT 288.15 K 567

Therefore, the average equilibrium constants ration at 288.15 K using Equation (8). In (lnKaver) of equilibrium solid salts were used to cal- Figure 4(a), the mean activity coefficients of magne- culate the solubilities in this study. These average sium bromide increase with increasing concentra- equilibrium constants (lnKaver) and uncertainties for tions of magnesium bromide. The γ± values first de- the equilibrium solid salts of MgSO4·7H2O, crease with concentration to a wide minimum at low MgSO4·6H2O are presented in Table 4. to moderate concentration, and an additional increase in molality leads to a sharp increase up to the equi- Table 3: Single-salt and mixing ion-interaction librium precipitation of the corresponding solids. parameters of the systems at 288.15 K. The trend for the curve at 288.15 K is similar to that for the curve at 323.15 K, but the activity coeffi- Parameters Value Reference cients in bromide electrolyte systems at 288.15 K are (0) β (MgBr2) 0.409524 Christov, 2011 smaller than those for systems at 323.15 K (Meng et (1) β (MgBr2) 1.945165 Christov, 2011 (ø) al., 2013). This result represents another step that C (MgBr2) 0.005198 Christov, 2011 (0) validates the present parameters for the bromide β (MgSO4) 0.109518 Marion and Farren, 1999 (1) systems presented in Table 3. Compared with the β (MgSO4) 3.004927 Marion and Farren, 1999 (2) curve in Figure 4(a), the curve in Figure 4(b) shows β (MgSO4) 0.725033 Marion and Farren, 1999 (ø) C (MgSO4) 0.067418 Marion and Farren, 1999 the opposite trend. The γ± values of magnesium sul- θ Br,SO4 0.03 Christov, 2012b phate first decrease sharply with concentration and Ψ 0.138242 This work Mg,Br,SO4 then change relatively smoothly with concentration. The solubilities for the ternary system at 288.15 K Table 4: Values for the average equilibrium con- were also calculated using Eqs. (2)-(7) to validate the stants of the ternary system at 288.15 K. accuracy of the model. It should be noted that solutes below their saturation were fixed at their Species lnKsp Uncertainty experimental values and the saturated solubilities

MgBr2·6H2O 11.6742 ±0.0342 were calculated. The comparison of the calculated

MgSO4·7H2O -3.4955 ±0.6120 and the experimental phase diagrams of the ternary

MgSO4·6H2O 2.7152 ±0.3701 system is shown in Figure 5. The calculated phase diagram and the experimental phase diagram are Validation and Application of the Model found to be in good agreement. These results indi- cate that the model obtained in this work that com- In Figure 4, we calculated the mean activity coef- bines the Pitzer parameters and the equilibrium con- ficients of magnesium bromide and magnesium sul- stants is reliable and is capable of predicting equilib- phate in the solutions (γ± vs. molality) up to the satu- rium in the system studied.

60 100

(b) 4

2 (a)

50 80

40 60 Hex 30 40 20 Eps

20 10 mean activity coefficient of MgBr mean activity coefficient of MgSO of coefficient activity mean 0 0 0123456 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -1 -1 m( MgBr2) /( mol∙kg ) m( MgSO4) /( mol∙kg ) Figure 4: Mean activity (γ±) calculated from the model of magnesium bromide and magnesium sulphate in the MgBr2 + MgSO4 + H2O system at 288.15 K; ▲, calculated data; —, calculated curve; (a) MgBr2; (b) MgSO4.

Brazilian Journal of Chemical Engineering Vol. 31, No. 02, pp. 561 - 570, April - June, 2014

568 Dan Li, Bo Huang, Lingzong Meng and Qinhong Xu

30 Experimental data Calculaed data A

2 Eps 10

× 20 ) 4

MgSO Hex (

w 10

Mb E F 0 0 102030405060B H O 2 2 w( MgBr 2) ×10 Figure 5: Comparison of the experimental and calculated phase diagrams of the stable ternary system MgBr2 + MgSO4 + H2O at 288.15 K; ○, Experimental data;▲, calculated data; —, experimental isotherm curve; …, calculated isotherm curve; Eps, MgSO4·7H2O; Hex, MgSO4·6H2O; Mb, MgBr2·6H2O.

