kister equation
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2021 ◽  
Vol 17 (2) ◽  
pp. 9-15
Author(s):  
SONU DWIVEDI ◽  

Ultrasonic velocity (U), density (ρ) for the ternary mixture of (Toluene + Chlorobenzene + Cyclohexane) in the various range of composition has been carried out at 298.15K. The observed data have been utilized to calculate various acoustical parameters like Isentropic compressibility (KS), Intermolecular free length (Lf) and acoustic impedance (Z). The various excess properties like excess ultrasonic velocity(UE ), excess acoustic impedance (ZE ), excess Isentropic compressibility (KS E ) and excess Inter molecular free length (Lf E ) have been calculated and using standard relations to the Redlich-Kister equation. The trend of acoustical and physicochemical parameters confirm the dynamics of molecules at temperature and the magnitude of intermolecular interactions among the constituents of the mixture always reflects the nature of substance. The variations in sign and values of these parameters are help us to know the interaction between component molecules and structural arrangement of the liquid mixture.


2021 ◽  
Vol 26 (1) ◽  
pp. 51-56
Author(s):  
N. Panthi ◽  
I. B. Bhandari ◽  
R. C. Pangeni ◽  
I. Koirala

Concentration-dependent thermophysical properties of molten Mg-Pb and Mg-Ga alloys at 1000 K was compared using the Redlich Kister equation by optimizing exponential interaction energy parameters based on the R-K polynomials framework.  The mixing behavior was investigated by giving more emphasis to the role of temperature-dependent interaction energy parameters. Our study shows that the magnesium gallium alloy is slightly interacting than the magnesium lead alloy. The surface tension and viscosity of both alloys was compared using the Butler equation as improved by Kaptay and KRP (Kozlov-Ronanov-Petrov) approach respectively. The surface tension of Mg-Pb liquid alloy increases but decreases in Mg-Ga alloy with an increase in the concentration of Mg. The viscosity has a nonlinear variation for both alloys with the increase in the concentration of magnesium.


2021 ◽  
Vol 33 (11) ◽  
pp. 2796-2802
Author(s):  
Mohammad Aftabuzzaman ◽  
Mohammad Monirul Islam ◽  
Nasiruddin ◽  
Farhana Rahman Rima ◽  
Mohammad Nazrul Islam ◽  
...  

Densities and sound velocities of the binary liquid mixtures of sulfolane + aniline, sulfolane + N,N-dimethylaniline, sulfolane + N,N-diethylaniline over the whole range of composition and their pure component were measured at temperatures (T = 303.15, 308.15, 313.15 K) and atmospheric pressure. A high precision vibrating-tube densitometer was used for the measurements. From the measured values, excess adiabatic compressibility (βs E), excess sound velocity (uE), excess internal pressure (Pi E) and deviation of surface tension (Δγ) were calculated for each of the systems. The excess properties and surface tension deviation were fitted to the Redlich-Kister equation. All these properties have been discussed in terms of molecular interactions.


2020 ◽  
Vol 20 (9) ◽  
pp. 5693-5702
Author(s):  
Gang Tian ◽  
Cong Yang ◽  
Li Wang ◽  
Yongjun Han ◽  
Lijuan Wu ◽  
...  

The refractive indexes of three ionic liquids, glutamic acid tetrafluoroborate ([GA]BF4), glutamic acid double trifluoromethyl sulfonyl amine salts ([GA]TF2N), glutamic acid hexafluorophosphate ([GA]PF6), with ethanol and/or water systems under 10~35 °C were studied. The excessive refractive index of the systems and the relationship between the refractive index and the constituent molar fraction at 20 °C, and the empirical relationship between the excess refractive rate and the constituent mole fraction were established. The experimental results show that the excess refractive index is positive in the measured concentration range, and the refractive index of ethanol+water with the increase in the composition appears maximum and the refractive index of ethanol/water+ [GA]BF4, ethanol/water+[GA]PF6, ethanol/water+[GA]TF2N system is increased with the increase in composition. By using the Redlich-Kister equation to correlate the binary system and the excess refractive index of ternary system, the fitting results show that the refractive index of ternary system can be estimated using the refractive index of the polynomial equation of binary system.


2020 ◽  
Author(s):  
Noritoshi Nambu

The relative permittivity is a measure of the solvent’s ability to insulate opposite charges from each other and has a very significant effect on the strength of the interactions between ions especially in dilute solution. I describe the relative permittivities, εr(sln) of nonaqueous mixtures as a function of the composition at 25 ºC. Experimental data were fitted with the Redlich-Kister equation. I explained the deviation from the ideal solution in terms of the magnitude of the coefficient a0. a0 is a dominant factor governing the Redlich-Kister equation. The decrease in a0 made a plot of εr(sln) vs. x2 close to a straight line, which corresponded to the ideal solution. The cohesive forces between dissimilar components resulted in the increased effective dipole moment and, consequently, in the small negative value of a0.


