# Vapor pressure **Vapor pressure** (or vapour pressure) is the [[Pressure|pressure]] exerted by a vapour that is in [[Thermodynamic_equilibrium|thermodynamic equilibrium]] with its own liquid or solid in a closed container at a given [[Temperature|temperature]]. It measures the escaping tendency of the condensed phase: molecules leave the surface by [[Evaporation|evaporation]] and return by condensation, and the vapour pressure is where the two rates balance. It rises steeply with temperature, and a liquid boils when its vapour pressure reaches the pressure pressing on it from outside, so the [[Boiling_point|boiling point]] of a liquid is simply the temperature at which its vapour-pressure curve crosses the ambient pressure.[^averill-t104] For [[Water|water]] that crossing is at 100 °C when the outside pressure is 760 mmHg, one standard atmosphere.[^os-af-503] On the Chemistry flagship the article serves the section *Vapour pressure and boiling* (Part III — Phase). In the microsim below the reader slides the temperature of a water bath from 0 to 110 °C and watches the marker climb the vapour-pressure curve of water, tabulated from the Portal Book's Table 10.4; the readouts answer two questions. The first is the dry-gas correction for a gas collected over water, `P_gas = P_total − p_H₂O(T)`, which says how much of the pressure in a collection bottle is the gas that was made and how much is water. The second is where the curve crosses the three horizontal lines at 760, 630 and 234 mmHg — sea level, Denver, and the summit of Everest — because each crossing is the temperature at which water boils in that place.[^averill-baro] ## Measurement and units Vapour pressure is measured with the instruments that measure any pressure: a barometer for the atmosphere, a manometer for a gas in a vessel. The Portal Book's manometer example makes the arithmetic concrete. A difference of 0.200 atm between the two arms of a mercury manometer stands 152 mm of [[Mercury_(element)|mercury]] apart, and the same difference would need 2.06 m of water, because the two liquids have densities of 13.53 and 0.9970 g/cm³.[^averill-mano] The classical vapour-pressure method is exactly this: seal the liquid in an evacuated tube above a mercury column, let it reach equilibrium at a fixed temperature, and read how far the mercury has been pushed down. That is why the historic unit is the millimetre of mercury, and why the Portal Book tabulates water in mmHg.[^averill-t104] The units are related by 1 atm = 760 mmHg = 101.325 kPa, and 1 mmHg = 133.322 Pa.[^mitofsky-184] Two things are easy to get wrong. The vapour pressure is a property of the substance and the temperature only: it does not depend on the amount of liquid present, provided some remains, nor on the size of the container, because the equilibrium is set by the rates of escape and return per unit surface. And the temperature that matters for a gas collected over water is the temperature of the water, not of the room, because it is the water's escaping tendency that adds vapour to the bottle.[^averill-overwater] Modern low-pressure measurements use capacitance gauges or the rate of [[Effusion|effusion]] through a small hole, but they report the same quantity the mercury column does. ## Estimating vapor pressures with Antoine equation Because a vapour-pressure curve rises so steeply, it is usually stored not as a table but as a three-parameter fit, the Antoine equation, `log₁₀ p = A − B/(C + T)`, proposed by the French engineer Louis Charles Antoine in 1888 as an improvement on the two-parameter form that the [[Clausius–Clapeyron_relation|Clausius–Clapeyron relation]] suggests.[^antoine1888] The constants A, B and C are fitted to measurements over a stated temperature range and are tabulated for thousands of substances; the NIST Chemistry WebBook is the standard open source, and each entry carries its own range, outside which the fit should not be trusted.