PSRK: A Group Contribution Equation of State Based on UNIFAC

A group contribution equation of state called PSRK (Predictive Soave-Redlich-Kwong) which is based on the Soave-Redlich-Kwong equation (Soave, 1972) has been developed. It uses the UNIFAC method to calculate the mixture parameter a and includes all already existing UNIFAC parameters. This concept makes use of recent developments by Michelsen (1990b) and has the main advantage, that vapor-uquid-equilibria (VLB) can be predicted for a large number of systems without introducing new model parameters that must be fitted to experimental VLB-data. The PSRK equation of state can be used for VLB-predictions over a much larger temperature and pressure range than the UNIFAC γ--approach and is easily extended to mixtures containing supercritical compounds. Additional PSRK parameters, which allow the calculation of gas/gas and gas/alkane phase equilibria, are given in this paper. In addition to those mixtures covered by UNIFAC, phase equilibrium calculations may also include gases like CH₄ C₂H₆, C₃H₆, c₄H₁₀, CO₂, N₂, H₂ and CO.     

Vapor–liquid equilibria and excess molar volumes of diethylamine(1) + acetone(2) and diethylamine(1) + acetonitrile(2) binary systems

Isothermal vapor–liquid equilibrium (VLE) data for diethylamine(1)+acetone(2) and diethylamine(1)+acetonitrile(2) binary systems were obtained at 323.15 K by dynamic method. Excess molar volumes at 298.15 K for these systems were measured by a dilution dilatometer. VLE data have been checked for thermodynamic consistency and correlated by Wilson, NRTL and UNIQUAC equations. UNIFAC group interaction parameters for CH₂NH---CH₃CO and CH₂NH---CH₃CN pairs are also obtained from the experimental VLE data.     

PVTx measurements for N2O + CH3F, N2O + CH2F2, and N2O + CHF3 binary systems

Isochoric PVTx measurements have been performed for the binary system of nitrous oxide + CH₃F (R41), +CH₂F₂ (R32), and +CHF₃ (R23) using a new experimental set-up. The experiments covered both the two-phase region and the superheated vapor region and were performed within the temperature range 214–358 K and within a pressure range from 270 to 5600 kPa. Data have been collected for not less than four compositions for each system. The vapor–liquid equilibrium data were derived correlating the experimental data by means of the Carnahan–Starling–De Santis equation of state. The studied systems show a positive deviation from the Raoult's law. The results obtained were compared with the Burnett PVTx data. The two methods showed a mutual consistency within an acceptable margin of error. No other experimental PVTx data were found in the literature for these binary systems.     

Liquid phase equilibria of (water + propionic acid + oleyl alcohol) ternary system at several temperatures

(Liquid–liquid) equilibrium (LLE) data are investigated for mixtures of (water + propionic acid + oleyl alcohol) at 298.15, 308.15 and 318.15 K and atmospheric pressure. The solubility curves and the tie-line end compositions of liquid phases at equilibrium were determined, and the tie-line results were compared with the data predicted by the UNIFAC method. The phase diagrams for the ternary mixtures including both the experimental and correlated tie-lines are presented. The distribution coefficients and the selectivity factors for the immiscibility region are calculated to evaluate the effect of temperature change. The reliability of the experimental tie-lines was confirmed by using Othmer–Tobias correlation. It is concluded that oleyl alcohol may serve as an adequate solvent to extract propionic acid from its dilute aqueous solutions. The UNIFAC model correlates the LLE data for 298.15, 308.15 and 318.15 K with a root mean square deviation of 5.89, 6.46, and 6.69%, respectively, between the observed and calculated mole concentrations.     

Phase equilibria in binary systems containing N-monosubstituted amides and hydrocarbons

The binary vapour-liquid equilibrium of seven systems of -caprolactam + octane, + decane, + dodecane, octane, + decane, + dodecane, of N-methylacetamide + octane, of N-ethylacetamide of N-methylpropionamide + octane and of N-methylpropionamid + -caprolactam was measured in the temperature range from 363 to 423 K and in the low pressure region. A static equilibrium apparatus for the measurements was constructed.

In the system N-methylpropionamide + octane measurements of liquid-liquid equilibrium were carried out in the temperature range from 310 K up to the critical solution temperature.

The experimental results were correlated applying activity coefficients models such as NRTL. The data obtained from our measurements were used to estimate UNIFAC interaction parameters for the groups CH₂/CONHCH₂, CH₂/C₅H₁₀CONH and CONHCH₂/C₅H₁₀CONH.     

