Correlation of the Prigogine-Flory theory with isothermal compressibility and excess enthalpy data for cyclohexane + alkane mixtures

The Prigogine-Flory theory is applied to isothermal compressibilities, at 25, 35, 45 and 60°C and to heats of mixing at 25°C for cyclohexane + n-alkane systems. To this purpose, the van der Waals and the Lennard-Jones potentials have been adopted. The energy parameter ₁₂ has been calculated from the experimental data, and its dependence on the n-alkane number of carbons has been studied. Taking the ₁₂ value obtained for the equimolecular mixture, the excess functi¹/ns (V^E/P)_T, H^E and V^E have been calculated and the results compared with experimental values.     

Isomer effects in the excess enthalpies of mixtures of alkanes and cycloalkanes

Using the Picker flow calorimeter, excess molar enthalpies H ^E have been obtained at 25°C for mixtures of 1,2-, 1,3- and 1,4-cis- and trans-dimethylcyclohexane and cis- and trans-decalin with n-hexadecane and the highly branched C₁₆ isomer, 2,2,4,4,6,8,8-heptamethylnonane. Values of H ^E are also obtained for cis- and trans-decalin mixed with C₆, C₇, and C₉ isomers. Anomalously low values of H ^E occur for normal alkanes mixed with cycloalkanes in the di-equatorial configuration, suggesting the presence of a negative contribution in H ^E possibly due to a restriction of n-alkane molecular motion by the flat, plate-like cycloalkane.     

Molar excess heat capacities and volumes for mixtures of benzonitrile with cyclohexane between 10 and 45°C

The heat capacities and volumes for binary mixtures of benzonitrile with cyclohexane were determined at 10, 25, and 45°C. The dependence of the molar excess heat capacities on temperature and composition are interpreted in terms of the thermal relaxation of associated benzonitrile molecules into monomeric species.To whom correspondence should be addressed.     

Prediction of vapor-liquid equilibrium from excess enthalpy data for binary ether +n-alkane or cyclohexane mixtures

Vapor liquid equilibrium (VLE) is successfully predicted from excess enthalpy H^E data for binary ether + n-alkane or cyclohexane mixtures. Parameters for the continuous linear association model (CLAM) and for the UNIQUAC Model for the excess Gibbs energy G^E were determined from H^E data measured at a low temperature (ambient temperature). These parameters are used to predict VLE data at low and high temperatures. The dependence of the accuracy of predictions on the set of H^E data chosen to evaluate the parameters and on the model for G^E are discussed.     

Treatment of excess thermodynamic quantities for liquid mixtures

Thermodynamic data on mixtures of liquids are usually expressed as excess quantitiesY ^EX and analyzed with the Redlich-Kister equation. This approach can in some cases be misleading and hide strong interactions at low concentrations. In agreement with the original statement of Redlich and Kister, it is therefore better to plot such data asY ^EX/X ₂(1-X ₂). This quantity, which is directly related to the apparent molar quantities of both components, is often a more useful quantity and has just as much a thermodynamic significance asY ^EX.     

Molar excess heat capacities and volumes for mixtures of alkanoates with cyclohexane at 25°C

Molar excess volumes V ^E at 25°C have been determined by vibrating-tube densimetry, as a function of mole fraction x for different series of an alkanoate (H _2m+1 C _m COOC _n H _2n+1 )+cyclohexane. Three types of alkanoates were investigated, i.e., methanoates (m=0, with n=3 and 4), ethanoates (m=1, with n=2, 3, and 4) and propanoates (m=2, with n=1, 2, and 3). In addition, a Picker flow calorimeter was used to obtain molar excess heat capacities C _p ^E at constant pressure at the same temperature. V ^E is positive for all systems and rather symmetric, with V ^E (x=0.5) amounting to almost identical values in a series of mixtures containing an alkanoate isomer of same formula (say C₄H₈O₂, C₅H₁₀O₂, or C₆H₁₂O₂). The composition dependence of C _p ^E is rather unusual in that two more or less marked minima are observed for most of the mixtures, especially when the alkanoate is a methanoate or an ethanoate. These results are discussed in terms of possible changes in conformation of both the ester and cyclohexane.     

