Thermodynamics of (1,4-difluorobenzene + an n-alkane) and of (hexafluorobenzene + an n-alkane)

Excess molar enthalpies H^E and excess molar volumes V^E have been measured, as a function of mole fraction x₁, at 298.15 K and atmospheric pressure for the five liquid mixtures (x₁1,4-C₆H₄F₂ + x₂n-C_lH_2l+2), l = 7, 8, 10, 12 and 16. In addition, H^E and excess molar heat capacities C_P^E at constant pressure have been determined for the two liquid mixtures (x₁C₆F₆ + x₂n-C_lH_2l+2), l = 7 and 14, at the same temperature and pressure. The instruments used were flow microcalorimeters of the Picker design (the H^E version was equipped with separators) and a vibrating-tube densimeter, respectively.

The excess enthalpies of the five difluorobenzene mixtures are all positive and quite large; they increase with increasing chain length l of the n-alkane from H^E(x₁ = 0.5)/(J mol⁻¹) = 1050 for l = 7 to 1359 for l = 16. The corresponding excess volumes V^E are all positive and also increase with increasing l: V^E(x₁ = 0.5)/(cm³ mol⁻¹) = 0.650 for l = 7 and 1.080 for l = 16. Interestingly, the excess enthalphies of the corresponding mixtures with hexafluorobenzene are only about 5% larger, whereas the excess volumes of (x₁C₆F₆ + x₂n-C_lH_2l+2) are roughly twice as large as those of their counterparts in the series containing 1,4-C₆H₄F₂. Specifically, at 298.15 K H^E(x₁ = 0.5)/(J mol⁻¹) = 1119 for (x₁C₆F₆ + x₂n-C₇H₁₆) and 1324 for (x₁C₆F₆ + x₂n-C₁₄H₃₀), and for the same mixtures V^E(x₁ = 0.5)/(cm³ mol⁻¹) = 1.882 and 2.093, respectively. The excess heat capacities for both systems are negative and of about the same magnitude as the excess heat capacities of mixtures of fluorobenzene with the same n-alkanes (Roux et al., 1984): C_P^E(x₁ = 0.5)/(J K⁻¹ mol⁻¹) = −1.18 for (x₁C₆F₆ + x₂n-C₇H₁₆), and −2.25 for (x₁C₆F₆ + x₂n-C₁₄H₃₀). The curve C_P^E vs. (x₁ for x₁C₆F₆ + x₂n-C₁₄H₃₀) shows a sort of “hump” for x₁ 0.5, which is presumed to indicate emerging W-shape composition dependence at lower temperatures.     

Thermoynamic properties (Hm, CP,m, Vm, κT) of binary mixtures {x1,3-Dioxane + (1−x)Cyclohexane} at 298.15 K

Molar excess enthalpies H_m^E, isobaric heat capacities C_P,m^E, volumes V_m^E and isothermal compressibilities κT^E for the 1,3-dioxane(3DX) + cyclohexane mixture were measured at 298.15 K, in order to compare to those of the 1,4-dioxane(4DX) + cyclohexane mixture. H_m^E is endothermic and the maximum value about 1.5 kJ mol⁻¹ at x ≈ 0.45, and lower than that of the 4DX mixture by about 80 J mol⁻¹. V_m^E is positive over the whole concentration and the maximum value is about 0.85 cm³ mol⁻¹ at x ≈ 0.45, and lower than that of the 4DX mixture. The above results suggest the energetic unstabilization, resulting in the volume expansion in the mixture. C_P,m^E shows the characteristic W-shaped concentration dependence, which has maximum at x ≈ 0.45 and two minima at x ≈ 0.1 and 0.9. The maximum C_P,m^E value for 3DX mixture shifts toward the positive side, compared to that of 4DX mixture. κT^E were estimated from speeds of sound, densities, thermal expansion coefficients and isobaric heat capacities of the pure component liquids and the mixtures. The κT^E result shows the positive concentration dependence over the whole composition range. The 3DX mixture has the similar thermodynamic properties to the 4DX mixture, despite that 4DX is the nonpolar solvent and 3DX is the dipolar liquid. this means that there exists the local dipolar interaction between 4DX molecules, and the prevalence of “microheterogeneity” in the both mixtures.     

