Pairwise additive third virial coefficients for multipolar molecules : Application to water vapour

1971 ◽  
Vol 24 (8) ◽  
pp. 1567 ◽  
Author(s):  
CHJ Johnson ◽  
TH Spurling
Keyword(s):  
Water Vapour ◽  
Potential Function ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Axially Symmetric ◽  
Multidimensional Integration ◽  
Third Virial Coefficient ◽  
Qualitative Effect ◽  
Experimental Values

Pairwise additive third virial coefficients for axially symmetric multipolar molecules have been calculated using a non-product multidimensional integration formula. Results for the Stockmayer potential agree with the corrected results of Rowlinson. It is found that the inclusion of the dipole-quadrupole and quadrupole-quadrupole terms in the potential function has a marked qualitative effect on the shape of the C-T curve. Values of the third virial coefficient for water vapour calculated using a potential function derived from gaseous viscosity and second virial coefficient data are in good agreement with the experimental values.

The statistical mechanics of assemblies of axially symmetric molecules - II. Second virial coefficients

1954 ◽  
Vol 221 (1147) ◽  
pp. 508-516 ◽  
Keyword(s):  
Carbon Dioxide ◽  
General Theory ◽  
Force Field ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Crystal Data ◽  
Axially Symmetric ◽  
Second Virial Coefficients

A general theory of the second virial coefficient of axially symmetric molecules is developed, the directional part of the intermolecular field being treated as a perturbationon the central-force part. The method is applicable to any type of intermolecular potential, particular models of directional interaction being obtained by suitable choices of parameters. Simple expressions are given for the second virial coefficient due to several types of directional force. The theory is illustrated by some calculations on the force field of carbon dioxide and its relation to the second virial coefficient and crystal data. These indicate that there is strong quadrupole interaction between carbon dioxide molecules.

INVESTIGATION OF THE PERTURBED VIRIAL EQUATIONS WITH ARBITRARY TEMPERATURE-DEPENDENT SECOND AND THIRD VIRIAL COEFFICIENTS

2011 ◽  
Vol 25 (19) ◽  
pp. 2593-2600 ◽  
Author(s):  
JIANXIANG TIAN
Keyword(s):  
Virial Coefficient ◽  
Equations Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Compressibility Factor ◽  
Critical Properties ◽  
Temperature Dependent ◽  
Packing Factor ◽  
Third Virial Coefficient ◽  
Real Fluids

In this paper, the perturbed virial equations of state with temperature-dependent virial coefficients are constructed using the Carnahan–Starling (CS) hard sphere equation as reference. Considering the second virial coefficient, some critical properties are interaction-independent and the critical packing factor is in the range of that of real fluids. But the critical compressibility factor and the liquid–vapor equilibrium properties disagree with experiments. When both the second and the third virial coefficient are considered, the critical properties are interaction-dependent but are out of the range of experimental results of real fluids. As a conclusion, the fourth virial coefficients are required for further consideration.

The Bender Equation of State and Virial Coefficients

2000 ◽  
Vol 65 (9) ◽  
pp. 1464-1470 ◽  
Author(s):  
Anatol Malijevský ◽  
Tomáš Hujo
Keyword(s):  
Equation Of State ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Low Density ◽  
Second Virial Coefficients ◽  
The Third ◽  
Temperature Dependences ◽  
Experimental Values

The second and third virial coefficients calculated from the Bender equation of state (BEOS) are tested against experimental virial coefficient data. It is shown that the temperature dependences of the second and third virial coefficients as predicted by the BEOS are sufficiently accurate. We conclude that experimental second virial coefficients should be used to determine independently five of twenty constants of the Bender equation. This would improve the performance of the equation in a region of low-density gas, and also suppress correlations among the BEOS constants, which is even more important. The third virial coefficients cannot be used for the same purpose because of large uncertainties in their experimental values.

The second virial coefficients of mixed polar vapours

1959 ◽  
Vol 249 (1258) ◽  
pp. 414-426 ◽  
Keyword(s):  
Methyl Acetate ◽  
Virial Coefficient ◽  
Methyl Formate ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Ethyl Formate ◽  
Carbonyl Oxygen ◽  
Second Virial Coefficients ◽  
Theoretical Significance ◽  
Boyle’S Law

The second virial coefficients of binary mixtures of chloroform with methyl formate, n -propyl formate, methyl acetate, ethyl acetate and diethylamine have been measured in a ‘Boyle’s law apparatus’ at temperatures between 50 and 95 °C. The measured values are consistently higher than predicted by the theory of corresponding states, and a quantitative interpretation is proposed, based on the hypothesis that the esters and amine are partially dimerized and are involved in association with the chloroform by hydrogen bonding. A linear relation is shown to exist between the heats and entropies of association for the various mixtures, and the theoretical significance of this is discussed. There is some evidence that hydrogen bonds are formed through the alkoxyl oxygen by formate esters and through the carbonyl oxygen by acetate esters. The paper includes data on the second virial coefficient for the pure esters and for ethyl formate and methyl propionate.

