Cross Virial Coefficients Research Articles

Second virial coefficients of normal alkanes, linear 1-alkanols and their binaries

Abstract

Estimation of the second cross virial coefficient from complete vapor—liquid equilibrium data. a simulation study

A method recently proposed for estimating the second cross virial coefficient from complete vapour—liquid equilibrium data has been tested by Monte Carlo simulation. The precision of B 12 estimation, the bias due to the method, the effect of systemitic errors in xyPT data, and the effect of statistical weighting of the individual measured variables have been thoroughly assessed. In general, the applicability of the method depends on the shape of the P− x ( y− x) curve, the measurement precision and the distribution of experimental points. If reliable, precise and numerous VLE data are available, then in favourable cases defined by a criterion formulated for this purpose, the error in B 12 is estimated to be 50–100 cm 3 mol −1. The most obvious use of the method appears to be for systems with strong specific interactions between the components in the vapour phase.

An empirical model for calculating second virial coefficients

A model for calculating the second virial coefficients of pure compounds and mixtures is proposed. This model derives from a new equation of state which obeys some theoretical constraints and it requires only the molar volume and the vaporization enthalpy at the normal boiling point as input parameters. The new relation is applied to correlate the B values of nearly 70 compounds which represent several molecular types, including strongly associated or dimerizing compounds. Rules are given to generalize the empirical constants of both models in order to predict the B values. The extension to correlate or to predict the second cross virial coefficient is also examined for 20 binary mixtures. The reliability of the proposed model is evaluated by comparison with the Tsonopoulos correlation.

Solubilities and second cross-virial coefficients of caffeine in ammonia

The solubility of caffeine in ammonia has been measured between 73.3 and 224°C up to 300 bar. The results can be reproduced by a simple equation. This equation allows the calculation of the solubility at higher and lower pressures. Using derived equations, cross virial coefficients have been calculated.

(Vapour + liquid) equilibria, limiting activity coefficients, and excess molar volumes of {1-bromo-1-chloro-2,2,2-trifluoroethane (halothane) + tetrachloromethane or trichloromethane or 1,1,1-trichloroethane}

The thermodynamic behaviour of {1-bromo-1-chloro-2,2,2-trifluoroethane (halothane) + tetrachloromethane or trichloromethane or 1,1,1-trichloroethane} has been investigated. Excess molar volumes were determined at 298.15 K with a tilting dilution dilatometer, vapour-liquid equilibria were measured at 318.15 K by a dynamic method, and limiting activity coefficients were determined by comparative ebulliometry. The results obtained for the (vapour + liquid) equilibria were verified by effective statistical procedures and used to calculate excess Gibbs molar energies. The unknown second cross virial coefficients were calculated on the basis of redundant information provided by complete results for the (vapour + liquid) equilibria. The results support the hypothesis of weak solvation effects in (halothane + trichloromethane or 1,1,1-trichloroethane).

Phase equilibria in very dilute mixtures of water and chlorinated hydrocarbons. Part I—experimental results

Activity coefficients at infinite dilution have been measured for six chlorinated alkane/water mixtures in the temperature range 293–323 K. Water-rich mixtures have been studied using gas liquid chromatography and measurements for organic-rich mixtures have been made using an isopiestic apparatus. The chromatographic experiments also provide estimates of the second cross virial coefficients for chlorinated alkane/nitrogen mixtures.

Dynamic solubility measurements of caffeine in carbon dioxide and in carbon dioxide saturated with water

The solubility of caffeine in dry carbon dioxide has been measured between 310 and 430 K up to 70 MPa. The solubility of caffeine in carbon dioxide saturated with water has been measured between 303 and 363 K up to 30 MPa. The results can be reproduced by simple equations. These equations allow a calculation of the solubilities at higher and lower pressures. Using these equations, cross virial coefficients have been calculated for both systems.

Prediction of second and cross virial coefficients of blended mobile phases in gas chromatography

The second-interaction virial coefficients of vapors of potential interest as carriers in gas chromatography are considered in detail. Those examined include the monatomic gases helium, neon, argon, and krypton, the homonuclear diatomic compounds hydrogen, nitrogen, and oxygen, the heteronuclear inorganic species carbon monoxide, carbon dioxide, nitrous oxide, sulfur dioxide, water, hydrogen chloride, and ammonia, and the organic materials methane through n-pentane, carbon tetrachloride, and fluorotrichloromethane. Experimentally derived pure-component virial coefficients B/sub ii/ for all species except water and hydrogen chloride are shown to fit quadratic equations of the form (chosen so as to reflect the principle of corresponding states) B/sub ii//V/sub ii//sup c/ = f(T/sub ii//sup c//T), where the superscripts c indicate a critical value. The temperature range to which the temperature-invariant coefficients apply spans for all substances that for which accurate experimental data are available which, for many, is 200-950 K. Methods of prediction of the cross virial coefficient B/sub ii/ are detailed, and the results are then employed with B/sub ii/ for quantitative theoretical evaluation of the compositional variation of second-interaction virial coefficients B/sub M/.

