Thermodynamic evaluation and optimization of the (Na2SO4 + K2SO4 + Na2S2O7 + K2S2O7) system

A complete, critical evaluation of all phase diagram and thermodynamic data was performed for all phases of the (Na₂SO₄ + K₂SO₄ + Na₂S₂O₇ + K₂S₂O₇) 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 were assumed to mix on an anionic sublattice. The Compound Energy Formalism was used for modelling the solid solutions of (Na,K)₂SO₄ and (Na,K)₂S₂O₇. 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.     

Thermodynamic representation of the NaCl + Na2SO4 + H2O system with electrolyte NRTL model

A comprehensive thermodynamic model based on the electrolyte NRTL (eNRTL) activity coefficient equation is developed for the NaCl + H₂O binary, the Na₂SO₄ + H₂O binary and the NaCl + Na₂SO₄ + H₂O ternary. The NRTL binary parameters for pairs H₂O-(Na⁺, Cl⁻) and H₂O-(Na⁺, SO₄²⁻), and the aqueous phase infinite dilution heat capacity parameters for ions Cl⁻ and SO₄²⁻ are regressed from fitting experimental data on mean ionic activity coefficient, heat capacity, liquid enthalpy and dissolution enthalpy for the NaCl + H₂O binary and the Na₂SO₄ + H₂O binary with electrolyte concentrations up to saturation and temperature up to 473.15 K. The Gibbs energy of formation, enthalpy of formation and heat capacity parameters for solids NaCl_(s), NaCl·2H₂O_(s), Na₂SO_4(s) and Na₂SO₄·10H₂O_(s) are obtained by fitting experimental data on solubilities of NaCl and Na₂SO₄ in water. The NRTL binary parameters for the (Na⁺, Cl⁻)-(Na⁺, SO₄²⁻) pair are regressed from fitting experimental data on dissolution enthalpies and solubilities for the NaCl + Na₂SO₄ + H₂O ternary.     

High-pressure phase behavior of CO2 + 1-butyl-3-methylimidazolium chloride system

The phase behavior of carbon dioxide (CO₂) and the ionic liquid (IL) 1-butyl-3-methylimidazolium chloride ([bmim][Cl]) was measured and correlated at high pressures up to ∼40 MPa and at temperatures between 353.15 K and 373.15 K. The solubility data of CO₂ in [bmim][Cl] were obtained by observing the bubble point pressure at specific temperatures. A variable-volume view cell, which is a high-pressure equilibrium apparatus, was used to measure the CO₂ + [bmim][Cl] system solubility under varying pressure and temperature conditions. In addition, liquid–liquid–vapor (LLV) three-phase behavior was investigated using the equilibrium cell to be able to determine the classification of phase-behavior type by Scott and Van Konynenburg. Based on the LLV phase behavior, this system most likely has type III phase-behavior which is common for IL + CO₂ systems. The resulting data showed that CO₂ dissolved well in the IL at low CO₂ concentrations, but that the pressure derivative of CO₂ solubility dramatically decreased as the mole fraction of CO₂ was increased. The experimental data were well fitted by the Peng–Robinson equation of state with a quadratic mixing rule and cubic parameters estimated by the Joback method.     

High-pressure phase behaviour of binary (CO2 + nicotine) and ternary (CO2 + nicotine + solanesol) mixtures

This work paper presents vapour–liquid equilibrium (VLE) data for binary (CO₂ + nicotine) and ternary (CO₂ + nicotine + solanesol) mixtures, at 313.2 K and 6, 8 and 15 MPa. The (CO₂ + nicotine) system exhibits three phases (L₁L₂V) in equilibrium at 8.37 MPa. It is estimated that this system most likely follows the type-III phase behaviour. In the ternary system, the presence of solanesol in the vapour phase was detected only at the pressure of 15 MPa. At this pressure, partition coefficients and separation factors for solanesol/nicotine were calculated for different initial nicotine/solanesol compositions and a strong influence of composition was found. The results were modelled using the Peng–Robinson equation of state (PR EOS) coupled with the Mathias–Klotz–Prausnitz (MKP) mixing rule (PR–MKP model). Good correlations of the binary data, particularly in the case of the (CO₂ + nicotine) mixture, were obtained. However, the model could not correlate the ternary data.     

