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.     

Thermodynamic evaluation and optimization of the (NaCl + Na2SO4 + Na2CO3 + KCl + K2SO4 + K2CO3) system

A complete, critical evaluation of all phase diagrams and thermodynamic data was performed for all condensed phases of the (NaCl + Na₂SO₄ + Na₂CO₃ + KCl + K₂SO₄ + K₂CO₃) system, and optimized parameters for the thermodynamic solution models were obtained. The Modified Quasichemical Model in the Quadruplet Approximation was used for modelling the liquid phase. The model evaluates first- and second-nearest-neighbour short-range order, where the cations (Na⁺ and K⁺) were assumed to mix on a cationic sublattice, while anions $({\text{CO}}_3^{2-}\text{,}{\text{SO}}_4^{2-}\text{,}\text{and}{\text{Cl}}^{-})$ were assumed to mix on an anionic sublattice. The thermodynamic properties of the solid solutions of (Na,K)₂(SO₄,CO₃) were modelled using the Compound Energy Formalism, and (Na,K)Cl was modelled using a substitutional model in previous studies. Phase transitions in the common-cation ternary systems (NaCl + Na₂SO₄ + Na₂CO₃) and (KCl + K₂SO₄ + K₂CO₃) were studied experimentally using d.s.c./t.g.a. The experimental results were used as input for evaluating the phase equilibrium in the common-cation ternary systems. The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature are reproduced within experimental error limits.     

Salt effect on the (polyethylene glycol 8000 + sodium sulfate) aqueous two-phase system: Relative hydrophobicity of the equilibrium phases

The relative hydrophobicity of the phases of several {polyethylene glycol (PEG) 8000 + sodium sulfate (Na₂SO₄)} aqueous two-phase systems (ATPSs), all containing 0.01 mol · L^?1 sodium phosphate buffer (NaPB, pH 7.4) and increasing concentration of a salt additive, NaCl or KCl, up to 1.0 mol · L^?1, was measured by the free energy of transfer of a methylene group between the phases, ΔG(CH₂). The ΔG(CH₂) of the systems was determined by partitioning of a homologous series of five sodium salts of dinitrophenylated (DNP) – amino acids with aliphatic side chains in three different tie-lines of each biphasic system. The relative hydrophobicity of the phases ranged from ?0.125 to ?0.183 kcal · mol^?1, being the NaCl salt the one to provide the more effective changes. The results show that, within each system, there is a linear relationship between the ΔG(CH₂) and the tie-line length (TLL), and biphasic systems with high salt additive concentration present the most negative ΔG(CH₂) values. Therefore, the feasibility of establishing a relationship between the relative hydrophobicity of the phases in a given TLL and the ionic strength of the salt additive was investigated and a satisfactory correlation was found for each salt.     

(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.     

(Solid + liquid) metastable equilibria in quaternary system (Li2SO4 + K2SO4 + Li2B4O7 + K2B4O7 + H2O) at T = 288 K

Metastable equilibrium solubilities and properties such as densities, conductivity, pH, refractive index, and viscosity of the solution were determined experimentally. According to the experimental data, the metastable equilibrium phase diagram was plotted. In the phase diagram, there are three invariant points, seven univariant curves, five fields of crystallization: Li₂SO₄ · H₂O, K₂SO₄, Li₂B₄O₇ · 3H₂O, K₂B₄O₇ · 4H₂O, and K₂SO₄ · Li₂SO₄. The double salt K₂SO₄ · Li₂SO₄ was found in the quaternary system metastable equilibria. Lithium sulfate (Li₂SO₄) has the highest concentration and strong salting-out effects on other salts.Also, the relationship diagram between the properties and the ion concentration of solution was constructed. It can be seen from the relationship diagram that the equilibrium solution density values, viscosity values, and refractive index values are increased apparently with the rise of sulfate ion concentration, reaching the maximum values at eutonic point F3. Electrical conductivity values and pH values, however, fall down with the rise of ion concentration on the whole.     

Cloud-point measurements of the {H2O + poly(ethylene glycol) + NaNO3} system

The cloud-point (CP) temperatures and phase separation of {H₂O + poly(ethylene glycol) + NaNO₃} ternary system is studied by the turbidimetry method using a reaction calorimeter. The phase separation was also observed by visual inspection. Differences between the CP measured using the turbidimetry method and visual inspection, was up ±0.5 K. The Flory–Huggins model with a temperature and concentration-dependent interaction parameter was employed to correlate the phase diagram of the system. As a result of the correlation an average absolute deviation of 0.002 is obtained.     

