Thermodynamic consistency of experimental VLE data for asymmetric binary mixtures at high pressures

A thermodynamic consistency of isothermal vapor–liquid equilibrium data for 9 non-polar and 8 polar binary asymmetric mixtures at high pressures has been evaluated. A method based on the isothermal Gibbs–Duhem equation was used for the test of thermodynamic consistency using a Φ–Φ approach. The Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the vapor–liquid equilibrium (VLE) within the thermodynamic consistency test. The VLE parameters calculations for asymmetric mixtures at high pressures were highly dependent on bubble pressure calculation, making more convenient to eliminate the data points yielding the highest deviations in pressure. However the results of the thermodynamic consistencies test of experimental data for many cases were found not fully consistent. As a result, the strategies for solving these problems were discussed in detailed.     

Thermodynamic consistency of high pressure ternary mixtures containing a compressed gas and solid solutes of different complexity

A thermodynamic consistency test applicable to high pressure binary gas–solid mixtures is extended to ternary mixtures containing a compressed gas and two solid solutes. A high pressure mixture containing carbon dioxide as solvent and two chemically similar solutes (2,3 dimethylnaphthalene and 2,6 dimethylnaphthalene) and a high pressure mixture containing carbon dioxide as solvent and two chemically different solutes (capsaicin and β-carotene), are considered in the study. Several sets of isothermal solubility data for binary and ternary mixtures are considered in the study. The Peng–Robinson equation of state with the mixing rules of Wong and Sandler have been employed for modeling the solubility of the solid in the case of binary mixtures, while the classical van der Waals mixing rules were used for modeling the ternary mixtures containing two solid solutes. Then the proposed thermodynamic consistency test has been applied. The results show that the thermodynamic test for ternary mixtures can be applied with confidence determining consistency or inconsistency of the experimental data used.     

Revised Phase Diagram of the System NaF–NaBF4

Summary. The phase diagram of the binary system NaF–NaBF₄ was determined using the thermal analysis method. Subsequent coupled analysis of the thermodynamic and phase diagram data was carried out to calculate the thermodynamically consistent phase diagram. The system NaF–NaBF₄ forms a simple eutectic phase diagram with the calculated coordinates of the eutectic point: 8.1 mol% NaF, 91.9 mol% NaBF₄, and 385.7°C. The probable inaccuracy in the calculated binary phase diagram is 9°C.     

Solid–Liquid Phase Equilibria in the Ternary Systems (LiBO 2 + NaBO 2 + H 2 O) and (LiBO 2 + KBO 2 + H 2 O) at 288.15 K and 0.1 MPa

Solid–liquid phase equilibria for the two aqueous systems (LiBO2 + NaBO2 + H2O) and (LiBO2 + KBO2 + H2O) at T = 288.15 K and p = 0.1 MPa were determined using the isothermal dissolution equilibrium method. The experimental results show that the phase diagrams consist of one two-salt co-saturated invariant point, two univariant solubility isotherms, and three crystallization fields. The two systems belong to simple co-saturated type, and neither double salt nor solid solution were found. The densities change regularly as the sodium metaborate (potassium metaborate) concentration increases in solution, and reach their maximum values at the invariant point. Based on the Pitzer and its extended Harvie–Møller–Weare (HMW) model, the solubilities for the ternary systems at 288.15 K were represented, and the calculated results agree well with the experimental values.     

Volumetric and Viscosimetric Measurements for Methanol + CH 3 –O–(CH 2 CH 2 O) n –CH 3 ( n = 2, 3, 4) Mixtures at (293.15–303.15) K and Atmospheric Pressure: Application of the ERAS Model

