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 (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.     

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.     

Thermodynamic evaluation and optimization of the (LiF + NaF + KF + MgF2 + CaF2 + SrF2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (LiF + NaF + KF + MgF₂ + CaF₂ + SrF₂) system, and optimized model parameters have been found. The (LiF + NaF + KF + MgF₂ + CaF₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase, and the low-temperature and high-temperature (CaF₂ + SrF₂) solid solutions were modelled 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 (Li, Na, K)(Mg, Ca, Sr)F₃ perovskite phase was modelled using the Compound Energy Formalism.     

Activity coefficients of electrolyte and amino acid in the systems (water + potassium chloride + dl -valine) at T = 298.15 K and (water + sodium chloride + l -valine) at T = 308.15 K

The activity coefficient data were reported for (water  +  potassium chloride  + dl -valine) at T =  298.15 K and (water  +  sodium chloride  + l -valine) at T =  308.15 K. The measurements were performed in an electrochemical cell using ion-selective electrodes. The maximum concentrations of the electrolytes and the amino acids studied were 1.0 molality and 0.4 molality, respectively. The results of the activity coefficients of dl -valine are compared with the activity coefficients of dl -valine in (water  +  sodium chloride  + dl -valine) system obtained from the previous study. The results show that the presence of an electrolyte and the nature of its cation have a significant effect on the activity coefficient of dl -valine in aqueous electrolyte solutions.     

Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl2 + CaCl2 + ZnCl2) 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 (NaCl + KCl + MgCl₂ + CaCl₂ + ZnCl₂) system, and optimized model parameters have been found. The (NaCl + KCl + MgCl₂ + CaCl₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase.     

Thermodynamic properties of (tetradecane + benzene, + toluene, + chlorobenzene, + bromobenzene, + anisole) binary mixtures at T = (298.15, 303.15, and 308.15) K

Density ρ, viscosity η, and refractive index n_D, values for (tetradecane + benzene, + toluene, + chlorobenzene, + bromobenzene, + anisole) binary mixtures over the entire range of mole fraction have been measured at temperatures (298.15, 303.15, and 308.15) K at atmospheric pressure. The speed of sound u has been measured at T = 298.15 K only. Using these data, excess molar volume V^E, deviations in viscosity Δη, Lorentz–Lorenz molar refraction ΔR, speed of sound Δu, and isentropic compressibility Δk_s have been calculated. These results have been fitted to the Redlich and Kister polynomial equation to estimate the binary interaction parameters and standard deviations. Excess molar volumes have exhibited both positive and negative trends in many mixtures, depending upon the nature of the second component of the mixture. For the (tetradecane + chlorobenzene) binary mixture, an incipient inversion has been observed. Calculated thermodynamic quantities have been discussed in terms of intermolecular interactions between mixing components.     

Experimental determination of the rate constants of the reactions of HO2 + DO2 and DO2 + DO2

The rate constants of the reactions of DO₂ + HO₂ (R1) and DO₂ + DO₂ (R2) have been determined by the simultaneous, selective, and quantitative measurement of HO₂ and DO₂ by continuous wave cavity ring-down spectroscopy (cw-CRDS) in the near infrared, coupled to a radical generation by laser photolysis. HO₂ was generated by photolyzing Cl₂ in the presence of CH₃OH and O₂. Low concentrations of DO₂ were generated simultaneously by adding low concentrations of D₂O to the reaction mixture, leading through isotopic exchange on tubing and reactor walls to formation of low concentrations of CH₃OD and thus formation of DO₂. Excess DO₂ was generated by photolyzing Cl₂ in the presence of CD₃OD and O₂, small concentrations of HO₂ were always generated simultaneously by isotopic exchange between CD₃OD and residual H₂O. The rate constant k₁ at 295 K was found to be pressure independent in the range 25–200 Torr helium, but increased with increasing D₂O concentration k₁ = (1.67 ± 0.03) × 10⁻¹² × (1 + (8.2 ± 1.6) × 10⁻¹⁸ cm³ × [D₂O] cm⁻³) cm³ s⁻¹. The rate constant for the DO₂ self-reaction k₂ has been measured under excess DO₂ concentration, and the DO₂ concentration has been determined by fitting the HO₂ decays, now governed by their reaction with DO₂, to the rate constant k₁. A rate constant with insignificant pressure dependence was found: k₂ = (4.1 ± 0.6) × 10⁻¹³ (1 + (2 ± 2) × 10⁻²⁰ cm³ × [He] cm⁻³) cm³ s⁻¹ as well as an increase of k₂ with increasing D₂O concentration was observed: k₂ = (4.14 ± 0.02) × 10⁻¹³ × (1 + (6.5 ± 1.3) × 10⁻¹⁸ cm³ × [D₂O] cm⁻³) cm³ s⁻¹. The result for k₂ is in excellent agreement with literature values, whereas this is the first determination of k₁.     