Rate constant of the reaction of NO3 with CH2I2 measured with use of cavity ring-down spectroscopy

We have applied cavity ring-down spectroscopy to a kinetic study of the reaction of NO₃ with CH₂I₂ in 25–100 Torr of N₂ diluent at 298 K. The rate constant of reaction of NO₃ + CH₂I₂ is determined to be (4.0 ± 1.2) × 10⁻¹³ cm³ molecule⁻¹ s⁻¹ in 100 Torr of N₂ diluent at 298 K. The rate constant increases with increasing pressure of buffer gas below 100 Torr. The reaction of CH₂I₂ with NO₃ has the potential importance at nighttime in the atmosphere.     

Isothermal vapor–liquid equilibria for different binary mixtures involved in the alcoholic distillation

Isothermal vapor–liquid equilibrium (VLE) data for five binary systems ethyl acetate + 3-methyl-1-butanol, ethanol + 3-methyl-1-butanol, ethyl acetate + 2-methyl-1-butanol, ethanol + 2-methyl-1-butanol, ethyl acetate + 2-methyl-1-propanol, involved in the alcoholic distillation have been determined experimentally by headspace gas chromatography. The composition in the liquid phase was corrected with the help of an iterative method by means of a G^E model. However, due to the large density difference between the liquid and the vapor, the correction of the liquid phase composition is nearly negligible. All the binary mixtures show positive deviations from Raoult's law. The experimental VLE data are well predicted by using the modified UNIFAC model (Dortmund).     

Phase diagram for the system KVO3 + NH4HCO3 + NH4VO3 + KHCO3 + H2O at 303 K

Solubility data of the KVO₃ + NH₄HCO₃ + NH₄VO₃ + KHCO₃ + H₂O system at 303 K were determined under varying pressure conditions. The results were used to construct a phase diagram in the oblique projection according to Jänecke's method. At constant p and T this diagram includes two invariant points, five double saturated liquid curves, and four crystallization fields corresponding to KVO₃, NH₄HCO₃, NH₄VO₃, and KHCO₃. It has been found that ammonium meta-vanadate is a sparingly soluble salt. NH₄VO₃ and KHCO₃ compose the stable pair of salts, whereas KVO₃ and NH₄HCO₃ form the unstable salt-pair. A thorough knowledge of the solubility phase diagram for this reciprocal quaternary salt system is the theoretical basis of the carbonation process of the potassium meta-vanadate saturated ammonia solution.     

(Liquid + liquid) equilibria of the (water + acetic acid + dibasic esters mixture) system

(Liquid + liquid) equilibrium (LLE) data for the {water + acetic acid + dibasic esters mixture (dimethyl adipate + dimethyl glutarate + dimethyl succinate)} system have been determined experimentally at T = (298.2, 308.2, and 318.2) K. Complete phase diagrams were obtained by determining solubility curve and tie-line data. The reliability of the experimental tie-line data was confirmed by using the Othmer-Tobias correlation. The UNIFAC model was used to predict the phase equilibrium in the system using the interaction parameters determined from experimental data between CH₂, CH₃COO, CH₃, COOH, and H₂O functional groups. Distribution coefficients and separation factors were compared with previous studies.     

Theoretical calculational studies on the mechanism of thermal dissociations for RN3 (R=CH3, CH3CH2, (CH3)2CH, (CH3)3C)

Mechanisms of RN₃ (R=CH₃, CH₃CH₂, (CH₃)₂CH, (CH₃)₃C) dissociations are proposed based on CAS, MP2 and B3LYP methods. The energy gaps between the ground-state reactants RN₃ and the intersystem crossing (ISC) points are only a little lower than respective potential energy barriers of the spin-allowed reactions, ¹RN₃ → ¹RN + ¹N₂. The ISC point, therefore, is considered as a transition state of the spin-forbidden reactions, ¹RN₃ → ³RN + ¹N₂. The methods of IRC and topological analysis of electron density are used to explain and predict the thermal dissociation pathways of the reactions studied.     

Liquid phase equilibria for mixtures of (an aliphatic hydrocarbon + toluene + γ-butyrolactone) at 298.2 K and atmospheric pressure

Liquid–liquid equilibrium (LLE) data for three ternary systems consisting of {n-heptane or n-hexane or cyclohexane (1) + toluene (2) + γ-butyrolactone (3)} were measured at 298.2 K and atmospheric pressure. The reliability of the experimental tie-line data was verified by using the Othmer–Tobias correlation. Distribution coefficients, separation factors and selectivity were evaluated for the immiscibility region. The experimental tie-line data were correlated by the UNIQUAC equation and also predicted with the UNIFAC model. The calculated results were compared with the experimental data. Better agreement with the experimental data was obtained by the UNIQUAC equation. The UNIFAC model does not provide reasonable correlations.     