Excess molar volumes of binary mixtures of γ-butyrolactone and a glycol at 303.15 K

Excess molar volumes at 303.15 K for the binary mixture of ethylene glycol+, diethylene glycol+, triethylene glycol+ and tetraethylene glycol+ γ-butyrolactone were determined from precise density measurements over the whole mole fraction range. The excess molar volumes are positive over the whole mole fraction range for ethylene glycol and diethylene glycol systems. For triethylene glycol and tetraethylene glycol systems, V^E curves are sigmoid with a positive lobe at low mole fraction of glycol and a negative lobe at high mole fraction. The excess molar volumes V^E, results are interpreted qualitatively in terms of several opposing effects.     

Experimental study and modelling using the ERAS-Model of the excess molar volume of acetonitrile–alkanol mixtures at different temperatures and atmospheric pressure

Densities of {(1−x)CH₃(CH₂)_n−1OH + xCH₃CN} for n=1, 2, 3 or 4 have been determined as a function of composition at 288.15, 293.15, 298.15 and 303.15 K at atmospheric pressure using a vibrating-tube densimeter (Anton Paar DMA 4500, resolution 1×10⁻⁵ g cm⁻³). Excess molar volumes were calculated. The V_m^E values were negative for acetonitrile–methanol mixtures and sigmoid for acetonitrile–alkanols (C₂–C₄) mixtures over the complete mole fraction range. V_m^E values increase in a positive direction with increase in chain length of the alkanols and with the temperature. The Extended Real Associated Solution Model (ERAS-Model) calculations allowing for self-association for the alkanols and complex formation between acetonitrile and alkanols have been used to correlate experimental data. The model is able to reproduce the asymmetrical V_m^E behavior of the studied systems, although agreement between theoretical and experimental values is less satisfactory for some concentration ranges.     

Thermodynamics of mixtures with strongly negative deviations from Raoult’s law: Part 5. Excess molar volumes at 298.15 K for 1-alkanols+dipropylamine systems: characterization in terms of the ERAS model

Excess molar volumes, V_m^E, at 298.15 K and atmospheric pressure over the entire composition range for binary mixtures of methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol, 1-heptanol and 1-octanol with dipropylamine are reported from densities measured with a vibrating-tube densimeter. All the excess volumes are large and negative over the whole mole fraction range, indicating strong interactions between unlike molecules, which are more important for the system involving methanol, characterized by the most negative V_m^E. For the remainder mixtures, V_m^E at equimolar composition, is approximately constant. The V_m^E curves are nearly symmetrical.

V_m^E and excess molar enthalpies, H_m^E, of the mixtures studied are consistently described by the ERAS model. The ERAS parameters confirm that the strongest interactions between unlike molecules are encountered in the methanol+dipropylamine system.     

Excess volumes of binary mixtures of anisole with bromobenzene, o-dichlorobenzene, o-chloroaniline and p-dioxane at 298.15, 303.15, 308.15 and 313.15 K

Excess molar volumes, V^E, and partial molar volumes, _i, have been calculated for binary liquid mixtures of anisole with bromobenzene, o-dichlorobenzene, o-chloroaniline and p-dioxane from the results of densities measured at 298.15, 303.15, 308.15 and 313.15 K over the entire range of composition. In the temperature interval studied the values of V^E are positive for anisole + p-dioxane, anisole + bromobenzene and anisole + o-dichlorobenzene, whereas negative values are observed for anisole + o-chloroaniline. The negative V^E for the latter system was due to specific interactions between mixing components. The positive V^E for the remaining systems was ascribed to the dispersion-type interactions.     

Viscometric and volumetric studies on binary mixtures of 1,2-dichloroethane and chlorinated methanes or their binary equimolar mixtures at 303.15 K

Excess viscosities, η^E and molar excess volumes V^E were obtained for binary mixtures of 1,2-dichloroethane and chlorinated methanes and for pseudobinary mixtures of 1,2-dichloroethane and equimolar binary mixtures from chlorinated methanes at 303.15 K. The chlorinated methanes include carbon tetrachloride, chloroform and dichloromethane. Grunberg—Nissan interaction parameter d and interaction energy for flow of activation W_vis were also presented. The relationship between the η^E's and the V^E's has been quantitively considered using Singh's equations. The excess viscosities for all the systems are negative over the entire compositions. There are specific interactions between 1,2-dichloroethane and chlorinated methanes, but the specific interactions are not strong. The interactions of 1,2-dichloroethane with chlorinated methanes decrease in the order: chloroform > dichloromethane > carbon tetrachloride. ‘Pseudochloroform’ has been defined by us for the first time as the equimolar mixture of dichloromethane and carbon tetrachloride.     