Hot band spectroscopy of CCO in the C–O stretching region: The (ν1 + 2ν3) − 2ν3 and (2ν1 + ν3) − (ν1 + ν3) bands

Two C–O stretching hot bands, (ν₁ + 2ν₃) − 2ν₃ and (2ν₁ + ν₃) − (ν₁ + ν₃), of the CCO radical in the ground electronic state were measured. These hot bands are red shifted by approximately 70 cm⁻¹ compared to the C–O stretching fundamental. CCO was produced in a discharge through a flowing mixture of carbon suboxide and helium. The spectra were recorded using a diode laser spectrometer. The band origins were determined to be 1904.32512(62) and 1902.69130(56) cm⁻¹ for (ν₁ + 2ν₃) − 2ν₃ and (2ν₁ + ν₃) − (ν₁ + ν₃), respectively. The measurements in this band together with previously reported frequencies in the C–C and C–O stretching regions were analysed to determine harmonic frequencies and anharmonicity constants.     

Thermodynamic investigation of the (LiF + NaF + CaF2 + LaF3) system

In this work a thermodynamic assessment of the (LiF + NaF + CaF₂ + LaF₃) system is reported. For the thermodynamic modeling of the liquid phase, the classical polynomial model, and the modified quasi-chemical model were used in parallel and compared. The extrapolation to higher order systems was done according to the Toop mathematical formalism. Furthermore, differential-scanning calorimetry data of the ternary (LiF + CaF₂ + LaF₃), (NaF + CaF₂ + LaF₃), and the quaternary (LiF + NaF + CaF₂ + LaF₃) mixtures are presented. Good agreement between the experimental data and the thermodynamic assessment was obtained.     

Phase behavior of (CO2 + methanol + lauric acid) system

In this study the phase equilibrium behaviors of the binary system (CO₂ + lauric acid) and the ternary system (CO₂ + methanol + lauric acid) were determined. The static synthetic method, using a variable-volume view cell, was employed to obtain the experimental data in the temperature range of (293 to 343) K and pressures up to 24 MPa. The mole fractions of carbon dioxide were varied according to the systems as follows: (0.7524 to 0.9955) for the binary system (CO₂ + lauric acid); (0.4616 to 0.9895) for the ternary system (CO₂ + methanol + lauric acid) with a methanol to lauric acid molar ratio of (2:1); and (0.3414 to 0.9182) for the system (CO₂ + methanol + lauric acid) with a methanol to lauric acid molar ratio of (6:1). For these systems (vapor + liquid), (liquid + liquid), (vapor + liquid + liquid), and (solid + fluid) transitions were observed. The phase equilibrium data obtained for the systems were modeled using the Peng–Robinson equation of state with the classical van der Waals mixing rule with a satisfactory correlation between experimental and calculated values.     

Isopiestic measurement and solubility evaluation of the ternary system (CaCl2 + SrCl2 + H2O) at T = 298.15 K