Parameters of the Bender Equation of State for Chloro Derivatives of Methane and Chlorobenzene

2001 ◽  
Vol 66 (6) ◽  
pp. 833-854 ◽  
Author(s):  
Ivan Cibulka ◽  
Lubomír Hnědkovský ◽  
Květoslav Růžička
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Liquid Equilibrium ◽  
Second Virial Coefficients ◽  
Equilibrium Data ◽  
State Behaviour ◽  
Derivatives Of

Values of adjustable parameters of the Bender equation of state evaluated for chloromethane, dichloromethane, trichloromethane, tetrachloromethane, and chlorobenzene from published experimental data are presented. Experimental data employed in the evaluation included the data on state behaviour (p-ρ-T) of fluid phases, vapour-liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas-liquid critical point. The description of second virial coefficient by the equation of state is examined.

Intermolecular forces and properties of fluid. I. The automatic calculation of higher virial coefficients and some values of the fourth coefficient for the Lennard-Jones potential

1960 ◽  
Vol 254 (1279) ◽  
pp. 487-498 ◽  
Keyword(s):  
Virial Coefficient ◽  
Mathematical Problem ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Lennard Jones ◽  
Experimental Values ◽  
First Time

The prediction of the virial coefficients for particular intermolecular potentials is generally regarded as a difficult mathematical problem. Methods have only been available for the second and third coefficient and in fact only few calculations have been made for the latter. Here a new method of successive approximation is introduced which has enabled the fourth virial coefficient to be evaluated for the first time for the Lennard-Jones potential. It is particularly suitable for automatic computation and the values reported here have been obtained by the use of the EDSAC I. The method is applicable to other potentials and some values for these will be reported subsequently. The values obtained cannot yet be compared with any experimental results since these have not been measured, but they can be used in the meantime to obtain more accurate experimental values of the lower coefficients.

A POTENTIAL FUNCTION FOR LIQUID HELIUM AT 0°K.

1954 ◽  
Vol 32 (12) ◽  
pp. 759-763 ◽  
Author(s):  
C. F. A. Beaumont
Keyword(s):  
Liquid Helium ◽  
Potential Function ◽  
High Temperatures ◽  
Radial Distribution ◽  
Isothermal Compressibility ◽  
Virial Coefficient ◽  
Distribution Curve ◽  
Second Virial Coefficient ◽  
Fair Agreement ◽  
Radial Distribution Curve

A new potential function for liquid helium is obtained by modifying the Margenau potential function and summing over a suggested structure for the liquid. The new potential function leads to fair agreement with the first peak of the radial distribution curve for liquid helium, with the isothermal compressibility, and with second virial coefficient data at high temperatures.

The second virial coefficients of mixed organic vapours

1952 ◽  
Vol 210 (1103) ◽  
pp. 557-564 ◽  
Keyword(s):  
Hydrogen Bonding ◽  
Binary Mixtures ◽  
Diethyl Ether ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Corresponding States ◽  
Linear Variation ◽  
Second Virial Coefficients

The second virial coefficients of some binary mixtures of organic vapours have been measured at temperatures between 50 and 120° C. Mixtures of n -hexane with chloroform and of n -hexane with diethyl ether show a linear variation of second virial coefficient with composition. This is shown to be in accordance with prediction from the principle of corresponding states. Mixtures of chloroform with diethyl ether show a linear variation at 120° C, but pronounced curvature at lower temperatures. This is interpreted quantitatively as being due to association by hydrogen bonding with an energy of 6020 cal/mole.

Frequency-and Temperature-Dependence of Second Refractivity Virial Coefficients

1993 ◽  
Vol 48 (3) ◽  
pp. 505-513
Author(s):  
Uwe Hohm
Keyword(s):  
Temperature Dependence ◽  
Small Molecules ◽  
Frequency Dependence ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Heuristic Approach ◽  
Experimental Values

Abstract A reasonable heuristic extrapolation of a theory given by Buckingham is used to estimate the frequency-and temperature-dependence of the second refractivity virial coefficient. The calculations are carried out for the atoms He, Ne, Ar, Kr, Xe and the small molecules H2 , N2 , O2 , HCl, CO2 , N2O, NH3 , CH4 , C2H4 , and SF6 . In some cases the frequency-dependence of BR (ω, T) is compared with experimental values, showing sometimes considerable deviations between experiment and the heuristic approach used in this work.

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