Correlation of the prigogine-flory theory with isothermal compressibility data. I. Systems with quasi-spherical molecules

The isothermal compressibilities K_T for cyclohexane + benzene, cyclohexane + toluene and benzene + toluene systems at 25, 35, 45 and 60°C have been used to test the Prigogine-Flory theory using Van der Waals and Lennard-Jones energy potentials. Flory's energy parameter X ₁₂ was calculated for these systems at the four temperatures. From X ₁₂ for the equimolar mixture, the following excess functions were calculated: (?V^E/?_p)_T which is related to K _T ^E , the heat of mixing H ^E , and the excess volume V ^E . The theory and any of the two potentials give (?V^E/?_p)_T which fit the experimental data, but H ^E and V ^E , calculated using the same X ₁₂ parameter, depart appreciably from the experimental data even though they agree in sign and have the essential features of the excess functions. The departure is apparent in both magnitude (in particular for the cyclohexane + benzene, and cyclohexane + toluene systems) and in the temperature dependence. The conclusion is that the X ₁₂ parameter does not predict the thermodynamic properties of these systems and the Lennard-Jones potential, involving a more complicated expression, does not contribute any improvement over the Van der Waals potential.     

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.     

Thermodynamic properties of liquid mixtures of carbon monoxide and methane

The equations of state of liquid methane at 125.00 K and of six liquid mixtures of carbon monoxide and methane at 116.30, 120.00 and 125.00 K have been measured from just above the saturation vapour pressure to the freezing pressure of methane. The results show that the excess volume V^E is large and negative at low pressures but becomes less negative as the pressure is increased, being almost zero at the highest pressures. The curve of V^E against the mole fraction x is very asymmetrical at low pressures, but becomes more symmetrical with rising pressure.The effect of pressure on the excess functions G^E, H^E and T·S^E has been calculated. H^E and T·S^E prove to be much more sensitive to pressure than G^E.Conformal solution theory, in the van der Waals one-fluid form, reproduces the experimental results very successfully.     

Temperature dependence of the volumetric properties of some alkoxypropanols + n-alkanol mixtures

The excess molar volumes V_m^E for binary liquid mixtures containing dipropylene glycol monomethyl ether or dipropylene glycol monobutyl ether and methanol, 1-propanol, 1-pentanol and 1-heptanol have been measured as a function of composition using a continuous dilution dilatometer at T=(288.15, 298.15, and 308.15) K and atmospheric pressure over the whole concentration range. The excess volume results allowed the following mixing quantities to be reported in all range of concentrations or at equimolar concentrations: α, volume expansivity; (∂V_m^E/∂T)_p; (∂H^E/∂P)_T at T=298.15 K. The obtained results have been compared at T=298.15 K with the calculated values by using the Flory theory of liquid mixtures. The theory predicts the α, and α^E values rather well, while the calculated values of (∂V_m^E/∂T)_p and (∂H^E/∂P)_T show general variation with the alkyl chain length of the alkoxypropanols. The results are discussed in terms of order or disorder creation.     

Thermodynamics of (1-alkanol + linear monoether) systems

Densities, ρ, and speeds of sound, u, of systems formed by 1-heptanol, or 1-octanol, or 1-decanol and dibutylether have been measured at a temperature of (293.15, 298.15, and 303.15) K and atmospheric pressure using a vibrating tube densimeter and sound analyser Anton Paar model DSA-5000. The ρ and u values were used to calculate excess molar volumes, V^E, and deviations from the ideal behaviour of the thermal expansion coefficient, Δα_p and of the isentropic compressibilities, Δκ_S. The available database on molar excess enthalpies, H^E, and V^E for (1-alkanol + linear monoether) systems was used to investigate interactional and structural effects in such mixtures. The enthalpy of the OH?O bonds is lower for methanol solutions, and for the remainder systems, it is practically independent of the mixture compounds. The V^E variation with the chain length of the 1-alkanol points out the existence of structural effects for systems including longer 1-alkanols. The ERAS model is applied to the studied mixtures. ERAS represents quite accurately H^E and V^E data using parameters which consistently depend on the molecular structure.     

