Isopiestic Investigation of the Osmotic and Activity Coefficients of {yMgCl2+(1−y)MgSO4}(aq) and the Osmotic Coefficients of Na2SO4⋅MgSO4(aq) at 298.15 K

Miladinović, Jelena; Ninković, Rozalija; Todorović, Milica; Rard, Joseph A.

doi:10.1007/s10953-007-9238-y

Cited by 14 publications

(9 citation statements)

References 46 publications

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“…By using the binary and ternary parameters in Tables , , and , we calculated the solubility isotherms of the four ternary systems at 298.15 K (solid lines in Figures , , , and ), which show satisfactory agreement with the experimental data. In addition, we predicted the water activities in the four ternary systems using our model and compared them with the experimental values. − Figure shows that the predictions become more consistent with the experimental values when the mixing parameters are used in the calculation.…”

Section: Modelingmentioning

confidence: 75%

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Solubility Phase Diagram of the Quaternary System Li⁺, Mg²⁺//Cl^–, SO₄^2––H₂O at 298.15 K: Experimental Redetermination and Model Simulation

Zeng

Yao

et al. 2014

Ind. Eng. Chem. Res.

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Solubility isotherms for the ternary system MgCl 2 −MgSO 4 −H 2 O and the quaternary reciprocal system Li + , Mg 2+ //Cl − , SO 4 2− −H 2 O were determined at 298.15 K by an isothermal dissolution method. In the ternary phase diagram, there are six solubility branches corresponding to the solid phases MgSO 4 •nH 2 O (s) (n = 7, 6, 5, 4, 1) and MgCl 2 •6H 2 O (s) . In the quaternary equilibrium phase diagram, there are 16 solubility co-saturated lines corresponding to the solid phases MgSO 4 • nH 2 O (s) (n = 7, 6, 5, 4, 1), MgCl 2 •6H 2 O (s) , Li 2 SO 4 •H 2 O (s) , LiCl•MgCl 2 •7H 2 O (s) , and LiCl•H 2 O (s) . This report describes for the first time that the equilibrium solid phases MgSO 4 •H 2 O (s) and MgSO 4 •4H 2 O (s) have been found to exist in this quaternary system. However, the phase field of MgSO 4 •H 2 O (s) overlaps with the phase fields of MgSO 4 •4H 2 O (s) and MgSO 4 •5H 2 O (s) , which indicates that MgSO 4 •4H 2 O (s) and MgSO 4 •5H 2 O (s) are metastable phases; MgSO 4 •H 2 O (s) is a relatively more stable phase in both the ternary and quaternary systems. A Pitzer−Simonson−Clegg thermodynamic model was used to simulate the properties of the sub-binary and subternary systems and to predict the solubility phase diagram of the quaternary system. The results of the modeling are in reasonable agreement with the experimental data.

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Section: Modelingmentioning

confidence: 75%

“…Full-filled symbols: model values calculated by binary parameters and mixing parameters. Experimental values: ○ •, Zhang et al; 33 □ ■ , Song et al; 34 Δ ▲, Yao et al; 35 ◇ ⧫ , Rard et al36…”

mentioning

confidence: 99%

Solubility Phase Diagram of the Quaternary System Li⁺, Mg²⁺//Cl^–, SO₄^2––H₂O at 298.15 K: Experimental Redetermination and Model Simulation

Zeng

Yao

et al. 2014

Ind. Eng. Chem. Res.

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“…Pavićević et al [11] and Miladinović et al [12] analyzed isopiestic data for mixed electrolyte solutions with Scatchard's neutral-electrolyte model [3] with the single electrolyte osmotic coefficients being represented by Pitzer's standard ioninteraction model [9] or an extended (Archer-type) [17] ion-interaction model. The extended equation can be written as:…”

Section: Scatchard's Neutral-electrolyte Model Equationmentioning

confidence: 99%

“…2)) there is nothing inherent in his model that limits it to that choice of functional form for the binary solutions. In several studies [11,12], Pitzer's ion-interaction equations for the single electrolyte solutions have been combined with mixing terms from Scatchard's neutral-electrolyte model to yield very accurate representations of their isopiestic data for common-ion aqueous electrolyte mixtures. This hybrid model gave significantly more accurate fits than the corresponding ones with Pitzer's two-parameter mixing function.…”

