Collision Factor Theory Research Articles

Theoretical Evaluation of Ultrasonic Velocities in Ternary Liquid Mixtures of Dibutylether + Toluene + 1‐Alkanols at 303K

A comparison of ultrasonic velocity evaluated from Nomoto’s relation, Van Deal‐Vangeel ideal mixtures relation, impedance dependence relation and collision factor theories with experimental values have been made in three ternary systems of 1‐alkanol with common binary mixture of toluene and dibutylether at 303 K. The relative applicability of these theories to the present systems has been checked and discussed.

Speed of sound, isentropic compressibilities and viscosities of ternary non-electrolyte solutions at 303.15 K

Measurements of ultrasonic speeds, isentropic compressibilities and viscosities were carried out for six ternary mixtures namely dimethylsulphoxide (1) + 1,2-dichlorobenzene (2) + 1-alkanols (3) at 303.15 K. The 1-alkanols include 1-propanol, 1-butanol, 1-pentanol, 1-hexanol, 1-heptanol and 1-octanol. The ultrasonic speeds of these ternary mixtures were also evaluated on the basis of Jacobson's free length theory and Schaaff's collision factor theory. From the viscosity data, deviations in viscosity and interaction parameters for various models were also calculated. An attempt has also been made to explain the nature of intermolecular interactions in the light of deviation in isentropic compressibilities and interaction parameter.

Ultrasonic velocities, isentropic compressibilities and excess molar volumes of octan-1-ol with chloroform, 1,2-dichloroethane and 1,1,2,2-tetrachloroethane at 298.15 and 308.15 K

Densities (ρ), and ultrasonic velocities (u) of binary mixtures of octan-1-ol with chloroform, 1,2-dichloroethane, and 1,1,2,2-tetrachloroethane (TCE) have been measured over the entire range of composition at 298.15 and 308.15 K and at atmospheric pressure. From the experimental values of density and ultrasonic velocity, the excess molar volumes (V E), deviations in ultrasonic velocity (Δu), intermolecular free lengths (L f), mean molecular radii (r), molar sound velocities (Rm ), acoustic impedances (Z), excess isentropic compressibilities (), excess intermolecular free lengths () and excess acoustic impedances (Z E) have been calculated. These excess functions have been fitted to the Redlich–Kister polynomial equation to derive the binary coefficients and the standard errors between the experimental and the calculated quantities. The experimental ultrasonic velocities have been analysed in terms of Nomoto (N), Van Dael (VD), Jacobson's free length theory, Schaaffs collision factor theory and thermoacoustical parameters.

Excess Volumes, Isentropic Compressibilities and Viscosities for Binary Mixtures of tert-Butylamine with Alkyl Acetates at 303.15 K

The data on excess volume (V E), density (ρ), viscosity (η) and speeds of sound (u) for the binary mixtures of tert-butylamine (TBA) + methyl acetate (MA), + ethyl acetate (EA), + butyl acetate (BA) and + isoamyl acetate (IAA) at 303.15 K were measured experimentally over the entire range of composition. Speeds of sound were evaluated using Jacobson’s free length theory (FLT) and Schaaffs’ collision factor theory (CFT). The viscosity data were analyzed on the basis of the corresponding states approach and the Grunberg and Nissan treatment. The experimental results for excess volume, deviation in isentropic compressibility and deviation in viscosity were discussed in terms of molecular interactions between unlike molecules. A Redlich-Kister type equation was used to fit the experimental data on excess volume, deviation in compressibility and deviation in viscosity.

Thermophysical and sonochemical behavior of binary mixtures of hexan-1-ol with halohydrocarbons at 303.15 K

Densities and ultrasonic velocities of binary mixtures of hexan-1-ol with 1,2-dichloroethane, 1,2-dibromoethane and 1,1,2,2-tetrachloroethene have been measured over the entire range of composition at 303.15 K at the atmospheric pressure. From these experimental data, the excess molar volumes, molar free volumes, molar isentropic compressibilities, limiting excess partial molar volumes and isentropic compressibilities; deviations in ultrasonic velocity, molecular radii, Rao's molar sound functions, parameters related to space-filling ability, Beyer's parameters of non-linearity, available volumes and intermolecular free lengths by three methods have been estimated. The excess functions have been fitted to the Redlich–Kister polynomial functions and the results have been analyzed in terms of Nomoto's relation (N), Van Dael's relation (VD), Jacobson's free length theory (FLT), Schaaffs' collision factor theory (CFT), thermoacoustical parameters (TAP) and Prigogine–Flory–Patterson theory (PFP).