Activity coefficient at infinite dilution, azeotropic data, excess enthalpies and solid–liquid-equilibria for binary systems of alkanes and aromatics with esters

Binary azeotropic data have been measured at different pressures for ethyl acetate + heptane, methyl acetate + heptane, isopropyl acetate + hexane and isopropyl acetate + heptane by means of a wire band column. Additionally activity coefficients at infinite dilution have been determined for ethyl acetate and isopropyl acetate in decane and dodecane in the temperature range between 303.15 and 333.15 K with the help of the dilutor technique. Furthermore excess enthalpies for the binary systems methyl acetate + hexane, methyl acetate + decane, ethyl acetate + hexane and ethyl acetate + decane at 363.15 and 413.15 K have been studied with the help of isothermal flow calorimetry. Finally solid–liquid equilibria for the systems ethyl myristate + benzene and ethyl myristate + p-xylene have been investigated by a visual technique. All these data have been used for the revision and extension of the group interaction parameters of the group contribution method modified UNIFAC (Dortmund) and the group contribution equation of state VTPR. The experimental data was compared with the results predicted using the group contribution method modified UNIFAC (Dortmund) and the group contribution equation of state VTPR.     

Novel CO2 selectively permeating membranes containing PETEDA dendrimer

Pentaerythrityl tetraethylenediamine (PETEDA) dendrimer was synthesized from pentaerythrityl tetrabromide and ethylenediamine. Its molecular structure was characterized by elemental analysis, Fourier transform infrared resonance (FT-IR) and hydrogen nuclear magnetic resonance (¹H NMR) spectroscopy. The composite membranes for selectively permeating CO₂ were prepared by using PETEDA-PVA blend polymer as the active layer and polyethersulfone (PES) ultrafiltration membrane as the support layer and their permselectivity was tested by pure CO₂ and CH₄ gases and the gas mixture containing 10 vol.% CO₂ and 90 vol.% CH₄, respectively. For pure gases, the membrane containing 78.6 wt% PETEDA and 21.4 wt% PVA in the blend has a CO₂ permeance of 8.14 × 10⁻⁵ cm³ (STP) cm⁻² s⁻¹ cmHg⁻¹ and CO₂/CH₄ selectivity of 52 at 143.5 cmHg feed gas pressure. While feed gas pressure is 991.2 cmHg, CO₂ permeance reaches 3.56 × 10⁻⁵ cm³ (STP) cm⁻² s⁻¹ cmHg⁻¹ and CO₂/CH₄ selectivity is 19. For the gas mixture, the membrane has a CO₂ permeance of 6.94 × 10⁻⁵ cm³ (STP) cm⁻² s⁻¹ cmHg⁻¹ with a CO₂/CH₄ selectivity of 33 at 188.5 cmHg feed gas pressure, and a CO₂ permeance of 3.29 × 10⁻⁵ cm³ (STP) cm⁻² s⁻¹ cmHg⁻¹ with a CO₂/CH₄ selectivity of 7.5 at a higher feed gas pressure of 1164 cmHg. A possible gas transport mechanism in the composite membranes is proposed by investigating the permeating behavior of pure gases and the gas mixture and analyzing possible reactions between CO₂/CH₄ gases and the PETEDA-PVA blend polymer. The effect of PETEDA content in the blend polymer on permselectivity of the composite membranes was investigated, presenting that CO₂ permeance and CO₂/CH₄ selectivity increase and CH₄ permeance decreases, respectively with PETEDA content. This is explained by that with increasing PETEDA content, the carrier content increases, and the crystallinity and free volume of the PETEDA-PVA blend decrease that were confirmed by the experimental results of X-ray diffraction spectra (XRD) and positron annihilation lifetime spectroscopy (PALS).     

Liquid–liquid equilibria of water + ethanol + reformate

Liquid–liquid equilibria (LLE) of the multicomponent system water + ethanol + a synthetic reformate (composed of benzene, n-hexane, 2,2,4-trimethylpentane, and cyclohexane) was studied at atmospheric pressure and at 283.15 and 313.15 K. The mutual reformate–water solubility with addition of anhydrous ethanol was investigated. Different quantities of water were added to the blends in order to have a wide water composition spectrum, at each temperature. We conclude from our experimental results, that this multicomponent system presents a very small water tolerance and that phase separation could result a considerable loss of ethanol that is drawn into the aqueous phase. The results were also used to analyse the applicability of the UNIFAC group contribution method and the UNIQUAC model. Both models fit the experimental data with similar low average root mean square deviations (rsmd ≤ 2.05%) yielding a satisfactory equilibrium prediction for the multicomponent system, although the predicted ethanol (rsmd ≤ 4.6%) compositions are not very good. The binary interaction parameters needed for the UNIQUAC model were obtained from the UNIFAC method.     

