In the top pane of figs. 8 and 9, we numerically integrate two sets of temperature dependent data and compare to reference vapor pressure data, taking our reference state to be the triple point. In the first case, we set ∆Z vap = 1, which corresponds to numerically integrating ∆H vap /R. The predicted data matches the reference vapor pressure at the triple point by construction, but diverges at the critical point due to propagation of errors and the assumption of ∆Z vap = 1 breaks down with increasing temperature. Clearly then ∆Z vap is important for accurate calculations. In the second case we numerically integrate ∆H vap / (R∆Z vap ). The resulting predictions match the reference data as expected. Clapeyron plots of NIST reference data for water of the log vapor pressure relative to the vapor pressure at the triple point (ln P/P 0 ) versus the inverse absolute temperature times 1000 (1000/T) as compared to predictions made by numerical integrating the Clapeyron equation . In the top pane, reference (ref) is compared to predictions made by numerically integrating ∆H vap / (R∆Z vap ) and ∆H vap /R, as indicated, where the latter assumes ∆Z vap = 1. In the middle pane, reference (ref) is compared to predictions made by numerically integrating ∆H vap / (R∆Z vap ) which is taken to be constant. We compare use of the value at the lowest temperature (the triple point, min), the average value (avg) and the average (natural) log value (Lavg), and the value at the highest temperature (0.097 K below the critical point, max). In the bottom pane, reference (ref) is compared to predictions made by numerically integrating ∆H vap /R which is taken to be constant and assumes ∆Z vap = 1. The plots span from the triple point (T = 273.16 K, P = 0.0061165 bar) to approximately the critical point (T c = 647.096 K, P c = 220.640 bar). Clapeyron plots of NIST reference data for hexane of the log vapor pressure relative to the vapor pressure at the triple point (ln P/P 0 ) versus the inverse absolute temperature times 1000 (1000/T) as compared to predictions made by numerical integrating the Clapeyron equation . In the top pane, reference (ref) is compared to predictions made by numerically integrating ∆H vap / (R∆Z vap ) and ∆H vap /R, as indicated, where the latter assumes ∆Z vap = 1. In the middle pane, reference (ref) is compared to predictions made by numerically integrating ∆H vap / (R∆Z vap ) which is taken to be constant. We compare use of the value at the lowest temperature (the triple point, min), the average value (avg) and the average (natural) log value (Lavg), and the value at the highest temperature (0.82 K below the critical point, max). In the bottom pane, reference (ref) is compared to predictions made by numerically integrating ∆H vap /R which is taken to be constant and assumes ∆Z vap = 1. The plots span from the triple point (T = 177.83 K, P = 1.189 × 10 -5 bar) to approximately the critical point (T c = 507.82 K, P c = 30.441 bar).