Interaction Virial Coefficients Research Articles

Gaseous speed of sound and virial coefficients for 2,3,3,3-tetrafluoropropene (R1234yf) + 1,1,1,2-tetrafluoroethane (R134a) binary mixture

The binary mixture 2,3,3,3-tetrafluoropropene (R1234yf) + 1,1,1,2-tetrafluoroethane (R134a) is commercially interesting and is widely studied in thermodynamics properties, but except for gaseous speed of sound. In this work, we modified the experimental procedure of the cylindrical fixed-path acoustic resonance method for the sound speed measurement of mixtures. Then we obtained the first two sets of gaseous sound speed data at the molar fraction of about (0.207/0.793) and (0.580/0.420) with a combined relative expanded uncertainty (k = 2) of 0.03%. The accurate molar fractions along each isotherm line were determined by extrapolating the experimental data with the absolute expanded uncertainty (k = 2) of 0.003. The interaction virial coefficients were derived from the experimental sound speed data and were used to establish a hard-core square-well molecular potential model. A previous virial coefficient correlation was modified to predict the virial coefficients for mixtures. The experimental results and model calculations agree well with each other, confirming the correctness of the experimental method. The data could provide references to test and develop the mixing model.

Thermodynamic characterization of the (CO2 + O2) binary system for the development of models for CCS processes: Accurate experimental (p, ρ, T) data and virial coefficients

Continuing our study on (CO2 + O2) mixtures, this work reports new experimental (p, ρ, T) data for two oxygen-rich mixtures with mole fractions x(O2) = (0.50 and 0.75) mol·mol−1, in the temperature range T = (250–375) K and pressure range p = (0.5–20) MPa, using a single-sinker densimeter. Experimental density data were compared to two well-established equation-of-state models: EOS-CG and GERG-2008. In the p, T-range investigated, the EOS-CG gave a better reproduction for the equimolar mixture (x(O2) = 0.5), whereas the GERG-2008 performed significantly better for the oxygen-rich mixture (x(O2) = 0.75). The EOS-CG generally overestimates the density, while the GERG-2008 underestimates it. This complete set of new experimental data, together with previous measurements, is used to calculate the virial coefficients B(T, x) and C(T, x), as well as the second interaction virial coefficient B12(T) for the (CO2 + O2) system.

Accurate Experimental (p, ρ, and T) Data for the Introduction of Hydrogen into the Natural Gas Grid (II): Thermodynamic Characterization of the Methane–Hydrogen Binary System from 240 to 350 K and Pressures up to 20 MPa

Most of the experimental density data of the methane–hydrogen binary system available at the time of the development of the equation of state for natural gases and related mixtures, GERG-2008, at temperatures above 270 K were limited to hydrogen contents higher than 0.20 (amount-of-substance fraction). On the contrary, for mixtures with hydrogen contents lower than 0.20, experimental data were limited to temperatures below 270 K. This work intends to close the gap and provides accurate experimental (p, ρ, and T) data for three binary mixtures of methane and hydrogen, (0.95 CH4 + 0.05 H2), (0.90 CH4 + 0.10 H2), and (0.50 CH4 + 0.50 H2), at temperatures of 240, 250, 260, 275, 300, 325, and 350 K, thus extending the range of available experimental data to higher temperatures for mixtures with hydrogen contents lower than 0.20 and, accordingly, to lower temperatures for mixtures with hydrogen contents higher than 0.20. The density measurements were performed by using a single-sinker densimeter with magnetic suspension coupling at pressures up to 20 MPa. Experimental data were compared to the corresponding densities calculated from the GERG-2008 and the AGA8-DC92 equations of state, respectively. The experimental data are within the uncertainty of both equations of state, except at the lower temperatures of 240 and 250 K and pressures over 14 MPa for the mixtures with a hydrogen content of 0.05 and 0.10, respectively. The virial coefficients B(T, x) and C(T, x), as well as the second interaction virial coefficient B12(T) for the methane–hydrogen binary system, were also calculated from the experimental data set at temperatures from 240 to 350 K using the virial equation of state.

Vapour-phase (p, ρ, T, x) behaviour and virial coefficients for the (ethane + carbon dioxide) system

Accurate density measurements on three binary (ethane + carbon dioxide) mixtures with ethane mole fractions of 0.05023, 0.20031, and 0.49954 were carried out at temperatures from T = (273.15 to 323.15) K with pressures up to the dew-point pressure or 6.0 MPa, whichever was lower. The gas mixtures were prepared gravimetrically and a well-proven two-sinker magnetic suspension densimeter was utilized for the measurements. It was observed that sorption effects have an impact on the reproducibility of the density measurements of up to 0.04%. Considering all measurement uncertainties in temperature, pressure, density, and composition, the relative combined expanded uncertainty (k = 2) in density was estimated to be less than or equal to 3.8 × 10−4. Relative deviations of the experimental densities from the GERG-2008 equation of state were less than 0.5%, which is clearly within the uncertainty of this equation. Values and uncertainties of the second and third virial coefficients were calculated by correlating the isothermal experimental data to a third-order virial equation. Second interaction virial coefficients were determined as well, and excellent agreement with literature was obtained. The new experimental data presented in this work can be especially used to further improve the performance of multi-parameter equations of state for mixtures, particularly in the vicinity of the dew line.

