The substance-specific constants formula_26 and formula_27 can be calculated from the critical properties formula_28 and formula_29 (noting that formula_29 is the molar volume at the critical point) as:  Also written as  Proposed in 1873, the van der Waals equation of state was one of the first to perform markedly better than the ideal gas law. In this landmark equation formula_26 is called the attraction parameter and formula_27 the repulsion parameter or the effective molecular volume. While the equation is definitely superior to the ideal gas law and does predict the formation of a liquid phase, the agreement with experimental data is limited for conditions where the liquid forms. While the van der Waals equation is commonly referenced in text-books and papers for historical reasons, it is now obsolete. Other modern equations of only slightly greater complexity are much more accurate. The van der Waals equation may be considered as the ideal gas law, "improved" due to two independent reasons:  With the reduced state variables, i.e. formula_45, formula_46 and formula_47, the reduced form of the Van der Waals equation can be formulated:  The benefit of this form is that for given formula_49 and formula_50, the reduced volume of the liquid and gas can be calculated directly using Cardano's method for the reduced cubic form:  For formula_52 and formula_53, the system is in a state of vapor–liquid equilibrium. The reduced cubic equation of state yields in that case 3 solutions. The largest and the lowest solution are the gas and liquid reduced volume. Introduced in 1949, the Redlich-Kwong equation of state was a considerable improvement over other equations of the time. It is still of interest primarily due to its relatively simple form. While superior to the van der Waals equation of state, it performs poorly with respect to the liquid phase and thus cannot be used for accurately calculating vapor–liquid equilibria. However, it can be used in conjunction with separate liquid-phase correlations for this purpose. The Redlich-Kwong equation is adequate for calculation of gas phase properties when the ratio of the pressure to the critical pressure (reduced pressure) is less than about one-half of the ratio of the temperature to the critical temperature (reduced temperature):  Where ω is the acentric factor for the species. This formulation for formula_61 is due to Graboski and Daubert. The original formulation from Soave is:  for hydrogen:  We can also write it in the polynomial form, with:  then we have: where formula_67 is the universal gas constant and Z=PV/(RT) is the compressibility factor.