Section: Introductionmentioning

confidence: 99%

Conversion of Parameters Among Variants of Scatchard’s Neutral-Electrolyte Model for Electrolyte Mixtures that Have Different Numbers of Mixing Terms

Rard

Wijesinghe

2008

J Solution Chem

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Various model equations are available for representing the excess Gibbs energy properties (osmotic and activity coefficients) of aqueous and other liquid mixedelectrolyte solutions. Scatchard's neutral-electrolyte model is among the simplest of these equations for ternary systems and contains terms that represent both symmetrical and asymmetric deviations from ideal mixing behavior when two single-electrolyte solutions are mixed in different proportions at constant ionic strengths. The usual form of this model allows from zero to six mixing parameters. In this report we present an analytical method for transforming the mixing parameters of neutral-electrolyte-type models with larger numbers of mixing parameters directly to those of models with fewer mixing parameters, without recourse to the source data used for evaluation of the original model that was applied by them to binary systems. It was found that the use of this approach with a constant ionic-strength cutoff of I ≤ 6.2 mol·kg -1 (the NaCl solubility limit) yielded parameters for the NaCl + SrCl 2 + H 2 O and NaCl + MgCl 2 + H 2 O systems that predicted osmotic coefficients φ in excellent agreement with those calculated using the same sets of parameters whose values were evaluated directly from the source data by least-squares, with root mean square differences of RMSE(φ) = 0.00006 to 0.00062 for the first system and RMSE(φ) = 0.00014 to 0.00042 for the second. If, however, the directly evaluated parameters were based on experimental data where the ionic strength cutoff varied with the ionic-strength fraction, i.e. because they were constrained by isopiestic ionic strengths (MgCl 2 + MgSO 4 + H 2 O) or solubility / oversaturation ionic strengths (NaCl + SrCl 2 + H 2 O and NaCl + MgCl 2 + H 2 O), then parameters converted by this approach assuming a 2 constant ionic-strength cutoff yield RMSE(φ) differences about an order of magnitude larger than the previous case. This indicates that for an accurate conversion of model parameters when the source model is constrained with variable ionic strength cutoffs, an extension of the parameter conversion method described herein will be required.However, when the source model parameters are evaluated at a constant ionic strength cuttoff, such as when source isopiestic data are constrained to ionic strengths at or below the solubility limit of the less soluble component, or are Emf measurements that are commonly made at constant ionic strengths, then our method yields accurate converted models.

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“…LiCl + MgSO 4 + H 2 O is a subsystem of the quaternary reciprocal system of Li + + Mg 2+ + Cl – + SO 4 2– + H 2 O, which occurs in many salt lake brines and ground brines of oil field and is important to the utilization of brine resources. The thermodynamic properties of the binary subsystems of LiCl + H 2 O, MgCl 2 + H 2 O, Li 2 SO 4 + H 2 O, and MgSO 4 + H 2 O have been extensively studied, and their models are available over a wide range of molality and temperature. − The ternary subsystems with a common ion like LiCl + MgCl 2 + H 2 O, Li 2 SO 4 + MgSO 4 + H 2 O, LiCl + Li 2 SO 4 + H 2 O, and MgCl 2 + MgSO 4 + H 2 O at T = 298.15 K have been measured. − Experimental redetermination and model simulation of the solubility phase diagram for the quaternary system of Li + , Mg 2+ //Cl – , SO 4 2– –H 2 O at 298.15 K and 323.15 K and the solubility phase diagram of the ternary system of MgCl 2 –MgSO 4 –H 2 O at (323.15 and 348.15) K have been reported. The thermodynamic properties and phase diagrams predicted by using the Pitzer ion interaction model for some seawater systems at various temperatures, , as well as for salt lake brine systems containing lithium at 298.15 K, have also been reported. − However, the studies for the salt lake brine system and its ternary subsystems containing lithium at a wide range of temperatures are lacking.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic Properties of LiCl + MgSO₄ + H₂O at Temperatures from 273.15 K to 373.15 K and Representation with Pitzer Ion-Interaction Model