[^nist-webbook] The Portal Book gives no Antoine constants, so a fit made here shows what the equation can do (ILLUSTRATIVE: a display fit through three rows of the book's table, not a measured law). Forcing the curve through Table 10.4's values at 0 °C (4.58 mmHg), 50 °C (92.6 mmHg) and 100 °C (760.0 mmHg) gives `A = 8.064`, `B = 1728.6` and `C = 233.49` for p in mmHg and T in °C. The fit then reproduces every other row of the table to within 0.2 %: it predicts 23.82 mmHg at 25 °C against the tabulated 23.77, 233.6 mmHg at 70 °C against 233.8, and 1075.8 mmHg at 110 °C against 1074.4.[^averill-t104] Three numbers therefore carry fourteen, which is the point of the form. The microsim does not use this fit; it interpolates the table directly, because the table is exact where the data are and the fit is not. Beyond the table the constants would need re-fitting, and near the [[Critical_point_(thermodynamics)|critical point]] the form fails altogether. ## Relation to boiling point of liquids A liquid boils when bubbles of its own vapour can form inside it and survive, which requires the vapour pressure in the bubble to equal the pressure on the liquid. The normal boiling point is the temperature at which the vapour pressure equals 1 atm; for water it is 100 °C, where Table 10.4 reads 760.0 mmHg.[^averill-t104] Lower the outside pressure and the liquid boils cooler; raise it and the boiling point climbs, which is how a pressure cooker works and why a sealed vessel of water at 25 °C sits under only 0.03 atm of its own vapour but reaches 218 atm at 374 °C, the critical point, above which liquid and vapour merge into a [[Supercritical_fluid|supercritical fluid]].[^os-af-506] The shape of the curve is governed by the [[Enthalpy_of_vaporization|enthalpy of vaporization]], the [[Latent_heat|latent heat]] of the phase change, through the Clausius–Clapeyron relation, which in its integrated two-point form reads `ln(p₂/p₁) = −(ΔH_vap/R)·(1/T₂ − 1/T₁)`. With water's ΔH_vap = 40.67 kJ/mol and the anchor 760 mmHg at 373.15 K,[^os-af-502] the relation predicts 28.1 mmHg at 25 °C, about 18 % above the tabulated 23.77 mmHg (derived). The gap is a lesson: the two-point form assumes a constant ΔH_vap, but water's enthalpy of vaporization grows as the temperature falls, so the real curve drops faster than the fit. Used near its anchor the relation is good, predicting boiling at 94.7 °C under 630 mmHg and at 69.2 °C under 234 mmHg, against 94 °C and 70 °C read from the table (derived). The sim's header says so: the curve drawn is the table, and the Clausius–Clapeyron line is ILLUSTRATIVE. ## Liquid mixtures: Raoult's law Above a [[Mixture|mixture]] of volatile liquids each component contributes its own [[Partial_pressure|partial pressure]], and for an ideal solution [[Raoult's_law|Raoult's law]] gives each one as the pure-liquid vapour pressure scaled by the component's [[Mole_fraction|mole fraction]] in the liquid: `p = x_A·p*_A + x_B·p*_B`.[^os-af-ch11] The total vapour pressure of the mixture is therefore a straight line between the two pure values, and the vapour is richer than the liquid in whichever component has the larger `p*`, which is the basis of [[Fractional_distillation|fractional distillation]]. A solute that has no vapour pressure of its own simply dilutes the solvent's, `p = x_solvent·p*_solvent`. At 100 °C a [[Solution_(chemistry)|solution]] in which water is 98 % of the molecules has a vapour pressure of `0.98 × 760.0 = 744.8 mmHg` and so does not yet boil under a standard atmosphere; it must be heated a little further until its lowered curve reaches 760 mmHg. That shift is the boiling-point elevation, one of the [[Colligative_properties|colligative properties]], and it depends only on how many solute particles are present, not on what they are.[^os-af-ch11] Real mixtures depart from the straight line when unlike molecules attract each other more or less than like ones; the sibling article on Raoult's law treats those deviations. ## Solids Solids have vapour pressures too, usually small, and the [[Phase_transition|phase transition]] a solid makes into its vapour is sublimation. [[Ice|Ice]] at −10 °C exerts 0.20 kPa, about 1.5 mmHg, which is why frost disappears from a windscreen on a dry day below freezing without ever becoming liquid.