Water activities in the ternary system (CaCl₂ + SrCl₂ + H₂O) and its sub-binary system (CaCl₂ + H₂O) at T = 298.15 K have been elaborately measured by an isopiestic method. The data of the measured water activity were used to justify the reliability of solubility isotherms reported in the literature by correlating them with a thermodynamic Pitzer–Simonson–Clegg (PSC) model. The model parameters for representing the thermodynamic properties of the (CaCl₂ + H₂O) system from (0 to 11) mol ⋅ kg⁻¹ at T = 298.15 K were determined, and the experimental water activity data in the ternary system were compared with those predicted by the parameters determined in the binary systems. Their agreement indicates that the PSC model parameters can reliably represent the properties of the ternary system. Under the assumption that the equilibrium solid phases are the pure solid phases (SrCl₂ ⋅ 6H₂O and CaCl₂ ⋅ 6H₂O)_(s) or the ideal solid solution consisting of CaCl₂ ⋅ 6H₂O_(s) and SrCl₂ ⋅ 6H₂O_(s), the solubility isotherms were predicted and compared with experimental data from the literature. It was found that the predicted solubility isotherm agrees with experimental data over the entire concentration range at T = 298.15 K under the second assumption described above; however, it does not under the first assumption. The modeling results reveal that the solid phase in equilibrium with the aqueous solution in the ternary system is an ideal solid solution consisting of SrCl₂ ⋅ 6H₂O_(s) and CaCl₂ ⋅ 6H₂O_(s). Based on the theoretical calculation, the possibility of the co-saturated points between SrCl₂ ⋅ 6H₂O_(s) and the solid solution (CaCl₂ ⋅ 6H₂O + SrCl₂ ⋅ 6H₂O)_(s) and between CaCl₂ ⋅ 6H₂O_(s) and the solid solution (CaCl₂ ⋅ 6H₂O + SrCl₂ ⋅ 6H₂O)_(s), which were reported by experimental researchers, has been discussed, and the Lippann diagram of this system has been presented.     

(Liquid + liquid) equilibrium of (water + 2-propanol + 1-butanol + salt) systems at T = 313.15 K and T = 353.15 K: Experimental data and correlation

(Liquid + liquid) equilibrium data for the quaternary systems (water + 2-propanol + 1-butanol + potassium bromide) and (water + 2-propanol + 1-butanol + magnesium chloride) were measured at T = 313.15 K and T = 353.15 K. The overall salt concentrations were 5 and 10 mass percent. Ternary (liquid + liquid) equilibrium data for the salt-free system (water + 2-propanol + 1-butanol) were also determined and found to be in good agreement with data from the literature. The NRTL model for the activity coefficient was used to correlate the data. New interaction parameters were estimated, using the Simplex minimization method and a concentration-based objective function. The results are very satisfactory, with root mean square deviations between experimental and calculated compositions of both phases being less than 0.5%.     

Isopiestic study of (calcium chloride + water) and (calcium chloride + magnesium chloride + water) atT = 313.15 K

The osmotic coefficients of aqueous calcium chloride solutions were experimentally determined atT =  313.15 K by the isopiestic method. Magnesium chloride served as the isopiestic standard for the calculation of osmotic coefficients. The molality range covered in this study correspond to about 0.1mol · kg ^− 1to 3.0mol · kg ^− 1. In addition, the osmotic coefficients of aqueous mixtures of calcium chloride and magnesium chloride were determined over the range of ionic strength levels of about 0.1mol · kg ^− 1to 9mol · kg ^− 1and at various mole fractions. The results obtained were correlated by the Pitzer equation.     

Speeds of sound in {(1 − x)CH4 + xN2} with x = (0.10001, 0.19999, and 0.5422) at temperatures between 170 K and 400 K and pressures up to 30 MPa

The speed of sound in {(1 − x)CH₄ + xN₂} has been measured with a spherical acoustic resonator. Two mixtures with x = (0.10001 and 0.19999) were studied along isotherms at temperatures between 220 K and 400 K with pressures up to 20 MPa; a few additional measurements at p = (25 and 30) MPa are also reported. A third mixture with x = 0.5422 was studied along pseudo-isochores at amount-of-substance densities between 0.2 mol · dm⁻³ and 5 mol · dm⁻³. Corrections for molecular vibrational relaxation are discussed in detail and relaxation times are reported. The overall uncertainty of the measured speeds of sound is estimated to be not worse than ±0.02%, except for those measurements in the mixture with x = 0.5422 that lie along the pseduo-isochore at the highest amount-of-substance density. The results have been compared with the predictions of several equations of state used for natural gas systems.     