Variation of gas chromatographic retentions with carrier pressure and composition

The second-interaction cross virial coefficients B/sub 1M/ are calculated for the solutes n-hexane, trans-3-hexene, benzene, 3,3-dimethylpentane, and cyclohexane with hydrogen, helium, nitrogen, carbon monoxide, carbon dioxide, argon, water, methane, ethane, carbon tetrachloride, and fluorotrichloromethane. The results are then used to evaluate the regression of In (solute specific retention volume) (V/sub g/..pi..) with carrier pressure and composition, and it is shown theoretically as well as demonstrated experimentally that retentions as well as retention order can accordingly be altered. Plots of solute V/sub g//sup 0/ or of (V/sub g/..pi..)/sup -1/ against mole fraction of the fluoroalkane mobile phase in admixture with hydrogen are found to be curved, although the curvature is slight at column pressure drops of 1.1 atm and less. The linear variation of solute capacity factors K' against partial pressure of steam + nitrogen as reported by Pretorius is thereby explained.

Vapor-liquid equilibrium behavior of six light gases at infinite dilution in hydrogen-dibenzofuran and hydrogen-9-methylanthracene systems

A sophisticated perturbation-chromatography apparatus has been used to study the vapor-liquid equilibrium behavior of six light gases in two hydrogen-coal-liquid model-compound systems. Infinite-dilution K values are reported for methane, ethane, propane, n-butane, carbon dioxide and hydrogen sulfide in (a) the hydrogen-dibenzofuran system at 373.2 and 398.2 K and up to 6 MPa, and (b) the hydrogen-9-methylanthracene system at 373.2, 398.2, 423.2, 448.2 and 473.2 K and up to 21 MPa. Henry's constants were determined for the light gases in 9-methylanthracene. Second cross-virial coefficients and vapor-phase infinite-dilution fugacity coefficients were calculated for the hydrocarbon gases in hydrogen. The results were combined with the experimental K-value measurements to obtain Henry's constants in hydrogen-9-methylanthracene mixtures of fixed liquid composition. The constants thus obtained show a significant dependence on hydrogen solubility.

The quantum-mechanical second virial coefficients of electron-spin-polarized atomic hydrogen and its admixtures with the isotopes of helium

The quantum-mechanical second virial coefficient of electron-spin-polarized atomic hydrogen H↑ and the second cross virial coefficients of H↑–3He and H↑–4He have been calculated for a range of temperatures using a Lennard-Jones 12-6 potential in each case. Our results indicate that the exchange (spin and quantum statistics) contributions for H↑ drop rapidly with increasing temperature. The Boyle temperature for H↑ occurs at a reduced temperature T*B = 0.25. Those for H↑–3He and H↑–4He are at T*B = 0.53 and 0.74, respectively.

Second cross virial coefficients B12 for gas mixture (carbon dioxide+water) from 300 to 1000 K

Values of the second cross virial coefficient B 12 for the gas mixture (carbon dioxide+water) were evaluated from a review of ( p, V, T) measurements reported in the literature. Values of B 12 are presented for the temperature range 300 to 1000 K. The results permit evaluation of the fugacity coefficients of the mixture components over a substantial pressure range.

Solubility of acetone and isopropyl ether in compressed nitrogen, methane, and carbon dioxide

Little fundamental information exists concerning the interaction between a small nonpolar molecule and a large polar one. Measuring the second virial cross-coefficient, B/sub 12/, which is directly related to the intermolecular potential, helps obtain this information. Experimental measurements that yield B/sub 12/ provide the fundamental information needed to calculate solvent losses in an absorption gas-purification process operating at high pressures. The University of California measured the vapor-phase solubilities of acetone and isopropyl either in compressed nitrogen, methane, and carbon dioxide at -58/sup 0/ to +122/sup 0/F and 246-913 psi. These experimental solubilities, when reduced, yielded the second virial cross-coefficients. The potential-energy-function fits were good for the nitrogen- and the methane-containing binary systems; the results for the carbon dioxide-containing binaries were less reliable.

Henry's constants and second virial coefficients from perturbed-hard-chain theory

The perturbed-hard-chain theory for pure fluids is extended to asymmetric mixtures for two limiting regions of composition and density: Henry's constants H and second virial cross coefficients B 12. The extension is made through a modified one-fluid theory approximation which accounts for non-randomness of the mixture. Final equations for H and B 12 require three pure-component parameters but only one binary constant, k 12, characteristic of each molecular pair; k 12 is the same for both H and B 12. The approximate partition function developed here is applicable to multi-component mixtures over the entire fluid density region and appears to be useful for mixtures of nonpolar (or slightly polar) molecules of arbitrary size and shape.