Densities, $$\rho$$, and kinematic viscosities, $$\nu$$, have been determined at atmospheric pressure and at 293.15–303.15 K for binary mixtures formed by methanol and one linear polyether of the type CH3–O–(CH2CH2O)n–CH3 (n = 2, 3, 4). Measurements on $$\rho$$ and $$\nu$$ were carried out, respectively, using an Anton Paar DMA 602 vibrating-tube densimeter and an Ubbelohde viscosimeter. The $$\rho$$ values were used to compute excess molar volumes, $$V_{{\text{m}}}^{{\text{E}}}$$, and, together with the $$\nu$$ results, dynamic viscosities ($$\eta$$). Deviations from linear dependence on mole fraction for viscosity, $$\Delta \eta$$, are also provided. Different semi-empirical equations have been employed to correlate viscosity data. Particularly, the equations used are the: Grunberg–Nissan, Hind, Frenkel, Katti–Chaudhri, McAllister and Heric. Calculations show that better results are obtained from the Hind equation. The $$V_{{\text{m}}}^{{\text{E}}}$$ values are large and negative and contrast with the positive excess molar enthalpies, $$H_{{\text{m}}}^{{\text{E}}}$$, available in the literature, for these systems. This indicates that structural effects are dominant. The $$\Delta \eta$$ results are positive and correlate well with the difference in volumes of the mixture compounds, confirming the importance of structural effects. The temperature dependences of $$\eta$$ and of the molar volume have been used to calculate enthalpies, entropies and Gibbs energies, $$\Delta G^{*}$$, of viscous flow. It is demonstrated that $$\Delta G^{*}$$ is essentially determined by enthalpic effects. Methanol + CH3–O–(CH2CH2O)n–CH3 mixtures have been treated in the framework of the ERAS model. Results for $$H_{{\text{m}}}^{{\text{E}}}$$ are acceptable, while the composition dependence of the $$V_{{\text{m}}}^{{\text{E}}}$$ curves is poorly represented. This has been ascribed to the existence of strong dipolar and structural effects in the present solutions.     

Solubility of Acetaminophen and Ibuprofen in Polyethylene Glycol 600, N-Methyl Pyrrolidone and Water Mixtures

The solubility of acetaminophen and ibuprofen in binary and ternary mixtures of N-methyl pyrrolidone, polyethylene glycol 600 and water at 25 °C were determined and the solubilities are mathematically represented by the Jouyban–Acree model. The density of the solute-free solvent mixtures was measured and employed to train the Jouyban–Acree model and then the densities of the saturated solutions were predicted. The overall mean relative deviations (OMRDs) for fitting the solubility data of acetaminophen and ibuprofen in binary mixtures are 3.2% and 6.0%, respectively. The OMRDs for fitting the solubilities in ternary solvent mixtures for acetaminophen and ibuprofen are 15.0% and 28.6%, respectively, and the OMRD values for predicting all solubilities of acetaminophen and ibuprofen by a trained version of the Jouyban–Acree model are 9.4% and 17.8%, respectively. The prediction OMRD for the density of saturated solutions is 1.9%.     

Excess Molar Volumes,Viscosities and Speeds of Sound of the Ternary Mixture 1-Heptanol (1) + Tetrachloroethylene (2) + Methylcyclohexane (3) at 298.15 K

Densities (ρ), viscosities (η) and speeds of sound (u) of the ternary mixture (1-heptanol + tetrachloroethylene + methylcyclohexane) and the corresponding binary mixtures (1-heptanol + tetrachloroethylene), (1-heptanol + methylcyclohexane) and (tetrachloroethylene + methylcyclohexane) at 298.15 K were measured over the whole composition range. The data obtained are used to calculate the excess molar volumes (V ^E), excess isobaric thermal expansivities (α ^E), viscosity deviations (Δη), excess Gibbs energies of activation of viscous flow (ΔG ^*E) and excess isentropic compressibilities (κ _S ^E) of the binary and ternary mixtures. The data from the binary systems were fitted by the Redlich–Kister equation whereas the best correlation method for the ternary system was found using the Nagata equation. Viscosities, speeds of sound and isentropic compressibilities of the binary and ternary mixtures have been correlated by means of several empirical and semi-empirical equations. The best correlation method for viscosities of binary systems is found using the Iulan et al. equation and for the ternary system using the Heric and McAllister equations. The best correlation method for the speeds of sound and isentropic compressibilities of the binary system (1-heptanol + methylcyclohexane) is found using IMR (Van Deal ideal mixing relation) and for the binary system (tetrachloroethylene + methylcyclohexane) it is found using the NR (Nomoto relation) and for the binary system (1-heptanol + tetrachloroethylene) and the ternary system (1-heptanol + trichloroethylene + methylcyclohexane) it is obtained from the FLT (Jacobson free length theory).     

Experimental Determination and Correlation of Liquid–Liquid Equilibria Data for the Ternary Systems of Water + 1-Butanol + Solvents (Isophorone and Mesityl Oxide) at Different Temperatures

Liquid–liquid equilibria (LLE) data for {water + 1-butanol + isophorone} and {water + 1-butanol + mesityl oxide} ternary systems were investigated systematically at different temperatures under atmospheric pressure. The Othmer–Tobias and Bachman equations were applied to analyze the dependability of the experimental LLE data. Selectivities and distribution coefficients were used to evaluate the extractive efficiency of the extractants. The Non-Random Two Liquid (NRTL) and Universal Quasi-Chemical (UNIQUAC) models were applied to correlate the studied systems and were well represented with all root mean square deviations (RMSD) less than 0.2%. Meanwhile, binary interaction parameters among these compounds were acquired during the correlation process.     

