Modelling (vapour + liquid) and (vapour + liquid + liquid) equilibria of {water (H2O) + methanol (MeOH) + dimethyl ether (DME) + carbon dioxide (CO2)} quaternary system using the Peng–Robinson EoS with Wong–Sandler mixing rule

The (vapour + liquid) equilibria (VLE) and (vapour + liquid + liquid) equilibria (VLLE) binary data from literature were correlated using the Peng–Robinson (PR) equation of state (EoS) with the Wong–Sandler mixing rule (WS). Two group contribution activity models were used in the PRWS: UNIFAC–PSRK and UNIFAC–Lby. The systems were successfully extrapolated from the binary systems to ternary and quaternary systems. Results indicate that the PRWS–UNIFAC–PSRK generally displays a better performance than the PRWS–UNIFAC–Lby.     

Vapor–liquid equilibrium of the (water + ethanol + glycerol) system: Experimental and modelling data at normal pressure

In this work, vapor-liquid equilibrium data of the ethanol–water–glycerol system were measured in an Othmer-type ebulliometer at normal pressure. The choice for this system was due to the importance of the ethanol–water separation. The samples analyses were done in a digital densimeter, and the methodology was previously validated with data available in the literature. Since the mean relative deviation was less than 5% in temperature and vapor composition, new data from mixtures of ethanol–water–glycerol were obtained. The experiments showed that glycerol is a promising solvent to ethanol dehydration since it eliminates the azeotrope and promotes the production of anhydrous ethanol. A thermodynamic model for this system was developed using the NRTL model to describe the non-ideality of the liquid phase. The modeling results were compared with experimental data and the deviations were lower than 7%. In this way, the model developed in this work can be used for simulation of ethanol dehydration.     

(Vapour + liquid) equilibria for the binary mixtures (cis-pinane + α-pinene) and (cis-pinane + 1-butanol)

The isothermal and isobaric (vapour + liquid) equilibria for (cis-pinane + α-pinene) and (cis-pinane + 1-butanol) measured with an inclined ebulliometer are presented. The experimental results are analysed using the UNIQUAC equation with the temperature-dependence binary parameters with satisfactory results. Experimental vapour pressures of cis-pinane are also included.     

(Liquid + liquid) equilibria for (water + 1-propanol or acetone + β-citronellol) at different temperatures

On this paper, experimental (liquid + liquid) equilibrium (LLE) results are presented for systems composed of β-citronellol and aqueous 1-propanol or acetone. To evaluate the phase separation properties of β-citronellol in aqueous mixtures, LLE values for the ternary systems (water + 1-propanol + β-citronellol) and (water + acetone + β-citronellol) were determined with a tie-line method at T = (283.15, 298.15, and 313.15 ± 0.02) K and atmospheric pressure. The reliability of the experimental tie-lines was verified by the Hand and Bachman equations. Ternary phase diagrams, distribution ratios of 1-propanol and acetone in the mixtures are shown. The effect of the temperature on the ternary (liquid + liquid) equilibria was examined and discussed. The experimental LLE values were satisfactorily correlated by extended UNIQUAC and modified UNIQUAC models.     

Ebulliometric determination and prediction of (vapor + liquid) equilibria for binary and ternary mixtures containing alcohols (C1–C4) and dimethyl carbonate

(Vapor + liquid) equilibrium (VLE) data for a ternary mixture, namely {methanol + propan-1-ol + dimethyl carbonate (DMC)}, and four binary mixtures, namely an {alcohol (C₃ or C₄) + DMC}, containing the binary constituent mixtures of the ternary mixture, were measured at p = (40.00 to 93.32) kPa using a modified Swietoslawski-type ebulliometer. The experimental data for the binary systems were correlated using the Wilson model. The Wilson model was also applied to the ternary system to predict the VLE behavior using parameters from the binary mixtures. The modified UNIFAC (Dortmund) model was also tested for the predictions of the VLE behavior of the binary and ternary mixtures. In addition, the experimental VLE data for the ternary and constituent binary mixtures were correlated using the extended Redlich–Kister (ERK) model, which can completely represent the azeotropic points. For the ternary system, a comparison of the experimental and the predicted or correlated boiling points obtained using the Wilson and ERK models showed that the ERK model is more accurate. The valley line, i.e., the curve which divides the patterns of vapor–liquid tie lines, was found in the (methanol + propan-1-ol + DMC) system. This valley line could be represented by the ERK model. Finally, the composition profile for simple distillation of this ternary mixture was obtained by analysis of the residue curves from the estimated Wilson parameters of the constituent binary mixtures.     