Measurements of HmE and VmE for (n-butane + sulphur hexafluoride) in the supercritical region at the pressure 6.00 MPa

A flow mixing calorimeter followed by a vibrating-tube densimeter has been used to measure excess molar enthalpies H_m^E and excess molar volumes V_m^E of {xC₄H₁₀+(1−x)SF₆}. Measurements over a range of mole fractions x have been made in the supercritical region at the pressure p=6.00 MPa and at seven temperatures in the range T=311.25 K to T=425.55 K. The H_m^E(x) measurements at T=351.35 K were found to exhibit an unusual double maximum. Measurements at all temperatures are compared with the Patel–Teja equation of state with the parameters determined by solving a cubic equation as recommended, and also with parameters determined by the method suggested by Valderamma and Cisternas who proposed equations which are a function of the critical compression factor. The overall fit to the H_m^E and V_m^E measurements obtained using Valderamma and Cisternas equations was found to be better than that obtained using the parameters according to the method suggested by Patel and Teja.     

The excess molar volumes and enthalpies of (N-methyl-2-pyrrolidinone + an alcohol) atT = 298.15 K and the application of the ERAS theory

Excess molar volumes V_m^EatT =  298.15 K and atmospheric pressure are reported for (N -methyl-2-pyrrolidinone  +  propan-2-ol, or butan-1-ol, or butan-2-ol, or 2-methylpropan-1-ol ). TheV_m^E have been calculated from measured values of density using the vibrating tube technique. The results are discussed in terms of the hydrogen bonding and other intermolecular association. Excess molar enthalpiesH_m^E at T =  298.15 K and atmospheric pressure are reported for (N -methyl-2-pyrrolidinone  +  propan-1-ol, or propan-2-ol, or butan-1-ol, or butan-2-ol, or 2-methylpropan-1-ol). The H_m^Ehave been obtained using flow calorimetry. The experimental results have been correlated and compared with the results from the Extended Real Associated Solution (ERAS) theory. The parameters adjusted to the mixtures properties are two cross association parameters and the interaction parameter responsible for the exchange energy of the van der Waals interactions. Self-association parameters of the alcohols and NMP are taken from the literature.     

Studies of some acoustical properties in binary solutions

Various acoustical properties such as isentropic compressibility, specific impedance, molar sound velocity, molar compressibility, van der Waals constant, intermolecular free length, excess molar volume (V^E), excess viscosity, excess adiabatic compressibility, Gibb’s free energy of activation for viscous flow etc. have been calculated in three binary systems: anisole+methanol, anisole+chloroform and anisole+dimethyl foramide from sound velocity (2 MHz), density and viscosity measurements at 30°C. The results are interpreted in terms of molecular interactions occurring in the solutions.     

Excess enthalpy,excess heat capacity and excess volume of 1,2,4-trimethylbenzene +, and 1-methylnaphthalene + an n-alkane

