Application of the wilson-equation to azeotropic mixtures

Stephan, K. and Wagner, W., 1985. Application of the Wilson-equation to azeotropic mixtures. Fluid Phase Equilibria, 19: 201-219. The Wilson model is appropriate to describe low pressure phase equilibria. For binary mixtures only two parameters are needed. A diagram was developed, based on the Wilson model, allowing us to distinguish azeotropic from nonazeotropic binary systems. To apply this diagram the Wilson constants, and in addition the vapour pressure or boiling temperature and the molar entropy of vaporization of the pure componentes must be known. A few examples for the application of the method are discussed.     

Single and Mixed Gas Adsorption Equilibria of Carbon Dioxide/Methane on Activated Carbon

Single gas adsorption isotherms of methane and carbon dioxide on micro-porous Norit RB1 activated carbon were determined in a gravimetric analyser in the temperature range of 292 to 349 K and pressures to 0.8 Mpa. Furthermore binary isotherms of carbon dioxide and methane mixtures were determined at 292 K and pressures up to 0.65 MPa. Adsorbed phase compositions were determined from the gravimetric data by the rigorous thermodynamic method of Van Ness.These experimental binary equilibrium data were compared with equilibrium data calculated by the Ideal Adsorbed Solution (IAS) model. Only moderate agreement could be obtained.Finally, activity coefficients, accounting for the non-ideality of the adsorbate mixture, were calculated from the experimental data. The Wilson equation, derived for bulk solutions, was fitted on these activity data and the Wilson interaction parameters were determined. The Wilson equation proved to correlate the experimental data reasonably. However, the Wilson interaction parameters are not only completely different from those found for bulk solutions, but also the physical interpretation of these parameter values is completely lacking.It is concluded that new solution models should be developed encompassing both non-ideal solution behaviour and surface heterogeneity.     

Review of rate constants and exploration of correlations of the halogen transfer reaction of trisubstituted carbon-centered radicals with molecular halogens

Rate constants for the reaction (R'(3)C(?) + X(2) → R'(3)CX + X(?); X = F, Cl, Br, I) are reviewed. Because of curved Arrhenius plots and negative E(X) values, empirical structure-reactivity correlations are sought for log k(X,298) rather than E(X). The well-known poor correlation with measures of reaction enthalpy is demonstrated. The best quantitative predictor for R'(3)C(?) is Σσ(p), the sum of the Hammett σ(p) constants for the three substituents, R'. Electronegative substituents with lone pairs, such as halogen and oxygen, thus appear to destabilize the formation of a polarized prereaction complex and/or TS ((δ+)R-?-?-X-?-?-X(δ-)) by σ inductive/field electron withdrawal while simultaneously stabilizing them by π resonance electron donation. The best quantitative predictor of the reactivity order of the halogens, I(2) > Br(2) ? Cl(2) ≈ F(2), is the polarizability of the halogen, α(X(2)). For the data set of 60 rate constants which span 6.5 orders of magnitude, a modestly successful correlation of log k(X,298) is achieved with only two parameters, Σσ(p) and α(X(2)), with a mean unsigned deviation of 0.59 log unit. How much of this residual variance is the result of inaccuracies in the data in comparison with oversimplification of the correlation approach remains to be seen.     

Temperature dependence of the spin-lattice relaxation rates in the triplet state of pyrazine at low temperatures

The electron spin-Lattice relaxation, (SLR) rate constants have been measured for the triplet state at pyrazine-d₄ in a cyclohexane matrix from 1 to 8 K by resolving the phosphorescent decay curve into three exponential components. A matrix kinetics is presented that gives the relationship between the SLR rate constants and the observed decay component rate constants and the decay component intensities of the three zero-field levels. An exact numerical procedure based on the Newton-Raphson technique is described in detail for systems of two and three coupled levels. This procedure was used to find the SLR rate constants starting from either the decay component rate constants or the decay component intensities. Both the matrix kinetics and the numerical procedure should be useful in many other studies involving multilevel systems whose sublevels are connected by some combination of SLR and microwaves. The observed SLR rate constants are best explained as a function of temperature as the sum of a direct process (linear in T) and a Raman process (T² dependence). Their relative magnitudes indicate that the Raman process is probably antharmonic. Vancus mechanisms for SLR in this system are examined, and a short review of SLR theory and experiment is given. The nature of the zero-field sublevels in pyrazine-J₄ is also discussed as is the effect of the choice of matrix solvent upon SLR rate constants and the phosphorescent spectrum.     