Pitzer ion-interaction parameters for Fe(II) and Fe(III) in the quinary {Na + K + Mg + Cl + SO4 + H2O} system at T=298.15 K

This paper describes a chemical model that calculates (solid + liquid) equilibria in the {m₁FeCl₂ + m₂FeCl₃}(aq), {m₁FeSO₄ + m₂Fe₂(SO₄)₃}(aq), {m₁NaCl + m₂FeCl₃}(aq), {m₁Na₂SO₄ + m₂FeSO₄}(aq), {m₁NaCl + m₂FeCl₂}(aq), {m₁KCl + m₂FeCl₃}(aq), {m₁K₂SO₄ + m₂Fe₂(SO₄)₃}(aq), {m₁KCl + m₂FeCl₂}(aq), {m₁K₂SO₄ + m₂FeSO₄}(aq), and {m₁MgCl₂ + m₂FeCl₂}(aq) systems, where m denotes molality at T=298.15 K. The Pitzer ion-interaction model has been used for thermodynamic analysis of the experimental activity data in binary FeCl₂(aq) and FeCl₃(aq) solutions, and ternary solubility data, presented in the literature. The thermodynamic functions needed (binary and ternary parameters of ionic interaction, thermodynamic solubility products) have been calculated and the theoretical solubility isotherms have been plotted. The mixed solution model parameters {θ(MN) and ψ(MNX)} have been chosen on the basis of the compositions of saturated ternary solutions and data on the pure water solubility of the K₂SO₄ · FeSO₄ · 6H₂O double salt. The standard chemical potentials of four ferrous {FeCl₂ · 4H₂O, Na₂SO₄ · FeSO₄ · 4H₂O, K₂SO₄ · FeSO₄ · 6H₂O, and MgCl₂ · FeCl₂ · 8H₂O} and three ferric {FeCl₃ · 6H₂O, 2KCl · FeCl₃ · H₂O, and 2K₂SO₄ · Fe₂(SO₄)₃ · 14H₂O} solid phases have been determined. Comparison of solubility predictions with experimental data not used in model parameterization is given. The component activities of the saturated {m₁MgSO₄ + m₂FeSO₄}(aq) and in the mixed crystalline phase were determined and the change of the molar Gibbs free energy of mixing Δ_mixG^∘_m(s) of crystals was determined as a function of the solid phase composition. It is established that at T=298.15 K the mixed (Mg,Fe)SO₄ · 7H₂O and (Fe,Mg)SO₄ · 7H₂O crystals show small positive deviations from the ideal mixed crystals. Limitations of the {Fe(II) + Fe(III)} model due to data insufficiencies 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.     

The partition coefficients of ethylene between vapor and hydrate phase for methane + ethylene + THF + water systems

The vapor-hydrate equilibria were studied experimentally in detail for CH₄ + C₂H₄ + tetrahydrofuran (THF) + water systems in the temperature range of 273.15–282.15 K, pressure range of 2.0–4.5 MPa, the initial gas–liquid volume ratio range of 45–170 standard volumes of gas per volume of liquid and THF concentration range of 4–12 mol%. The results demonstrated that, because of the presence of THF, ethylene was remarkably enriched in vapor phase instead of being enriched in hydrate phase for CH₄ + C₂H₄ + water system. This conclusion is of industrial significance; it implies that it is feasible to enrich ethylene from gas mixture, e.g., various kinds of refinery gases or cracking gases in ethylene plant, by forming hydrate.     

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.     

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%.     

Thermodynamic evaluation and optimization of the (Na2CO3 + Na2SO4 + Na2S + K2CO3 + K2SO4 + K2S) system

A critical evaluation of all phase diagram and thermodynamic data were performed for the solid and liquid phases of the (Na₂CO₃ + Na₂SO₄ + Na₂S + K₂CO₃ + K₂SO₄ + K₂S) system and optimized model parameters were obtained. The Modified Quasichemical Model in the Quadruplet Approximation was used for modelling the liquid phase. The model evaluates first- and second-nearest-neighbour short-range ordering, where the cations (Na⁺ and K⁺) are assumed to mix on a cationic sublattice, while anions $({\text{CO}}_3^{2-}\text{,}{\text{SO}}_4^{2-}\text{,}\text{and}{\text{S}}^{2-})$ are assumed to mix on an anionic sublattice. The Compound Energy Formalism was used for modelling the solid solutions of (Na, K)₂(CO₃, SO₄, S). The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature were reproduced within experimental error limits.     

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.     

Vapour pressure osmometry determination of water activity of binary and ternary aqueous (polymer + polymer) solutions

Precise water activity measurements at T = 308.15 K were carried out on several binary (water + polymer) and ternary {water + polymer (1) + polymer (2)} systems using the vapour pressure osmometry (VPO) technique. Polymers were polyethylene glycol 400 (PEG400), polyethylene glycol 6000 (PEG6000), polypropylene glycol 400 (PPG400), polyvinylpyrrolidone (PVP) and dextran (DEX). The water activity results obtained were used to calculate the vapour pressure of solutions as a function of concentration and the segment-based local composition models, NRTL and Wilson, were used to correlate the experimental water activity values. It was found that, for the polymer concentration range studied here, the values of the water activity obtained for the binary (water + polymer) solutions decrease in the order DEX > PVP > PEG6000 > PPG400 > PEG400. Furthermore, water activities of solutions of each polymer in the aqueous solutions of (5, 10, 15 and 20)% (w/w) other polymers investigated were also measured at T = 308.15 K. The ability of polymer (1) in decreasing the water activity of binary {water + polymer (2)} solutions was discussed on the basis of the (polymer + water) and {polymer (1) + polymer (2)} interactions.     