[^os-af-504] On the [[Phase_diagram|phase diagram]] the solid–vapour curve runs up to the [[Triple_point|triple point]], where it meets the liquid–vapour curve; below the triple-point pressure no liquid can exist at any temperature, so a solid heated at such a pressure passes straight into vapour. Freeze-drying uses exactly this: frozen food or a frozen pharmaceutical is held under vacuum below the triple-point pressure and the ice sublimes away, leaving the structure intact.[^os-af-504] Carbon dioxide is the everyday example of a solid whose triple point lies above atmospheric pressure. Its liquid cannot exist at 1 atm, so dry ice sublimes, and the Portal Book's phase diagram for CO₂ is drawn with a logarithmic pressure axis to fit the solid, liquid and gas regions on one page.[^os-af-505] Solids with an appreciable vapour pressure at room temperature, such as naphthalene and [[Iodine|iodine]], announce it by their smell and by the slow disappearance of a crystal left in the open; the sim tabulates water alone. ## Boiling point of water The microsim's curve is Table 10.4 of the Portal Book, the vapour pressure of water from 0 to 110 °C: 4.58 mmHg at 0 °C, 9.21 at 10, 17.54 at 20, 19.84 at 22, 23.77 at 25, 31.84 at 30, 55.4 at 40, 92.6 at 50, 149.5 at 60, 233.8 at 70, 355.3 at 80, 525.9 at 90, 760.0 at 100 and 1074.4 at 110 °C.[^averill-t104] The book gives no formula, so the sim stores a monotone interpolation of these rows. Three horizontal lines cross the curve. At 760 mmHg the crossing is 100 °C. Denver's barometer reads about 630 mmHg,[^averill-baro] and linear interpolation between the 90 °C and 100 °C rows puts the crossing at 94 °C (derived). At 14,000 ft the pressure is 454 mmHg, crossed near 86 °C (derived).[^averill-baro] The summit of Everest stands at 0.308 atm, which is 234 mmHg, almost exactly the table's 233.8 mmHg at 70 °C, so water boils there at about 70 °C.[^averill-baro] The Portal Book's phase-diagram exercise reads the boiling point at 50 kPa (375 mmHg) off its figure as 78 °C; the table interpolates to 81 °C, the difference being the resolution of a figure read by eye.[^os-af-505] The same table answers the other question the sim asks. A gas made in the laboratory is often collected by bubbling it into an inverted bottle of water, and the bottle then holds a mixture of the gas and water vapour at the water's vapour pressure, so by [[Dalton's_law|Dalton's law]] `P_gas = P_total − p_H₂O(T)`.[^averill-overwater] In the Portal Book's airbag example, 0.115 mol of [[Nitrogen|nitrogen]] from 5.00 g of [[Sodium|sodium]] azide is collected at 22 °C and a total pressure of 762 mmHg; subtracting the 19.84 mmHg of water vapour leaves 742 mmHg of nitrogen, which occupies 2.85 L.[^averill-airbag] In its exercise, 1.00 g of [[Zinc|zinc]] dissolved in hydrochloric acid gives 0.0153 mol of hydrogen, collected at 30 °C under 760 mmHg total, so 728 mmHg of hydrogen and a volume of 0.397 L.[^averill-zn] The sim's "aha" is what happens as the bath warms toward the local boiling point: the correction grows until it consumes the whole pressure and no room is left for the collected gas, because at the boiling point the bottle would hold nothing but steam. Gases that dissolve in water or react with it cannot be collected this way at all.[^averill-overwater] ## Dühring's rule Dühring's rule is an empirical observation about solutions: if the temperature at which a solution reaches a given vapour pressure is plotted against the temperature at which pure water reaches the same vapour pressure, the points fall on a nearly straight line, `T_solution = a·T_water + b`, whose slope and intercept depend on the concentration of the solution but not on the pressure. The lines for a family of concentrations are called Dühring lines, and the classic chart is for [[Sodium_hydroxide|sodium hydroxide]] in water, which is used to find the boiling point of a caustic solution at the pressure inside an evaporator.[^mccabe-evap] Because the rule is a straight-line fit to data, a Dühring chart is a display fit in the sense this wiki labels ILLUSTRATIVE; it is a good one for concentrated aqueous solutions, and it lets the whole of Table 10.4 be reused for a solution through one multiplication and one addition. ## Examples Water's table above is the worked example of a liquid. The other end of every vapour-pressure curve is the critical point, where the liquid–vapour line stops, and the Portal Book's critical data give the points at which seven common substances' curves end.