(Liquid + liquid) equilibria of the (water + propionic acid + Aliquat 336 + organic solvents) at T = 298.15 K

In this work, trioctyl methyl ammonium chloride (Aliquat 336) was studied for its ability to extract propionic acid at various amine concentrations. The extraction of propionic acid with Aliquat 336 dissolved in five single solvents (cyclohexane, hexane, toluene, methyl isobutyl ketone, and ethyl acetate ) and binary solvents (hexane + MIBK, hexane + toluene, and MIBK + toluene) was investigated under various experimental conditions. The loading factors Z, extraction efficiency E and overall particular distribution coefficients were determined. All measurements were carried out at T = 298.15 K. The obtained results and the observed phenomena were discussed by taking into consideration the mechanism of extraction and the concentration of the interaction product in the aqueous phase.     

The P, V, T,x properties of binary aqueous chloride solutions up to T = 573 K and 100 MPa

A highly accurate P, V, T,x model is developed for aqueous chloride solutions of the binary systems, viz. (LiCl + H₂O), (NaCl + H₂O), (KCl + H₂O), (MgCl₂ + H₂O), (CaCl₂ + H₂O), (SrCl₂ + H₂O), and (BaCl₂ + H₂O). The applied ranges of temperature, pressure, and concentrations for the systems (LiCl + H₂O), (NaCl + H₂O), (KCl + H₂O), (MgCl₂ + H₂O), (CaCl₂ + H₂O), (SrCl₂ + H₂O), and (BaCl₂ + H₂O) are (273 K to 564 K, 0.1 MPa to 40 MPa, and 0 to 10 molal), (273 K to 573 K, 0.1 MPa to 100 MPa, and 0 to 6.0 molal), (273 K to 543 K, 0.1 MPa to 50 MPa, and 0 to 4.5 molal), (273 K to 543 K, 0.1 MPa to 40 MPa, and 0 to 3.0 molal), (273 K to 523 K, 0.1 MPa to 60 MPa, and 0 to 6.0 molal), (298 K to 473 K, 0.1 MPa to 2 MPa, and 0 to 2.0 molal) and (273 K to 473 K, 0.1 MPa to 20 MPa, and 0 to 1.6 molal), respectively. Comparison of the model with thousands of experimental data points concludes that the average deviation over the above T, P, m range is 0.020% to 0.066% in density (or volume) for these systems, which indicates high accuracy. From this model, various volumetric properties, such as the apparent molar volume at infinite dilution and isochores of fluid inclusions, can be calculated, thus having a wide range of geological applications, such as reservoir fluid flow simulation and fluid-inclusion study. A computer code is developed for this model and can be downloaded from the website: www.geochem-model.org/programs.htm and online calculations is made available on: www.geochem-model.org/models.htm     

(Liquid + liquid) equilibria of (tert -amyl ethyl ether + ethanol + water) at several temperatures

(Liquid  +  liquid) equilibrium data of (tert amyl ethyl ether  +  ethanol  +  water) were determined experimentally atT =  (298.15, 308.15, and 318.15) K. The experimental results were correlated with the NRTL and UNIQUAC equations. The correlations were made at each temperature and for the three temperatures simultaneously. The best results were achieved with the NRTL equation, using α =  0.2 for the individual correlations at each temperature and α =  0.1 for the overall correlation. The experimental data were also compared with predicted values by the UNIFAC method.     

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.     

(Liquid + liquid) equilibria of three ternary systems: (heptane + benzene + N-formylmorpholine), (heptane + toluene + N-formylmorpholine), (heptane + xylene + N-formylmorpholine) from T = (298.15 to 353.15) K

(Liquid + liquid) equilibrium (LLE) data for ternary systems: (heptane + benzene + N-formylmorpholine), (heptane + toluene + N-formylmorpholine), and (heptane + xylene + N-formylmorpholine) have been determined experimentally at temperatures ranging from 298.15 K to 353.15 K. Complete phase diagrams were obtained by determining solubility and tie-line data. Tie-line compositions were correlated by Othmer–Tobias and Bachman methods. The universal quasichemical activity coefficient (UNIQUAC) and the non-random two liquids equation (NRTL) were used to predict the phase equilibrium in the system using the interaction parameters determined from experimental data. It is found that UNIQUAC and NRTL used for LLE could provide a good correlation. Distribution coefficients, separation factors, and selectivity were evaluated for the immiscibility region.