Molecular Interaction Studies in Binary Liquid Mixtures from Ultrasonic Data

Ultrasonic velocities and densities of the binary liquid mixtures of dimethy1 sulphoxide (DMSO) with phenol, o‐cresol, m‐cresol, p‐cresol and p‐chlorophenol at 318.15 K, over the entire composition range were measured. The theoretical values of ultrasonic velocity were evaluated using the Nomoto’s Relation (NR), Ideal Mixture Relation (IMR), Free Length Theory (FT) and Collision Factor Theory (FLT). The validity of these relations and theories was tested by comparing the computed sound velocities with experimental values. Further, the molecular interaction parameter (α) was computed by using the experimental and the theoretical ultrasonic velocity values. The variation of this parameter with composition of the mixtures has been discussed in terms of molecular interaction in these mixtures.

Studies on thermodynamic properties of binary mixtures of hexan-1-ol with halogenated compounds at T = (308.15 and 313.15) K

Densities, ρ, and ultrasonic velocities, u of binary mixtures of hexan-1-ol with 1,2-dichloroethane, 1,2-dibromoethane, and 1,1,2,2-tetrachloroethene have been measured over the entire range of composition and temperature at (308.15 and 313.15) K. From these experimental results, the excess molar volumes, V E, excess molar isentropic compressibility, K S,m E , molar free volumes, V f, intermolecular free lengths, L f, mean molecular radii, r, Beyer’s parameters of non-linearity, B/ A, and limiting excess partial molar volumes, V ¯ i E, ∘ , have been estimated. The excess functions have been fitted to the Redlich–Kister polynomial equations. The experimental ultrasonic velocities have been analyzed in terms of Nomoto’s relation, Van Dael’s ideal mixture relation, Jacobson’s free length theory, Schaaffs collision factor theory and thermoacoustical parameters.

Densities, viscosities, speeds of sound and refractive indices of binary mixtures of tetrahydrofuran with 1-hexanol, 1-heptanol, 1-octanol, 1-nonanol and 1-decanol at 298.15, 303.15, 308.15 and 313.15 K

Densities (ρ), dynamic viscosities (η), refractive indices (n D) and speeds of sound (u) of binary mixtures of tetrahydrofuran with 1-hexanol, 1-heptanol, 1-octanol, 1-nonanol and 1-decanol over the entire range of mole fraction, at temperatures 298.15, 303.15, 308.15 and 313.15 K and atmospheric pressure have been measured. Excess functions such as excess molar volume (V E), deviations in molar refractivity (ΔR m), deviations in speed of sound (u D), excess isentropic compressibilities () and viscosity deviations (Δη) have been calculated and fitted to the Redlich–Kister-type polynomial equation. The viscosity data were correlated with semi-empirical equations. The speeds of sound have been analysed in terms of collision factor theory and free length theory. The behaviour of V E, ΔR m and u D over the entire range of mole fraction, exhibited positive deviations, while and Δη showed negative variations.

Excess molar volumes and ultrasonic studies of N-methyl-2-pyrrolidone with ketones at T=303.15K

Excess molar volumes (VE) and ultrasonic studies at T = 303.15 K and atmospheric pressure have been measured over the whole composition range for the binary mixtures of N-methyl-2-pyrrolidone (NMP) with ketones. The ketones studied in the present investigation include methyl ethyl ketone (MEK), diethylketone (DEK), methyl propyl ketone (MPK), methyl isobutyl ketone (MIBK), and cyclohexanone (CH). The VE values were measured using a dilatometer and were negative over the entire mole fraction range for NMP with MEK, DEK, MPK, and MIBK and were positive for NMP with CH. The ultrasonic sound velocities for the above systems were measured with a single crystal interferometer at a frequency of 3 MHz. The sound velocity (u) results have been used to calculate isentropic compressibility (Ks) and deviation in isentropic compressibility (ΔKs) over the entire range of volume fraction. The sound velocity results have been predicted in terms of free length theory (FLT), collision factor theory (CFT), and Nomoto relation. The results reveal that all the theories gave a satisfactory estimate of the sound velocity. The deviation values of the isentropic compressibilities (ΔKs) were negative over the entire range of volume fraction in all the binary liquid mixtures except in the binary system NMP with CH, where we observed positive ΔKs values. The results are interpreted on possible molecular interactions between components.