Accurate experimental (p, ρ, T) values and virial coefficients for the (methane and helium) binary system

This work provides accurate experimental (p, ρ, T) values for three binary mixtures of methane with helium: (0.95 (amount-of-substance fraction) CH4+0.05 He) and (0.90 CH4+0.10 He) at temperatures of (240, 250, and 260)K and (0.50 CH4+0.50 He) from (240 to 400)K. This work is a continuation of a previous one which reported accurate experimental (p, ρ, T) values for the (0.95 CH4+0.05 He) and the (0.90 CH4+0.10 He) binary mixtures over the temperature range from (250 to 400)K. All density measurements were performed by using a single-sinker densimeter with magnetic suspension coupling at pressures up to 20MPa. Experimental values were compared with the corresponding densities calculated from the GERG-2008 and the AGA8-DC92 equations of state, respectively. Deviations from the GERG-2008 are much larger than from the AGA8-DC92 (up to −6.5%). These deviations increase with decreasing temperature, with increasing pressure, and with increasing helium fraction. In contrast, deviations from the AGA8-DC92 are within the 0.5% band. The experimental values were also used to calculate the second and the third virial coefficients, B(T,x) and C(T,x), as well as the second interaction virial coefficient B12(T) for this mixture.

Thermophysical properties of CF4/O2 and SF6/O2 gas mixtures

Fitting formulae are presented for the calculation of the second interaction virial coefficients, mixture viscosities and binary diffusion coefficients for CF4/O2 and SF6/O2 gas mixtures in the temperature range between 200 K and 1000 K. The data recommended are obtained from the isotropic (n-6) Lennard-Jones intermolecular interaction potentials of the pure substances by using the Hohm-Zarkova-Damyanova mixing rules. In general, a good agreement is observed between our results and the experimental and theoretical data found in the literature.

Vapor-Phase (p, ρ, T, x) Behavior and Virial Coefficients for the (Methane + Propane) System

The (p, ρ, T, x) behavior of three (methane + propane) mixtures was measured with a two-sinker magnetic suspension densimeter over the temperature range of (248.15 to 373.15) K with pressures up to the dew-point pressure or 6 MPa, whichever was lower. The compositions of the gravimetrically prepared mixtures were (0.74977, 0.50688, and 0.26579) mole fraction methane. A detailed uncertainty analysis is presented. The relative combined expanded uncertainty (k = 2) in density considering all effects, including the uncertainty in composition, was 0.05 % or lower for most points, except it was larger at densities less than 5 kg·m–3. Comparisons to the GERG-2008 equation of state for natural-gas mixtures showed significant deviations in density (as large as −1.3 %) that increased with decreasing temperature, with increasing pressure, and with increasing propane fraction in the mixture. The experimental values were also used to calculate interaction virial coefficients B12(T) for this system. The B12(T) agreed well with literature values. They were constant (within experimental uncertainty) with composition, as expected from theory. In contrast, the B12(T) calculated with the GERG-2008 equation of state varied with composition.

First-Principles Calculation of the Air–Water Second Virial Coefficient

Recent theoretical work has produced quantitatively accurate potential-energy surfaces for water with common gases. These pair potentials have been used to calculate second interaction virial coefficients with an accuracy superior to that obtained by most experiments. In this work, results for water–nitrogen, water–oxygen, and water–argon are combined to calculate an effective second virial coefficient for water with air. The results are in agreement with the existing experimental data, but they cover a wide range of temperatures while the experimental data extend only from 253 to 348 K. These results will be useful for humidity standards and other applications requiring thermodynamic properties of moist air.

