Theory Of Liquid Mixtures Research Articles

NpT-ensemble Monte Carlo calculations for binary liquid mixtures

A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12-6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.

Molar excess volumes of ternary mixtures containing ether

Molar excess volumes (VEijk) of 1,3-dioxolane (i) + benzene (j) + cyclohexane (k); 1,3-dioxolane (i) + benzene (j) + n-hexane (k); and 1,3-dioxolane (i) + benzene (j) + n-heptane (k) ternary mixtures have been measured dilatometrically as a function of composition at 298.15 K. The observed data have been analysed in terms of (i) Graph theoretical approach; (ii) Flory's theory; and (iii) Lacombe and Sanche's theory of liquid mixtures. It has been observed that VEijk values predicted by graph theoretical approach compare better with the corresponding experimental values than with the VEijk data predicted by other approaches.Key words: molar excess volumes, molar volume interaction parameters, connectivity parameter of third degree 3ξ.

Excess molar enthalpies and volumes of (1-hexyne, or 1-heptyne, or 1-octyne + di-1-methylethyl ether, or 1,1-dimethylethyl methyl ether, or 1,1-dimethylpropyl methyl ether) at the temperature 298.15 K

Excess molar enthalpies HmEand volumes VmEwere measured at T= 298.15 K and atmospheric pressure for (1-hexyne, or 1-heptyne, or 1-octyne + di-1-methylethyl ether, or 1,1-dimethylethyl methyl ether, or 1,1-dimethylpropyl methyl ether). The results were compared with the values of HmEfor the related mixtures, and the possible hydrogen bonding between the alkyne and the ether noted. Various theories of liquid mixtures were fitted with the results. The HmEresults were discussed in terms of the NRTL and UNIQUAC models, and were calculated by using the values of VmE(x= 0.5) by the Prigogine–Flory–Patterson (PFP) theory using Flory’s equation of state and a free volume contribution.

Excess molar volumes of binary mixtures of toluene and ethylbenzene with propylbenzene, butylbenzene and hexylbenzene at 298.15, 308.15 and 318.15 K

Excess molar volumes of binary mixtures of toluene and ethylbenzene with propylbenzene, butylbenzene and hexylbenzene were determined at 298. 15, 308. 15 and 318. 15 K (except for toluene+butylbenzene for which the excess molar volume was determined only at 298. 15 K) using a vibrating tube densitimeter. The experimental excess molar volumes are compared with the calculated values based upon Flory's theory of liquid mixtures.

Speed of sound and isentropic compressibilities of nonelectrolyte liquid mixtures. I. Binary mixtures containingp-dioxane

The speed of sound was measured for mixtures of p-dioxane with cyclohexane, n-hexane, benzene, toluene, carbon tetrachloride, chloroform, 1,1,2,2-tetrachloroethane, pentachloroethane and ethyl acetate over the whole mole fraction range at 30°C. These data were combined with densities and molar volumes to obtain isentropic compressibilities and Rao's molar sound functions. Excess isentropic compressibilities and excess speeds of sound have also been calculated. The behavior of the present mixtures is discussed in terms of possible molecular interactions and the Prigogine-Flory-Patterson theory of liquid mixtures.

Thermodynamic properties for binary liquid mixtures of 1-chlorobutane+n-alkanes

Isothermal compressibilities KΥ and isobaric thermal expansion coefficients αp have been measured at 25 and 45°C for pure components and the following binary mixtures: 1-chlorobutane+normal alkanes (n-Cn) where n=6, 8, 10, 12, 14 and 16. With these results and other thermodynamic data from literature the next mixing quantities have also been reported: (∂V E/∂T)P, − (∂V)E/∂P)T, K S v , ∂H E/∂P)T, Δ(αpγVT and ΔCv. The obtained results have been compared at 25°C with the calculated values by using the Prigogine-Flory-Patterson theory of liquid mixtures. The theory predicts the excess volume VE and ∂V E/∂P)T values rather well, the C P E quite poorly, while for ∂V E/∂T)P and ∂V E/∂P)T it is only predicted the trend with the chain length of the n-alkane. The last two quantities show deviations between theoretical and experimental, slightly higher in systems with longer n-alkanes than for shorter ones. Our conclusion is that a nonrigid linear molecule, like 1-chlorobutane, has a low ability as a breaker of the pure n-Cn orientation correlations, in between that which we found for toluene and p-xylene and much smaller than for cyclohexane or benzene.