Experimentally measured data for viscosity and refractive index of (o-Xylene + n-Nonane) binary mixture are reported in this research paper for various compositions for three different temperatures at atmospheric pressure. Modified Ubbelholde viscometer and Abbe-3L Refractometer were used for experimental measurements. Deviation in molar refraction (ΔR) and deviation in viscosity (Δη) w.r.t composition have been calculated from the experimental data. ‘Grunberg and Nissan’ equation and Herric’s Correlation were used to correlate the viscosity data. Excess thermodynamic properties were fitted to Redlich-Kister equation. Coefficients and standard deviations, hence obtained are reported. Variation in Excess Thermodynamic properties for the mixture have been discussed in terms of intermolecular interactions


2020 ◽  
Vol 74 (3) ◽  
pp. 163-185
Author(s):  
Divna Majstorovic ◽  
Marija Mirkovic ◽  
Mirjana Kijevcanin ◽  
Emila Zivkovic

The aim of this research is the experimental determination of density, viscosity, refractive index and speed of sound for binary mixtures of the ester ethyl acetate and alcohols. Experimental measurements were carried out for two systems with 1-propanol and 1-butanol at atmospheric pressure and in a temperature range 288.15 - 323.15 K. Results of experimental measurements were further used to determine excess molar volumes, viscosity deviations, refractive index deviations, and excess isentropic compressibility for each investigated mixture. These calculated data were correlated using the empirical Redlich-Kister equation. Positive values of the excess molar volume and isentropic compressibility appear for both analysed systems, while values of viscosity and refractive index deviations are negative. The structure and specific characteristics of different molecules in considered mixtures and determined non-ideal behaviour allow the insight into the possible type of interactions in the mixture, interstitial accommodation and structural effects.


2019 ◽  
Vol 31 (4) ◽  
pp. 820-824
Author(s):  
Husam S. Khalaf ◽  
Zainab A.H. Al-Dulaimy ◽  
Ahmed M. Abbas ◽  
Maida H. Saleem

At the temperature 298.15 K, some physical properties such as: refractive indices (nD), viscosities (η) and densities (ρ) were studied in four liquid-liquid mixtures: carboxylic acids (HCOOH, CH3COOH, CH3CH2COOH and CH3CH2CH2COOH) with tetrahydrofurfuryl alcohol (THFA) with the identified configuration set. These empirical data were utilized to estimate the excess molar volumes (Vm E), refractive index perversions (ΔR), viscosity deviations (ηE) and excess molar Gibbs free energy (ΔG*E). Values of Vm E, ηE , ΔG*E and ΔR were plotted versus mole fraction of tetrahydrofurfuryl alcohol. In all cases, the values of Vm E, ηE , ΔG*E and ΔR that obtained in this study were found to be negative at 298.15 K. The excess parameters were applied in the Redlich-Kister equation by utilizing multi-parameter coefficients that concluded binary coefficients and in respect to the standard deviation. The difference of these characteristics with the formation of binary liquid systems indicates the absence of bipolar bond, variation in the shape and size of component molecules, hydrogen bonding and dipolar interaction among unlike molecules.


2018 ◽  
Vol 284 ◽  
pp. 575-580
Author(s):  
E.A. Trofimov ◽  
O.V. Samoilova ◽  
E.R. Vakhitova

The Na–Cu and Na–K systems present a big interest for the study due to the use of liquid sodium and melt of sodium and potassium in the nuclear industry as a coolant in nuclear reactors. In the present work, thermodynamic modeling of phase equilibria in the Na–Cu and Na–K systems is carried out, based on the available published experimental data. This modeling was done using the “FactSage” software package (version 7.0). The set of Redlich–Kister equation parameters was obtained, that allows to describe the dependence of Gibbs energy from composition and temperature for solutions that can be formed in the studied systems. Phase diagrams (T–x diagrams) of the investigated systems were calculated.


Metals ◽  
2018 ◽  
Vol 8 (8) ◽  
pp. 629 ◽  
Author(s):  
Evgeny Trofimov ◽  
Olga Samoilova ◽  
Olga Zaitseva ◽  
Elena Vakhitova

The Na-Cu and Na-K systems are of significant interest due to the use of liquid sodium and melt of sodium and potassium in the nuclear industry as a cooling agent in nuclear reactors. In the present work, thermodynamic modeling of phase equilibria in the Na-Cu and Na-K systems is carried out, based on the available published experimental data. This modeling was done using the “FactSage” software package (version 7.0). The set of Redlich-Kister equation parameters was obtained, which allows one to describe the dependence of Gibbs energy from composition and temperature for solutions that can be formed in the studied systems. Phase diagrams (T-x diagrams) of the investigated systems were calculated.


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