[^os-af-506] | Substance | Critical temperature (°C) | Critical pressure (kPa) | |---|---|---| | Hydrogen | −240.0 | 1300 | | Nitrogen | −147.2 | 3400 | | Oxygen | −118.9 | 5000 | | Carbon dioxide | 31.1 | 7400 | | Ammonia | 132.4 | 11,300 | | Sulfur dioxide | 157.2 | 7800 | | Water | 374.0 | 22,000 | Read as vapour pressures, the table says that liquid [[Hydrogen|hydrogen]] never exerts more than 1300 kPa and liquid water never more than 22,000 kPa, however hot they are made; beyond those points there is no liquid to exert anything.[^os-af-506] A gas whose critical temperature lies below room temperature, such as [[Oxygen|oxygen]] or nitrogen, has no vapour pressure at all at room temperature because it cannot be liquefied there by pressure, while [[Ammonia|ammonia]] and carbon dioxide can be stored as liquids under their own vapour pressure in a steel cylinder at 20 °C.[^os-af-507] Water's own row is the top of the curve the microsim draws, some 260 °C past the table's last entry. ## Estimating vapor pressure from molecular structure When no measurement exists, a vapour pressure can be estimated from the normal boiling point alone. Trouton's rule states that the entropy of vaporization at the normal boiling point, `ΔS_vap = ΔH_vap/T_b`, is close to the same value, roughly 85–88 J·K⁻¹·mol⁻¹, for many liquids whose molecules do not associate.[^trouton1884] Given a boiling point, the rule supplies an enthalpy of vaporization, and the Clausius–Clapeyron relation then supplies the curve to the accuracy of a constant-ΔH fit. Water is the standard exception: `40,670/373.15 = 109 J·K⁻¹·mol⁻¹` (derived), well above the Trouton value, because the [[Hydrogen_bond|hydrogen bonds]] that order liquid water make its vaporization entropy unusually large.[^os-af-502] The underlying variable is the strength of the [[Intermolecular_force|intermolecular forces]]: the stronger the attraction between [[Molecule|molecules]], the lower the vapour pressure at a given temperature and the higher the boiling point, so polar and hydrogen-bonded liquids sit below nonpolar molecules of similar mass, and vapour pressure falls along a series of alkanes as the molecules lengthen and their [[London_dispersion_force|dispersion forces]] grow.[^blackstock-imf] Group-contribution methods turn that pattern into arithmetic by assigning each structural fragment a contribution to the boiling point or directly to log p; the estimation programs used in environmental screening, such as the United States Environmental Protection Agency's EPI Suite, predict this way how readily a new compound will enter the air.[^epa-episuite] ## Meaning in meteorology In meteorology the vapour pressure is the partial pressure of water vapour actually present in the air, written *e*, and the saturation vapour pressure *e_s(T)* is the equilibrium value from the curve above, the most the air can hold in the presence of liquid water at that temperature.[^ams-vp] Relative humidity is the ratio of the two, `RH = 100·e/e_s(T)`, and the dew point is the temperature to which the air must be cooled, at constant *e*, for *e* to become the saturation value, the temperature at which dew or fog begins to form.[^ams-dew] The table makes the definitions numerical. Air at 22 °C, where `e_s = 19.84 mmHg`, holding water vapour at 9.21 mmHg has a relative humidity of `100 × 9.21/19.84 = 46 %`, and because 9.21 mmHg is the saturation value at 10 °C its dew point is 10 °C (derived).[^averill-t104] Read this way the sim's slider is a dew-point calculator: every point on the curve is both a boiling temperature at that pressure and a dew point for that vapour pressure. The [[Atmosphere_of_Earth|atmosphere]] rarely reaches saturation, which is why evaporation continues; when air cools below its dew point at night the excess condenses, and the same curve sets how much water a warm air mass can carry and release as rain. ## See also - [[Clausius–Clapeyron_relation]] - [[Boiling_point]] - [[Evaporation]] - [[Raoult's_law]] - [[Phase_diagram]] - [[Triple_point]] - [[Critical_point_(thermodynamics)]] - [[Enthalpy_of_vaporization]] ## Notes The Portal Book