A flow microcalorimeter of the Picker design was used to measure excess molar enthalpies H^E at 298.15 K as a function of mole fraction χ₁ for several mixtures belonging to series I: {χ₁1,2,4-C₆H₃(CH₃)₃ + χ₂n-C_ℓH_2ℓ+2}, and series II: {χ₁1-C₁₀H₇CH₃ + χ₂n-C_ℓH_2ℓ+2}. The chain length ℓ of the n-alkanes ranged between 7 and 16. 1,2,4-trimethylbenzene and 1-methylnaphthalene have about the same size and shape as the previously investigated chloro derivatives 1,2,4-C₆H₃Cl₃ and 1-C₁₀H₇Cl but a much smaller reduced dipole moment. The calorimeter was used in the discontinuous mode. A plot of H^E_max (i.e., the maximum value of H^E with respect to composition) against ℓ for series I shows a shallow minimum around ℓ = 11 with H^E_max (ℓ = 11) ≈ 250 J mol⁻¹, whereas H^E_max for series II decreases over the whole range 7 ⩽ ℓ ⩽ 16: H^E_max (ℓ = 7) ≈ 760 J mol⁻¹, and H^E_max (ℓ = 16) ≈ 595 J mol⁻¹. The corresponding enthalpic interaction parameters h₁₂, calculated from zeroth-order KGB (Kehiaian-Guggenheim-Barker) theory, decrease with increasing ℓ, and the rate of decrease, dh₁₂/dℓ, diminishes for larger chain lengths.For three mixtures belonging to series I (ℓ = 7, 10, 14), excess molar volumes V^E and excess molar heat capacities C^E_P at constant pressure were mesured at the same temperature. V^E was determined with a vibrating-tube densimeter (flow conditions), and C^E_P was obtained with another type of flow calorimeter (stepwise procedure). V^E(χ₁ = 0.5)/(cm³ mol⁻¹) = −0.207 for ℓ = 7, 0.060 for ℓ = 10, and 0.145 for ℓ = 14. The corresponding values for C^E_P x₁ = 0.5)/(J K⁻¹ mol⁻²) are 0.32, 0.66 and −0.09. Thus the chain length dependence of the excess molar heat capacity is qualitatively similar to that observed for the series with the homomorphic chloro derivative, (1,2,4-C₆H₃Cl₃ + n-C_ℓH_2ℓ+2), and to that of (1-C₁₀H₇Cl+n-C_ℓH_2ℓ+2).     

Thermodynamic study of 2-methyl-tetrahydrofuran with isomeric chlorobutanes

Excess molar volumes, V^E, isentropic compressibility deviations, Δκ_S, and excess molar enthalpies, H^E, for the binary mixtures 2-methyl-tetrahydrofuran with 1-chlorobutane, 2-chlorobutane, 2-methyl-1-chloropropane and 2-methyl-2-chloropropane have been determined at temperatures 298.15 and 313.15 K, excess molar enthalpies were only measured at 298.15 K. We have applied the Prigogine-Flory-Patterson (PFP) theory to these mixtures at 298.15 K.     

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.     

Volumes of mixing of n-octylacetate + n-alkanes: an interpretation in terms of the Prigogine-Flory-Patterson theory

The results of measurements of molar excess volumes V^E at 303.15 K over the whole mole fraction range for eight mixtures: n-octylacetate + n-hexane; +n--heptane; + n-octane; +nn-nonane; + n-decane; +nn-dodecane; + n-tetradecane and + n-hexadecane are presented. The experimental values of V^E show a regular pattern of behaviour for the eight sets of binary mixtures. The magnitude of V^E for this class of mixtures decreases as the n-alkane chain-length decreases. In order to explain the observed behaviour, the Prigogine-Flory-Patterson theory is used to predict the total V^E and the three different contributions to V^E. Agreement between the theoretical and experimental V^E is reasonable for the eight systems     

Excess molar volumes at 298.15 K of binary liquid organic mixtures containing n-alkanones and linear ethers: Application of Flory’s theory

Excess molar volumes, V_m^E, at 298.15 K and atmospheric pressure over the entire composition range for binary mixtures of 2-butanone with di-n-butyl ether and 2-pentanone and 3-pentanone with di-n-butyl ether and 2,5-dioxahexane, 2-heptanone and 4-heptanone with di-n-butyl ether, 2,5-dioxahexane and 3,6,9-trioxaundecane are reported from densities measured with a vibrating-tube densimeter. All the excess volumes present strong contractions when compared to those of n-alkanone+n-alkane systems.Molar excess enthalpies H_m^E and V_m^E of the considered mixtures vary similarly. This may be attributed to interactional effects which prevail over structural effects.Flory’s theory has been applied to the systems under study. As expected, results for H_m^E are better when the difference in polarity of the components of the mixture decreases. V_m^E is often poorly represented.     