Thermodynamic evaluation and optimization of the (NaF + AlF3 + CaF2 + BeF2 + Al2O3 + BeO) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases and relevant gaseous species of the (NaF + AlF₃ + CaF₂ + BeF₂ + Al₂O₃ + BeO) system, and optimized model parameters have been found. The (NaF + AlF₃ + CaF₂ + Al₂O₃) subsystem, which is the base electrolyte used for the electro-reduction of alumina in Hall–Héroult cells, has been critically evaluated in a previous article. The Modified Quasichemical Model in the Quadruplet Approximation for short-range ordering was used for the molten salt phase. The thermodynamic database developed is a first step towards a quantitative study of the beryllium mass balance in an electrolysis cell. In particular, the predominant Be-containing species in the gas phase evolved at the anode were identified; and, for a given beryllium content of the alumina, the beryllium content of the electrolytic bath at steady state was assessed under several approximations.     

The effect of temperature and molar mass on the (liquid + liquid) equilibria of (poly ethylene glycol dimethyl ether + di-sodium hydrogen citrate + water) systems: Experimental and correlation

The (liquid + liquid) equilibrium for the {polyethylene glycol dimethyl ether 2000 (PEGDME₂₀₀₀) + di-sodium hydrogen citrate + H₂O} system was studied at T = (298.15, 308.15 and 318.15) K and atmospheric pressure (≈85 kPa). The free energies, enthalpies and entropies of cloud points were calculated in order to investigate the driving force formation of this two-phase system. To investigate the effect of molar mass of the polymer on the binodals and tie-lines, similar measurements were also made at T = 298.15 K on this two-phase system consisting of the PEGDME with molar masses of 500 and 250 g ⋅ mol⁻¹. The effective excluded volume model was used for representation of the phase-forming ability in PEGDME systems. An empirical and the Merchuck equations with the temperature dependency were used to correlate the binodal curves. The Othmer–Tobias and Bancraft and Setschenow equations, the osmotic virial and the extended NRTL models were used to fit the tie-line data.     

(Solid + liquid) isothermal evaporation phase equilibria in the aqueous ternary system (Li2SO4 + MgSO4 + H2O) at T = 308.15 K

The solubility and the density in the aqueous ternary system (Li₂SO₄ + MgSO₄ + H₂O) at T = 308.15 K were determined by the isothermal evaporation. Our experimental results permitted the construction of the phase diagram and the plot of density against composition. It was found that there is one eutectic point for (Li₂SO₄ · H₂O + MgSO₄ · 7H₂O), two univariant curves, and two crystallization regions corresponding to lithium sulphate monohydrate (Li₂SO₄ · H₂O) and epsomite (MgSO₄ · 7H₂O). The system belongs to a simple co-saturated type, and neither double salts nor solid solution was found. Based on the Pitzer ion-interaction model and its extended HW models of aqueous electrolyte solution, the solubility of the ternary system at T = 308.15 K has been calculated. The predicted solubility agrees well with the experimental values.     

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.     

Cation effect on the (PEG 8000 + sodium sulfate) and (PEG 8000 + magnesium sulfate) aqueous two-phase system: Relative hydrophobicity of the equilibrium phases

The partitioning of four dinitrophenylated (DNP-) amino acids in aqueous two-phase systems of (polyethylene glycol (PEG)-8000 + sodium sulfate) and (polyethylene glycol (PEG)-8000 + magnesium sulfate) in five different tie-lines was experimentally determined at T = 298.15 K. The Gibbs energy of transfer of a methylene group between the two phases was calculated from the measured partition coefficients. This characterizes the relative hydrophobicity of the equilibrium phases. Values of ΔG¹(CH₂) were in range from (−0.674 to −1.012) kJ · mol⁻¹. A comparison of both systems was carried out. The results show that the cation type has a strong influence on the amino acids partitioning process. The largest relative hydrophobicity was noted for the ATPS system formed by sodium sulfate. This showed to be a better system for the separation.     

(Surfactant + polymer) interaction parameter studied by (liquid + liquid) equilibrium data of quaternary aqueous solution containing surfactant,polymer, and salt

(Liquid + liquid) equilibrium (LLE) data of quaternary aqueous system containing polyoxyethylene (20) cetyl ether (with abbreviation name Brij 58, non-ionic surfactant), diammonium hydrogen phosphate, and poly ethylene glycol (PEG) with three molar masses {M_W = (1000, 6000, and 35,000) g · mol^?1} have been determined experimentally at T = 313.15 K.Furthermore, the Flory–Huggins theory with two electrostatic terms (Debye–Hückel and Pitzer–Debye–Hückel equations) have been used to calculate the phase behavior of the quaternary systems and (surfactant + polymer) interaction parameter as well as interaction parameters between other species. Temperature dependency of the parameters of the Flory–Huggins theory has been obtained.Also an effort have been done to show that addition of PEG as well as increasing the temperature can shift the binodal curves of the ternary aqueous system containing surfactant and salt to lower mole fraction of salt. Also the effect of polymer molar mass on the binodal diagram displacement has been discussed.