How this instrument works
Vapor pressure is the pressure exerted by a liquid's vapor when it's in equilibrium with the liquid phase at a given temperature — it rises with temperature, since more molecules have enough energy to escape the liquid into the vapor phase as things heat up. The Clausius-Clapeyron relation connects vapor pressure at two different temperatures to the substance's molar heat of vaporization (deltaHvap), the energy needed to convert one mole of liquid to vapor: ln(P2/P1) = -(deltaHvap/R) x (1/T2 - 1/T1), where R is the gas constant and T is in kelvin.
This calculator solves that relation for P2 — the vapor pressure at a new temperature, T2 — given a known reference pressure and temperature (P1, T1, commonly the substance's normal boiling point, where vapor pressure equals 1 atmosphere) and the substance's heat of vaporization. It's the inverse pairing of solving for a boiling point at a new pressure: same physical law, same four known quantities, just rearranged for the other unknown.
The relation assumes deltaHvap stays constant across the temperature range between T1 and T2 — a reasonable approximation over a modest temperature span, but deltaHvap actually decreases somewhat as temperature rises (it goes to zero exactly at the critical point), so extrapolating across a wide temperature gap trades away some accuracy. Water extrapolated the roughly 75-degree gap from its 100C boiling point down to 25C, for instance, comes out a bit above its real measured 25C vapor pressure — a known, disclosed limitation of the constant-deltaHvap approximation, not a computation error.
- Enter a known reference pressure into Reference pressure, P1 (kPa) — commonly 101.325 kPa (1 atm) if you're using the normal boiling point as your reference.
- Enter the temperature at which that reference pressure applies into Reference temperature at P1 (degC) — the normal boiling point, if P1 is 101.325 kPa.
- Enter the substance's molar heat of vaporization into Latent heat of vaporization, substance-specific (J/mol).
- Enter the new temperature you want the vapor pressure at into New temperature, T2 (degC).
- Read Vapor pressure at T2 (kPa) below the inputs — accuracy is best when T2 is reasonably close to T1, since the underlying approximation assumes constant deltaHvap across that gap.
Worked example — water's vapor pressure at room temperature
Enter 101.325 into Reference pressure, P1 (kPa), 100 into Reference temperature at P1 (degC) (water's normal boiling point), 40700 into Latent heat of vaporization, substance-specific (J/mol) (water's standard molar heat of vaporization), and 25 into New temperature, T2 (degC). Vapor pressure at T2 (kPa) reads about 3.74 kPa.
Water's real, measured vapor pressure at 25C is closer to 3.17 kPa, so this estimate runs a bit high — expected, since it extrapolates the constant-deltaHvap approximation across a wide 75-degree gap from the 100C reference point, and deltaHvap itself actually decreases somewhat as temperature drops from 100C toward 25C. Run the same calculation over a much smaller gap — say, from 100C down to 90C — and the approximation lands very close to water's real measured vapor pressure at that temperature, since deltaHvap barely changes across such a small span.
Questions
Why does the estimate drift from the real value over a large temperature range?
Because the Clausius-Clapeyron relation, as used here, assumes the substance's heat of vaporization (deltaHvap) is constant across the whole temperature range from T1 to T2 — but deltaHvap actually decreases as temperature rises, reaching zero exactly at the critical point. Extrapolating water's vapor pressure from its 100C boiling point down to 25C spans 75 degrees, over which deltaHvap has already shifted noticeably from its 100C value, which is exactly why that particular estimate runs somewhat above the true measured figure.
What reference point should I use for P1 and T1?
The substance's normal boiling point is the most convenient and commonly available choice — the temperature at which vapor pressure equals standard atmospheric pressure, 101.325 kPa, a figure that's tabulated for essentially every common substance. Any other pressure-temperature pair you know accurately for the substance works equally well as a reference, though; the calculation doesn't require the reference specifically be the boiling point.
Where do I find a substance's heat of vaporization?
Standard chemistry references like the CRC Handbook of Chemistry and Physics tabulate molar heat of vaporization for common substances at their normal boiling point — water's is about 40,700 J/mol, ethanol's is about 38,600 J/mol. Some sources report it in different units (kJ/mol or cal/g); convert to J/mol before entering it here, since that's the unit this formula's gas-constant term expects.
Is this the same relationship used to calculate a boiling point at a different pressure?
Yes — a boiling-point-at-altitude or boiling-point-at-pressure calculation uses the exact same Clausius-Clapeyron relation, just solved for the temperature (T2) instead of the pressure (P2). Both start from the identical physical law and the same four known quantities (a reference pressure/temperature pair and a heat of vaporization); which one you use depends only on whether your unknown is a pressure or a temperature.
Does this work for any liquid, or just water?
Any pure substance, as long as you supply that substance's own heat of vaporization and a valid reference pressure/temperature pair for it — the relation itself isn't water-specific. Water is used in the worked example because its properties are so well known and easy to sanity-check, but the same formula applies to ethanol, acetone, or any other single-component liquid with a known deltaHvap.