1More than a hundred equations of state relating the pressure, volume, and temperature of gases have been proposed according to Dodge ( 7 ) , but only a very few of them have attained any practical importance as the majority do not represent the data with sufficient accuracy. In this work the significant pressure-volume-temperature (hereafter referred to as P V T ) characteristics of pure gases have been examined in detail, and an equation has been developed to fit precisely the characteristics common t o different gases.PVT data may be plotted on different types of graphs, of which probably the oldest is that of pressure vs. volume with temperature as a parameter, as shown in Figure 1. From this graph van der Waals deduced two properties of the critical isotherm namely, that at the critical point the slope is zero and an inflection occurs.' Van der Waals expressed these two properties algebraically in the following well-known manner :where P is pressure, V is volume, and T is temperature, as indicated above. Van der Waals employed these two conditions to evaluate the two arbitrary constants in the equation of state he proposed.A number of other two-constant (exclusive of the gas constant) equations of state have been proposed, the best known being those of Berthelot and Dieterici. None of them, however, actually represent the PVT data over a wide range *Some investinations ( 1 3 ) indicate that the critical isothermis not the smoothly inflected curve shown in Figure 1. This result seems to be attributed to the indefiniteness of the critical state and possibly to the lack of attainment of true equilibrium.with any great degree of precision and not one of them is considered suitable for the calculation of accurate thermodynamic diagrams. This does not imply, however, that these two-constant equations have not been extremely useful. Van der Waals' equation was of the greatest value in leading to the principle of corresponding states.In one form the correspondingstate principle suggests that the compressibility factor, x = PVIRT, depends only on the reduced temperature and pressure, which are defined respectively as T , = T I T , and P,= PIP,. On a generalized compressibility chart for many different compounds single average lines are drawn for each isotherm; however, to demonstrate that the principle is approximate, Figure 2 has been constructed to emphasize the differences which actually exist among compounds.From the compressibility chart it is noted that all gases follow the ideal-gas law as the pressure approaches zero, regardless of the temperature. This may be expressed as Z = PV/RT= 1 at P = 0 for all temperatures (3) With any isotherm t,aken at Po = 0, 2, = 1.0, (dZ/dP,) = lim (2 -1) / (P, -0 ) as P, -+ 0 = lim RT (Z -I)/RTP, as P, -+ 0 = (P,/RT) Iim(ZRT/P-RT/P) (5) FIG. 1. PRESSURE-VOLUME DIAGRAM. ~ A curious corollary of this is the seemingly contradictory fact that in general V does not equal R T I P at P=O. By definition of a derivative a t any point ( P o , 2,) on the compressibility chart, ----------(...