Application of the ERAS-Model to binary mixtures of diethylamine and s-butylamine with acetonitrile in the temperature range (288.15–303.15) K

Densities for binary mixtures of diethylamine and s-butylamine with acetonitrile have been measured at 288.15, 293.15, 298.15 and 303.15 K using a vibrating-tube densimeter. Excess molar volumes (V_m^E) were determined. Both systems exhibit negative V_m^E values over the entire composition range in the temperature range studied. ERAS-Model calculations allowing for self-association for the amines and complex formation between acetonitrile and amines were performed. The agreement between theoretical and experimental results is satisfactory only for mole fractions of amines less than 0.50. A simplified version of the model, without the chemical contribution, gives similar results.     

Excess molar volumes and enthalpies for the binary systems propyl propanoate + o-xylene, m-xylene, and p-xylene at 298.15 K

This paper reports excess molar enthalpies, H_m^E, and excess molar volumes, V_m^E, of the binary systems {propyl propanoate + o-xylene}, {propyl propanoate + m-xylene} and {propyl propanoate + p-xylene} at the temperature 298.15 K and atmospheric pressure, over the whole composition range. V_m^E was calculated from the experimental measurement of the corresponding densities, while H_m^E was measured directly. The excess magnitudes were correlated to a Redlich-Kister type equation. Finally, we will discuss the results of the three mixtures studied here and by comparison with other binary systems containing propyl propanoate and a benzene-based compound previously published.     

Excess volumes of ternary mixtures of N,N-dimethylformamide-diethyl ketone-1-alkanols at 303.15K

Volume changes on mixing of ternary liquid mixtures of N,N-dimethylformamide and diethyl ketone with 1-alkanols have been measured as a function of composition at 303.15 K. The alkanols include 1-propanol, 1-butanol, 1-pentanol and 1-hexanol. The measured V^E values are negative in the mixtures of N,N-dimethylformamide, diethyl ketone and 1-propanol, or 1-butanol. The V^E data exhibits an inversion in sign in the mixture containing 1-pentanol and positive excess volumes are observed in the mixture containing 1-hexanol. The measured data are compared with predicted values based upon empirical relations. The excess volume for the binary mixture of N,N-dimethylformamide with diethyl ketone has been measured over the entire range of composition at 303.15 K. The V^E values are negative for the binary mixture.     

Isothermal vapor–liquid equilibria and excess molar volumes for 2-methyl pyrazine (2MP) containing binary mixtures

2-Methyl pyrazine (2MP) has led to significant interest for its industrial and pharmaceutical uses. The new vapor–liquid equilibria (VLE) at 353.15 K and excess molar volumes (V^E) at 298.15 K over the whole mole fraction range for seven binaries (water, n-hexane, cyclohexane, n-heptane, methylcyclopentane (MCP), methylcyclohexane (MCH) and ethyl acetate (EA) with 2MP) have been measured. VLE were measured by using headspace gas chromatography and V^E were determined using precision density meter. The water+2MP system has only the minimum boiling azeotrope. The experimental VLE and V^E data were well correlated in terms of common g^E models and Redlich–Kister equation, respectively.     

Excess properties of binary alkanol-ether mixtures and the application of the ERAS model

Experimental results are reported of excess molar volumes V^E and excess molar enthalpies H^E for binary mixtures of 1-propanol, 2-propanol, 1-butanol and 2-butanol with diisopropyl ether (DIPE) and dibutyl ether (DBE) at 298.15 K. A vibrating-tube densitometer was used to determine V^E, and H^E was measured using a quasi-isothermal flow calorimeter. The applicability of the ERAS model has been investigated for describing the experimental data as well as literature data of alkanol-ether mixtures containing DBE or dipropyl ether (DPE).     

Excess differential thermodynamic properties

A strategy is described for the systematic generation of a complete set of partial derivatives of the four energy functions from a basis set of five measured properties: V_m, S_m, C_p,m (δV_m/δT)_p and either (δV_m/δp)_T or (δV_m/δp)_s. The same set of equations applies to both pure substances and either real or ideal mixtures.

Examples are given of some excess differential properties of binary mixtures which exhibit unusual sensitivity to changes in composition.     

On the extremum property of electron density functions in position and momentum spaces

For statistically uncorrelated wave functions, the electron density ρ(r) is known to be an extremum function of the generalized electron-pair density g(q;a,b), which smoothly connects ρ(r), the electron-pair intracule (relative motion) density h(u), and the electron-pair extracule (center-of-mass motion) density d(R). The present systematic examination of the numerical Hartree–Fock results of moments rⁿ, uⁿ, Rⁿ and density values at the origin ρ(0), h(0), d(0) for 102 neutral atoms and 96 singly charged ions suggests that ρ(r) is local maximum for a small q and is local minimum for a large q of the function g(q;a,b). Analogous results are obtained for the momentum-space counterparts Π(p) and .     

