Avoiding interpolation errors for computed second virial coefficients of noble gases

The second virial coefficients characterize the real-gas non-ideality caused by the interaction between molecular pairs and ensure a link between macroscopic thermodynamic properties and microscopic molecular interactions because they depend on intermolecular interaction energy and temperature. Therefore, the second virial coefficients that are suitable for calculating the thermodynamic properties of gases used in the many fields in this work are preferred. In this study, a semi-analytic representation for the second virial (SV) coefficient over exponent–spline-Morse-spline-van der Waals potential (ESMSV), investigating the thermodynamic properties of rare gases, is presented. In the study the series formulae of the hypergeometric function, exponential function, gamma function, Meijer function, and binomial expansion have used in the suggested method. The numerical approach has been used mostly to evaluate the SV coefficient with ESMSV potential in literature. This unified formula can be applied and tested for rare gases. The obtained results for the SV coefficient over ESMSV potential of 4He–4He, 4He–Ne, 4He–Ar, 4He–Kr, 4He–Xe, Ne–Ne, O2–O2, and Ar–O2 rare gases have been compared with alternative experimental data and numerical calculations and shown that semi-analytical expression can be successfully applied to evaluate simple fluids.

Earlier work on the group contribution method applied to the Kihara potential is extended to noble gases for the estimation of second virial coefficients, dilute gas viscosities and diffusivities with a single set of gas group parameters. Group parameters are determined when second virial coefficient and viscosity data of pure gases are satisfactorily fitted within the experimental uncertainties. Parameters for gas groups (He, Ne, Ar, Kr and Xe) are found to provide good predictions of mixture properties: second virial cross coefficients, mixture viscosities, and binary diffusion coefficients. Application of the model shows that second virial coefficient data are represented with good results comparable to the values by means of the corresponding states correlation. The reliability of the present model in viscosity predictions is proved by comparison with the Lucas method. Prediction results of diffusivity are in excellent agreement with literature data and compare well with values obtained by means of the Fuller method.

Rare gases form compounds of a loose complex nature such as hydrates, solvates or mercury complexes. Such molecular aggregates contain a molecule of permanent dipole moment or an excited atom or molecule of dipole character as the other reaction partner besides the rare gas. The forces holding the complex molecule are the attraction between the permanent dipole and the dipole induced in the rare gas molecule due to its polarizability. Five lines of evidence are cited which indicate the formation of such complex molecules: (1) Band spectra of complex HgA and HgKr are known. (2) Rare gas hydrates have been described. (3) Isoelectronic systems similar to the rare gases have proton affinity. (4) Rare gas hydride ions have been found in the mass-spectrograph. (5) The P-V-T relation of gaseous mixtures show that interaction between the unlike molecules exists. The second Virial coefficient is determined experimentally for Kr–HCl mixtures as a function of composition and it is shown that interaction exists between the rare gas atom Kr and the permanent dipole HCl.

We present an analytical equation of state based on statistical-mechanical perturbation theory for hard spheres, using the Weeks–Chandler–Andersen decomposition of the potential and the Carnahan–Starling formula for the pair distribution function at contact, g(d+), but with a different algorithm for calculating the effective hard-sphere diameter. The second virial coefficient is calculated exactly. Two temperature-dependent quantities in addition to the second virial coefficient arise, an effective hard-sphere diameter or van der Waals covolume, and a scaling factor for g(d+). Both can be calculated by simple quadrature from the intermolecular potential. If the potential is not known, they can be determined from the experimental second virial coefficient because they are insensitive to the shape of the potential. Two scaling constants suffice for this purpose, the Boyle temperature and the Boyle volume. These could also be determined from analysis of a number of properties other than the second virial coefficient. Thus the second virial coefficient serves to predict the entire equation of state in terms of two scaling parameters, and hence a number of other thermodynamic properties including the Helmholtz free energy, the internal energy, the vapor pressure curve and the orthobaric liquid and vapor densities, and the Joule–Thomson inversion curve, among others. Since it is effectively a two-parameter equation, the equation of state implies a principle of corresponding states. Agreement with computer-simulated results for a Lennard-Jones (12,6) fluid, and with experimental p–v–T data on the noble gases (except He) is quite good, extending up to the limit of available data, which is ten times the critical density for the (12,6) fluid and about three times the critical density for the noble gases. As expected for a mean-field theory, the prediction of the critical constants is only fair, and of the critical exponents is incorrect. Limited testing on the polyatomic gases CH4, N2, and CO2 suggests that the results for spherical molecules (CH4) may be as good as for the noble gases, nearly as good for slightly nonspherical molecules (N2), but poor at high densities for nonspherical molecules (CO2). In all cases, however, the results are accurate up to the critical density. Except for the eight-parameter empirical Benedict–Webb–Rubin equation, this appears to be the most accurate analytical equation of state proposed to date.

