Effect of the course of the second derivative of Gibbs' energy in binary mixtures on the liquid-liquid equilibrium in ternary system

1981 ◽  
Vol 46 (12) ◽  
pp. 3003-3017
Author(s):  
Josef P. Novák ◽  
Jaroslav Matouš ◽  
Josef Šobr ◽  
Jiří Pick
Keyword(s):  
Gibbs Energy ◽  
Ternary System ◽  
Binary Mixtures ◽  
Binary Systems ◽  
Second Derivative ◽  
Curve Shape ◽  
Liquid Equilibrium ◽  
Model Calculations ◽  
Tie Lines ◽  
Heterogeneous Region

The effect of the course of G11(x1) in binary systems is studied on the binodal curve shape, the extent of heterogeneous region and the inclination of tie-lines in the ternary system. The effect of individual quantities is shown both on model calculations and on the systems acetonitrile-benzene-n-heptane, water-benzene-ethanol and water-benzene-2-propanol. The UNIQUAC and the modified Wilson equations were employed for calculating.

scholarly journals MODELING OF THERMODYNAMIC PROPERTIES OF THE MELTS OF TERNARY Ge-Mn-Gd SYSTEM

2019 ◽  
pp. 18-22
Author(s):  
N. Golovata ◽  
N. Kotova ◽  
N. Usenko
Keyword(s):  
Thermodynamic Properties ◽  
Gibbs Energy ◽  
Ternary System ◽  
Binary Systems ◽  
Thermodynamic Characteristics ◽  
Published Data ◽  
Liquid Alloys ◽  
Model Calculations ◽  
Enthalpies Of Mixing ◽  
Gibbs Energies

In the present work, the Gibbs energies of mixing of liquid alloys of the Ge-Mn-Gd ternary system were determined, which was made on the basis of an analysis of published data on the thermodynamic properties of liquid alloys of boundary binary systems that form the ternary Ge-Mn-Gd, as well as on the basis of the model calculations in these binary systems. To determine the activities of the components, the Gibbs energies of mixing, and the enthalpies of mixing of liquid alloys of the Ge-Mn(Gd) systems, for which alloying process is accompanied by significant heat release, an ideal associated solution model was applied. For the melts of the Mn-Gd system, which are characterized by rather insignificant exothermic effects, a model of regular solutions was used. The surface of the Gibbs energy of mixing for the alloys of the Ge-Mn-Gd ternary system has been determined on the basis of the concentration dependences of the Gibbs energies of mixing obtained for constituent binary systems under the assumption of additivity of pair interactions using the Redlich-Kister-Muggianu method. The obtained topology of the Gibbs energy isolines projections is compared with the thermochemical properties of liquid alloys of this system that we have determined earlier. A comparative analysis of the topology of these surfaces in the Ge-Mn-Gd system led to the conclusion that the surfaces of ΔG and ΔmH monotonically decrease from the manganese-rich angle of the diagram towards the Ge-Gd side of the concentration triangle. The minimum value of the thermodynamic characteristics of mixing of the ternary liquid alloys corresponds to the composition, which coincides with the composition of the most stable intermetallic compound in the Ge-Gd system. From the course of isolines of free energies and integral enthalpies of mixing, one can also conclude about the influence of a short-range order, existed in the Ge-Mn system near the composition with a mole fraction of mangan greater than 0.7, on the properties of ternary alloys in the vicinity of this composition. Thus, the topology of isolines and the large exothermic values of the obtained thermodynamic properties allow us to make a reasonable conclusion that the strong interaction between unlike components inherent in the Ge-Gd system in the solid state is also maintained for liquid alloys of the Ge-Mn-Gd system.

Determination of the concentration dependence of the second derivative of Gibbs' energy with respect to composition on the basis of vapour-liquid equilibrium data

1981 ◽  
Vol 46 (12) ◽  
pp. 2989-3002 ◽  
Author(s):  
Josef P. Novák ◽  
Jaroslav Matouš ◽  
Josef Šobr ◽  
Jiří Pick
Keyword(s):  
Gibbs Energy ◽  
Concentration Dependence ◽  
Binary Systems ◽  
Second Derivative ◽  
Liquid Equilibrium ◽  
Equilibrium Data

