Pressure–temperature nomograph
Pick a compound or enter a boiling point you know. Get the boiling point at any pressure, or the vacuum you need to boil it at a given temperature.
What you know
Nomograph
drag a markerThe line runs through the values from the compound's own vapour pressure data. Where it crosses the middle scale is the chart's generic estimate of the normal boiling point; the hollow dot is the measured one.
At typical pressures
| Pressure | Boiling point |
|---|---|
| 1013.25 mbarAtmosphere | 110.6 °Cextrapolated |
| 500 mbar | 87.5 °C |
| 200 mbar | 61.9 °C |
| 100 mbar | 45.3 °C |
| 50 mbar | 30.5 °C |
| 20 mbarWater aspirator | 13.2 °C |
| 10 mbar | 1.7 °Cextrapolated |
| 5 mbarDiaphragm pump | −8.7 °Cextrapolated |
| 2 mbar | −21.1 °Cextrapolated |
| 1 mbar | −29.5 °Cextrapolated |
| 0.5 mbar | −37.3 °Cextrapolated |
| 0.1 mbarRotary vane pump | −53.0 °Cextrapolated |
| 0.01 mbarRotary vane pump, cold trap | −71.4 °Cextrapolated |
| 0.001 mbarDiffusion pump | −86.1 °Cextrapolated |
Details
- Antoine constants
- A 6.95464, B 1344.8, C 219.48log₁₀(P/mmHg) = A − B/(C + T/°C), fitted 8 to 100 °C, NIST WebBook
- ΔHvap at the normal boiling point
- 34.8 kJ/molClausius–Clapeyron slope of the Antoine curve
- Liquid type
- not hydrogen-bonded by O–H
How the boiling point is calculated
When the compound has Antoine constants in our database (NIST WebBook), the boiling point solves log10(P/mmHg) = A − B/(C + T) exactly. Outside the temperature range the constants were fitted for, the value is marked as extrapolated. Constants that contradict a measured boiling point of the same compound are not used.
Otherwise the vapour pressure curve is estimated from one boiling point, the normal one or one measured under vacuum. The curve has the Antoine form with the Calingaert–Davis constant C = −43.15 K (230 in the °C form). Its slope at the boiling point follows from the entropy of vaporization by Trouton's rule in the temperature-dependent Trouton–Hildebrand–Everett form, ΔSvap/R = 4.4 + ln(Tb/K), divided by ΔZ = 0.95 for the non-ideal vapour at 1 atm. Alcohols, glycols and water are hydrogen-bonded and have a larger entropy of vaporization; for them it is multiplied by 1.29, the value that best fits the NIST vapour pressure curves of water, methanol, ethanol, 2-propanol, 1-butanol, ethylene glycol and 2-phenoxyethanol between 1 and 400 mmHg. The slopes of those curves at the boiling point give 1.23 to 1.31; for hexane the same ratio is 1.00. Carboxylic acids dimerise in the vapour and follow the plain rule.
We checked it against the 31 NIST Antoine curves in our database that agree with a measured boiling point, at 149 pressures from 1 to 400 mmHg inside their fitted ranges, anchoring each estimate at the curve's own normal boiling point. It is off by 2.4 K on average; 79 % of the values are within 3 K and nine in ten within 6.1 K. The largest error, 15 K, is 2-phenoxyethanol at 1 mmHg, a large molecule with a single O–H group. Below 1 mmHg the estimate is marked as extrapolated.
Reading the nomograph
A straight line through the normal boiling point on the middle scale and the pressure on the right crosses the left scale at the boiling point at that pressure. Because the estimate above is written as a relation that can be drawn exactly, the three points are collinear to drawing precision; the middle scale is curved, with one curve for hydrogen-bonded liquids and one for the rest.
Drag the marker on the pressure scale to change the pressure, or the one on the left scale to find the pressure for a temperature. With a known boiling point at 1 atm the middle marker moves too. A boiling point measured under vacuum draws a second, lighter line that finds the normal boiling point first.
The classic printed nomograph uses the Clausius–Clapeyron equation with one Trouton constant for every liquid, so it cannot tell ethanol from toluene. Here, a compound with its own vapour pressure data is read from those data, and the chart shows how far the generic scale would be off.
Sources
- Antoine constants: NIST Chemistry WebBook, as stored with their fitted ranges.
- Boiling points: CAS Common Chemistry, as stored in our catalogue.
- C. Antoine, C. R. Acad. Sci. 107 (1888) 681 and 836: the vapour pressure equation.
- G. Calingaert and D. S. Davis, Ind. Eng. Chem. 17 (1925) 1287: C = 230 in the °C form.
- J. H. Hildebrand, J. Am. Chem. Soc. 37 (1915) 970: entropies of vaporization compared at equal vapour concentration, the basis of the Trouton–Hildebrand–Everett form.