Prediction of phase equilibrium in mixtures containing ionic liquids using UNIFAC

The UNIFAC model is extended to mixtures of ionic liquids consisting of the imidazolium cation and the hexafluorophosphate anion with alkanes, cycloalkanes, alcohols and water. Two new main groups, the imidazolium and the hexafluorophosphate groups, are introduced in UNIFAC. The required group interaction parameters between these groups and the existing UNIFAC main groups, CH₂, OH and H₂O, are determined by fitting binary liquid–liquid equilibrium and infinite dilution activity coefficient experimental data. The predictive capability of the extended UNIFAC model is examined against experimental data for vapour–liquid equilibrium, liquid–liquid equilibrium and activity coefficients at infinite dilution of binary and ternary systems containing 1-alkyl-3-alkyl′-imidazolium hexafluorophosphate ionic liquids, alkanes, cycloalkanes, alcohols and water. The results indicate that UNIFAC is a reliable model for phase equilibrium predictions in mixtures containing this type of ionic liquids.     

Liquid–liquid equilibria of ternary mixture (propargyl alcohol + diisopropyl ether + water)

The liquid–liquid equilibria (LLE) of ternary mixture (propargyl alcohol + diisopropyl ether + water) were measured under atmospheric pressure and at different temperatures of 297.25, 304.35, 313.15, and 323.25 K. It was found that the end points of tie-lines at the four temperatures were located almost on a common solubility curve but the tie-lines possessed different slopes that described different equilibrium relations. A comparison of the predicted values through use of UNIFAC method with the measured LLE data was carried out but the predicted values showed remarkable deviations from the experimental data.     

Using vibrational modes in the search for global minima of atomic and molecular clusters

The reaction between dimethyl sulfide (CH₃SCH₃) and nitrate radical (NO₃) is studied using density functional theory and ab initio methods. The transition state for this reaction is optimized at different levels of theory and basis sets, and then used for kinetics calculations of the rate constant. The CH₃SCH₃ + NO₃ reaction leading to CH₃SCH₂ and HNO₃ is shown to have a negative activation energy and thus negative temperature dependence. The study confirms that the NO₃ radical is a significant contributor to the oxidation of DMS in the troposphere.     

Spatial structure of β-substituted alkoxyvinyl trifluoromethyl ketones

Spatial structure of six β-substituted enones, with common structure R₁O–CR₂CH–COCF₃, were R₁ = C₂H₅, R₂ = H (ETBO); R₁ = R₂ = CH₃ (TMPO); R₁ = C₂H₅, R₂ = C₆H₅ (ETPO); R₁ = C₂H₅, R₂ = 4- O₂NC₆H₄ (ETNO); R₁ = C₂H₅, R₂ = C(CH₃)₃ (ETDO) were investigated by ¹H and ¹⁹F NMR, infrared spectroscopy and AM1 calculations. NMR spectra revealed that enones (MBO), (ETBO) and (TMPO) are exclusively (3E) isomers, whereas in (ETPO), (ETNO) and especially in (ETDO) the percentage of (3Z) isomers is significant and depends on the nature of solvents. Conformational behaviour of studied enones are determined by the rotation around of CC double bond, C–C and C–O single bonds (correspondingly trifluoroacetyl and alkoxy groups), and (EZZ) conformer being the most stable in all cases. IR spectra revealed that with the exception of (ETDO) (EZZ) conformer is most populated in all cases. Bulky substituents like phenyl or tert-butyl group at β-position of enone result in the equilibrium mainly between (EZZ) and (ZZZ) forms, whereas β-hydrogen and β-methyl substituents determine the equilibrium between (EZZ) and (EEZ) or (EZE) conformers.     

Vapour pressures and excess functions of N, N, N′, N′-tetramethylalkanediamine + cyclohexane. A group contribution study of the N---N proximity effect

The vapour pressuresof liquid cyclohexane + N, N, N′, N′-tetramethylalkanediamine, (CH₃)₂ N(CH₂)_uN(CH₃)₂ (u = 1,2) + cyclohexane mixtures were measured by a static method between 303.15 and 343.15 K at 10 K intervals. The excess molar enthalpies at 303.15 K were also measured.

The molar excess Gibbs energies, calculated from the vapour-liquid equilibrium data, and the molar excess enthalpies compare satisfactorily with group contribution (DISQUAC) predictions.

The proximity effect of N atoms produces a regular decrease of the interactional parameters.     

Theoretical investigations on the SO2 + HO2 reaction and the SO2–HO2 radical complex

The mechanism of the SO₂ + HO₂ reaction was studied theoretically for the first time. Three product channels were revealed, namely, O₂ + HOSO, O₂ + HSO₂, and OH + SO₃. The O₂ + HOSO channel dominates the reaction under combustion conditions. A five-member-ring complex [SO₂–HO₂] exists at the entrance of the reaction. The structure and binding energy (D_e and D₀) of the SO₂–HO₂ complex have been calculated. In view of D₀ = 21.2 ± 2.0 kJ mol⁻¹, the SO₂–HO₂ complex should be stable at low temperature. The infrared spectra and frequency shifts were calculated for both SO₂–HO₂ and SO₂–DO₂, and compared with the available experimental data.