shows the behavior of argon in its gaseous and liquid phases. represents the potential contributed from the term, and represents the contributions from the term. When n < 30, would interfere with and lower significantly the volume of liquid. It is surprising that n has to be greater than 20 to produce a solid phase. It is well known that the Lenard-Jones 6-12 potential can be used to compute the second virial coefficient from quantum mechanical principles. Quantum mechanical reasoning relates the second virial coefficient to bimolecular attraction, and the third coefficients to tri-molecular repulsion, etc. In the liquid phase of argon, one atom is surrounded by 12 nearest neighbors and up to 32 next-to-nearest neighbors. In the solid phase, all atoms are locked in place, and the number of interacting neighbors is infinite. Therefore, n = 30, or even greater, is reasonable. As a result, we have a virial equation of state to describe quantitatively the gas-liquid-solid equilibrium for argon, and all fluids which observe the principle of corresponding states, at its triple point: Virial equations of state From Benedict-Webb-Rubin and Starling equations of state, it was determined that the best virial equation of state should take the form of The second and third virial coefficients in this equation can be computed from experimental PρT data using a linear regression. After removing the first three virial terms, the residue in compressibility factor could then be used to obtain the sixth virial coefficient. See also Virial theorem Statistical mechanics Equation of state References Statistical mechanics