Modeling of the quaternary NaCl + KCl + CH3OH + H2O mixed electrolyte system: Binary and ternary mixing (ion + ion) and (ion + nonelectrolyte) interaction parameters

The purpose of this work is modeling of the quaternary system of mixed NaCl + KCl electrolyte in mixed CH₃OH + H₂O solvent, with different alcohol mass fractions by using particularly, the Pitzer (P) and Pitzer–Esteso (PE) equations and based on potentiometric measurement technique. The experimental data are obtained by different molal salt ratio r (r = m_NaCl/m_KCl = 100, 150, 200 and 250) in mixed solvent with different alcohol mass fractions x (x = 0.10, 0.20, 0.30, 0.40, and 0.50) in water. A galvanic cell is employed for collecting the potentiometric data by combining a Na⁺ glass membrane and Ag/AgCl electrodes and using different series of electrolyte solutions, at defined constant ionic strengths, with the molality ranging from 0.0005 up to 3.5 mol · kg⁻¹, at T = 298.15 ± 0.05 K of experiments. Comparison of the models shows that the modified Pitzer equation by Esteso (PE) present a better fit of the experimental data.     

Quaternary (liquid + liquid) equilibria for (water + 2-propanol + 1,1-dimethylethyl methyl ether + diisopropyl ether) at the temperature 298.15 K

(Liquid + liquid) equilibrium tie-lines were measured for one ternary system {x₁H₂O + x₂(CH₃)₂CHOH + (1 − x₁ − x₂)CH₃C(CH₃)₂OCH₃} and one quaternary system {x₁H₂O + x₂(CH₃)₂CHOH + x₃CH₃C(CH₃)₂OCH₃ + (1 − x₁ − x₂ − x₃)(CH₃)₂CHOCH(CH₃)₂} at T = 298.15 K and P^∘ = 101.3 kPa. The experimental (liquid + liquid) equilibrium results were satisfactorily correlated by modified and extended UNIQUAC models both with ternary and quaternary parameters in addition to binary ones.     

Vapour pressures,densities, and viscosities of the (water + lithium bromide + potassium acetate) system and (water + lithium bromide + sodium lactate) system

Measurements of thermophysical properties (vapour pressure, density, and viscosity) of the (water + lithium bromide + potassium acetate) system LiBr:CH₃COOK = 2:1 by mass ratio and the (water + lithium bromide + sodium lactate) system LiBr:CH₃CH(OH)COONa = 2:1 by mass ratio were measured. The system, a possible new working fluid for absorption heat pump, consists of absorbent (LiBr + CH₃COOK) or (LiBr + CH₃CH(OH)COONa) and refrigerant H₂O. The vapour pressures were measured in the ranges of temperature and absorbent concentration from T = (293.15 to 333.15) K and from mass fraction 0.20 to 0.50, densities and viscosities were measured from T = (293.15 to 323.15) K and from mass fraction 0.20 to 0.40. The experimental data were correlated with an Antoine-type equation. Densities and viscosities were measured in the same range of temperature and absorbent concentration as that of the vapour pressure. Regression equations for densities and viscosities were obtained with a minimum mean square error criterion.     

Thermodynamic study of the system (LiCl + LiNO3 + H2O)

The solubility of the binary system (LiNO₃ + H₂O) from T = 273.15 K to T = 333.15 K and solubility isotherms of the ternary system (LiCl + LiNO₃ + H₂O) were elaborately measured at T = 273.15 K and T = 323.15 K. These solubility data, as well as water activities in the binary systems from the literature, were treated by an empirically modified BET model. The isotherms of the ternary system (LiCl + LiNO₃ + H₂O) were reproduced and a complete phase diagram of the ternary system in the temperature range from 273.15 K to 323.15 K predicted. It is shown that the solubility data for the binary system (LiNO₃ + H₂O) measured in this work are slightly different from the literature data. Simulated results showed that the saturated salt solution of (2.8LiCl + LiNO₃) is in equilibrium with the stable solid phase LiNO₃(s) over the temperature range from 283.15 K to 323.15 K, other than the solid phases LiNO₃ · 3H₂O(s) and LiClH₂O(s) as reported by Iyoki et al. [S. Iwasaki, Y. Kuriyama. T. Uemura, J. Chem. Eng. Data 38 (1993) 396–398].     

Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (NaCl + KCl + MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) system, and optimized model parameters have been found. The (MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model was used for the molten salt phase, and the (MgCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) solid solution was modeled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. Finally, the (Na,K)(Mg,Ca,Mn,Fe,Co,Ni)Cl₃ and the (Na,K)₂(Mg,Mn,Fe,Co,Ni)Cl₄ solid solutions were modeled using the Compound Energy Formalism.     

Calorimetric investigation of mixing enthalpy of liquid (Co + Cu + Zr) alloys at T = 1873 K

The enthalpies of mixing of liquid (Co + Cu + Zr) alloys have been determined using the high-temperature isoperibolic calorimeter. The measurements have been performed along three sections (x_Co/x_Cu = 3/1, 1/1, 1/3) with x_Zr = 0 to 0.55 at T = 1873 K. Over the investigated composition range, the partial mixing enthalpies of zirconium are negative. The limiting partial enthalpies of mixing of undercooled liquid zirconium in liquid (Co + Cu) alloys are (−138 ± 18) kJ · mol⁻¹ (the section x_Co/x_Cu = 3/1), (−155 ± 10) kJ · mol⁻¹ (the section x_Co/x_Cu = 1/1), and (−130 ± 22) kJ · mol⁻¹ (the section x_Co/x_Cu = 1/3). The integral mixing enthalpies are sign-changing. The isenthalpic curves have been plotted on the Gibbs triangle. The main features of the composition dependence of the integral mixing enthalpy of liquid ternary alloys are defined by the pair (Co + Zr) and (Cu + Zr) interactions.     

(Liquid + solid) metastable equilibria in quinary system Li2CO3 + Na2CO3 + K2CO3 + Li2B4O7 + Na2B4O7 + K2B4O7 + H2O at T=288 K for Zhabuye salt lake

An experimental study on metastable equilibria at T=288 K in the quinary system Li₂CO₃ + Na₂CO₃ + K₂CO₃ + Li₂B₄O₇ + Na₂B₄O₇ + K₂B₄O₇ + H₂O was done by isothermal evaporation method. Metastable equilibrium solubilities and densities of the solution were determined experimentally. According to the experimental data, the metastable equilibrium phase diagram under the condition saturated with Li₂CO₃ was plotted, in which there are four invariant points; nine univariant curves; six fields of crystallization: K₂CO₃ · 3/2H₂O, K₂B₄O₇ · 5H₂O, Li₂B₂O₄ · 16H₂O, Na₂B₂O₄ · 8H₂O, Na₂CO₃ · 10H₂O, NaKCO₃ · 6H₂O. Some differences were found between the stable phase diagram at T=298 K and the metastable one at T=288 K.     

Salt effect on (liquid + liquid) equilibrium of (water + tert-butanol + 1-butanol) system: Experimental data and correlation

(Liquid + liquid) equilibrium data for the quaternary systems (water + tert-butanol + 1-butanol + KBr) and (water + tert-butanol + 1-butanol + MgCl₂) were experimentally determined at T = 293.15 K and T = 313.15 K. For mixtures with KBr, the overall salt concentrations were 5 and 10 mass percent; for mixtures with MgCl₂, the overall salt concentrations were 2 and 5 mass percent. The experimental results were used to estimate molecular interaction parameters for the NRTL activity coefficient model, using the Simplex minimization method and a concentration-based objective function. The correlation results are extremely satisfactory, with deviations in phase compositions below 1.7%.     