Phase Behavior of Aqueous Na–K–Mg–Ca–Cl–NO<Subscript>3</Subscript> Mixtures: Isopiestic Measurements and Thermodynamic Modeling

A comprehensive model has been established for calculating thermodynamic properties of multicomponent aqueous systems containing the Na⁺, K⁺, Mg²⁺, Ca²⁺, Cl⁻ and NO₃⁻ ions. The thermodynamic framework is based on a previously developed model for mixed-solvent electrolyte solutions. The framework has been designed to reproduce the properties of salt solutions at temperatures ranging from the freezing point to 300 °C and concentrations ranging from infinite dilution to the fused salt limit. The model has been parameterized using a combination of an extensive literature database and new isopiestic measurements for thirteen salt mixtures at 140 °C. The measurements have been performed using Oak Ridge National Laboratory’s (ORNL) previously designed gravimetric isopiestic apparatus, which can also detect solid phase precipitation. In addition to various Na–K–Mg–Ca–Cl–NO₃ systems, results are reported for LiCl solutions. Water activities are reported for mixtures with a fixed ratio of salts as a function of the total apparent salt mole fraction. The isopiestic measurements reported here simultaneously reflect two fundamental properties of the system, i.e., the activity of water as a function of solution concentration and the occurrence of solid–liquid transitions. The thermodynamic model accurately reproduces the new isopiestic data as well as literature data for binary, ternary and higher-order subsystems. Because of its high accuracy in calculating vapor–liquid and solid–liquid equilibria, the model is suitable for studying deliquescence behavior of multicomponent salt systems.     

Phase equilibria and critical phenomena in the potassium perchlorate-water-<Emphasis Type="Italic">n</Emphasis>-butoxyethanol ternary system

Phase equilibria and critical phenomena in the potassium perchlorate-water-n-butoxyethanol ternary system, where the boundary liquid binary system is characterized by the presence of a closed stratification region, were studied by the visual-polythermal method over the temperature range 40–150°C. The temperature of the formation of the critical monotectic equilibrium tie line (141.0°C) and temperature dependences of the compositions of mixtures corresponding to the critical solubility points of the stratification region over the temperature ranges 47.7–130.3 and 141.0–150.0°C were determined. The isotherms of phase states constructed at 10 temperatures were used to reveal the topological transformation of the phase diagram of the ternary system depending on temperature. At low concentrations (up to 5.8 wt %), potassium perchlorate had a salting in action on heterogeneous water-n-butoxyethanol mixtures. The solubility of the salt increased as the temperature grew, and, above 141.0°C, potassium perchlorate had a salting out action. The salting out of n-butoxyethanol from aqueous solutions by potassium perchlorate grew stronger as the temperature increased.     

Phase Transitions and Critical Behaviour of Binary Liquid Mixtures

Summary.  Compared to the simple one-component case, the phase behaviour of binary liquid mixtures shows an incredibly rich variety of phenomena. In this contribution we restrict ourselves to so-called binary symmetric mixtures, i.e. where like-particle interactions are equal (Φ₁₁(r) = Φ₂₂(r)), whereas the interactions between unlike fluid particles differ from those of likes ones (Φ₁₁(r) ≠ Φ₁₂(r)). Using both the simple mean spherical approximation and the more sophisticated self-consistent Ornstein-Zernike approximation, we have calculated the structural and thermodynamic properties of such a system and determine phase diagrams, paying particular attention to the critical behaviour (critical and tricritical points, critical end points). We then study the thermodynamic properties of the same binary mixture when it is in thermal equilibrium with a disordered porous matrix which we have realized by a frozen configuration of equally sized particles. We observe – in qualitative agreement with experiment – that already a minute matrix density is able to lead to drastic changes in the phase behaviour of the fluid. We systematically investigate the influence of the external system parameters (due to the matrix properties and the fluid–matrix interactions) and of the internal system parameters (due to the fluid properties) on the phase diagram. Received June 27, 2001. Accepted July 2, 2001     

Phase Transitions and Critical Behaviour of Binary Liquid Mixtures

 Compared to the simple one-component case, the phase behaviour of binary liquid mixtures shows an incredibly rich variety of phenomena. In this contribution we restrict ourselves to so-called binary symmetric mixtures, i.e. where like-particle interactions are equal (Φ₁₁(r) = Φ₂₂(r)), whereas the interactions between unlike fluid particles differ from those of likes ones (Φ₁₁(r) ≠ Φ₁₂(r)). Using both the simple mean spherical approximation and the more sophisticated self-consistent Ornstein-Zernike approximation, we have calculated the structural and thermodynamic properties of such a system and determine phase diagrams, paying particular attention to the critical behaviour (critical and tricritical points, critical end points). We then study the thermodynamic properties of the same binary mixture when it is in thermal equilibrium with a disordered porous matrix which we have realized by a frozen configuration of equally sized particles. We observe – in qualitative agreement with experiment – that already a minute matrix density is able to lead to drastic changes in the phase behaviour of the fluid. We systematically investigate the influence of the external system parameters (due to the matrix properties and the fluid–matrix interactions) and of the internal system parameters (due to the fluid properties) on the phase diagram.     

