Antoine Equation Vapor Pressure Calculator

Vapour pressure is the pressure of vapour in equilibrium with its own liquid at a given temperature, and it rises steeply with temperature because the fraction of molecules carrying enough energy to escape the surface grows roughly exponentially. The Clausius-Clapeyron relation gives the theoretical shape, dln(P)/dT = enthalpy of vaporisation divided by R times T squared, which on integration at constant enthalpy yields a straight line of log P against 1/T. Real substances curve away from that line because the enthalpy of vaporisation falls as temperature rises, vanishing at the critical point. The Antoine equation, log10(P) = A - B/(C + T), absorbs that curvature into a single extra parameter: setting C to zero recovers the two-constant August form, while a positive C shifts the temperature axis and bends the fit. Rearranging for the normal boiling point gives T = B/(A - log10(760)) - C when pressure is in mmHg. The constants are pure curve-fitting parameters with no physical meaning individually, and they are inseparable from their units and their fitted range. That last point is the dominant practical caveat. A set of constants quoted for mmHg and degrees Celsius produces nonsense if fed kelvin or read as bar, and published tables use all these conventions, so the units must be checked before the numbers are trusted. The water constants A = 8.07131, B = 1730.63, C = 233.426 are fitted over roughly 1 to 100 degrees C and return 760.96 mmHg at 100 degrees C, close to the defined 760; a second set is normally used from 100 to 374 degrees C, and mixing the two across the boundary produces a visible discontinuity. Within its stated range the equation is typically accurate to within one to three percent, but extrapolation degrades quickly, especially towards the critical point where no three-parameter form can follow the real curve. For wide-range work, extended Antoine variants with additional terms or the Wagner equation are used instead. The equation also applies only to a pure component; mixtures require Raoult's law with activity coefficients, and it says nothing about supercooled liquids or solid sublimation pressures unless constants fitted specifically to the solid are used.

Measuring how vapour pressure changes with temperature was a central problem of early thermodynamics. John Dalton and Joseph Louis Gay-Lussac published measurements on water and other liquids in the first decade of the nineteenth century, and Ernst Ferdinand August proposed the two-constant logarithmic form log P = A - B/T around 1828, which fitted data adequately near the boiling point but drifted badly elsewhere. The theoretical footing came from Benoit Paul Emile Clapeyron in 1834, who derived the relation between the slope of the phase boundary and the latent heat, and from Rudolf Clausius, who recast it in 1850 in terms of the second law to give the form now taught as the Clausius-Clapeyron equation. Henri Victor Regnault meanwhile produced the era's definitive vapour pressure measurements, providing the accurate data that any correlation had to reproduce. The French engineer Louis Charles Antoine published his three-constant modification in 1888 in the Comptes Rendus de l'Academie des Sciences, showing that inserting an additive constant into the temperature denominator dramatically improved the fit across a working range without adding computational burden. Its simplicity kept it in use as slide rules gave way to calculators and then to process simulators. Large compilations of constants followed as chemical engineering industrialised, notably the tables in successive editions of Perry's Chemical Engineers Handbook, the Dortmund Data Bank, the DIPPR project begun in 1978 under the American Institute of Chemical Engineers, and the Yaws handbooks. Wilhelm Wagner introduced a more accurate wide-range correlation in 1973 for work extending to the critical point, and the NIST Chemistry WebBook now distributes Antoine coefficients with their explicit validity ranges and source references so that users can check the fit before applying it.