(53k) Compressibility Determination By Volumetric Property Measurements: A Non-Burnett Technique of Estimating Virial Coefficients for Pure Substances

Over the period starting from 1921 to 1957, the Laboratory of Sage et al. at California Institute of Technology reported volumetric property data for hydrocarbons (methane, ethane, propane, i-butane, n-butane, n-pentane, n-hexane, n-heptane, n-nonane, n-decane, benzene, cyclohexane, propene, 1-butene and trans-2-butene), non-hydrocarbons (nitrogen, carbon dioxide, hydrogen sulfide), water, ammonia, nitric acid (HNO₃), nitric oxide, nitrogen dioxide and their respective binary and ternary systems. Those volumetric property data are analyzed by graphical and least squared methods and are used to validate and augment the existing data on the second to fourth virial coefficients. However, as the virial coefficients essentially depend on temperature, the large uncertainties of deriving virial coefficients at low temperature by the graphical approaches give way to a new method for re-determining a(T) and b(T) of the Van der Waals generic cubic equation of state as typified by the design of the Lawal-Lake-Silberberg (LLS) cubic equation of state and the improved a(T) and b(T) are used to accurately predict the volumetric properties of pure substances reported by Sage et al. The LLS cubic equation with the improved a(T) and b(T) is then used to derive virial coefficients for polar and nonpolar pure substances. The analyses of results in comparison with the second virial coefficients derived by the Burnett method are in agreements but deviations are exhibited at low temperatures for the third virial coefficient. Also, the LLS cubic equation is used to establish the even- and odd-terms of n-order virial coefficients for structurally well-defined asymmetric pure substances without regard to polarity, size, shape and structure. Furthermore, the inverted second virial coefficients of binary species i and j provides a basis for the cross-second virial coefficient that can be used to establish the force-parameter to approximate the Van der Waals intermolecular parameter for species i and j through the ratio of the molecular volumes.