The curvature of the liquid–vapor reduced pressure curve and its relation with the critical region

For most fluids, there exist a maximum and a minimum in the curvature of the reduced vapor pressure curve, pr=pr(Tr)pr=pr(Tr) (with pr=p/pcpr=p/pc and Tr=T/Tc,pc and TcTc being the pressure and temperature at the critical point). By analyzing National Institute of Standards and Technology (NIST) data on the liquid-vapor coexistence curve for 105 fluids, we find that the maximum occurs in the reduced temperature range 0.5⩽Tr⩽0.80.5⩽Tr⩽0.8 while the minimum occurs in the reduced temperature range 0.980⩽Tr⩽0.9950.980⩽Tr⩽0.995. Vapor pressure equations for which d2pr/dTr2 diverges at the critical point present a minimum in their curvature. Therefore, the point of minimum curvature can be used as a marker for the critical region. By using the well-known Ambrose–Walton (AW) vapor pressure equation we obtain the reduced temperatures of the maximum and minimum curvature in terms of the Pitzer acentric factor. The AW predictions are checked against those obtained from NIST data.

► The curvature of the reduced vapor pressure curve has two extrema for most fluids.
► The Ambrose–Walton vapor pressure equation yields the extrema in terms of the acentric factor.
► The maximum in the curvature occurs in for reduced temperatures in the range [0.5, 0.8].
► The minimum in the curvature of the vapor pressure curve is a delimiter for the critical region.