Zhang

Yao

et al. 2016

J. Chem. Eng. Data

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Osmotic coefficients, water activities, and vapor pressures for the systems of LiCl + H 2 O, MgSO 4 + H 2 O, and LiCl + MgSO 4 + H 2 O over the ionic strength ranges from I = (0.5552 to 7.0004, 4.1028 to 22.6048, and 1.1982 to 20.5863) mol·kg −1 respectively at T = (273.15, 298.15, 323.15, 348.15, and 373.15) K were determined by the isopiestic method with an improved simple apparatus. Aqueous CaCl 2 solution was chosen as a reference standard. The measured osmotic coefficients for the binary solutions of LiCl + H 2 O and MgSO 4 + H 2 O were in agreement with those from the literature. The experimental data of osmotic coefficients for the ternary mixtures were represented by using the Pitzer ion-interaction model; the expressions for the temperature dependencies of the model parameters were given. The standard deviations of all the measured osmotic coefficient data from those calculated by using the model over the temperature range were estimated. A set of model equations of apparent molar enthalpy and excess heat capacity for the mixtures as functions of molality and temperature were obtained by differentiating the model equations of excess Gibbs free energy. The mean activity coefficients, relative apparent molar enthalpies, and excess heat capacities were calculated by using the corresponding equations. The effects of composition and temperature on these thermodynamic properties were discussed.

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Isopiestic Investigation of the Osmotic and Activity Coefficients of {yMgCl2+(1−y)MgSO4}(aq) and the Osmotic Coefficients of Na2SO4⋅MgSO4(aq) at 298.15 K

Cited by 14 publications

References 46 publications

Solubility Phase Diagram of the Quaternary System Li⁺, Mg²⁺//Cl^–, SO₄^2––H₂O at 298.15 K: Experimental Redetermination and Model Simulation

Solubility Phase Diagram of the Quaternary System Li⁺, Mg²⁺//Cl^–, SO₄^2––H₂O at 298.15 K: Experimental Redetermination and Model Simulation

Conversion of Parameters Among Variants of Scatchard’s Neutral-Electrolyte Model for Electrolyte Mixtures that Have Different Numbers of Mixing Terms

Thermodynamic Properties of LiCl + MgSO₄ + H₂O at Temperatures from 273.15 K to 373.15 K and Representation with Pitzer Ion-Interaction Model

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Isopiestic Investigation of the Osmotic and Activity Coefficients of {yMgCl2+(1−y)MgSO4}(aq) and the Osmotic Coefficients of Na2SO4⋅MgSO4(aq) at 298.15 K

Cited by 14 publications

References 46 publications

Solubility Phase Diagram of the Quaternary System Li+, Mg2+//Cl–, SO42––H2O at 298.15 K: Experimental Redetermination and Model Simulation

Solubility Phase Diagram of the Quaternary System Li+, Mg2+//Cl–, SO42––H2O at 298.15 K: Experimental Redetermination and Model Simulation

Conversion of Parameters Among Variants of Scatchard’s Neutral-Electrolyte Model for Electrolyte Mixtures that Have Different Numbers of Mixing Terms

Thermodynamic Properties of LiCl + MgSO4 + H2O at Temperatures from 273.15 K to 373.15 K and Representation with Pitzer Ion-Interaction Model

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Solubility Phase Diagram of the Quaternary System Li⁺, Mg²⁺//Cl^–, SO₄^2––H₂O at 298.15 K: Experimental Redetermination and Model Simulation

Solubility Phase Diagram of the Quaternary System Li⁺, Mg²⁺//Cl^–, SO₄^2––H₂O at 298.15 K: Experimental Redetermination and Model Simulation

Thermodynamic Properties of LiCl + MgSO₄ + H₂O at Temperatures from 273.15 K to 373.15 K and Representation with Pitzer Ion-Interaction Model