Equilibrium solubility of sodium 2-naphthalenesulfonate in binary (sodium chloride + water), (sodium sulfate + water), and (ethanol + water) solvent mixtures at temperatures from (278.15 to 323.15) K

The equilibrium solubility of sodium 2-naphthalenesulfonate in binary (sodium chloride + water), (sodium sulfate + water), and (ethanol + water) solvent mixtures was measured at elevated temperatures from (278.15 to 323.15) K using a steady-state method. With increasing temperatures, the solubility increases in aqueous solvent mixtures. The results of these results were regressed by a modified Apelblat equation. The dissolution entropy and enthalpy determined using the method of the least-squares and the change of Gibbs free energy calculated with the values of Δ_diffS^o and Δ_diffH^o at T = 278.15 K.     

(Liquid + liquid) equilibria of the (water + butyric acid + dodecanol) ternary system

(Liquid + liquid) equilibrium (LLE) data for the (water + butyric acid + dodecanol) ternary system have been determined experimentally at T = (298.2, 308.2 and 318.2) K. Complete phase diagrams were obtained by determining binodal curves and tie lines. The reliability of the experimental tie lines was confirmed by using the Othmer–Tobias correlation. The UNIFAC method was used to predict the phase equilibrium in the ternary system using the interaction parameters determined from experimental data of CH₃, CH₂, COOH, OH and H₂O functional groups. Distribution coefficients and separation factors were evaluated for the immiscibility region.     

(Liquid + liquid) equilibria for ternary mixtures of (alkane + benzene + [EMpy] [ESO4]) at several temperatures and atmospheric pressure

In this work, the separation of benzene from aliphatic hydrocarbons (hexane, or heptane) is investigated by extraction with 1-ethyl-3-methylpyridinium ethylsulphate ionic liquid, [EMpy][ESO₄]. (Liquid + liquid) equilibria (LLE) data are determined for the ternary systems: {hexane (1) + benzene (2) + [EMpy][ESO₄] (3)} at T = (283.15, 293.15, 298.15, and 303.15) K and {heptane (1) + benzene (2) + [EMpy][ESO₄] (3)} at T = (283.15 and 298.15) K and atmospheric pressure. The selectivity and distribution coefficient, derived from the tie line data, were used to determine whether the ionic liquid is a good solvent for the extraction of aromatic from aliphatic compounds. The consistency of the tie line data was ascertained by applying the Othmer–Tobias and Hand equations. The experimental results for the ternary systems were well correlated with the NRTL equation. A study of the temperature effect and the influence of the chain length of the alkanes were realized. The results obtained were compared with other ionic liquids. There are no literature data for the mixtures discussed in this paper.     

(Solid + solute) phase equilibria in aqueous solution. XIII. Thermodynamic properties of hydrozincite and predominance diagrams for (Zn2 + + H2O + CO2)

The thermodynamic properties ofZn₅(OH)₆(CO₃)₂ , hydrozincite, have been determined by performing solubility and d.s.c. measurements. The solubility constant in aqueous NaClO₄media has been measured at temperatures ranging from 288.15 K to 338.15 K at constant ionic strength (I =  1.00 mol · kg ^− 1). Additionally, the dependence of the solubility constant on the ionic strength has been investigated up to I =  3.00 mol · kg ^− 1NaClO₄at T =  298.15 K. The standard molar heat capacity C_{p, m}^ofunction fromT =  318.15 K to T =  418.15 K, as well as the heat of decomposition of hydrozincite, have been obtained from d.s.c. measurements. All experimental results have been simultaneously evaluated by means of the optimization routine of ChemSage yielding an internally consistent set of thermodynamic data (T =  298.15 K): solubility constant log ^* K_{ps 0}⁰ =  (9.0  ±  0.1), standard molar Gibbs energy of formationΔ_fG_m^o {Zn₅(OH)₆(CO₃)₂ }  =  ( − 3164.6  ±  3.0)kJ · mol ^− 1, standard molar enthalpy of formation Δ_fH_m^o{Zn₅(OH)₆(CO₃)₂ }  =  ( − 3584  ±  15)kJ · mol ^− 1, standard molar entropy S_m^o{Zn₅(OH)₆(CO₃)₂ }  =  (436  ±  50)J · mol ^− 1· K ^− 1and C_p,m^o / (J · mol ^− 1· K ^− 1)  =  (119  ±  11)  +  (0.834  ±  0.033)T / K. A three-dimensional predominance diagram is introduced which allows a comprehensive thermodynamic interpretation of phase relations in(Zn^2 +  +  H₂O  +  CO₂) . The axes of this phase diagram correspond to the potential quantities: temperature, partial pressure of carbon dioxide and pH of the aqueous solution. Moreover, it is shown how the stoichiometric composition{n(CO₃) / n(Zn)} of the solid compoundsZnCO₃ and Zn₅(OH)₆(CO₃)₂can be checked by thermodynamically analysing the measured solubility data.     