氯仿,乙醇,苯有关二元体系加压相平衡研究

氯仿、乙醇、苯有关二元体系加压相平衡研究马忠明，陈庚华，王琦，严新焕，韩世钧，余淑娴（浙江大学化学系，杭州，３１００２７）（江西大学化学系）关键词加压汽液平衡，醇烃体系，氯仿，乙醇，苯醇是极性分子，烃是非极性或弱极性分子，醇与醇、烃与烃分子及醇与烃分...     

Correlations between molecular parameters and the spin–spin coupling constants of vicinal protons: Criticism of the karplus equations

Conformationally rigid systems such as xylopyranose 1,2,4-ortho esters ( 1a ) and ( 1b ) and 10-methoxy-6-aza-isoadamantane ( 2 ), for which the identity of conformations both in the crystalline state and in solution can reasonably be assumed, provide good models for the study of experimental correlations between the spin–spin coupling constants (J) of the vicinal protons and the dihedral bond angles (DBA) determined from an X-ray study in the H? C? C? H bond system. The Karplus equations and their modifications (with and without corrections for the electronegativity of adjacent groups) were found to be unable to provide satisfactory correlations between these parameters. Optimum coefficients for the equations connecting the J and DBA values with corrections for electronegativity were calculated by the least squares method. The same procedure was used to obtain an equation connecting the J with DBA values using the sum of the chemical shifts as a measure of the electronic factors affecting the J ∝ DBA dependence. The accuracy of the equation thus obtained lies within ±18% as opposed to ±48% for the original Karplus equations. A similar correlation was obtained for the angles between the intercrossing lines formed by the directions of the vicinal C? H bonds (ILA). When combined with the sum of chemical shifts, ILA provides a better correlation with the coupling constants J than the conventional parameter DBA.     

An analytical expression for the variation of the vapour pressure of liquids with temperatures up to critical conditions

In development of previous observations, the author proposes a four-constant equation which accurately reproduces the vapour pressures of liquids from about 0.04 mm to critical conditions. The equation holds for: (a) a variety of substances ranging from hydrogen and the lowest inert gases through non-polar and polar organic compounds and (b) fused salts and liquid metals to the upper limits of vapour pressures available. It satisfactorily accounts for infection points, and correlates previous work on entropies of vaporisation in terms of an aspherical factor.Of the four constants, one is universal and a second nearly so; below about 5 atm therefore, the equation reduces to one containing only two specific constants. The theoretical significance of the latter equation is discussed in terms of a free-volume theory of the liquid state.     

19F n.m.r. spectrum of hexafluoroquinazoline long-range inter-ring F?F coupling constants

The ¹⁹F n.m.r. spectrum of hexafluoroquinazoline has been analyzed giving the signs and magnitudes of all but two of the coupling constants, and supporting the analyses of the ¹⁹F n.m.r. spectra of heptafluoroquinoline and heptafluoroisoquinoline. Long range F? F inter-ring coupling constants are a guide for assessing π-electron delocalization pathways. In addition, nitrogen in the β position enhances the distant F-5, F-7 meta-coupling constant, implying a π-contribution to J(FF)meta. A rationalization of changes in peri-coupling constants is also presented. The observed changes appear to be the sum of two effects: (i) ring contraction by the insertion of shorter C? N bonds into the aromatic ring and (ii) a secondary effect which is dependent on the existence of a β-nitrogen, adjacent to the peri nuclei.     

Molecular dynamics of germylacetylene

A complete vibrational analysis has been carried out for germylacetylene and germylacetylene-d₃ molecules and a set of molecular constants, i.e. kinetic constants and potential constants, is reported. The physical understanding of the nature of the potential constants and kinetic constants in molecules leads to a stringent application of provisions of group theoretical technique, introduced by Wilson in the study of molecular vibrations. This procedure is applied here to the evaluation of mean amplitudes of vibration. Coriolis coupling constants and centrifugal distortion constants of these cases, with highly satisfactory results. The values of Coriolis coupling constants and centrifugal distortion constants are in good agreement with the observed values for the germylacetylene molecule showing the significance of the procedure adopted in the present study.     

Role of the Crystal Lattice Constants and Band Structures in the Optoelectronic Spectra of CdGa2S4 by DFT Approaches

The electronical and optical properties of CdGa₂S₄ under high pressures were studied using the full potential linearized augmented plane wave (FP‐LAPW) method within the GGA and mBJ exchange correlation potentials from 0.0 to 16.92 GPa. The obtained results show that the lattice constants, bandgap values, and optoelectronic properties are sensitive to applied external pressures. The mBJ results indicate that the bandgap increases and the static dielectric constants decrease with increasing the pressure. The two none zero dielectric tensor components show considerable anisotropy between the perpendicular and parallel components. The maximum absorption for x direction in all pressures takes place in vacuum UV region. Also, the plasma frequency shifts to the higher energies with increasing the pressure for application in optical devices. The calculated results by mBJ are in close agreement with the experimental values.     