High pressure phase equilibria in methane + waxy systems. 2. Methane + waxy ternary mixture

Liquid–vapour and fluid–solid phase transitions were experimentally determined under pressure on the system methane + a ternary waxy mixture using a full visibility cell. The wax was an approximately equimolar mixture of n-C₁₆, n-C₁₇ and n-C₁₈, the composition being chosen to obtain a mixture with an average molecular weight similar to heptadecane. Measurements were performed according to the synthetic method on different mixtures ranging from 0 to 99.5 mol% of methane. The liquid–solid phase transitions were investigated up to 100 MPa and fluid phase boundary was studied in the temperature domain from 293 to 373 K. Measurements performed on this pseudo-binary system were compared to the phase diagram of the binary system methane + heptadecane.     

Phase behavior of the system hyperbranched polyglycerol + methanol + carbon dioxide

Phase equilibrium data have been measured for the ternary system hyperbranched polyglycerol + methanol + carbon dioxide at temperatures of 313–450 K and pressures up to 13.5 MPa. Phase changes were determined according to a synthetic method using the Cailletet setup. At elevated temperatures the system shows a liquid–liquid–vapor region with lower solution temperatures. Besides the vapor–liquid and liquid–liquid equilibria, the vapor–liquid to vapor–liquid–liquid and vapor–liquid–liquid to liquid–liquid phase boundaries are reported at different polymer molar masses and can serve as test sets for thermodynamic models. A distinct influence of the polymer molar mass on the vapor–liquid equilibrium can be noticed and indicates the existence of structural effects due to the polymer branching. Modeling the systems with the PCP-SAFT equation of state confirms these findings.     

Thermodynamic properties on quaternary aqueous solutions of chlorides charge-type 1-1*2-1*2-1: XCl + MgCl2 + CaCl2 + H2O with (X ≡ Na; NH4)

In this investigation, the quaternary aqueous solutions of chlorides charge-type 1-1*2-1*2-1 with a cation (Na⁺; NH₄⁺; Mg²⁺; Ca²⁺) have been studied using the hygrometric method at 298.15 K. The water activities of the systems NH₄Cl + MgCl₂ + CaCl₂ + H₂O and NaCl + MgCl₂ + CaCl₂ + H₂O are measured at total molalities from 0.60 mol kg⁻¹ to saturation for different ionic-strength fractions NH₄Cl or NaCl, y = 0.20, 0.50, 0.80, and z ratio ionic-strength for other solutes, with z = 0.20, 0.50 and 0.80 for each y. The obtained data allow the deduction of osmotic coefficients.     

Solid-liquid phase equilibria in the system water + methanol + MgSO4·7H2O + MnSO4·4H2O

The solubilities and complex phase equilibria for the system of MnSO₄·4H₂O + MgSO₄·7H₂O + H₂O + CH₃OH were determined at the temperatures 291.2 and 301.2 K over the methanol mole fraction range of 0.00–0.12.The solubility data were used for modelling with the modified extended electrolyte non-random two-liquid equation. The salting-out effect of MgSO₄ and methanol on the solubilities of two manganese salts (MnSO₄·H₂O and MnSO₄·4H₂O) are represented in the several thermodynamic figures as a function of temperature. The solventing-out effect was stronger than the salting-out effect, which results in a decrease of the solubilities of manganese, salts even though the solubility of MnSO₄·H₂O decreased and solubility of MgSO₄·4H₂O increased as temperature increased.     

New isothermal vapor–liquid equilibria for the CO2 + n-nonane,and CO2 + n-undecane systems

Experimental vapor–liquid equilibria (VLE) for the CO₂ + n-nonane and CO₂ + n-undecane systems were obtained by using a 100-cm³ high-pressure titanium cell up to 20 MPa at four temperatures (315, 344, 373, and 418 K). The apparatus is based on the static-analytic method; which allows fast determination of the coexistence curve. For the CO₂ + n-nonane system, good agreement was found between the experimental data and those reported in literature. No literature data were available for the CO₂ + n-undecane system at high temperature and pressure. Experimental data were correlated with the Peng–Robinson equation of state using the classical and the Wong–Sandler mixing rules.     

The DFT and ab initio investigations on the mechanism of CF3O2 + H reaction

The mechanisms for the reaction of CF₃O₂ with atomic hydrogen were studied with ab initio and DFT methods. The results reveal that the reaction could take place on the singlet and triplet potential energy surfaces (PES). For the singlet PES, addition/elimination and substitution mechanisms are determined, and the former one is dominant. The most favorable channel involves the association of CF₃O₂ with H atom to form CF₃O₂H (IM1) via a barrierless process, and then the O–O bond dissociates to give out CF₃O + OH. The secondary product might be CF₃OH + O, formed from the O–O bond cleavage in the initial adduct CF₃O(H)O (IM2). Other products such as CF₃ + O₂H, HF + CF₂O₂ and O₂ + CHF₃ are of no importances because of higher barriers. On the triplet PES, only substitution mechanism is located. With higher barriers involving, the channels on the triplet PES could be negligible compared with the channels on the singlet PES.     