Temperature dependence of excess enthalpies for systems containing normal hexadecane

Excess enthalpies, and heat capacities derived therefrom, have been obtained between 25 and 65 or 75°C at a constant concentration for cyclohexane and octamethylcyclotetrasiloxane mixed with normal hexadecane and with a highly branched C₁₆ isomer, 2,2,4,4,6,8,8-heptamethylnonane, and also forcis-andtrans-decalin mixed withn-C₁₆. Theh ^E values withn-C₁₆ are positive and much larger than with the branched-C₁₆. They decrease rapidly withT so thatc _p ^E is large and negative. These results imply the presence of orientational order in then-C₁₆, which is destroyed on mixing with the other component and which decreases withT. Theh ^E fortrans-decalin+n-C₁₆ is much smaller than forcis-decalin+n-C₁₆, and becomes negative with increase ofT. This change of sign, which is unexplained by current theory, is interpreted as due to an interference of the flat, plateliketrans-decalin molecule with the molecular motion of then-C₁₆ chain.     

DISQUAC predictions of phase equilibria,molar and standard partial molar excess quantities for 1-alkanol+cyclohexane mixtures

Literature data for phase equilibria: vapor-liquid VLE, liquid-liquid LLE, and solid-liquid SLE; molar excess Gibbs energies G ^E , molar excess enthalpies H ^E ; activity coefficients _i and partial molar excess enthalpies H _i ^E,o at infinite dilution for 1-alkanol (1)+cyclohexane (2) mixtures are examined by the DISQUAC group contribution model. For a more sensitive test of DISQUAC, the azeotropes, obtained from the reduction of the original isothermal VLE data, are also examined for systems characterized by hydroxyl, alkane and cyclohexane groups. The alkane/cyclohexane and alkane/hydroxyl interaction parameters have been estimated previously. The cyclohexane/hydroxyl interaction parameters are reported in this work. The first dispersive parameters increase regularly with the size of the alkanol; from 1-octadecanol they are constant; an opposite behavior is encountered for the third dispersive parameters, which are constant from 1-dodecanol. The second dispersive parameters decrease as far as 1-propanol and then increase regularly; from 1-octadecanol they are constant. The quasichemical parameters are equal to those for the alkane/hydroxyl interactions. Phase equilibria, the molar excess functions, and activity coefficients at infinite dilution are reasonably well reproduced. Poor results are found for H _i ^E,o and DISQUAC predictions for H _i ^E,o are strongly dependent on temperature.     

Topological and thermodynamic investigations of binary mixtures: Molar excess volumes, molar excess enthalpies and isentropic compressibility changes of mixing

Molar excess volumes, V^E, molar excess enthalpies, H^E, and speeds of sound, u, of o-toluidine (i) + cyclohexane or n-hexane or n-heptane (j) binary mixtures have been determined over entire range of composition at 308.15 K. Speeds of sound data have been utilized to predict isentropic compressibility changes of mixing, of (i + j) mixtures. The observed V^E, H^E and data have been analyzed in terms of Graph theory. The analysis of V^E data by Graph theory reveals that o-toluidine exists as an associated molecular entity and (i + j) mixtures contain 1:1 molecular complex. It has been observed that V^E, H^E and values calculated by Graph theory compare well with their corresponding experimental values. The observed data have also been analyzed in term of Flory theory.     

Excess molar heat capacities and excess molar volumes of some mixtures of propylene carbonate with aromatic hydrocarbons