Thermal analysis of the system triamterene-d-mannitol

Thermal analysis (DSC and HSM), and equilibrium solubility determinations were carried out to elucidate the mechanism of interaction at the solid state in the binary system triamterene-D-mannitol. Physical mixtures (5–90% w/w triamterene) and solid dispersions (5 up to 40% w/w triamterene) were prepared and studied. From DSC and HSM results, the thermal changes were associated with the variations in composition of the binary mixture, being more pronounced in the range 20–50% w/w. The binary phase diagram was proposed, although the exact position of the eutectic was uncertain. This is in accordance with a partial dissolution process detected by HSM. A linear increase in the solubility of triamterene with increasing aqueous mannitol concentration was obtained. The thermodynamic parameters of the solution properties were calculated, with an activation energy value of 96.081 kJ/mole. The solubilization increase was associated with complexation processes and hydrogen bonding formation. Dedicated to Professor Lisa Heller-Kallai on the occasion of her 65^th birthday     

Phase equilibria of binary mixtures containing methyl acetate,water, methanol or ethanol at 101.3 kPa

Isobaric vapor–liquid equilibria data at 101.3?kPa were reported for the binary mixtures (methyl acetate?+?(water or methanol or ethanol), methanol?+?(water or ethanol) and (ethanol?+?water)). The experimental data were tested for thermodynamic consistency by means of the Wisniak method and were demonstrated to be consistent. The experimental data were correlated using Wilson, NRTL and UNIQUAC models for the activity coefficients and predicted using the UNIFAC and PSRK equation of state for testing theirs capability. The results show that the obtained data for the studied binary systems are more reliable than other published data.     

Mercury(II) Biosorption Using <Emphasis Type="Italic">Lessonia</Emphasis> sp. Kelp

Lessonia nigrescens and Lessonia trabeculata kelps have been tested for the sorption of mercury from aqueous solutions. A pretreatment (using CaCl₂) allowed stabilizing the biomass that was very efficient for removing Hg(II) at pH 6–7. Sorption isotherms were described by the Langmuir equation with sorption capacities close to 240–270 mg Hg g⁻¹ at pH 6. The temperature had a negligible effect on the distribution of the metal at equilibrium. The presence of chloride anions had a more marked limiting impact than sulfate and nitrate anions. The uptake kinetics were modeled using the pseudo-second-order equation that fitted better experimental data than the pseudo-first-order equation. The particle size hardly influenced sorption isotherms and uptake kinetics, indicating that sorption occurs in the whole mass of the biosorbent and that intraparticle mass transfer resistance was not the limiting rate. Varying the sorbent dosage and the initial metal concentration influenced the equilibrium, but the kinetic parameters were not drastically modified. Metal can be eluted with hydrochloric acid, citric acid, or acidic KI solutions.     

Adsorption equilibrium of binary methane/ethane mixtures in BPL activated carbon: isotherms and calorimetric heats of adsorption

The adsorption of pure methane and ethane in BPL activated carbon has been measured at temperatures between 264 and 373 K and at pressures up to 3.3 MPa with a bench-scale high-pressure open-flow apparatus. The same apparatus was used to measure the adsorption of binary methane/ethane mixtures in BPL at 301.4 K and at pressures up to 2.6 MPa. Thermodynamic consistency tests demonstrate that the data are thermodynamically consistent. In contrast to two sets of data previously published, we found that the adsorption of binary methane/ethane in BPL behaves ideally (in the sense of obeying ideal adsorbed solution theory, IAST) throughout the pressure and gas-phase composition range studied. A Tian-Calvet type microcalorimeter was used to measure low-pressure isotherms, the isosteric heats of adsorption of pure methane and ethane in BPL activated carbon, and the individual heats of adsorption in binary mixtures, at 297 K and at pressures up to 100 kPa. The mixture heats of adsorption were consistent with IAST.     

