Thermodynamic consistency testing of PTx-data via the Gibbs-Helmholtz equation 2.: Methodology and limitations

Abstract

Measurement of mixture vapor-pressure data, Px or Tx (PTx) data, is a fast, efficient, and often more accurate method to determine low-pressure binary vapor–liquid equilibrium (VLE) data compared with measurement of PTxy data in re-circulating equilibrium stills. PTx data are the minimum necessary to specify VLE according to the phase rule so that Gibbs–Duhem slope and area thermodynamic consistency tests are not possible. However, GE/RT data derived from PTx data measured at several temperatures can be compared to measured HE data with the Gibbs–Helmholtz (GH) equation, GE/RT=HE/RT–SE/R. This comparison can be used as a thermodynamic consistency test for PTx data. Previous work (Fluid Phase Equilibria, 14 (1983) 383–392) showed that random errors in pressure measurement large enough to give GH inconsistency usually are not large enough to cause unacceptable errors in the vapor compositions calculated by Barker's method. This present work demonstrates that using a Redlich–Kister GE expansion at each temperature rather than using a Local Composition GE model, e.g., NRTL, fitted to all of the Px data over the entire temperature range is an effective methodology for GH testing; this methodology is demonstrated by analysis of high-precision ethanol + water Px data. In addition, the special GH testing problems presented by nearly-ideal systems are illustrated by analysis of recent high-precision ethanol + n-propanol Px data. Other limitations of and recommendations for Gibbs–Helmholtz testing of VLE data are discussed.