Solubilities of heavy hydrocarbons in compressed methane, ethane, and ethylene: Dew‐point temperatures for gas mixtures containing small and large molecules

AbstractSolubilities of heavy hydrocarbons in compressed gases were measured in the region 50° to 170°C for hexadecane, bicyclohexyl, diphenylmethane, and 1‐methyl naphthalene and in the region 165° to 272°C for eicosane and squalane. Measurements were made in the pressure region 9 to 80 atm. The solubility data were reduced to yield second virial cross coefficients B12. To interpret the B12 data, a square‐well potential was used; the characteristic size of the large molecule is given by the mean radius of gyration which takes into account the variety of molecular conformations. Calculated results give good agreement with new as well as previously published B12 data.Illustrative calculations indicate how the results obtained here may be used to make dew‐point calculations in multicomponent systems containing both small and large molecules.

The Second Interaction (Cross) Virial Coefficient for Moist Air.

The results of calculations of the second interaction (cross) virial coefficient B aw for water vapor and air, based on enhancement data obtained at NBS at 30, 40, and 50 °C, are presented. Comparisons are made with the results of calculations based on the enhancement data of Politzer and Strebel, Webster, and Goff et al. and with the results of the theoretical calculations of Mason and Monchick and of Chaddock. An empirical equation is given for interpolation and extrapolation. The random (one standard deviation) uncertainty in the mean values of B aw , arising from the scatter of previously obtained NBS values of the enhancement factor, is estimated to range from 0.7 percent at 30 °C to 1.4 percent of 50 °C. The estimated systematic uncertainties range from 4 percent at 30 °C to 6 percent at 50 °C, respectively.

Second Cross Virial Coefficients of Carbon Tetrachloride – Gas Mixtures Determined from Solubility Measurements at High Pressures

The solubility of carbon tetrachloride in compressed helium, hydrogen, nitrogen, argon, methane, carbon dioxide, and ethylene has been measured over pressure ranges of 1–60 atm at temperatures ranging from −10 to 75 °C. Second cross virial coefficients representing carbon tetrachloride – gas interactions are evaluated from the data. It is shown that when allowance is made for the effects of quantum deviations and quadrupolar interaction on the critical temperatures and volumes of helium, hydrogen, and carbon dioxide, respectively, ordinary combining rules produce pseudocritical parameters which reduce all of the measured cross virial coefficients to a single function of reduced temperature. When reduced on a Boyle point basis, it is found that the data are best represented by virial coefficients corresponding to a 7-28 Mie type potential or a Kihara core potential having a core radius somewhat smaller than the carbon–chlorine bond length in carbon tetrachloride.

Compressibilities and virial coefficients for methane, ethylene, and their mixtures

AbstractA Burnett type of apparatus was built for 12,000 lb./sq.in. pressure and temperatures of 25° to 100°C. Isothermal expansions were run on methane, ethylene, and four binary mixtures at 25°, 50°, and 75°C., and compressibility factors were derived from the pressure ratio observations.From the experimental data, second and third virial coefficients were derived by two techniques, that is, the slope‐intercept and the multiple regressions curve‐fit of the data by the density‐series virial equation. A comparison of these virial coefficients with those from the different empirical equations of state indicates areas of needed improvements in these equations. Second virial cross coefficients were also obtained.

Solubility of Anthracene in Compressed Methane, Ethylene, Ethane, and Carbon Dioxide: The Correlation of Anthracene–Gas Second Cross Virial Coefficients Using Pseudocritical Parameters

The solubility of anthracene in compressed methane, ethylene, ethane, and carbon dioxide has been measured over pressure ranges of 1–100 atm and temperature ranges of 63–185°C. Second cross virial coefficients representing anthracene–gas pair interactions have been evaluated from this data. It is shown that when allowance is made for the effect of the molecular quadrupole moment on the critical constants of carbon dioxide, ordinary combing rules produce pseudocritical parameters which reduce these anthracene–gas cross virial coefficients to a single function of reduced temperature. The functional behavior of these reduced virial coefficients is shown to be the same within experimental error as that exhibited by cross virial coefficients of phenanthrene with many of these same gases.

Solubility of Phenanthrene in Compressed Methane, Ethylene, Carbon Dioxide, and Nitrous Oxide: The Correlation of Phenanthrene–Gas Second Cross Virial Coefficients Using Pseudocritical Parameters

The solubility of phenanthrene in compressed methane, ethylene, carbon dioxide, and nitrous oxide has been measured over pressure ranges of 1–60 atm at temperatures ranging from 37 to 142°C. Second cross virial coefficients representing phenanthrene–gas pair interactions have been evaluated from this data. It is shown that when allowance is made for the effect of molecular quadrupole moments on the critical temperatures of carbon dioxide and nitrous oxide, ordinary combining rules produce pseudocritical parameters which reduce these phenanthrene–gas cross virial coefficients to a single function of reduced temperature. The data are fitted to several potential functions which are shown to be consistent with the reduced behavior of these systems.