The course of the second derivative of Gibbs' energy with respect to composition for binary systems is evaluated. The representation of this quantity in terms of different correlation relations (the Wilson, NRTL and UNIQUAC equations and the ASOG and UNIFAC methods) is also discussed.

scholarly journals Computation of Isobaric Vapor-Liquid Equilibrium Data for Binary and Ternary Mixtures of Methanol, Water, and Ethanoic Acid from T, p, x, and HmE Measurements

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Daming Gao ◽  
Hui Zhang ◽  
Peter Lücking ◽  
Hong Sun ◽  
Jingyu Si ◽  
...  
Keyword(s):  
Liquid Phase ◽  
Ternary System ◽  
Vapor Phase ◽  
Binary Systems ◽  
Model Parameters ◽  
Liquid Equilibrium ◽  
Vapor Liquid Equilibrium ◽  
Molar Excess ◽  
Ethanoic Acid ◽  
Vle Data

Vapor-liquid equilibrium (VLE) data for the strongly associated ternary system methanol + water + ethanoic acid and the three constituent binary systems have been determined by the total pressure-temperature-liquid-phase composition-molar excess enthalpy of mixing of the liquid phase (p, T, x, HmE) for the binary systems using a novel pump ebulliometer at 101.325 kPa. The vapor-phase compositions of these binary systems had been calculated from Tpx and HmE based on the Q function of molar excess Gibbs energy through an indirect method. Moreover, the experimental T, x data are used to estimate nonrandom two-liquid (NRTL), Wilson, Margules, and van Laar model parameters, and these parameters in turn are used to calculate vapor-phase compositions. The activity coefficients of the solution were correlated with NRTL, Wilson, Margules, and van Laar models through fitting by least-squares method. The VLE data of the ternary system were well predicted from these binary interaction parameters of NRTL, Wilson, Margules, and van Laar model parameters without any additional adjustment to build the thermodynamic model of VLE for the ternary system and obtain the vapor-phase compositions and the calculated bubble points.

Correlation and Prediction of Vapor-Liquid Equilibrium for the Propylene Oxide-Ethanol-Water Ternary System

2011 ◽  
Vol 396-398 ◽  
pp. 973-976
Author(s):  
Cheng Xue Wang ◽  
Rui Xia Jiang
Keyword(s):  
Experimental Data ◽  
Ternary System ◽  
Propylene Oxide ◽  
Binary Systems ◽  
Molar Fraction ◽  
Liquid Equilibrium ◽  
Vapor Liquid Equilibrium ◽  
Vle Data ◽  
Consistency Verification ◽  
Vapor Liquid

The vapor-liquid equilibrium (VLE) data for the binary systems ethanol-water (1), propylene oxide (PO)-ethanol (2), PO-water (3) and the ternary system PO-ethanol-water (4) were determined at 101.3kPa. The binary VLE data measured passed the thermodynamic consistency verification. The experimental VLE data of the binary systems were correlated with the nonrandom two-liquid (NRTL) models. The results show that the values of molar fraction of the ternary system (4) in vapor phase from the binary NRTL parameters agree well with the experimental data.

Liquid-Liquid Equilibrium for (Water + Palm Oil Biodiesel + Methanol) Ternary System at Different Temperatures

2012 ◽  
Vol 455-456 ◽  
pp. 867-871
Author(s):  
Xing Yue Yan ◽  
Yong Chun Cheng ◽  
Xiao Ping Hu
Keyword(s):  
Experimental Data ◽  
Ternary System ◽  
Palm Oil ◽  
Ternary Mixtures ◽  
Binary Interaction ◽  
Liquid Equilibrium ◽  
Different Temperatures ◽  
Tie Lines ◽  
Binary Interaction Parameters ◽  
Palm Oil Biodiesel

The liquid-liquid equilibrium (LLE) of ternary mixtures (water + palm oil biodiesel + methanol) was measured under atmospheric pressure and temperatures of 303.15K, 313.15K and 323.15K. The mutual solubility of biodiesel and water increased as the increasing of ratio of methanol. Also, the mutual dissolution of the mixture was slightly promoted by increasing temperature. The phase diagrams and tie lines for the ternary system were determined by high-temperature gas chromatography (HTGC). NRTL and UINQUAC models were applied to fit the experimental data for the ternary system, and the binary interaction parameters were obtained by regression on the experimental data. Both models could describe the LLE behavior of the systems fairly well.

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