Determination and measurement of solid–liquid equilibrium for binary fatty acid mixtures based on NRTL and UNIQUAC activity models

The estimation of solid–liquid phase equilibrium is important for the design, development, and operation of many industrial processes because of application in many manufacturing fields such as cosmetic, pharmaceutic, and biotechnology industries. In this work, we measured solid–liquid phase equilibrium of six fatty acid binary mixtures using the DSC technique and developed thermodynamic approaches for binary fatty acid mixtures to estimate melting temperatures as a function of mole fraction in solid–liquid phase equilibrium. Derivation of NRTL and UNIQUAC activity models was developed to predict melting temperatures and latent heat to achieve eutectic points of undecylic acid, pentadecylic acid, margaric acid, and stearic acid six pairwise binary mixtures. The fatty acids eutectic mixtures are appropriate for heat water systems, phase clothes, concrete, and other similar applications. The results showed low deviations from experimental data measured in this study.

     

Prediction and experimental verification of the salt effect on the vapour–liquid equilibrium of water–ethanol–2-propanol mixture

Experimental vapour–liquid equilibria of water–ethanol–2-propanol saturated with NaNO₃, NaCl, KCl and containing 0.05 mol CH₃COOK/mol total solvent compared well with those predicted by Tan–Wilson and Tan–non-random two liquid (NRTL) models for multicomponent solvent–solute mixture using a set of solvent–solvent interaction parameters obtained from the regression of the vapour–liquid equilibrium of the solvent mixture without the dissolved solute and a set of solute–solvent interaction parameters calculated from the bubble points of the individual solvent components saturated or containing the same molar ratio of solute/total solvents as the mixture. The results also showed that a solvent component i is salted-in or out of the liquid phase relatively more than solvent component j would depend on whether A_sj/A_si (Tan–Wilson model) or exp(τ_is−τ_js) (Tan–NRTL model) is less or greater than 1. This is consistent with earlier publications on the effect of dissolved solutes (electrolytes and non-electrolytes) on the binary solvents mixtures. These findings confirmed that Tan–Wilson and Tan–NRTL models for multicomponent solvent–solute system can provide an accurate and rapid screening of electrolytes and non-electrolytes for their suitability in facilitating solvent separation by salt distillation of ternary solvent mixtures simply by determining the relative ratios of the solute–solvent interaction parameters from the respective bubble points of the solvent components containing the dissolved solute. The results also suggest that this may also be extended to other multicomponent solvent mixtures.     

Thermodynamic aspects of phase equilibrium in binary water–organic solvent mixtures

It is shown that the boundary curves of liquid equilibria in binary systems characterize the temperature–concentration boundary of the existence of homogeneous mixtures whose formation is not accompanied by changes in the Gibbs energy of the system and are a combination of two branches that do not convert into each other but intersect at the temperature of homogenization of a mixture of critical composition. The phase diagrams of a number of water–organic solvent systems are analyzed to determine the thermodynamic particularities of the latter.

     

Solid–liquid phase equilibrium and mixing thermodynamic analysis of coumarin in binary solvent mixtures

The solubility of coumarin in three aqueous solvent mixtures (methanol + water, ethanol + water and acetone + water) was experimentally determined by a gravimetric method at atmospheric pressure. The experimental solubility data were fitted using the modified Apelblat equation, non-random two-liquid (NRTL) equation, the combined nearly ideal binary solvent/Redlich–Kister equation and the Jouyban?Acree equation, respectively. All the equations were proven to be able to correlate the experimental data, and the modified Apelblat equation could obtain better correlation results than the other three models. The solubility of coumarin increases with increase in temperature. At the same temperature, the solubility increases with increase in mole fraction of organic solvents except for the ethanol–water system which shows a unimodal curve. In addition, the apparent thermodynamic properties of the mixing process were calculated based on the NRTL model and the experimental solubility data.     

