(74t) Rationale for the Parameterization of Van Der Waals Equations-of-State: The Lawal-Lake-Silberberg Equation As Classic Prototype

As of yet and by judging from the State-of-The-Arts Reviews by Leland (1968), Tsonopoulos-Prausnitz (1969), Vera-Prausnitz (1972), Abbott (1973), Storvick-Sandler (1977),  Horvath (1974), Prausnitz (1977), Firoozabadi (1978), Martins (1979), Wong-Prausnitz (1985), Walas (1985), Anderko (1990), Wu-Prausnitz (1998), Poling et al. (2001), Wang-Pope (2002), Valderrama (2003) and Prausnitz -Tavares (2004), the issue of which Van der Waals (VDW) model with the same number of parameters is best does not have a universal and widely acceptable answer and there is still no obvious choice among the three- and four-parameter cubic equation of state models.

This contribution asserts the reformed four-parameter VDW 1873 equation of state, which has been affectionately named the Lawal-Lake-Silberberg (LLS) cubic equation, as the preferred choice among all categories of the VDW type of cubic equations of state by honoring the four properties of the VDW theory, the four critical constraint criteria and by being in accord with the theory of cubic polynomial equations of state which stipulates four-parameter for all cubic polynomial equations. A theoretical justification within the framework of the VDW empiricisms is provided for the LLS equation as the Substance-Based Cubic Equation of State for the individual pure substances, in agreement with the VDW objective which he stated toward the end of the 1910 Nobel Prize Lecture*** as “to determine the relation between p, v and T for a substance.”  However, we are still lacking the microscopic-level description for the two empirical parameters introduced into the reformed VDW 1873 equation, the LLS equation.

The LLS equation is applicable to all categories of pure substances, regardless of the chemical structure, polarity or molecular size and prediction of accurate volumetric and thermodynamic properties over the entire PVT states are guaranteed. But, the extension of the combining mixture rules to ternary and multicomponent systems is still being explored.

*** Van der Waals, J. D., 1910 Nobel Prize Lecture available from "J. D. van der Waals - Nobel Lecture: The Equation of State for Gases and Liquids". http://www.nobelprize.org/nobel_prizes/physics/laureates/1910/waals-lecture.html