CONCLUSIONS ACKNOWLEDGEMENTS

The stable equilibria of the aqueous ternary sys- Financial support from the Foundation of Tianjin tem MgBr2 + MgSO4 + H2O were investigated at Key Laboratory of Marine Resources and Chemistry 288.15 K. The phase diagram and diagram of the at Tianjin University of Science & Technology variation in the refractive indices with composition (Gant. 201101) and the Science Foundation of Linyi were plotted for this system at 288.15 K. It was University (Grant. BS201005) are greatly acknowl- found that there are two three-salt cosaturated invari- edged. We also thank Prof. P.S. Song from the ant points, three univariant solubility isotherms, and Qinghai Institute of Salt Lakes for his kind help. three stable crystallisation fields in the ternary sys- tem. Neither solid solutions nor double salts are found. The refractive indices of the solution are NOMENCLATURE positively correlated with the concentration of mag- nesium bromide, with the maximum value occurring AØ Debye–Hückel parameter at point F (Hex + Mb). No significant differences are BØ parametric functions of found among the diagrams of the ternary system at Pitzer parameter different temperatures; however, the crystallisation B parametric functions of fields are very different, especially the fields for Pitzer parameter hydrated magnesium sulphate. The empirical equa- B' parametric functions of tions were used to calculate the refractive indices; Pitzer parameter the coefficients have been fitted, and the calculated CØ single-salt Pitzer values for the refractive index are in good agreement parameter with the experimental data. C parametric functions of The parameter ψ at 288.15 K was fitted Mg,Br,SO4 Pitzer parameter γ using the measured solubility data in this study, and f parametric functions of the average equilibrium constants for stable equilib- Pitzer parameter ' rium solids at 288.15 K were obtained with a method g(x), g (x) parametric functions of using the activity product constant. Based on Pitzer Pitzer parameter theory and the HW approach, a new chemical model, I mol/kg including the Pitzer parameters and the equilibrium Ksp solubility equilibrium constants, was constructed for the ternary system at constant 288.15 K. The model gave very good agreement with m molality mol/kg the equilibrium solubility data of the magnesium M,C cation salts. n neutral molecules

Brazilian Journal of Chemical Engineering

Solubility Measurement and Solid-Liquid Equilibrium Model for the Ternary System MgBr2 + MgSO4 + H2O AT 288.15 K 569