Vapor–liquid equilibrium of binary mixtures of trichloroethylene with 1-pentanol, 2-methyl-1-butanol and 3-methyl-1-butanol at 100 kPa

Isobaric vapor–liquid equilibria (VLE) have been obtained for the systems trichloroethylene+1-pentanol, trichloroethylene+2-methyl-1-butanol and trichloroethylene+3-methyl-1-butanol at 100 kPa using a dynamic still. The experimental error in temperature is ±0.1 K, in pressure ±0.1 kPa, and in the liquid and vapor mole fraction ±0.001. The three systems satisfy the point-to-point thermodynamic consistency test. All the systems show positive deviations from ideality. The data have been correlated with the Margules, van Laar, Wilson, NRTL and UNIQUAC equations.     

Solid–liquid phase diagrams of binary mixtures

This study investigates the sorption of toluene and naphthalene by a sodium bentonite (BFN), an organoclay (WS35) and by their respective iron oxide hydrate composites Mag_BFN and Mag_S35. The organic matter content of WS35 and Mag_S35, determined by thermogravimetry, was used to obtain their organic matter sorption coefficients, which show that they are effective sorbents to remove organic contaminants from water, with a higher selectivity for naphthalene than for toluene sorption. The main iron oxide phase present in Mag_BFN and Mag_S35 is maghemite (γ-Fe₂O₃), which allows these sorbents to be separated from the effluent by a magnetic separation process after use.     

An approach to calculate solid–liquid phase equilibrium for binary mixtures

An approach is presented to calculate solid–liquid phase equilibrium for binary mixtures, using expressions for the temperature as a function of the molar fraction. For Margules model the expression gives explicitly the temperature, while for other liquid phase activity models an iterative procedure is required to calculate the temperature. The method is very easy to apply and it can be used for mixtures that have peritectic and eutectic points, or just a eutectic point. The approach was applied to five case studies with binary mixtures of fatty acids and triglycerides. The results were in good agreement with experimental data.     

Molecular simulation of the phase behaviour of ternary fluid mixtures: the effect of a third component on vapour–liquid and liquid–liquid coexistence

The Gibbs ensemble algorithm is implemented to determine the vapour–liquid and liquid–liquid phase coexistence of dilute ternary fluid mixtures interacting via a Lennard–Jones potential. Calculations are reported for mixtures with a third component characterised by different intermolecular potential energy parameters. Comparison with binary mixture data indicates that the choice of energy parameter for the third component affects the composition range of vapour–liquid substantially. The addition of a third component lowers the energy of liquid phase while slightly increasing the energy of the vapour phase.     

Solid and liquid phase equilibria and solid-hydrate formation in binary mixtures of water with amines

Solid and liquid phase diagrams have been constructed for {water+triethylamine,or+N,N-dimethylformamide(DMF) or+N,N-dimethlacetamide (DMA)} Solid-hydrates form with the empirical formulae N(C2H5)3 3H2O,DMF 3H2O,DMF 2H2O,DMA 3H2O and (DMA)2 3H2O.All are congruently melting except the first which melts incongruently.The solid-hydrate formation is attributed to hydrogen bond.The results are compared with the references     

Thermodynamic properties of binary mixtures containing n-alkylamines: I. Isothermal vapour–liquid equilibrium and excess molar enthalpy of n-alkylamine+toluene mixtures. Measurement and analysis in terms of group contributions

Molar excess enthalpies, H^E, at 303.15 K and atmospheric pressure, of n-propyl-, n-butyl-, n-pentyl-, n-octyl- or n-decylamine+toluene, as well as the isothermal vapour–liquid equilibria, VLE, of n-butylamine+toluene and of n-butylamine+benzene at 298.15 K have been determined. These experimental results, along with the data available in the literature on molar excess Gibbs energies, G^E, activity coefficients at infinite dilution, γ_i^∞, and molar excess enthalpies, H^E, for n-alkylamine+toluene mixtures are examined on the basis of the DISQUAC group contribution model. The modified UNIFAC is also used to describe the mixtures.     