The dielectric-constant gas thermometer of Physikalisch-Technische Bundesanstalt (PTB) developed for measuring the Boltzmann constant with a relative uncertainty of 1.9 parts per million was used for determining the virial coefficients of the three noble gases, helium, neon, and argon, at the triple point of water (0.01 ○C). For this purpose, isotherms were measured up to a maximum pressure of 7 MPa. The evaluation of the highly accurate data by fitting is required to derive an extended working equation for the dependence of the gas pressure on the dielectric constant. The following values have been obtained for the second B and third C virial coefficients, with the standard uncertainties given in parentheses as a multiple of the last digit, considering literature data for the dielectric virial coefficients: helium: BDCGT He0.01 ○C=11.925715 cm3/mol, CDCGT He0.01 ○C=113.4958 cm6/mol2; neon: BDCGT Ne0.01 ○C=10.994528 cm3/mol, CDCGT Ne0.01 ○C=215.815 cm6/mol2; argon: BDCGT Ar0.01 ○C=-21.233144 cm3/mol, CDCGT Ar0.01 ○C=1143.339 cm6/mol2. These values are compared with the results of the latest ab initio calculations of the second and third virial coefficients.

The approximate nonconformal (ANC) theory recently proposed has been very successful in determining interaction potentials for the noble gases and their mixtures. The ANC theory is used here to obtain effective angle averaged potentials of all homodiatomic gases for which experimental second virial coefficient data are available: H2, D2, N2, O2, F2 and Cl2. The cross virial coefficients in the mixtures of homodiatomics among themselves and with noble gases are predicted with excellent agreement with experiment for the heavier classical gases. The atom–atom interactions, which should be an improvement over previous results, are also determined and shown to behave regularly with atomic number. The critical temperatures and volumes of these gases vary smoothly when scaled with the parameters of the ANC potential.

The three-parameter Lennard-Jones(12-6)potential function is proposed to calculate thermodynamic property (second virial coefficient) and transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases (He, Ne, Ar, Kr, and Xe) and their mixtures at low density. Empirical modification is made by introducing a reduced temperature-correction parameterτto the Lennard-Jones potential function for this purpose. Potential parameters (σ,ε, andτ) are determined individually for each species when the second virial coefficient and viscosity data are fitted together within the experimental uncertainties. Calculated thermodynamic and transport properties are compared with experimental data by using a single set of parameters. The present study yields parameter sets that have more physical significance than those of second virial coefficient methods and is more discriminative than the existing transport property methods in most cases of pure gases and of gas mixtures. In particular, the proposed model is proved with better results than those of the two-parameter Lennard-Jones(12-6)potential, Kihara Potential with group contribution concepts, and other existing methods.

Osmotic second virial coefficients in dilute aqueous solutions of small nonpolar solutes are calculated from three different two-component equations of state. The solutes are five noble gases, four diatomics, and six hydrocarbons in the range C1-C4. The equations of state are modified versions of the van der Waals, Redlich-Kwong, and Peng-Robinson equations, with an added hydrogen-bonding term for the solvent water. The parameters in the resulting equations of state are assigned so as to reproduce the experimental values and temperature dependence of the density, vapor pressure, and compressibility of the solvent, the gas-phase second virial coefficient of the pure solute, the solubility and partial molecular volume of the solute, and earlier estimates of the solutes' molecular radii. For all 15 solutes, the calculations are done for 298.15 K, whereas for CH4, C2H6, and C3H8 in particular, they are also done as functions of temperature over the full range 278.15-348.15 K. The calculated osmotic virial coefficients are compared with earlier calculations of these coefficients for these solutes and also with the results derived from earlier computer simulations of model aqueous solutions of methane. They are also compared with the experimental gas-phase second virial coefficients of the pure gaseous solutes to determine the effect the mediation of the solvent has on the resulting solute-solute interactions in the solution.