Theoretical Prediction of Ultrasonic Velocity in Organic Liquid Mixtures

Theoretical values of ultrasonic velocity in the binary mixtures of cyclohexanone with 2‐propanol and 2‐methyl‐2‐propanol have been evaluated at 303 K using Nomoto’s relation, collision factor theory, free length theory, ideal mixture relation, Junjie’s method. Theoretical values are compared with the experimental values and the validity of the theories are checked by applying the chi‐square test for goodness of fit and by calculating the average percentage error (APE).

PHYSICOCHEMICAL PROPERTIES FOR BINARY MIXTURES OF ANISOLE WITH 1-HEXANOL, 1-HEPTANOL, 1-OCTANOL, 1-NONANOL, AND 1-DECANOL AT 298.15, 303.15, 308.15, AND 313.15 K

Densities (ρ), viscosities (η), and speeds of sound (u) of binary mixtures of anisole with 1-hexanol, 1-heptanol, 1-octanol, 1-nonanol, and 1-decanol over the entire range of mole fraction and at temperatures 298.15, 303.15, 308.15, and 313.15 K and atmospheric pressure have been measured. From the experimental data, excess molar volume (VE), deviations in speed of sound (uD), excess isentropic compressibilities (k), and viscosity deviations (Δη) have been calculated and fitted to the Redlich-Kister type polynomial equation. The viscosity data were correlated with semi-empirical equations. The speeds of sound have been analyzed in terms of collision factor theory (CFT) and free length theory (FLT). The behavior of VE and k, over the entire range of mole fraction, exhibited positive deviations, while uD and Δη showed negative variations.

Thermodynamics of mixtures containing alkoxyethanols. Part xxiii. Speed of sound predictions and ultrasonic studies of hydroxyether + organic solvent mixtures

The ability of different models to predict speeds of sound, u, of binary mixtures formed by alkoxyethanol and octane, oxaalkane or propylamine has been examined. The models applied are: the free length theory (LFT), the collision factor theory (CFT), and equations such as those proposed by Nomoto, Junjie or Van Dael. Collision factor theory, Nomoto's and Junjie's equations provide similar deviations between experimental and calculated u, which is represented quite accurately by these three models. Poorer predictions are obtained when applying the Junjie's equation to propylamine systems, probably due to the existence of strong interactions between unlike molecules in such mixtures. In contrast, slightly better u predictions from CFT are obtained for the systems 2-methoxyethanol + polyether, or hydroxyether + propylamine. The good u predictions obtained using Nomoto's equation remark the validity of Rao's assumption on additivity of molar sound velocity contributions from atoms, atom groups and chemical bonds of the constituent molecules. Discrepancies between experimental and calculated u are larger when using FLT than those obtained from CFT, Nomoto's or Junjie's equations. This has been ascribed to association and size or shape effects. The linear dependence on the molar fractions of the component liquids of the Rao's and Wada's constants suggests that there is no complex formation in the investigated mixtures, and that the interactions present in such systems are of dipolar type.

Thermodynamics of mixtures containing alkoxyethanols: Part XXVII. Predictions on isobaric thermal expansion coefficients, compressibilities and speeds of sound from the Flory theory

The Flory model is applied to predict the isobaric expansion coefficients, α P, isentropic, κ S , and isothermal, κ T , compressibilities and speeds of sound, u, of the highly complex mixtures: hydroxyether + alkane, + dibutylether, + 1-butanol or + 2-methoxyethanol, 1-alkanol + alkane, and 1-alkanol + dibutylether. Predictions were obtained using the energetic parameter, χ 12, determined from values of excess enthalpies, H E, and from values of the excess isochoric internal energies, U V E , at equimolar composition. No meaningful differences exist between such predictions. Deviations between experimental and calculated values are lower than 2% for mixtures containing alkoxyethanols. Poorer results are obtained for 1-alkanol + dibutylether mixtures with deviations up to 5%. It is shown that predictions on α P, κ S , κ T , and u essentially depend on structural effects and not on the orientational effects present in the studied mixtures. Results are improved using χ 12 values fitted to molar excess volumes. In this case, deviations are similar to those obtained from semiempirical models as free length theory, collision factor theory, or Nomoto or Junjie equations.