Thermodynamic properties of binary mixtures containing n-alkylamines: II. Isothermal vapour–liquid equilibrium and excess molar enthalpy of n-alkylamine+ethylbenzene mixtures. Measurement and analysis in terms of group contributions

Molar excess enthalpies, H^E, at 303.15 K and atmospheric pressure, of n-propyl-, n-butyl-, n-pentyl-, n-octyl- or n-decylamine+ethylbenzene, as well as the isothermal vapour–liquid equilibrium (VLE) of n-butylamine+ethylbenzene at 298.15 K have been determined. These experimental results, along with the data available in the literature on molar excess Gibbs energies, G^E, for n-alkylamine+ethylbenzene mixtures are examined on the basis of the DISQUAC group contribution model. The modified (mod.) UNIFAC is also used to describe the mixtures.     

The influence of the temperature on the liquid–liquid equilibrium of the ternary system 1-pentanol–ethanol–water

Liquid–liquid equilibrium data for the ternary system 1-pentanol–ethanol–water have been determined experimentally at 25, 50, 85 and 95°C. These results have been correlated simultaneously by the uniquac method obtaining two sets of interaction parameters: one of them independent of the temperature and the other with a linear dependence. Both sets of parameters fit the experimental results well.     

Isobaric vapour–liquid equilibrium for the binary systems formed by a cyclic ether and bromocyclohexane at 40.0 and 101.3 kPa

Experimental data of vapour–liquid equilibrium (VLE) for the binary systems tetrahydrofuran, or tetrahydropyran, or 2-methyl-tetrahydrofuran, or 2,5-dimethyl-tetrahydrofuran with bromocyclohexane have been measured in isobaric conditions at two pressures, 40.0 and 101.3?kPa. The equipment used was a dynamic recirculating still. The consistency of the measured VLE data has been tested with the Van Ness’ point-to-point method. The activity coefficients have been correlated with the mole fraction through Wilson, NRTL and UNIQUAC equations.     

Isothermal vapour–liquid equilibrium data for the binary propan-2-one+chloroalkanes mixtures at temperatures from 298.15 K to 313.15 K

Isothermal vapour–liquid equilibrium data are reported for binary mixtures of propan-2-one with 1,1,2,2-tetrachloroethane (I) and 1,4-dichlorobutane (II) within the 298.15–313.15 K temperature range. Total vapour pressures were measured by a static method, the mixtures beeing prepared by weight and degased directly into the working cell. The experimental data were correlated by Barker's method and different expressions for excess Gibbs energy were tested. The results indicate negative deviation from ideality for mixture (I), while mixture (II) behaves almost ideally, with slightly positive deviations.     

Isobaric vapor–liquid–liquid equilibrium and vapor–liquid equilibrium for the system water–ethanol-1,4-dimethylbenzene at 101.3 kPa

An all-glass, dynamic recirculating still equipped with an ultrasonic homogenizer has been used to determine vapor–liquid (VLE) and vapor–liquid–liquid (VLLE) equilibria. Consistent data have been obtained for the ternary water + ethanol + p-xylene system at 101.3 kPa for temperatures in the range of 351.16–365.40 K. Experimental results have been used to check the accuracy of the UNIFAC, UNIQUAC and NRTL models in the liquid–liquid region of importance in the dehydration of ethanol by azeotropic distillation.     