Excess molar volumes V ^E and excess molar heat capacities C _P ^E at constant pressure have been measured, at 25°C, as a function of composition for the four binary liquid mixtures propylene carbonate (4-methyl-1,3-dioxolan-2-one, C₄H₆O₃; PC) + benzene (C₆H₆;B), + toluene (C₆H₅CH₃;T), + ethylbenzene (C₆H₅C₂H₅;EB), and + p-xylene (p-C₆H₄(CH₃)₂;p-X) using a vibrating-tube densimeter and a Picker flow microcalorimeter, respectively. All the excess volumes are negative and noticeably skewed towards the hydrocarbon side: V ^E (cm³-mol^–1) at the minimum ranges from about –0.31 at x₁=0.43 for {x₁C₄H₆O₃+x₂p-C₆H₄(CH₃)₂}, to –0.45 at x₁=0.40 for {x₁C₄H₆O₃+x₂C₆H₅CH₃}. For the systems (PC+T), (PC+EB) and (PC+p-X) the C _P ^E s are all positive and even more skewed. For instance, for (PC+T) the maximum is at x _1,max =0.31 with C _P,max ^E =1.91 J-K^–1-mol^–1. Most interestingly, C _P ^E of {x₁C₄H₆O₃+x₂C₆H₆} exhibits two maxima near the ends of the composition range and a minimum at x _1,min =0.71 with C _P,min ^E =–0.23 J-K^–1-mol^–1. For this type of mixture, it is the first reported case of an M-shaped composition dependence of the excess molar heat capacity at constant pressure.Communicated at the Festsymposium celebrating Dr. Henry V. Kehiaian's 60^th birthday, Clermont-Ferrand, France, 17–18 May 1990.     

Variation of excess volumes with temperature for binary mixtures ofp-xylene withn-hexane andn-hexadecane

The variation of the molar volume with temperature from 25 to 50 °C of binary mixtures of p-xylene + n-hexane and p-xylene + n-hexadecane has been measured by a dilatometric method over the complete mole fraction range. From the experimental results we have calculated v^E/T)_p. Literature values of v^E at 25°C together with the integration of v^E/T)_p yield v^E as a function of temperature. The excess volumes of p-xylene + n-hexane at 40 °C and p-xylene + n-hexadecane at 40 and 45 °C have also been measured by a dilatometric method, and the results were compared to those obtained from the integration of . The results from both methods are in excellent agreement within experimental error.The experimental values of are negative for the system p-xylene + n-hexane and positive for p-xylene + n-hexadecane. We have interpreted our experimental results in terms of the order present in p-xylene and n-alkanes.     

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

Isobaric expansibilities _P and isothermal compressibilities _T have been determined at 25 and 45°C for binary mixtures of ethylbenzene + n-tetradecane and + n-hexadecane and the corresponding excess functions (V ^E /T)_P and (V ^E /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: _S ^E , (V ^E /P)_T, C_V and (VT). 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-C_n orientations is similar to what we found for toluene and higher than for p-xylene.     

Acoustical and excess thermodynamic studies of mixtures of 2-pyrrolidone with 1,3-propanediol and water as well as 1,3-propanediol with water at 308.15 K

The density (ρ), viscosity (η) and ultrasonic velocity (u) of three mixtures consisting of 2- pyrrolidone with 1,3-propanediol (PD) and water and also of PD and water have been measured as a function of mole fraction at 308.15 K. The experimentally collected data has been used to calculate the excess molar volume (V^E), deviation in viscosity (Δη), deviation in ultrasonic velocity (Δu), isentropic compressibility (κ_s), deviation in isentropic compressibility (Δκ_s) and excess Gibbs free energy of activation (ΔG*^E). The Redlich–Kister polynomial equation has been used to fit the derived parameters. The variation in excessive thermodynamic properties as a consequence of possible molecular interactions is discussed.     

An improvement for the excess enthalpy prediction by UNIFAC. 1. Binary mixtures containing alkanes

The UNIFAC model is tested for its ability to correlate and predict binary excess enthalpies. Besides the alkanes containing systems from earlier work, those for ester-alkane mixtures are also investigated. The model is fitted to binary excess enthalpy data. The influence of group surface area parameters is also examined by using values based on the van der Waals surface areas Q_s multiplied for all the groups by the factor n. A significant improvement of H^E calculation in most of the systems considered is observed if the factor n is taken equal to 3.     

Thermodynamics of liquid mixtures containing n-alkanes and strongly polar components: VE and C P E of mixtures with either pyridine or piperidine

