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 solubility 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 phase 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 solutions 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; Phase diagram; 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 temperatures 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 solubilities 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 solution 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 temperature 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 concentrations 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,