A thermodynamic study on solubility and liquid−liquid phase behaviour for 2,2,2-trifluoroethanol + cyclohexane + 1-butanol at three temperatures and pressure 101.3 kPa

This study demonstrates the course of solubility and (liquid + liquid) equilibrium (LLE) for the system (cyclohexane + 1-butanol + 2,2,2-trifluoroethanol) at temperatures of (288.15, 298.15, and 308.15) K and pressure 101.3 kPa. The titration method was used to assess solubility (binodal) curves, while a direct analytical method to acquire tie lines.The consistency of the binodal curves and phase diagrams data were well calculated by Hand and Othmer–Tobias empirical equations. The NRTL and UNIQUAC thermodynamic models gave accurate tie-line values for the systems. Plait-point, distribution coefficient, solvent selectivity, and NRTL and UNIQUAC binary interaction parameters were obtained.The immiscibility region of the system decreases significantly with increasing temperature. The results present an overview of the high efficiency of liquid extraction using 2,2,2-trifluoroethanol as solvent to yield pure cyclohexane from its 1-butanol azeotrope mixture at ambient temperatures.     

The liquid–liquid coexistence curves of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} in the critical region

Liquid + liquid coexistence curves for the binary solutions of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} have been measured in the critical region. The critical exponent β and the critical amplitudes have been deduced and the former is consistent with the theoretic prediction. It was found that the coexistence curves may be well described by the crossover model proposed by Gutkowski et al. The asymmetries of the diameters of the coexistence curves were also discussed in the frame of the complete scaling theory.     

Correlation of CO2 solubility in N-methyldiethanolamine + piperazine aqueous solutions using extended Debye–Hückel model

Solubility data of CO₂ in aqueous N-methyldiethanolamine (MDEA) solutions of concentration (2.52, 3.36, and 4.28) kmol/m³ were obtained at temperatures (313, 323, and 343) K and partial pressures ranging from about (30 to 5000) kPa. A thermodynamic model based on extended Debye–Hückel theory was applied to predict and correlate of CO₂ solubility in various aqueous amine solutions. The effect of piperazine (PZ) concentration on CO₂ loading in MDEA solutions was determined at PZ concentration (0.36, 0.86, and 1.36) kmol/m³. Using experimental data in various temperatures the interaction parameters of activity coefficient model for these systems were determined. The results show the model consistency with experimental and literature data and PZ is beneficial to the CO₂ loading. The comparison of results of this study with previous data work shows the wide range of CO₂ loading considered in this work and the better agreement of model with experimental data. The average absolute relative deviation percent (δ_AAD) for all data points were 8.11%.     

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

The (vapor + liquid) equilibrium values reported by Mohsen-Nia and Memarzadeh appear to be flawed. In particular, neither the reported experimental activity coefficients are consistent with the reported composition data nor the reported model parameters can be used to adequately represent their experimental data.     

Phase diagrams of (vapour + liquid) equilibrium for binary mixtures of α,α,α-trifluorotoluene with ethanol,or benzene,or chloroform at pressure 101.4 kPa

(Vapour + liquid) equilibrium (VLE) of binary mixtures of (ethanol + α,α,α-trifluorotoluene), (benzene + α,α,α-trifluorotoluene), and (chloroform + α,α,α-trifluorotoluene) have been investigated at the pressure 101.4 kPa using the dynamic-ebulliometry method over the whole composition range. The correlated VLE phase diagrams were adequately described by means of NRTL and UNIQUAC thermodynamic models. Fair attractive energies in the first two systems are capable to yield azeotropes, while moderate repulsive energies in the later system make it zeotrope.     

Vapor–liquid equilibrium measurement and modeling for the difluoromethane + pentafluoroethane + propane ternary mixture

Vapor–liquid equilibrium data for the difluoromethane (R32) + pentafluoroethane (R125) + propane (R290) ternary mixture were measured at 5 isotherms between 263.15 K and 323.15 K. The measurement was carried out using a circulation-type apparatus recently developed, which was validated with binary mixtures. With binary interaction parameters obtained for the three corresponding binary mixtures, VLE modeling and prediction were performed for the ternary mixture using the Peng–Robinson equation of state with the classical mixing rules and MHV1 mixing rules. Hou's group contribution model for VLE of new refrigerant mixtures was further tested with the experimental data for the ternary system. The predicted pressure and vapor phase composition were compared with experimental ones.     

Measurement and prediction of (solid + liquid) equilibria of gun powder’s and propellant’s stabilizers mixtures

A differential scanning calorimetry (d.s.c.) was used to determine binary (solid + liquid) phase equilibria (SLE) for four binary mixtures, viz. (n-nitrosodiphenylamine + diphenylamine), (2-nitrodiphenylamine + ethyl centralite), (2,4-dinitro-N-ethylaniline + methyl centralite), and (2,4-diphenylamine + 4,4′-dinitroethylcentralite). These compounds are used as stabilizers in gun powders and propellants. Results obtained with this technique are compared with those correlated by NRTL and ideal models. It was found out that all the systems are simple eutectic systems and deviations between experimental and predicted SLE results were observed.     