On oxoacidic properties and solubilities of beryllium and magnesium oxides in molten (CsCs + KCl + NaCl) eutectic at T = 783 K

Reactions of Be²⁺ and Mg²⁺ with O^2– in molten eutectic mixture (CsCs + KCl + NaCl) (0.455:0.245:0.30) at T = 783 K were studied by a potentiometric method using Pt(O₂)|ZrO₂(Y₂O₃) indicator electrode. Addition of O^2– ions to the melt containing Mg²⁺ results in precipitation of MgO (pK_s,MgO = 11.89 ± 0.3, molality) whereas interaction of Be²⁺ with O^2– is accompanied with sequential formation of Be₂O²⁺ (pK = 15.68 ± 0.5, molality) and precipitation of BeO (pK_s,BeO = 9.62 ± 0.3, molality). On the basis of the obtained and known data pK_s,MgO–T⁻¹ dependence in molten (CsCs + KCl + NaCl) eutectic is constructed. The slope of the said dependence in T/K = (from 583 to 1073) range is in good agreement with the value predicted by the Shreder equation, that extends the range of use of the Shreder equation for predictions of metal oxide solubilities in molten halides.     

(Liquid + liquid) equilibrium of (NaClO4 + PEG 4000 + H2O) ternary system at different temperatures

Phase diagram and (liquid + liquid) equilibrium (LLE) results for {NaClO₄ + polyethylene glycol 4000 (PEG 4000) + H₂O} have been determined experimentally at T = (288.15, 298.15, and 308.15) K. The Chen-NRTL, modified Wilson and UNIQUAC models were used to correlate the values for the experimental tie-lines. The results show that the quality of fitting is better with the modified Wilson model.     

Study of bromide salts solubility in the (m1NaBr + m2MgBr2)(aq) system at T = 323.15 K. Thermodynamic model of solution behavior and (solid + liquid) equilibria in the (Na + K + Mg + Br + H2O) system to high concentration and temperature

The bromide minerals solubility in the mixed system (m₁NaBr + m₂MgBr₂)(aq) have been investigated at T = 323.15 K by the physico-chemical analysis method. The equilibrium crystallization of NaBr·2H₂O(cr), NaBr(cr), and MgBr₂·6H₂O(cr) has been established. The solubility-measurements results obtained have been combined with all other experimental equilibrium solubility data available in literature at T = (273.15 and 298.15) K to construct a chemical model that calculates (solid + liquid) equilibria in the mixed system (m₁NaBr + m₂MgBr₂)(aq). The solubility modeling approach based on fundamental Pitzer specific interaction equations is employed. The model gives a very good agreement with bromide salts equilibrium solubility data. Temperature extrapolation of the mixed system model provides reasonable mineral solubility at high temperature (up to 100 °C). This model expands the previously published temperature variable sodium–potassium–bromide and potassium–magnesium–bromide models by evaluating sodium–magnesium mixing parameters. The resulting model for quaternary system (Na + K + Mg + Br + H₂O) is validated by comparing solubility predictions with those given in literature, and not used in the parameterization process. Limitations of the mixed solution models due to data insufficiencies at high temperature are discussed.     

(Liquid + liquid) equilibrium of (NaNO3 + PEG 4000 + H2O) ternary system at different temperatures

Phase diagram and (liquid + liquid) equilibrium (LLE) data for the (NaNO₃ + polyethylene glycol 4000 (PEG 4000) + H₂O) system have been determined experimentally at T = (288.15 and 308.15) K. The effects of temperature on the binodal curves and tie-lines have been studied and it was found that an increasing in temperature caused the expansion of two-phase region. The Chen-NRTL, modified Wilson and UNIQUAC models were used to correlate the experimental tie-line data. The results show that the quality of fitting is better with the UNIQUAC model.     