苯+环己烷、苯+正庚烷和环己烷+正庚烷的蒸汽压和过量Gibbs自由焓研究

本文采用简单的装置,测定了苯+环己烷(313.25K),苯+正庚烷(308.19K)和环已烷+正庚烷(298.15K)三个体系的蒸汽压-液相组成关系,并由此求得了体系的过量Gibbs自由焓,结果良好。     

An ab initio study of the relationship between the O?H bond length and the harmonic and anharmonic stretching force constants for planar molecules containing C?OH,N?OH,and O?OH groups

The O? H bond length and the quadratic, cubic, and quartic stretching force constants, calculated ab initio using the unscaled 4-31G basis set with full geometry optimization, are reported for 30 planar conformers of ten molecules contaning either the C? OH, N? OH, or O? OH group. The data are analyzed in terms of the general form of Clark's equation, and the power functions and exponential functions proposed by Herschbach and Laurie. In the case of the quadratic constants, significant trends are found in the values of the parameters depending on whether the O? H group is bonded to carbon, nitrogen, or oxygen, and whether it is non-hydrogen-bonded or involved in intramolecular hydrogen bond formation in four-, five-, or six-membered rings. Using data for diatomic molecules, O? H, and C? H bonds, and the C?O and C? C bonds in planar monosubstituted carbonyl compounds, the parameter d_ij in the power function equation for quadratic constants, which can be regarded as the distance of closest approach of the two nuclei, is shown to increase progressively along the series (i) diatomic molecule; (ii) similar bond in a polyatomic environment with one of the two atoms covalently bonded to a neighboring atom; (iii) as in (ii) but with the second atom hydrogen bonded; and (iv) with both atoms covalently bonded to neighboring atoms.     

Mathematical functions for the analysis of luminescence decays with underlying distributions: 2. Becquerel (compressed hyperbola) and related decay functions

The Becquerel (compressed hyperbola) decay law is analyzed in detail and shown to be an interesting approach for the analysis of complex luminescence decays. A decay function unifying the modified Kohlrausch and Becquerel decay laws is also introduced. It is proposed that the analysis of luminescence decays with a sum of Becquerel functions is a powerful alternative to the usual sum of exponentials. It is also shown that some complex decay laws can be written as a sum of an infinite number of exponentials and have for this reason an infinite but discrete spectrum of rate constants.     

The effect of the spatial nonlocality of the Kirkwood g-factor on the determination of the long wavelength dielectric functions in dipolar fluids

The Kirkwood g-factor that determines the long wavelength dielectric constant of a simple, isotropic, translationally invariant dipolar fluid is given by an integral of a dipole-dipole correlation function over a spherical region of a nonzero radius R(K) chosen such that any further increase in the radius leads to no change in the value of the integral, thereby defining a Kirkwood correlation length R(K). For radii less than the correlation length the integral defines a radius dependent (nonlocal) Kirkwood g-factor, implying a nonlocal dielectric function. The nonlocal nature of these quantities has important consequences for the determination of the long wavelength dielectric function from dipole fluctuations via the Kirkwood-Fro?hlich connection. The dipole-dipole correlation function (the volume dipole auto-correlation function) commonly used in this determination involves particles residing solely within a sphere of radius R, unlike the correct correlation function which involves either a single particle with those particles in a spherical volume of radius R(K) or those particles in a spherical volume of radius R with those residing within a spherical volume of radius R+R(K). A procedure is suggested for extracting the infinite system dipole-dipole correlation function from results of simulations performed on finite spherical samples. Using some results reported in the recent literature, relative to the accurate correlation function the commonly used correlation function ranges from 27% too small for a sphere having a radius comparable to the Kirkwood correlation length to 4% too small at a radius of seven times that correlation length. As a result, the apparent dielectric constants, as determined by the conventional procedure of using the fluctuations of the sum of dipoles in a finite fixed volume, are also too small. This suggests that a dielectric constant extracted from computer simulations using a total dipole-total dipole correlation function in a given volume with other geometries and/or boundary conditions will result in similar errors.     

Effects of memory on the coherent scattering function for the rouse–zimm model of dilute polymer solutions

We study the effect of the memory function on the coherent scattering function of a dilute polymer solution, taking into account hydrodynamic interactions among the polymer segments. The line shape, given by a sum of two exponentials, is very accurate numerically for ka ? 3 (with a the length of a polymer segment) and for times such that ω₀(k)t ? 1.5 [with ω₀(k) the initial slope]. However, this approximation to the scattering function is not nearly so accurate at the smaller values of ka encountered in light scattering experiments. The amplitudes and relaxation times associated with the two exponentials are found to be markedly dependent on the strength of the hydrodynamic interactions.     