Comparison of different alpha functions, α(Tr), applied in the prediction of supercritical properties of different polar and nonpolar fluids at Boyle temperature

Second virial coefficients as function of temperature are computed for the title molecular systems interacting with He, Ne, and Ar. The relevant anisotropic forces are obtained via accurate potential functions tested earlier through the analysis of several, different properties of the various systems. The relevant quantum corrections are also computed, in addition to the classical results, and their effects analyzed vis à vis the available experimental data. The influence of such corrections on the very low-T behavior of the virial coefficients and on the determination of the Boyle temperatures is also shown and discussed. All examined potential functions are found to yield B(T) values in rather good accord with experiments, in spite of their marked differences in anisotropic behavior and in the shape of their potential well regions.

Adsorption of rare gases on ferrierite has been measured to high accuracy over a wide pressure range (10–1–105 Pa). The adsorbed molecules behave as one-dimensional gases, for which the virial coefficients and their temperature dependences have been determined. The values for the second and third virial coefficients of xenon are well described by a repulsive pair potential which is obtained by neglecting the attractive part of the Lennard-Jones 6–12 potential. It is concluded that the drastic change in the pair potential was caused by a three-body effect.

This paper uses results from statistical-mechanical theory, applied through a combination of an extended principle of corresponding states with some knowledge of intermolecular potentials, to the calculation of the transport and equilibrium properties of gas mixtures at low density. The gases involved are: N2, O2, NO, CO, CO2, N2O, CH4, CF4, SF6, C2H4, C2H6, and He, Ar, Ne, Kr, Xe. The properties included are: second virial coefficient, viscosity, diffusion, and thermal diffusion, but not thermal conductivity. The calculations are internally, thermodynamically consistent and the resulting algorithms, which are fully programmable, operate in an entirely predictive mode by means of validated combination rules. This paper is a sequel to one on the five noble gases and all their possible mixtures and a second on the above eleven polyatomic gases. The paper contains ten tables (mainly intended for the checking of computer codes) and 201 graphs of deviation and comparison plots. An additional 98 tables have been deposited with the Physics Auxiliary Publication Service (PAPS) of the AIP. The algorithms presented in this paper, together with those mentioned above, make it possible to program calculations for a wide range of low-density equilibrium and transport properties of 16 gases and of all possible multicomponent mixtures formed with them, for a total of 65,535 systems. For each system, the program would cover the full range of compositions.

The approximate nonconformal (ANC) theory recently proposed has been very successful for determining effective interaction parameters from the measured gas imperfection B(T) for a variety of substances, from the noble gases to perfluoro-n-alkanes. Here we report the application of the ANC treatment to the polar substances: NO, CO, HCl, CO2, H2O, D2O, NH3, CH2:CH2 and SF6 and predict the cross interactions in the mixtures of these substances with noble gases. The theory is successful in describing B(T). It also permits us to extract atom–atom potential parameters for CO. The resulting C–C interaction follows the simple dependence on atomic number already found for other atoms. For NO, which is partially dimerised in the gas phase, and using the approach pioneered by Guggenheim and Scott, the ANC theory gives a very good account of the observed B(T) for partially dimerised NO. Lastly, the ANC prediction of the cross virial coefficient is in excellent agreement with experiment in all but one of the binary mixtures considered.

With a new development of corresponding states principle involving quasi-second virial coefficients of alkali metals, the free parameter of the ISM analytical equation of state, Γ, is shown to incorporate quantum effects. This observation is justified by the assumption that Γ adjusts itself with the value of a second virial coefficient so much that both describe the compressibility behavior of the system. Calculations along with the present data show that Li, and to some extent Na, deviates from the corresponding states behavior, succeeded by K, Rb, and Cs. By developing a corresponding states principle involving ΔHv, which the scaling factor used in the calculation of the quasi-second virial coefficients of alkali metals, the quantum effect in Γ is well justified. The same behaviors are observed among noble gases, where only He deviates. The statistical mechanical view of the open-shell electronic structure of alkalis must be considered as a special difference in physical behavior with noble gases.

Second virial coefficients for some polyatomic gases and their binary mixtures with noble gases