Hm and Vm thermodynamic surfaces for binary mixtures in the near critical region

Even for such simple mixtures as (argon+methane), the excess enthalpy H^E_m and the excess volume V^E_m in the near critical region are about two orders of magnitude higher than for the liquid mixture at low temperatures and pressures near ambient conditions. Mixtures for which the critical temperatures are close together, and for which the critical pressures are far apart, have similar H^E_m (x,p,T) and V^E_m (x,p,T) surfaces, and near critical isotherms show double maxima in the supercritical fluid region. Mixtures for which the critical pressures are close together, and the critical temperatures are far apart, also have similar H^E_m (x,p,T) and V^E_m (x,p,T) surfaces, but isobars on the surfaces are ‘S’ shaped. The shapes of these near-critical excess-function surfaces can be understood from an inspection of the enthalpy, or residual enthalpy curves of the mixture and of the pure components. Examples of both are given. Attention is drawn to the large value that these excess functions can have close to a pure component critical point.     

Pressure and temperature dependencies of excess molar enthalpies of two-component Lennard–Jones fluid mixtures in the supercritical region

Monte Carlo (MC) simulations have been carried out for mixtures of Lennard–Jones (LJ) fluids near or in the supercritical region. Excess molar enthalpy at equimolar concentration, H_p,x=0.5^E, has been obtained for four kinds of model mixtures each having different combining rule for unlike interactions. The pressure and temperature dependencies of H_p,x=0.5^E are investigated. The unique pressure and temperature dependencies of H_p,x=0.5^E for real systems such as (ethane+ethene) in the supercritical condition have been reproduced by the present simple model systems. Excess molar internal energies at constant volumes, U_V,x=0.5^E, are also evaluated. They are compared with H_p,x=0.5^E to investigate the volumetric contributions to H_p,x=0.5^E or excess molar internal energies at constant pressure, U_V,x=0.5^E. Calculated U_V,x=0.5^E for the present model systems are quite simple compared to the excess molar internal energy at constant pressure, U_V,x=0.5^E. They are very small in magnitude and show linear dependencies on the density of mixtures.     

Binding of acrylic and sulphonic polyanions by open-chain polyammonium cations

The interactions between some acrylic and sulphonic polyanions and some protonated amines (diamines NH₂-(CH₂)_x-NH₂, x=2,…,10; linear tri-, tetra-, penta- and hexa-amines) were studied potentiometrically in aqueous solution, at 25°C. For both types of polyanions AL₂H_i (L⁻, monomer of polyanion, A, amine) species are formed, with i=1,…,n (n=number of amino groups in the amine). The stability of these species is strictly dependent on the polyammonium cation charge, and fairly independent of the type of amine (in diamine species maximum stability is observed for x=4, 5). Acrylic and sulphonic polyanion complexes are considerably stronger than analogous species formed by low molecular weight anions. Mean stability can be expressed as log K=2.87ζ^2/3, for polyacrylic anions and log K=2.42ζ^2/3 for polysulphonic anions (ζ=absolute value for charge product of reactants).     

Prediction of specific retention volumes in gas chromatography by using Kováts and molecular structural coefficients

The Kováts coefficients, K_c,Z, of a stationary phase and the solute's molecular structural coefficients, S_c,i, depend both on the specific retention volume V_g, of a solute or homologous series and on the “log-plot” slope, b, of a chromatographic column. In view of this dependence, the feasibility of predicting V_g in three instances was investigated: (a) V_g prediction of any n-alkane from K_c,Z and retention data of n-decane; (b) V_g prediction of any solute from the temperature dependence of the above parameters and (c) V_g prediction of any term of a homologous series from the correlations of the S_c increments, ΔS_c, with the organic structural function. The possibilities of the method are evaluated in the light of the analysis of the deviations of the predicted V_g values from the measured values.     

Formation of cobalt, nickel and copper complexes with murexide in ethanol-water mixtures

The complexation reactions between murexide and Co²⁺, Ni²⁺ and Cu²⁺ in C₂H₅OH-H₂O mixtures have been investigated spectrophotometrically. The formation constants of the 1:1 complexes formed increase in the order Co²⁺ < Ni²⁺ < Cu²⁺ for all solvent mixtures studied, and log K_f is a linear function of the mole fraction of ethanol. The heat of complexation was determined calorimetrically for the nickel and copper complexes. The values of ΔH° and ΔS° are solvent-dependent, and all three complexes have negative ΔH° and positive ΔS° values.