First and second thermodynamic mixing properties of ethylbenzene +n-alkanes: Experimental and theory

Isobaric expansibilities αP and isothermal compressibilities κT have been determined at 25 and 45°C for binary mixtures of ethylbenzene + n-tetradecane and + n-hexadecane and the corresponding excess functions (∂VE/∂T)P and (∂VE/∂P)T have also been obtained. With these data and supplementary literature values, the following second order mixing properties are also reported at 25°C: κSE, (∂VE/∂P)T, ΔCV and Δ(ΔγVT). All mixing quantities have been compared with the results obtained at 25°C by using the Prigogine-Flory-Patterson theory of liquid mixtures. The predicted values suggest that the ability of ethylbenzene as a breaker of the pure n-Cn orientations is similar to what we found for toluene and higher than for p-xylene.

Excess molar volumes of binary mixtures of benzene +n-propylbenzene, +n-butylbenzene and +n-hexylbenzene at 298.15, 308.15 and 318.15 K

Excess molar volumes of binary mixtures of benzene+n-propylbenzene, +n-butylbenzene and +n-hexylbenzene at 298.15, 308.15 and 318.15 K have been determined using a vibrating-tube densimeter. Flory's theory of liquid mixtures has been used to calculate excess enthapies; the calculated values for equimolar mixtures are compared with our previously published experimental results.

Application of the Prigogine-Flory-Patterson theory part II. Mixtures of a bicyclic compound, benzene, cyclohexane,n-hexane with a 1-alkene and a 1-alkyne

The Prigogine-Flory-Patterson theory of liquid mixtures has been applied to the HmE and VmE for binary mixtures of an n-alkane with decalin, bicyclohexyl, tetralin, cyclohexylbenzene, benzene, cyclohexane and n-hexane with 1-hexene, 1-hexyne, 1-heptene and 1-heptyne. Furthermore the Prigogine-Flory theory has been used to predict activity coefficients at infinite dilution from the experimentally determined HmE at 25°C for the mixtures 1-hexene, 1-hexyne, 1-heptene, 1-heptyne with decalin, bicyclohexyl, tetralin and cyclohexylbenzene. The predictions are compared to experimental results.

Application of the Prigogine-Flory-Patterson theory part I. Mixtures ofn-alkanes with bicyclic compounds, benzene, cyclohexane andn-hexane

The Prigogine-Flory-Patterson theory of liquid mixtures has been applied to the HmE and VmE for binary mixtures of an n-alkane with decalin, bicyclohexyl, tetralin, cyclohexylbenzene, benzene, cyclohexane and n-hexane. Furthermore the Prigogine-Flory theory has been used to predict activity coefficients at infinite dilution from the experimentally determined HmE at 25°C and at finite concentrations for n-hexane and n-heptane with decalin, bicyclohexyl, tetralin and cyclohexylbenzene.

Application of the Prigogine-Flory-Patterson theory part III. Mixtures of a bicyclic compound, benzene, cyclohexane,n-hexane with a cycloalkane, cyclohexene, a cycloalkadiene and benzene

The Prigogine-Flory-Patterson theory of liquid mixtures has been qpplied to the H m E and V m E for binary mixtures of a bicyclic compound, benzene, cyclohexane and n-hexane with a cycloalkane, cyclohexene, a cycloalkadiene and benzene. Furthermore the Prigogine-Flory theory has been used to predict activity coefficients at infinite dilution from the experimentally determined H m E at 25°C for the mixtures cyclohexane, cyclohexene, 1,3-cyclohexadiene, 1,4-cyclohexadiene and benzene with a bicyclic compound. The predictions are compared to experimental results.

A two‐fluid, non‐random‐mixing theory for liquid mixtures

A two‐fluid, non‐random‐mixing theory for liquid mixtures

A Two‐Fluid Theory for Liquid Mixtures with an Application to Poly(dimethyl Siloxane) Solutions etc.

AbstractA free‐volume, two‐fluid theory for liquid mixtures is presented. It is based on Flory's equation‐of‐state theory. Two versions differing in the assumption concerning the relation between the reduced volumes of the hypothetical fluids are discussed. In both versions, two adjustable binary parameters are used, one related to the interaction energies and the other to segment core volumes. Correction for non‐randomness is, also, provided. The theory is tested against experimental data on heats of mixing, volumes of mixing and χ interaction parameters of five representative poly(dimethyl siloxane) solutions with satisfactory results. Relations with existing similar theories are discussed.

A free-volume, non-random-mixing theory for liquid mixtures

Flory's partition function for pure liquids is extended to binary mixtures using the two-fluid theory of mixtures and local compositions to allow for non-randomness and to take into account changes in molecular rotation and vibration which accompany the mixing process. This extension requires only two binary parameters: one for potential energy and the other for liquid structure (packing of molecules). For associated and/or solvated solutions, a chemical contribution is required to represent the mixture's Gibbs energy. Calculated activity coefficients agree well with experiment. For engineering work, this molecular theory offers no significant advantages over phenomenological equations now in common use. The theory, however, contributes toward the molecular understanding required to establish a truly satisfactory description of liquid mixtures.