Excess molar volumes V _E and excess molar heat capacities C _P ^/E at constant pressure have been obtained, as a function of mole fraction x₁, for several binary liquid mixtures belonging either to series I: pyridine+n-alkane (C_lH_2l+2), with l=7, 10, 14, 16, or series II: piperidine+n-alkane, with l=7, 8, 10, 12, 14. The instruments used were a vibrating-tube densimeter and a Picker flow microcalorimeter, respectively. V ^E of pyridine+n-heptane shows a S-shaped composition dependence with a small negative part in the region rich in pyridine (x₁>0.90). All the other systems show positive V ^E only. The excess volumes increase with increasing chain length l of the n-alkane. The excess molar heat capacities of the mixtures belonging to series II are all negative, except for a small positive part for piperidine+n-heptane in the region rich in piperidine (x₁>0.87). The C _P ^/E at the respective minima, C _P ^/E (x_1,min ), become more negative with increasing l, and the x_1,min values range from about 0.26 (l=7) to 0.39 (l=14). Most interestingly, mixtures of series I exhibit curves of C _P ^/E against x₁ with two minima and one maximum, the so-called W-shape curves.Dedicated to Professor A. Néckel on the occasion of his 65^th birthday. Communicated in part at the XVII^èmes Journées de Calorimétrie, d'Analyse Thermique et de Thermodynamique Chimique, Ferrara, Italy, 27–30 October, 1986.     

Prediction of free excess enthalpy and excess enthalpy of nonelectrolyte mixtures with the modified TASQUAC model

Summary Using the known models for liquid mixtures (NRTL, UNIQUAC,...), the excess free enthalpy and the heats of mixing cannot be calculated simultaneously in good agreement with experimental data using only two parameters (or three for NRTL) per temperature and binary system. The excess enthalpy can be estimated only qualitatively but not quantitatively. There is also much doubt about the sign of the predictedH ^E data if the absolute value ofH ^E is small [1]. In this work, we examined the possibilities of modified TASQUAC in simultaneous prediction ofVLE andH ^E data and the thermodynamic consistency of experimental data.

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Vorhersage von freier Exzessenthalpie und Exzessenthalpie von Nichtelektrolytmischungen mit Hilfe des modifizierten TASQUAC-Modells

Zusammenfassung Mit Hilfe der bekannten Modelle für flüssige Mischungen (NRTL, UNIQUAC,...) können die freie Exzeßenthalpie und die Mischungswärme nicht gleichzeitig in guter Übereinstimmung mit experimentellen Daten berechnet werden. Die Exzeßenthalpie kann, ausgehend von Parametern, die ausVLE-Daten erhalten wurden, nur qualitativ, nicht quantitativ beschrieben werden. Weiterhin ist das berechnete Vorzeichen der Mischungswärme bei betraglich kleinen Werten der Exzeßenthalpie unsicher [1]. In dieser Arbeit werden die Möglichkeiten des modifizierten TASQUAC-Modells zur simultanen Beschreibung vonVLE- undH ^E-Daten untersucht sowie die thermodynamische Konsistenz der verwendeten Daten überprüft.

     

Volumetric and transport properties of binary liquid mixtures of N-methylacetamide with lactones at temperatures (303.15 to 318.15) K

The values of density (ρ), viscosity (η) and speed of sound (u) have been measured for binary liquid mixtures of γ-butyrolactone (GBL), δ-valerolactone (DVL), and ε-caprolactone (ECL) with N-methylacetamide (NMA) over the whole composition range at T = (303.15 to 318.15) K and atmospheric pressure. From these data, excess molar volume (V^E), deviation in viscosity (Δη), and deviation in isentropic compressibility (Δκ_s), are calculated. The results are fitted to a Redlich–Kister type polynomial equation to derive binary coefficients and standard deviations.     

Excess thermodynamic properties of binary liquid mixtures containing dimethylsulfoxide at 30°C

The exess volumes of mixing of dimethylsulfoxide with n-, sec- and tertbutylamine, n-pentylamine, n-hexylamine, n-heptylamine, n-octylamine and cyclohexylamine have been measured as a function of composition at 30°C by a dilatometric method. For all amines V^E values are negative over the entire mole fraction range. The results are attributed to the interaction between unlike molecules.     

Excess thermodynamic properties of binary liquid mixtures containing cyclohexylamine at 30°C

The excess volumes of mixing of cyclohexylamine with n-hexane, n-heptene, n-octane, n-nonane, benzene, toluene, nitrobenzene, chlorobenzene and bromobenzene have been measured at 30°C. For all systems except for n-hexane, V ^E is positive over the entire mole fraction range. For the n-hexane mixtures, a sigmoid curve is obtained with negative V ^E at high mole fraction of amine.