Thermo physical properties of binary mixtures of n-butylamine with alkyl acetates at 303.15 K

Excess volumes, speeds of sound and viscosities were measured for binary mixtures of n-butylamine (NBA) with methyl acetate (MA), ethyl acetate (EA), butyl acetate (BA) and isoamyl acetate (IAA) at 303.15 K over the entire range of composition. Isentropic compressibilities were computed from speed of sound and density data. Densities were obtained from experimental excess volume data in case mixtures. Speeds of sound were evaluated using Jacobson free length theory (FLT) and Schaaffs collision factor theory (CFT). The viscosity data were analyzed on the basis of corresponding states approach and Grunberg and Nissan treatment. The experimental results on excess volume, deviation in isentropic compressibility and in viscosity were discussed in terms of molecular interactions between unlike molecules. A Redlich–Kister type equation was used to fit the experimental data on excess volume, deviations in compressibility and viscosity.

Thermodynamics of mixtures containing alkoxyethanols. Part XXV. Densities, excess molar volumes and speeds of sound at 293.15, 298.15 and 303.15 K, and isothermal compressibilities at 298.15 K for 2-alkoxyethanol + 1-butanol systems

Densities, ρ, and speeds of sound, u, of systems formed by 2-methoxyethanol (2ME), 2-ethoxyethanol (2EE), 2-propoxyethanol (2PE), or 2-butoxyethanol (2BE) and 1-butanol have been measured at 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, at those temperatures and deviations from the ideal behaviour of the thermal expansion coefficient, Δ α P, or of the isentropic and isothermal compressibilities, Δ κ S and Δ κ T at 298.15 K. From the data, it is apparent that the interactional contribution to V E is more important for systems with 2ME or 2EE, while structural effects are more relevant in the 2PE or 2BE mixtures, and that dipolar interactions decrease with the size of the 2-alkoxyethanol. Several methods are applied to predict speeds of sound: free length theory (FLT), collision factor theory (CFT), and Nomoto, Junjie and Van Dael equations. CFT and Nomoto's equation provide the better predictions. Finally, 1-butanol + 2-alkoxyethanol, or + 2-(2-alkoxyethoxy)ethanol mixtures have been studied using ERAS. Poorer results were obtained for systems including 2-(2-alkoxyethoxy)ethanols, which may be due to dipolar interactions and structural effects are more important in such solutions.

Speeds of sound and isentropic compressibilities of binary mixtures of 1-heptanol + 1,2-dichloroethane, +1,1,1-trichloroethane, +1,1,2,2-tetrachloroethane, +trichloroethylene and +tetrachloroethylene at 303.15 K – comparison with theories

Densities ρ, and speeds of sound u, of the binary mixtures of 1-heptanol with 1,2-dichloroethane, 1,1,1-trichloroethane, 1,1,2,2-tetrachloroethane, trichloroethylene, and tetrachloroethylene have been measured over the complete composition range at 303.15 K. Isentropic compressibility κs, and Isentropic compressibility deviations Δκs were calculated, and were correlated by a Redlich–Kister type function to determine the fitting parameters and the SDs. The results are consistent with the self-association of 1-heptanol and the polar and nonpolar characters of used chloroethanes or chloroethylenes, which produce the dissociation of 1-heptanol. Speeds of sound and isentropic compressibilities have been compared with calculated values from Jacobson free length theory, Schaaff collision factor theory, Nomoto relation, Junjie relation and Van Deal ideal mixing relation.

Excess molar volumes and ultrasonic studies of dimethylsulphoxide with ketones at T = 303.15 K

Excess molar volumes ( V E) and ultrasonic sound velocities at T = 303.15 K and ambient pressure have been measured as a function of composition for the binary liquid mixtures of dimethylsulphoxide (DMSO) with ketones. The ketones studied in the present investigation include ethyl methyl ketone (EMK), diethylketone (DEK), methyl propyl ketone (MPK), methyl isobutyl ketone (MIBK), and cyclohexanone (CH). The V E values were measured using a dilatometer and were positive over the entire mole fraction range for all systems except in the binary system DMSO with EMK where the V E exhibits an inversion in sign. The experimental V E values have been correlated using Redlich–Kister and Hwang et al. equations. The ultrasonic sound velocities for the above systems have been measured with a single crystal interferometer at a frequency of 3 MHz. The sound velocity ( u) data have been used to calculate isentropic compressibility ( K s) and deviation in isentropic compressibility (Δ K s) over the entire range of volume fraction. The sound velocity data have been predicted in terms of free length theory (FLT), collision factor theory (CFT), and Nomoto relation. The results reveal that all the theories gave a satisfactory estimate of the sound velocity. The deviations in values of isentropic compressibility (Δ K s) were negative over the entire range of volume fraction in all the binary liquid mixtures. The results are interpreted with respect to possible molecular interactions between components.