Phase behavior of ternary mixtures {aliphatic hydrocarbon + aromatic hydrocarbon + ionic liquid}: Experimental LLE data and their modeling by COSMO-RS

Separation of aromatic and aliphatic hydrocarbons is a complex process in the petrochemical industry due to overlapping boiling points and azeotrope formation. In this paper, liquid extraction of aromatic compounds (toluene and ethylbenzene) from aliphatic compounds (hexane and cyclohexene) using ionic liquids (1-butyl-3-methylimidazolium methylsulfate, BMimMSO₄, 1-propyl-3-methylimidazolium bis{trifluoromethylsulfonyl}imide, PMimNTf₂, and 1-butyl-3-methylimidazolium bis{trifluoromethylsulfonyl}imide, BMimNTf₂) as solvent was studied. (Liquid + liquid) equilibrium (ELL) data for the ternary systems {hexane (1) + ethylbenzene (2) + BMimMSO₄, or BMimNTf₂, or PMimNTf₂ (3)}, {hexane (1) + toluene (2) + BMimMSO₄ (3)} and {cyclohexene (1) + ethylbenzene (2) + BMimMSO₄ (3)} were experimentally determined at T = 298.15 K and atmospheric pressure. Moreover, an analysis of the influence of the structure of each compound on the phase behavior was also carried out. The ability of the studied ILs to separate aromatic from aliphatic compounds was evaluated in terms of the solute distribution ratio, β, and the selectivity, S. The Non Random Two-Liquid (NRTL) and UNIversal QUAsiChemical (UNIQUAC) thermodynamic models were used to correlate the experimental LLE data. Furthermore, the COnductor-like Screening MOdel for Real Solvents (COSMO-RS) was applied to predict the (liquid + liquid) equilibrium. The suitability of this model to describe the phase behavior of the studied mixtures was evaluated comparing the experimental and calculated data.     

Thermodynamic evaluation and optimization of the (MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) system, and optimized model parameters have been found. The model parameters obtained for the binary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model was used for the molten salt phase, and the (MgCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) solid solution was modeled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. This is the first of two articles on the optimization of the (NaCl + KCl + MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) system.     

Thermodynamic evaluation and optimization of the (NaNO3 + KNO3 + Na2SO4 + K2SO4) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (NaNO₃ + KNO₃ + Na₂SO₄ + K₂SO₄) ternary reciprocal system, and optimised model parameters have been found. The model parameters obtained for the four binary common-ion subsystems (i.e. (NaNO₃ + Na₂SO₄), (KNO₃ + K₂SO₄), (NaNO₃ + KNO₃) and (Na₂SO₄ + K₂SO₄)) are used to predict thermodynamic properties and phase equilibria for the entire system. The Modified Quasichemical Model in the Quadruplet Approximation for short-range ordering was used for the molten salt phase, and the Compound Energy Formalism was used for the various solid solutions.     

Volumetric study of (2-methoxyethanol + tetrahydrofuran + cyclohexane) at T=298.15 K

The excess molar volumes V_m^E at T=298.15 have been determined in the whole composition domain for (2-methoxyethanol + tetrahydrofuran + cyclohexane) and for the parent binary mixtures. Data on V_m^E are also reported for (2-ethoxyethanol + cyclohexane). All binaries showed positive V_m^E values, small for (methoxyethanol + tetrahydrofuran) and large for the other ones. The ternary V_m^E surface is always positive and exhibits a smooth trend with a maximum corresponding to the binary (2-methoxyethanol + cyclohexane). The capabilities of various models of either predicting or reproducing the ternary data have been compared. The behaviour of V_m^E and of the excess apparent molar volume of the components is discussed in both binary and ternary mixtures. The results suggest that hydrogen bonding decreases with alcohol dilution and increases with the tetrahydrofuran content in the ternary solutions.