Wagner liquid–vapour pressure equation constants from a simple methodology

A methodology to determine the A, B, C, and D constants from the Wagner equation is presented. The constants for 274 pure substances were determined by minimization in the sum of the squares of the relative deviation in liquid vapour pressure. For 69 chemical compounds, vapour pressures exist over the range from 1 kPa to the critical pressure and an average absolute deviation in vapour pressure of 0.039% was calculated. Using Antoine equation coefficients and initial guesses for a correlation in terms of the acentric factor, Wagner constants were estimated for substances with limited data within the range from (1 to 200) kPa. To validate the proposed methodology, vapour pressure predictions from 1 kPa to the critical pressure were made for 52 substances using Wagner parameters estimated from limited data. A value of 0.27% in average absolute deviation results for those substances. Finally the Waring criterion was applied to check the constants presented in this paper.     

Vapor pressures and apparent molal volumes of the solutions of ZnCl2 in ethanol at 298.15 K

Vapor pressures and apparent molal volumes of solutions of ZnCl₂ in ethanol are reported at 298.15 K. The vapor pressure of ethanol has been evaluated from the osmotic coefficients measured by an improved isopiestic method. The experimental osmotic coefficients have been correlated with the Pitzer model and local composition models including electrolyte non-random two liquid (e-NRTL), non-random factor (NRF), modified NRTL (MNRTL) and extended Wilson (EW) models. Apparent molal volumes have been calculated from the densities of the solutions measured by a vibrating-tube densimeter, and fitted with the volumetric equations based on the Pitzer model and the local composition models. All of the models successfully correlate the experimental osmotic coefficients and apparent molal volume data.     

NATURE OF THE A AND THE F MATRIX IN THE CALCULATION OF FORCE CONSTANTS OF MOLECULAR VIBRATION

In this paper,calculations of force constants of molecular vibrations are carried out by using Wilson GF matrix method.In the determination of force constants from frequencies and factorization of Gmatrix,an ordering relationship of A matrix(may be n dimensional) relative to L matrix was found according to the ordering of symmetry coordinates.With the help of inverse unitary transformation,a general method to calculate Ft from constants Fs was established.The additivity of Fr depending on the symmetry block was determined to be true.All the force constants in non-planar and planar of urea,thiourea and sclenouroa molecules were calculated by using the general va-leine force field.The calculated values of frequencies were com-pairec with other data given in the literature,and it was shown that the present calculation is in good agreement with the experimental     

Vapor-Liquid Phase Equilibria in the Multicomponent Systems Formed by Normal Alcohols and Esters of Ethanoic Acid

Boiling points of some multicomponent systems formed by aliphatic alcohols and esters of ethanoic acid were measured ebulliometrically at various pressures. The activity coefficients of solution components were calculated using the Wilson and Non-Random Two-Liquid equations. The computational results were verified experimentally.     

Impact of carbon dioxide on the surface tension of 1-hexanol aqueous solutions

Effects of carbon dioxide presence on the surface tension and adsorption kinetics of 1-hexanol solutions were investigated. Experiments were performed at a range of carbon dioxide vapor pressures and varying concentrations of 1-hexanol aqueous solution. Both dynamic and steady-state surface tensions of 1-hexanol aqueous solution were found to decrease with carbon dioxide pressure, and a linear relationship was observed between the steady-state surface tension and carbon dioxide pressure. To explain the experiments, adsorption and desorption of the two species (1-hexanol and carbon dioxide) from two sides of the vapor-liquid interface were considered. A modified Langmuir isotherm, the modified Langmuir equation of state and the modified kinetic transfer equation were developed. The resulting steady-state and dynamic surface tension data were modeled using the modified Langmuir equation of state and the modified kinetic transfer equation, respectively. Equilibrium constants and adsorption rate constants of 1-hexanol and carbon dioxide were evaluated through a minimization procedure for CO₂ pressures ranging from 0 to 690 kPa. From the steady-state modeling, the equilibrium parameters for 1-hexanol and carbon dioxide adsorption from vapor phase and liquid phase were found unchanged at different pressures of carbon dioxide. From the dynamic modeling, the adsorption rate constants for 1-hexanol and carbon dioxide from vapor phase and liquid phase were found to decrease with carbon dioxide pressure. Some fluctuations in the fitting parameters of the dynamic modeling (adsorption rate constants) were observed. These fluctuations may be due to experimental errors, or more likely the limitations of the model used. A major limitation of the model is related to large differences in adsorption/desorption between initial and final stages of the process, and a single set of property parameters cannot describe both initial and final states of the system. Variations may occur depending on which set of data, of initial or final states, is used in the model predictions over the entire time range.