Effect of temperature on mixing thermodynamics of a new ionic liquid: {2-Hydroxy ethylammonium formate (2-HEAF) + short hydroxylic solvents}

Density and ultrasonic velocity of the mixtures of the new ionic liquid 2-hydroxy ethylammonium formate (2-HEAF) and short hydroxylic solvents (water, methanol, and ethanol) have been measured at the range of temperature (288.15 to 323.15) K and atmospheric pressure. The corresponding apparent molar volume and the apparent molar isentropic compressibility values have been evaluated from the experimental data and fitted to a temperature dependent Redlich–Mayer equation. From these correlations, the limiting infinite dilution values of the apparent magnitudes have also been computed. Derived properties such as isobaric expansibility and isothermal coefficient of pressure excess molar enthalpy were computed due to their importance in the study of specific molecular interactions. The new experimental data were used to test the capability of prediction of the modified Heller temperature dependent equation (MHE) and collision factor theory (CFT). The obtained results indicate that ionic liquid interactions in water are weaker than in the studied alcoholic solutions. An intersection point in isotherms of isentropic compressibility was observed for aqueous solutions which may be an indication of the clathrate structural interactions at high solvent composition. The observed inverse dependence on temperature for aqueous or alcoholic mixtures points out the special trend of packing of this ionic liquid into hydroxylic solvents and its strong dependence on steric hindrance of aliphatic residues. As previously observed, the increase in van der Waals forces due to the presence of long alkyl chain (into ionic liquid and alcohols) leads to higher interactions on mixing.

Excess Molar Isentropic Compressibilities, Excess Molar Volumes, and Excess Sound Speeds of the 1-Propanol + Diethyl Ether + 1-Octanol Ternary Mixture and Constituent Binary Mixtures at 298.15 K

The sound speeds and densities of the 1 -propanol + diethyl ether + 1 -octanol ternary mixture and constituent binary mixtures, 1-propanol + diethyl ether, 1-propanol + 1-octanol, and diethyl ether + 1-octanol, have been measured at 298.15 K as a function of composition. Isentropic compressibilities, molar isentropic compressibilities, excess molar isentropic compressibilities, excess molar volumes, and excess sound speeds have been calculated from the experimental density and sound speed data. Excess molar volumes, excess molar isentropic compressibilities, and excess sound speeds of the binary mixtures were fitted to the Redlich-Kister equation. By using the free length theory (FLT), Schaaff's collision factor theory (CFT), Nomoto's relation (NR), Van Deal's ideal mixing relation (IMR), and Junjie's relation (JR), sound-speed values of the investigated mixtures were calculated. These values were compared with the experimental sound-speed results.

Densities, Viscosities, Speeds of Sound, and Refractive Indices for Binary Mixtures of Diethylcarbonate, Acetophenone, and 1-Hexanol at (293.15, 303.15, 313.15, and 323.15) K for the Liquid Region and at Ambient Pressure

Densities, viscosities, speeds of sound, and refractive indices of the binary systems formed by (diethylcarbonate + acetophenone), (diethylcarbonate + 1-hexanol), and (acetophenone + 1-hexanol) were measured at (293.15, 303.15, 313.15, and 323.15) K for the liquid region and at ambient pressure for the whole composition range. Deviations in viscosity (Δη) from the mole fraction average, deviations in isentropic compressibility (Δκs), and deviations in the refractive index (ΔnD) from the volume fraction average for the mixtures were derived from the experimental data. The binary data of Δη, Δκs, and ΔnD were correlated as a function of the mole fraction by using the Redlich−Kister-type function to determine the fitting parameters and the standard deviations. McAllister's four-body interaction model is used for correlating the kinematic viscosity of binary mixtures. The speeds of sound have been compared with values calculated from the free length theory (FLT) due to Jacobson and the collision factor theory...