Solubility Parameter of Gatifloxacin and Its Correlation with Antibacterial Activity

The solubility parameter of gatifloxacin was calculated theoretically by Fedors’ method and also determined experimentally using the standard solubility method. The molar volume of gatifloxacin was determined experimentally by the flotation method. Three solvents, ethyl acetate, propylene glycol and water were used to prepare nine binary mixtures having different solubility parameter values varying from 8.9 to 23.4 H. The δ ₂ solubility parameter of gatifloxacin was found to be 12.4 H. The cumulative transport of gatifloxacin from the binary solvent mixtures (ethyl acetate–propylene glycol and propylene glycol–water) exhibited an inverse parabolic relationship to the solubility parameter of the solvent mixtures. Transport studies revealed that the extent of gatifloxacin rejection from solvent mixtures was dependent on its solubility parameter and system composition. In the selected organisms (bacteria), a minimum zone of inhibition was observed in a solvent mixture having the solubility parameter nearest to the solubility parameter of gatifloxacin. Two models were employed for the evaluation of the antibacterial activity of gatifloxacin in binary mixtures.     

Water-soluble microgels made by radical polymerization in solution

The goal of this study was to prepare and characterize water-soluble, high-molecular-weight microgels. N-Vinylpyrrolidone (NVP) and vinylacetate (VAc) in combination with cross-linkers diethylene glycol dimethacrylate (DEGDMA) or diethylene glycol divinyl ether (DEGDVE) were copolymerized in solution to high conversion. Polymerization was performed in different solvents or solvent mixtures, with solubility parameters ranging from 16.0 to 47.6 J^0.5cm^−1.5, and at different initial monomer concentrations. In solvent mixtures with solubility parameters of 20–40 J^0.5cm^−1.5, macrogelation did not occur below a critical gelation concentration and microgels were formed. For NVP/VAc/DEGDMA (85.0/10.0/5.0 wt%, 84.8/12.9/2.4 mol%) and NVP/VAc/DEGDVE (85.0/10.0/5.0 wt%, 84.8/12.9/3.5 mol%) the critical gelation curves were determined. The molecular weights of the microgels depend on the solvent systems and the initial monomer concentration. Microgels of high molecular weight but low cross-linking density gave aqueous solutions with high viscosities. Increasing the amount of cross-linker to 20 wt% gave high-molecular-weight microgels with lower solution viscosity. Microgels with a monomer composition NVP/VAc/DEGDVE (65.0/15.0/20.0 wt%, 66.2/19.5/14.3 mol%) were prepared in ethanol at different monomer concentrations (3–20 wt%). The molecular weights were determined by a combination of field-flow fractionation and light scattering. By increasing the initial monomer concentration, the molecular weight and the molecular-weight distribution as well as the intrinsic viscosity increased. The exponent of the Mark–Houwink equation was 0.26. Received: 19 March 2001 Accepted: 20 July 2001     

Isobaric (vapour + liquid) equilibria for the (1-propanol + 1-butanol) binary mixture at (53.3 and 91.3) kPa

In this work, isobaric (vapour + liquid) equilibrium data have been determined at (53.3 and 91.3) kPa for the binary mixtures of (1-propanol + 1-butanol). The thermodynamic consistency of the experimental values was checked by means the traditional area test and the direct test methods. According to the criteria for the test methods, the (vapour + liquid) equilibrium results were found to be thermodynamically consistent. The experimental values obtained were correlated by using the van Laar, Margules, Wilson, NRTL, and UNIQUAC activity-coefficient models. The binary interaction parameters of the activity-coefficient models have been determined and reported. They have been compared with those calculated by the activity-coefficient models. The average absolute deviation in boiling point and vapour-phase composition were determined. The calculated maximum average absolute deviations were 0.86 K and 0.0151 for the boiling point and vapour-phase composition, respectively. Therefore, it was shown that the activity-coefficient models used satisfactorily correlate the (vapour + liquid) equilibrium results of the mixture studied. However, the performance of the UNIQUAC model was superior to all other models mentioned.     

Liquid–Liquid Equilibria of Oxygenate Fuel Additives with Water: Two Quaternary Aqueous Systems of Diisopropyl Ether + 2,2,4-Trimethylpentane with Methyl <Emphasis Type="Italic">tert</Emphasis>-Butyl Ether or Toluene

Experimental tie-line data for two quaternary systems, water + diisopropyl ether + 2,2,4-trimethylpentane + methyl tert-butyl ether or toluene, were investigated at 298.15 K and atmospheric pressure. The experimental liquid–liquid equilibrium data were correlated using a modified UNIQUAC activity coefficient model with ternary and quaternary parameters, in addition to the binary ones. The calculated results were further compared with those obtained with an extended UNIQUAC model from Nagata [Fluid Phase Equilib. 54, 191–206 (1990)].