X, A anion K2B4O7−H2O and KCl−KBr−K2SO4−H2O at 373 z valence of ions K. J. Chem. Eng. Data, 58, 477-481 (2013). Z parametric functions of the Harvie, C. E., Møller, N. and Weare, J. H., The pre- molality of species i diction of mineral solubilities in nature waters: The Na-K-Mg- Ca-H-SO4-OH-HCO3-CO3-H2O Greek Letters system to high ionic strengths at 25 °C. Geochim. Cosmochim. Acta, 48, 723-751 (1984). Harvie, C. E., and Weare, J. H., The prediction of αw water activity β(0) single-salt Pitzer parameter mineral solubilties in nature waters: The Na-K- β(1) single-salt Pitzer parameter Mg- Cl-SO4-H2O system from zero to high con- β(2) single-salt Pitzer parameter centration at 25 °C. Geochim. Cosmochim. Acta, υ number of ions in the 44, 981-997 (1980). molecule Howard, D. and Silcock, L., Solubilities of Inorganic γ activity coefficient of the and Organic Compounds. Pergamon Press, New ions York (1979). ø osmotic coefficients Marion, G. M. and Farren, R. E., Mineral solubilities θ mixing ion interaction Pitzer in the Na-K Mg-Ca-Cl-SO4-H2O system: A re- parameter evaluation of the sulfate chemistry in the Ψ mixing ion interaction Pitzer Spencer-Moller-Weare model. Geochim. Cosmo- parameter chim. Acta, 63, 1305-1318 (1999). Meng, L. Z., Deng, T. L., Guo, Y. F., Li, D. and Yang, L., Measurement and thermodynamic model study REFERENCES on solid + liquid equilibria and physicochemical properties of the ternary system MgBr2 + MgSO4 Christov, C., Study of bromide salts solubility in the + H2O at 323.15 K. Fluid Phase Equilib., 342, 88- 94 (2013). (m1KBr + m2CaBr2)(aq) system at T = 323.15 K. Thermodynamic model of solution behaviour and Meng, L. Z., Li, D., Guo, Y. F. and Deng, T. L., Stable phase equilibrium of the aqueous quaternary system (solid + liquid) equilibria in the ternaries (m1KBr (MgCl2 + MgSO4 + MgB6O10 + H2O) at 323.15 K. + m2CaBr2) (aq), and (m1MgBr2 + m2CaBr2)(aq), and in the quinary (Na + K + Mg + Ca + Br + J. Chem. Eng. Data, 56, 5060-5065 (2011). Pitzer, K. S., Thermodynamics of electrolytes I: H O) systems to high concentration and tem- 2 Theoretical general equation. J. Phys. Chem., 77, perature. J. Chem. Thermodyn., 55, 7-22 (2012). 268-277 (1973). Christov, C., Temperature variable chemical model Pitzer, K. S., Activity coefficients in electrolyte so- of bromide–sulfate solution interaction parame- lutions. 2nd Ed., CRC Press, London (1992). ters and solid–liquid equilibria in the Na–K–Ca–Br– Sang, S. H., Sun, M. L., Li, H., Zhang, X. and SO –H O system. CALPHAD, 36, 71-81 (2012). 4 2 Zhang, K. J., A study on equilibria of the quater- Christov, C., Study of bromide salts solubility in the + + - 2- nary system Na ,K //Br ,SO4 –H2O at 323 K. Chin. (m1NaBr + m2MgBr2)(aq) system at T = 323.15 J. Inorg. Chem., 27, 845-849 (2011). K. Thermodynamic model of solution behavior Song, P. S., Studies on the application of the wet and (solid + liquid) equilibria in the (Na + K + Mg residues method in phase equilibrium for the salt- + Br + H2O) system to high concentration and water systems. J. Salt Lake Res., (China), 1, 42- temperature. J. Chem. Thermodyn., 47, 335-340 46 (1991). (2012). Song, P. S., and Du, X. H., Phase equilibrium and Christov, C., Isopiestic investigation of the osmotic properties of the saturated solution in the quater- coefficients of MgBr (aq) and study of bromide 2 nary system Li2B4O7–Li2SO4–LiCl–H2O at 25 °C. salts solubility in the (m1KBr + m2MgBr2)(aq) Chin. Sci. Bull., (China), 3, 209-213 (1986). system at T = 323.15 K. Thermodynamic model Spencer, R. J., Moller, N., and Weare, J. H., The of solution behaviour and (solid + liquid) equilib- prediction of mineral solubilities in natural water: ria in the MgBr2(aq), and (m1KBr + m2MgBr2) A model for the Na-K-Ca- (aq) systems to high concentration and tempera- Mg- Cl-SO4-H2O system at temperature below ture. J. Chem. Thermodyn., 43, 344-353 (2011). 25 °C. Geochim. Cosmochim. Acta, 54, 575-590 Cui, R. Z., Sang, S. H., and Hu, Y. X., Solid−liquid (1990). equilibria in the quaternary systems KCl−KBr− Zhai, Z. X., Cheng, Z. B., Hu, F., Wu, G. L., Xiao,

Brazilian Journal of Chemical Engineering Vol. 31, No. 02, pp. 561 - 570, April - June, 2014

570 Dan Li, Bo Huang, Lingzong Meng and Qinhong Xu

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