A correlation of critical points

Critical points were correlated for fluids which obey the three-parameter equation of state according to which the compressibility factor, $\text{Z=}\text{P}\text{dRT}$, is given by Z=1 + k_Bδκ (θ, δ), in which κ (θ, δ) is a universal function of reduced temperature, $\text{θ =}\text{T}\text{T}{}_{\mathrm{B}}$, and reduced density, $\text{δ =}\text{d}\text{d}{}_{\mathrm{<mtext>O</mtext>}}$. The three parameters which distinguish one fluid from another are k_B, T_B, and d_O. It is shown that experimental inflection points of the pressure versus density isotherms of gases obeying this equation of state all fall on the same reduced curve of θ versus δ. Critical points also must lie on this curve, at a location dependent on k_B. Critical densities are too uncertain experimentally to permit a definite correlation, but the critical temperatures of sixteen fluids are shown to fall on a common θ_c versus k_B curve with an average deviation of 0.4 degrees. The critical pressures of these same fluids lie within a few tenths of an atmosphere on a common π_c ($\text{π =}\text{P}\text{d}{}_{\mathrm{<mtext>O</mtext>}}\text{RT}{}_{\mathrm{<mtext>B</mtext>}}$) versus k_B line. This correlation of critical points is accomplished using values of the three parameters that had previously been determined by fitting supercritical PVT data to the equation of state.