Vapor–liquid equilibrium data for the binary systems in the process of synthesizing diethyl carbonate

Vapor–liquid equilibrium data for the binary systems of carbon monoxide (CO) + diethyl carbonate (DEC) and carbon monoxide + ethyl acetate (EA) were measured at temperatures of 293.2 K, 313.2 K and 333.2 K and the elevated pressures up to 12.00 MPa. The measurements were carried out in a cylindrical autoclave with a moveable piston and an observation window. The experimental data were correlated using the Peng–Robisom (PR) equation of state (EOS) and Peng–Robinson–Stryjek–Vera (PRSV) equation of state with the two-parameter van der Waals II or Panagiotopoulos–Reid mixing rule. The interaction parameters were obtained while correlating. The comparison between calculation results and experimental data indicated that the method of PRSV equation of state with van der Waals II produced the better correlated results.     

Development of a new equation of state for mixed salt and mixed solvent systems,and application to vapour–liquid and solid (hydrate)–vapour–liquid equilibrium calculations

An equation of state that can be used for phase equilibrium and other thermodynamic property calculations at high pressures is developed for systems that contain aqueous solutions of strong electrolytes and molecular species. The proposed equation of state is based upon contributions to the Helmholtz free energy from a non-electrolyte term and three electrolyte terms. The non-electrolyte term comes from the Trebble–Bishnoi equation of state and the electrolyte terms consist of a Born energy term, a mean spherical approximation term and a newly developed hydration term. The application of the proposed equation of state to aqueous systems containing mixed salts and mixed solvents is illustrated by calculating the vapour–liquid equilibrium (VLE) and solid (Clathrate hydrate)–vapour–liquid equilibrium (SVLE) conditions for several systems. The solubility of CO₂ in salt water systems is examined at elevated pressures. As well, the new equation of state is used in conjunction with the model of van der Waals and Platteeuw to predict the SVLE conditions for gas hydrate forming systems in the presence of single salts, mixed salts and a mixture of aqueous salts and methanol. It is found that the new equation of state is able to accurately represent the experimental data over a wide range of pressure, temperature and salt concentration.     

Micellisation thermodynamics of sodium lauroylsarcosinate in water–alcohol binary mixtures

Aggregation of sodium lauroylsarcosinate (SLS) in aqueous solutions of methanol, ethanol, propanol and ethylene glycol at 288–313 K has been determined from conductivity measurement in the range 0–20% v/v of additives. The precise values of the critical micelle concentration (CMC) and the degree of counter-ion dissociation of micelles were obtained at each temperature by fitting the specific conductivity-surfactant concentration curve to the integrated form of the Boltzmann-sigmoid equation. The CMC was found to increase with increase in additive concentrations in the case of methanol and ethylene glycol, while it decreases with increase in ethanol and propanol concentration. The equilibrium model of micelle formation was applied to obtain the thermodynamic parameters of micellisation. The Gibbs free energies were observed to vary only slightly with temperature and additive concentrations. Enthalpy–entropy compensation was observed for all the systems with a constant compensation temperature of ≈300 K and negative compensation enthalpy.     

Prediction by the ASOG method of liquid–liquid equilibrium for binary and ternary systems containing 1-alkyl-3-methylimidazolium hexafluorophosphate

Ionic liquids are neoteric, environmentally friendly solvents (since they do not produce emissions) composed of large organic cations and relatively small inorganic anions. They have favorable physical properties, such as negligible volatility and wide range of liquid existence. Moreover, many different cations and anions can be used to synthesize ionic liquid, so the properties can be designed by the use of selected combinations of anions and cations. Liquid–liquid equilibrium (LLE) data for systems including ionic liquids, although essential for the design and operation of separation processes, are still scarce. However, some recent studies have presented ternary LLE data involving several ionic liquids and organic compounds such as alkanes, alkenes, alkanols, water, ethers and aromatics. In this work, the ASOG model for the activity coefficient is used to predict the LLE for 11 binary and 17 ternary systems including the ionic liquid 1-alkyl-3-methylimidazolium hexafluorophosphate plus alkanes, alkenes, alkanols, ketones, carboxylic acids and aromatics. New group interaction parameters were determined by using a modified Simplex method, minimizing a composition-based objective function. The results are satisfactory, with rms deviations of about 4%.