Ternary (liquid + liquid) equilibria of the azeotrope (ethyl acetate + 2-propanol) with different ionic liquids at T = 298.15 K

Experimental (liquid + liquid) equilibria involving ionic liquids {1,3-dimethylimidazolium methyl sulfate (MMIM MeSO₄)}, {2-propanol + ethyl acetate + 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM PF₆)} and {2-propanol + ethyl acetate + 1-hexyl-3-methylimidazolium hexafluorophosphate (HMIM PF₆)} were carried out to separate the azeotropic mixture ethyl acetate and 2-propanol. Selectivity and distribution ratio values, derived from the tie-lines data, were presented in order to analyze the best separation solvent in a liquid extraction process. Experimental (liquid + liquid) equilibria data were compared with the correlated values obtained by means of the NRTL, Othmer-Tobias and Hand equations. These equations were verified to accurately correlate the experimental data.     

Measurement of water activities of alanine + tri-potassium citrate + water system at temperatures between 293.15 and 313 K—Experimental and modeling

Water activity measurements by isopiestic method have been carried out on the aqueous solutions of alanine + tri-potassium citrate (K₃Cit) over a range of temperatures at atmospheric pressure. From these measurements, values of the vapor pressure of solutions were determined. The effect of temperature on the vapor–liquid equilibrium of alanine + K₃Cit + H₂O systems has been studied. The experimental water activities have been correlated successfully with the segment-based local composition Wilson and NRTL models. The agreement between the correlations and the experimental data is good.     

Isobaric vapor–liquid equilibria for the quaternary reactive system: Ethanol + water + ethyl lactate + lactic acid at 101.33 kPa

Isobaric vapor–liquid equilibrium (VLE) data of the reactive quaternary system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid (4) have been determined experimentally. Additionally, the reaction equilibrium constant was calculated for each VLE experimental data. The experimental VLE data were correlated using the UNIQUAC equation to describe the chemical and phase equilibria simultaneously. For some of the non-reactive binary systems, UNIQUAC binary interaction parameters were obtained from the literature. The rest of the binary UNIQUAC parameters were obtained by correlating the experimental quaternary VLE data obtained in this work. A maximum pressure azeotrope at high water concentration for the binary reactive system ethyl lactate + water has been calculated.     

Quinary liquid–liquid equilibria for mixtures of nonane + undecane + two pairs of aromatics (benzene/toluene/m-xylene) + sulfolane at 298.15 and 313.15 K

In this work, liquid–liquid equilibrium data were measured for three quinary mixtures (nonane + undecane + benzene + toluene + sulfolane), (nonane + undecane + benzene + m-xylene + sulfolane) and (nonane + undecane + toluene + m-xylene + sulfolane) at 298.15 and 313.15 K and ambient pressure. The experimental LLE data were determined by using a jacketed glass cell with temperature controlled. The quantitative analysis was performed by using a Varian gas chromatograph equipped with a flame ionization detector and a SPB™-1 column. The experimental quinary liquid–liquid equilibrium data have been satisfactorily correlated by using NRTL and UNIFAC-LLE models. The calculated values based on the NRTL model were found to be in a better agreement with the experiment than those based on the UNIFAC-LLE model.     

Clathrate hydrate formation in (methane + water + methylcyclohexanone) systems: the first phase equilibrium data

The present study experimentally demonstrated clathrate hydrate formation in the systems of (methane + water + each of the three methylcyclohexanone isomers, i.e., 2-methylcyclohexanone, 3-methylcyclohexanone, and 4-methylcyclohexanone) and measured the first data of the quadruple (water rich liquid + hydrate + methylcyclohexanone rich liquid + methane rich vapor) equilibrium pressure and temperature conditions in these systems over the temperatures from T=273 K to T=281 K. In the three systems with methylcyclohexanone, the measured equilibrium pressure at each given temperature is ∼1.3 MPa lower than that in a structure-I hydrate forming (methane + water) system without any methylcyclohexanone, which suggests the formation of structure-H hydrates with methylcyclohexanones as large-molecule guest substances. Among the three systems, 3-methylcyclohexanone provides the highest equilibrium pressure, and 2-methylcyclohexanone, the lowest.     