Second virial coefficients of fluorinated methanes CH4−xFx(x = 0–4) and their binary mixtures

Download options Please wait... Supplementary files Tables DOC (922K) Article information DOI https://doi.org/10.1039/B204839F Article type Paper Submitted 17 May 2002 Accepted 16 Jul 2002 First published 12 Aug 2002 Download Citation Phys. Chem. Chem. Phys., 2002,4, 4444-4448 BibTex EndNote MEDLINE ProCite ReferenceManager RefWorks RIS Permissions Request permissions Second virial coefficients of fluorinated methanes CH4−xFx (x = 0–4) and their binary mixtures J. A. Lamp, B. F. Schramm, S. M. Saad and S. A. El-Geubeily, Phys. Chem. Chem. Phys., 2002, 4, 4444 DOI: 10.1039/B204839F To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page. Read more about how to correctly acknowledge RSC content. Social activity Tweet Share Search articles by author Joachim A. Lamp Bernhard F. Schramm Shokry M. Saad Samia A. El-Geubeily

An Approximate Empirical Intermolecular Potential for CF4–Ar

An approximate empirical intermolecular potential for CF

Spectra of Ar–CO2 from ab initio potential energy surfaces

Potential energy surface for the interaction of Ar with CO2 has been calculated using different levels of symmetry-adapted perturbation theory (SAPT) and the supermolecular many-body perturbation theory (MBPT) and coupled-cluster methods. These potentials have been used to compute the rovibrational spectra of Ar–CO2 and the interaction virial coefficients. The best reproduction of experimental data was achieved by the SAPT potential at the level of theory similar to the second-order of MBPT. The accuracy of this potential is in fact very close to that of the recent semiempirical surface of Hutson et al. [J. Chem. Phys. 106, 9130 (1996)] which was fitted to this set of data. Somewhat surprisingly, the more advanced methods considered here performed not as well.

Second and third interaction virial coefficients of the (methane+propane) system determined from the speed of sound

The speed of sound has been measured in the binary gaseous mixture (0.85CH4+0.15C3H8) along seven isotherms at temperatures between 225 and 375 K and at pressures up to 1.4 M Pa. From the measurements, second and third acoustic virial coefficients of the mixture were obtained. These results were analyzed together with values of the second and third acoustic virial coefficients of the two pure components to obtain a set of model intermolecular potential-energy functions for the methane-propane system. Nonpairwise additivity of the intermolecular forces was included in this analysis. Ordinary second and third interaction virial coefficients calculated from the model are reported, as are the second and third virial coefficients of the pure components. Gas densities calculated by means of these virial coefficients for the mixture (0.9298CH4+0.0702C3H8) were found to agree with experimental values at temperatures between 280 and 330 K to within 0.02% at pressures up to 3 MPa and to within 0.08% at 4MPa.

Ab initio potential energy surface, infrared spectrum, and second virial coefficient of the He–CO complex

Symmetry-adapted perturbation theory has been applied to compute the intermolecular potential energy surface of the He–CO complex. The interaction energy is found to be dominated by the first-order exchange contribution and the dispersion energy. The ab initio potential has a single minimum of εm=−24.895 cm−1 for the linear CO–He geometry at Rm=6.85 bohr. The computed potential energy surface has been analytically fitted and used in converged variational calculations to generate bound rovibrational states of the He–CO molecule and the infrared spectrum, which corresponds to the simultaneous excitation of vibration and internal rotation in the CO subunit within the complex. The predicted positions and intensities of lines in the infrared spectrum are in good agreement with the experimental spectrum [C.E. Chuaqui et al., J. Chem. Phys. 101, 39 (1994)]. The theoretical potential was also checked by comparison of computed excess second virial coefficients with the experimental data. The ab initio interaction virial coefficients, including quantum corrections, lie within the experimental error bars over a wide range of temperatures.

Virial coefficients of methane-ethane mixtures in the temperature range from 0 to 60�C determined with an automated expansion apparatus

An automated expansion apparatus has been set up which can be used for PVT measurements on gases from Il to 60 C at pressures from 2 to 7 NIPa. It consists of two chambers connected by an expansion valve. The ratio of the two volumes is 1:54. The measurements along one isotherm. which take 20 h, can be per formed routinely and without operator attendance. The uncertainty of the com pressibility factor is estimated to be 10−3. The compressibility factors of binary mixtures of the main components of most natural gases, methane and ethane, were determined on high-grade gas, the mole fractions of ethane being 0.05, 0.15. and 0.25. Seven isotherms were measured of each of the mixtures. Data from the literature for the virial coefficients of the pure substances were used to establish a virial equation of state which approximates the measured com pressibility factors with a standard deviation of 0.4 x 10 '. This is substantially smaller than the uncertainty. The interaction virial coefficients were calculated from this equation of state. The results obtained are in good agreement with other available data.

N2–Kr interaction: A multiproperty analysis

An earlier anisotropic N2–Kr potential energy surface [Chem. Phys. Lett. 88, 197 (1982)] of Lennard-Jones form, obtained by inversion of molecular beam differential scattering data, has been found to provide calculated transport–relaxation phenomena in good agreement with experiment, but leads to calculated second interaction virial coefficients which are significantly too low, and does not provide adequate agreement with recent microwave van der Waals spectral data. A modification of this surface to include a recent ab initio determination of the C6 dispersion coefficient, and to bring in the virial and microwave data, gives a new potential surface that is in good agreement with all available experimental data.