The liquid–liquid coexistence curves of {x dimethyl adipate + (1 − x) n-hexane} and {x dimethyl adipate + (1 − x) n-heptane} in the critical region

The liquid–liquid coexistence curves for (dimethyl adipate + n-hexane), (dimethyl adipate + n-heptane) have been measured, from which the critical amplitudes and the critical exponents are deduced. The critical exponent β corresponding to the coexistence curves are consistent with the 3D-Ising value. The experimental results have also been analyzed to determine the critical amplitudes of Wegner-correction terms when β and Δ are fixed at their theoretical values, and to examine the asymmetry of the diameters for the coexistence curves.     

A reliable prediction of the global phase stability for liquid–liquid equilibrium through the simulated annealing algorithm: Application to NRTL and UNIQUAC equations

The simulated annealing algorithm is introduced to search the global optimal solutions for the multipeak phenomena which generally exist in the phase stability problems with continuous variables. The Gibbs free energy criterion was modeled by the NRTL and UNIQUAC activity coefficient equations. When previous approaches fail, it is usually because they locate local minima due to the nonconvex and nonlinear natures of the models used to predict phase equilibrium. In this paper, the preliminary results show that the global minimum of the tangent plane distance function (TPDF) can be obtained by using the simulated annealing algorithm. The effects of the initial and the final values of the control parameter, the decrement of the control parameter and the length of the Markov chains are analyzed. The optimal `cooling schedule' was obtained according to the calculation results of the phase stability problems for one ternary mixture. The liquid–liquid equilibrium compositions were calculated by the Newton–Raphson method on the basis of the global minimum of TPDF. The results of four examples show that the simulated annealing algorithm can effectively solve the global phase stability problem.     

Thermodynamics of the oxidation–reduction reaction {2 glutathionered(aq) + NADPox(aq)=glutathioneox(aq) + NADPred(aq)}

Microcalorimetry, spectrophotometry, and high-performance liquid chromatography (h.p.l.c.) have been used to conduct a thermodynamic investigation of the glutathione reductase catalyzed reaction {2 glutathione_red(aq) + NADP_ox(aq)=glutathione_ox(aq) + NADP_red(aq)}. The reaction involves the breaking of a disulfide bond and is of particular importance because of the role glutathione_red plays in the repair of enzymes. The measured values of the apparent equilibrium constant K^′ for this reaction ranged from 0.5 to 69 and were measured over a range of temperature (288.15 K to 303.15 K), pH (6.58 to 8.68), and ionic strength I_m (0.091 mol · kg⁻¹ to 0.90 mol · kg⁻¹). The results of the equilibrium and calorimetric measurements were analyzed in terms of a chemical equilibrium model that accounts for the multiplicity of ionic states of the reactants and products. These calculations led to values of thermodynamic quantities at T=298.15 K and I_m=0 for a chemical reference reaction that involves specific ionic forms. Thus, for the reaction {2 glutathione_red⁻(aq) + NADP_ox³⁻(aq)=glutathione_ox²⁻(aq) + NADP_red⁴⁻(aq) + H⁺(aq)}, the equilibrium constant K=(6.5±4.4)·10⁻¹¹, the standard molar enthalpy of reaction Δ_rH^o_m=(6.9±3.0) kJ · mol⁻¹, the standard molar Gibbs free energy change Δ_rG^o_m=(58.1±1.7) kJ · mol⁻¹, and the standard molar entropy change Δ_rS^o_m=−(172±12) J · K⁻¹ · mol⁻¹. Under approximately physiological conditions (T=311.15 K, pH=7.0, and I_m=0.25 mol · kg⁻¹ the apparent equilibrium constant K^′≈0.013. The results of the several studies of this reaction from the literature have also been examined and analyzed using the chemical equilibrium model. It was found that much of the literature is in agreement with the results of this study. Use of our results together with a value from the literature for the standard electromotive force E^o for the NADP redox reaction leads to E^o=0.166 V (T=298.15 K and I=0) for the glutathione redox reaction {glutathione_ox²⁻(aq) + 2 H⁺(aq) + 2 e⁻=2 glutathione_red⁻(aq)}. The thermodynamic results obtained in this study also permit the calculation of the standard apparent electromotive force E^′o for the biochemical redox reaction {glutathione_ox(aq) + 2 e⁻=2 glutathione_red(aq)} over a wide range of temperature, pH, and ionic strength. At T=298.15 K, I=0.25 mol · kg⁻¹, and pH=7.0, the calculated value of E^′o is −0.265 V.