ChemInform Abstract: THERMODYNAMIC PROPERTIES OF BINARY LIQUID MIXTURES

Excess volumes of the three binary mixtures: (1) cyclohexane – diethyl ketone, (2) cyclohexane–benzonitrile, and (3) toluene–benzonitrile have been measured at 303.15 K using a dilatometer. Excess volumes of the first two systems are positive over the whole range of composition and are negative for the third system. The measured excess volumes and the excess heats of mixing reported in the literature for the three binary systems have been analysed in the light of the statistical theory of liquid mixtures developed by Flory. The analysis has shown that the theory in its modified form is approximately applicable to the mixtures cyclohexane–diethylketone and cyclohexane–benzonitrile.

Thermodynamic properties of binary liquid mixtures

Excess volumes of the three binary mixtures: (1) cyclohexane – diethyl ketone, (2) cyclohexane–benzonitrile, and (3) toluene–benzonitrile have been measured at 303.15 K using a dilatometer. Excess volumes of the first two systems are positive over the whole range of composition and are negative for the third system. The measured excess volumes and the excess heats of mixing reported in the literature for the three binary systems have been analysed in the light of the statistical theory of liquid mixtures developed by Flory. The analysis has shown that the theory in its modified form is approximately applicable to the mixtures cyclohexane–diethylketone and cyclohexane–benzonitrile.

Excess enthalpies of liquid oxygen + argon, oxygen + nitrogen, and argon + methane

A new apparatus is described for the determination of the excess enthalpies of binary mixtures of condensed gases, which removes some of the uncertainty associated with earlier calorimeters. Values have been obtained for oxygen + argon at 86.6 K, oxygen + nitrogen at 80.3 K, and argon + methane at 91.5 K. Comparison is made with previous work, and with some theories of liquid mixtures.

Theory of Simple Mixtures

This review is devoted to recent progress in the theory of liquid mixtures of nonelectrolytes. Prior to about 1968 the theory of liquid mixtures was not at all well developed but, largely as a result of progress in the theory of pure liquids, it is now in a much more satisfactory state. Unfortunately, this fact is not very well known. Papers using theories now recognized as unsatisfactory are still common. A recent review of this field has been given by McDonald ( 1) in the Specialist Periodical Reports of the Chemical Society. This same volume also includes short discussions of the application of integral equation methods and perturbation theories to the theory of mixtures by Watts (2) and Smith (3), respectively. The earlier review of Henderson & Leonard (4) is still of value. Gubbins (5) has published a timely review of perturbation theories of mixtures. Mention must also be made of the articles on mixtures appearing regularly in this series. In addition, there is the invaluable Liquids and Liquid Mixtures by Rowlinson (6). Finally, there are some recent articles in this series which briefly mention or relate to the theory of mixtures (7-7c).

Thermodynamic properties of liquid mixtures: Selection of the pure liquid parameter

There has recently been a revival of interest in theories of liquid mixtures based on analytic equations of state for pure fluids. We have shown that the method used to determine the parameters of the pure-liquid equation of state has a significant effect on the excess thermodynamic properties obtained from such theories.

Theoretische Behandlung flüssiger Mischungen mit Hilfe von Gleichgewichtsmodellen. Teil I: Binäre symmetrische Mischungen / Theoretical Treatment of Liquid Mixtures by Means of Equilibrium Models

Abstract A thermodynamic theory of liquid mixtures based on a simple molecular model is developed which describes the equilibrium state as the result of a coupling between a "chemical" and a "statistical" equilibrium. The intermolecular interactions are taken into account by considering "complexes" formed between a given molecule and its z nearest neighbours. The equilibrium mole fractions of these complexes are calculated by application of the ideal law of mass action to an appropriate set of "exchange equilibria". Formulae for the excess functions GE and HE and for the activities of the components are derived for the cases z=1 and z=4. GE depends on an equilibrium constant K describing the deviation from random distribution of the equilibrium mole fractions of the complexes. HE depends on K and on an energy parameter w which is related to differences of pair interactions. K and w are independent parameters, and there is no limitation in respect to amount and sign of the excess functions. The conditions for the existence of a critical solution point are formulated; at this point GE has a value of about 0.56 R T. If a model with two equilibrium constants is used allowing for instance competition between "self-association" and "complex-formation", the existence of closed miscibility gaps becomes possible. Closed miscibility curves are calculated and the conditions for their appearance are discussed. The relations between this theory and Guggenheim's statistical lattice theory of symmetrical mixtures are pointed out.