A b i n i t i o potential energy surfaces of Ar–H2O and Ar–D2O

We present an ab initio potential energy surface for the van der Waals system argon–water. The points on the surface are computed as a sum of Heitler–London short range repulsion, damped dispersion, and damped induction. Damping is done in the manner first proposed by Tang and Toennies. We give the surface analytically in the form of a spherical harmonic expansion through l=7. The expansion coefficients are represented by functions depending on the distance between the centers of mass of the monomers. We also present an Ar–D2O potential obtained from the Ar–H2O potential by translating the center of mass of the water molecule. An analytic formula for the translation of polarizabilities is derived and applied to the computation of the long range energy of Ar–D2O. The short range part of the energy is translated numerically. Finally, the potential is checked by comparison of computed interaction virial coefficients with experimental data.

Precise Measurements of Second Virial Coefficients of Simple Gases and Gas Mixtures in the Temperature Range Below 300 K

AbstractA new apparatus for measurements of second virial coefficients of gases or gas mixtures at room temperature is described. It was used to determine virial coefficients of He, H2, N2, CO2, NH3, and the interaction virial coefficient of Ar/NH3. Furthermore, low temperature interaction virial coefficients of Ar/NH3and H2/CO are reported and finally a critical revision of second virial coefficients of He, H2, Ar, N2, and CO at 77.3 K is presented. The virial coefficients are discussed in their relation to new intermolecular potentials.

PVT data from refractive index measurements for the ethane + nitrogen system from 270 to 350 K and pressures to 28 MPa

The P, ϱ, T behaviour of three ethane + nitrogen mixtures (0.7515 C 2H 6, 0.5004 C 2H 6 and 0.2503 C 2H 6) was determined from P, n, T measurements for the isotherms 270, 290, 310, 330 and 350 K and for pressures up to 28 MPa. The refractive index n and the pressure P of the mixtures were measured with two coupled laser interferometers. The experimental P, n, N data were combined with the higher-order refractivity virial coefficients B R and C R of the Lorentz—Lorenz expansion to calculate the density ϱ. The experimental results were used to obtain tables of compressibility factors for each mixture. The P, ϱ, T data were reduced to obtain the second and third virial coefficients, B and C, for each mixture. Unlike interaction virial coefficients, B 12, C 112 and C 122, were determined from the mixture virial coefficients by using the like interaction virial coefficients of the pure components from Jaeschke and Hinze. The compressibility factors are considered accurate to 0.1%, and unlike interaction second virial coefficients to ±1.5 cm 3 mol −1. The values agree excellently with the B 12 results determined from the P, ϱ, T data of Reintsema et al. and the value at 311 K from Calvin and Reed.

PVT data from burnett and refractive index measurements for the nitrogen—hydrogen system from 270 to 353 K and pressures to 30 MPa

The P, ϱ and T behaviour of four nitrogen—hydrogen mixtures (0.8505 N 2, 0.7501 N 2, 0.4998 N 2 and 0.2503 N 2) was measured in the temperature range 270–353 K and pressures up to 30 MPa. Measurements were carried out with a Burnett apparatus and an optical device, also termed a grating interferometer. The experimental results were used to obtain tables of compressibility factors for each mixture. The compressibility factors obtained by the two methods, the Burnett and optical experiments, are accurate to ±0.1%. For pressures below 10 MPa the accuracy of the Burnett data is estimated to be ±0.07%. The P, ϱ and T data were used to determine the second and third virial coefficients, B and C, for each mixture. Unlike interaction virial coefficients, B 12, C 112 and C, 122 were determined from the mixture virial coefficients by using the like interaction virial coefficients, B 11, B 22, C 111 and C 222, of the pure components from Jaeschke and Hinze. The deduced values of B 12 are accurate to ±0.4 cm 3 mol −1. These values agree excellently with the B 12 results determined from the P, ϱ and T data of Michels and Wassenaar.

A b i n i t i o potential energy surfaces of Ar–NH3 for different NH3 umbrella angles

Four ab initio potential energy surfaces of the van der Waals system argon–ammonia are computed for the following four different HNH (‘‘umbrella’’) angles of ammonia: 100°, 106.67°, 113.34°, and 120°. These potentials have been obtained by Heitler–London short-range calculations and from multipole-expanded dispersion and induction long-range contributions. A Tang–Toennies-like damping is applied to the long-range energy. Each surface is given analytically in the form of a spherical harmonic expansion through l=7, where the expansion functions depend on the polar angles of the argon atom with respect to the principal axes of NH3. The expansion coefficients are represented by functions depending on the distance between the monomers. The potential for the equilibrium HNH angle 106.67° is applied to the computation of interaction virial coefficients in which quantum effects through ℏ2 are included.