Volatility and crystal lattice energy of palladium(II) chelates

Temperature dependence of saturated vapor pressure has been measured by gas saturation technique for volatile bis-chelates of palladium(II) with such ligands as acetylacetone, hexafluoroacetylacetone, diethyldithiocarbamate, diisopropyldithiophosphate, and also mixed ligand complex with acetylacetone and cyclooctadiene-2,4. Standard thermodynamic parameters of vaporization ΔH _T ⁰ and ΔS _T ⁰ were calculated. Crystal molecular packings and intermolecular interactions were analyzed basing on structural data. Atomatom potential calculation of van der Waals energy E_cryst in crystal lattice was performed and compared to the experimentally obtained values of sublimation enthalpy for the complexes under study.     

Excess molar volumes of (cyclohexanone+trichloromethane,or 1,2-dichloroethane,or trichloroethene,or 1,1,1-trichloroethane,or cyclohexane) at T=308.15 K,and of (cyclohexanone+dichloromethane) at T=303.15 K

Excess molar volumes V_m^E have been measured using a dilatometric technique for mixtures of cyclohexanone (C₆H₁₀O) with trichloromethane (CHCl₃), 1,2-dichloroethane (CH₂ClCH₂Cl), trichloroethene (CHClCCl₂), 1,1,1-trichloroethane (CCl₃CH₃), and cyclohexane (c-C₆H₁₂) at T=308.15 K, and for cyclohexanone+dichloromethane (CH₂Cl₂) at T=303.15 K. Throughout the entire range of the mole fraction χ of C₆H₁₀O, V_m^E has been found to be positive for χ C₆H₁₀O+(1−χ)c-C₆H₁₂, and negative for χ C₆H₁₀O+(1−χ)CH₂Cl₂, χ C₆H₁₀O+(1−χ)CHClCCl₂, χ C₆H₁₀O+(1−χ)CHCl₃, and χ C₆H₁₀O+(1−χ) CCl₃CH₃. For χ C₆H₁₀O+(1−χ)CH₂ClCH₂Cl, V_m^E has been found to be positive at lower values of χ and negative at high values of χ, with inversion of sign from positive to negative values of V_m^E for this system occurring at χ∼0.78. Values of V_m^E for the various systems have been fitted by the method of least squares with smoothing equation, and have been discussed from the viewpoint of the existence specific interactions between the components.     

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.     

Thermodynamic and transport properties of binary liquid mixtures of cyclohexanol with isomeric chlorotoluenes

Densities (ρ) at different temperatures from 303.15 to 318.15 K, speeds of sound (u) and viscosities (η) at 303.15 K were measured for the binary mixtures of cyclohexanol with 2-chlorotoluene, 3-chlorotoluene and 4-chlorotoluene over the entire range of composition. The excess volumes (V^E) for the mixtures have been computed from the experimental density data. Further, the deviation in isentropic compressibilities (Δκ_s) and deviation in viscosities (Δη) for the binary mixtures have been calculated from the speed of sound and viscosity data, respectively. The V^E values and Δκ_s values were positive and Δη data were negative for all the mixtures over the whole range of composition at the measured temperatures. The calculated excess functions V^E, Δκ_s and Δη were fitted to Redlich–Kister equation. The excess functions have been discussed in terms of molecular interactions between component molecules of the binary mixtures.     

Excess heat capacities and excess volumes of binary liquid mixtures of chloroform with cyclic ethers at 298.15 K

Molar excess heat capacities at constant pressure, C^E_p, of binary liquid mixtures chloroform + oxolane, chloroform + 1,3-dioxolane, chloroform + oxane, and chloroform + 1,4-dioxane have been determined at 298.15 K from measurements of volumetric heat capacities in a Picker flow microcalorimeter. A precision of ±0.04 J K^?1 mole^? was achieved by using the stepwise procedure. Experimental molar excess heat capacities are compared with values derived from H^E results at different temperatures. Excess molar volumes, V^E, for the same systems at 298.15 K have been determined by measuring the density of the pure liquids and solutions with a high-precision digital flow densimeter.