Microscopic phase behavior of supercritical carbon dioxide + non-ionic surfactant + water systems at elevated pressures

The microscopic phase behavior of the supercritical carbon dioxide (scCO₂) + polyethylene oxide-2,6,8-trimethyl-4-nonyl ether (TMN) + water systems at about 3 wt% of TMN were investigated using a synthetic method with a microscope. The two types of TMN (TMN-3 and TMN-10) used in this work had molecular weight distributions caused by the distribution of the number of ethylene oxide groups. Two different types of phase transition were observed when pressure was decreased gradually at a constant temperature from the high pressure at which the transparent phase was observed to the low pressure at which the separate vapor–liquid phases were observed for the scCO₂ + TMN-3 + water system at 3 wt% of TMN-3. The transparent phase was colorless under all experimental conditions and the phase transition from a transparent phase to a turbidity phase with small, dispersed droplets was observed at the higher side phase transition (higher phase transition pressure). As the pressure continued to decrease, another phase transition was observed from the phase with small droplets to a state with an accelerating aggregation of droplets (lower phase transition pressure). In the turbidity phase between the higher and the lower phase transition, the degree of turbidity became higher with decreasing pressure. On the other hand, in the phase observed below the lower phase transition, a new liquid phase adhered to the sapphire windows and the wall inside the optical cell.     

Phase diagram and thermodynamic modeling of PEO + organic salts + H2O and PPO + organic salts + H2O aqueous two-phase systems

The phase diagrams of PEO1500 + sodium tartrate + water, PPO400 + sodium tartrate + water, PEO1500 + sodium succinate + water, PPO400 + sodium succinate + water, PEO1500 + sodium citrate + water, PPO400 + sodium citrate + water and PPO400 + sodium acetate + water aqueous two-phase systems were determined at (283.15, 298.15, and 313.15) K. Both equilibrium phases composition were analyzed by conductimetry and refractive index. In this paper, the influences of polymer hydrophobicity, salt nature and temperature on the phase diagram were analyzed. The phase separation processes was endothermic and the hydrophobic increase make easier the phase splitting, while the electrolyte capacity to induce phase separation follow the order: citrate > tartrate > succinate. The consistency of the tie-line data was ascertained by applying the Othmer-Tobias correlation. The experimental data were correlated with the NRTL model for the activity coefficient, with estimation of new interaction energy parameters. The results, analyzed in terms of root mean square deviations between experimental and calculated compositions, were considered satisfactory.     

Liquid–liquid equilibria for quaternary mixtures of nonane + undecane + (benzene or toluene or m-xylene) + sulfolane at 298.15 and 313.15 K

Liquid–liquid equilibrium (LLE) data were measured for three quaternary systems containing sulfolane, nonane + undecane + benzene + sulfolane, nonane + undecane + toluene + sulfolane and nonane + undecane + m-xylene + sulfolane, at T = 298.15 and 313.15 K and ambient pressure. The experimental quaternary liquid–liquid equilibrium data have been satisfactorily represented by using NRTL and UNIFAC-LLE models for the activity coefficient. The calculated compositions based on the NRTL model were found to in a better agreement with the experiment than those based on the UNIFAC-LLE model.     

Modeling of the three-phase equilibrium in systems of the type water + nonionic surfactant + alkane

Liquid–liquid equilibria of systems water (A) + C_iE_j surfactant (B) + n-alkane (C) have been modeled by a mass-action law model previously developed and so far successfully applied to a series of binary water + C_iE_j systems and to the ternary system water + C₄E₁ + n-dodecane. These calculations provide the basis for the presented modeling. The aqueous systems give information about the association constants and the χ_AB-parameter of the Flory–Huggins theory and the ternary C₄E₁-system provides universal temperature functions for the χ_AC- and the χ_BC-parameter. The three-phase equilibrium for seven ternary C_iE_j systems (i = 6–12, j = 3–6) has been calculated by fitting one additional parameter for each of both temperature functions to the characteristic “fish-tail” point. The agreement with the experimental data is reasonably well. For systems with very small three-phase areas the results can considerably be improved by individual temperature functions that incorporate the experimental temperature maximum of the “fish” into the parameter fit. Based on the parameters of the system water + C₈E₄ + n-C₈H₁₈ the “fish-shaped” phase diagram of the system water + C₈E₄ + n-C₁₄H₃₀ was predicted reasonably well.