tabulates water's vapour pressure in millimetres of mercury, and this article keeps that unit so the numbers can be checked against the table; 1 mmHg = 133.322 Pa and 760 mmHg = 101.325 kPa. Values marked "derived" were computed here from the book's table or constants and are not printed in the book. The reused microsim is registered under the Energy Center of Excellence; a registry row for this article is to be added. Source footnotes are under References. ## References [^averill-t104]: Averill, Bruce; Eldredge, Patricia (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", Table 10.4, pp. 933–934 (vapour pressure of water, 0–110 °C, in mmHg; boiling where the vapour pressure equals the external pressure). Portal Book 050. https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^os-af-503]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. §10.4 "Phase Diagrams", p. 503 (water boils at 100 °C at 1 atm; critical point 374 °C and 218 atm). Portal Book 051. https://openstax.org/details/books/chemistry-atoms-first-2e [^averill-baro]: Averill, Bruce; Eldredge, Patricia (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", pp. 884–889 (barometric pressure: Denver about 630 mmHg, p. 884; 454 mmHg at 14,000 ft, p. 888; Everest 0.308 atm = 234 mmHg, p. 889). Portal Book 050. [^averill-mano]: Averill, Bruce; Eldredge, Patricia (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", pp. 890–891 (manometer example: 0.200 atm as 152 mm Hg or 2.06 m of water; densities 13.53 and 0.9970 g/cm³). Portal Book 050. [^mitofsky-184]: Mitofsky, Andrea (2018). *Direct Energy*. Chapter 8, p. 184 (1 mmHg = 133.322 Pa). Portal Book 055. https://open.umn.edu/opentextbooks/textbooks/direct-energy [^averill-overwater]: Averill, Bruce; Eldredge, Patricia (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", pp. 933–935 (gas collected over water as a mixture, `P_gas = P_total − P_H₂O`; the correction uses the water's temperature; gases that dissolve in or react with water cannot be collected this way). Portal Book 050. [^antoine1888]: Antoine, Ch. (1888). "Tensions des vapeurs; nouvelle relation entre les tensions et les températures." *Comptes rendus hebdomadaires des séances de l'Académie des sciences* 107: 681–684, 778–780, 836–837. [^nist-webbook]: NIST Chemistry WebBook, SRD 69. Antoine equation parameters, with their temperature ranges, in each substance's phase-change data. National Institute of Standards and Technology. https://webbook.nist.gov/chemistry/ [^os-af-506]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. §10.4 "Phase Diagrams", pp. 506–507 (sealed water at 0.03 atm at 25 °C and 218 atm at 374 °C; table of critical temperatures and pressures: H₂ −240.0 °C/1300 kPa, N₂ −147.2/3400, O₂ −118.9/5000, CO₂ 31.1/7400, NH₃ 132.4/11,300, SO₂ 157.2/7800, H₂O 374.0/22,000). Portal Book 051. [^os-af-502]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 10, p. 502 (enthalpy of vaporization of water 40.67 kJ/mol). Portal Book 051. [^os-af-ch11]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 11, "Solutions and Colloids", §11.4 "Colligative Properties" (Raoult's law, vapour-pressure lowering, boiling-point elevation; page to pin). Portal Book 051. [^os-af-504]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. §10.4 "Phase Diagrams", p. 504 (ice vapour pressure 0.20 kPa at −10 °C; no liquid below the triple-point pressure; freeze-drying). Portal Book 051. [^os-af-505]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. §10.4 "Phase Diagrams", p. 505 (CO₂ phase diagram with a logarithmic pressure axis and a triple point above 1 atm; Example 10.11 check: water at 50 kPa boils at 78 °C). Portal Book 051. [^averill-airbag]: Averill, Bruce; Eldredge, Patricia (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", pp. 934–935 (Example 14: 5.00 g NaN₃ → 0.115 mol N₂ collected at 22 °C and 762 mmHg over water; P_H₂O = 19.84 mmHg; P_N₂ = 742 mmHg; V = 2.85 L). Portal Book 050. [^averill-zn]: Averill, Bruce; Eldredge, Patricia (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", pp. 935–936 (1.00 g Zn + HCl at 30 °C and 760 mmHg over water → 0.397 L H₂). Portal Book 050. [^mccabe-evap]: McCabe, Warren L.; Smith, Julian C.; Harriott, Peter. *Unit Operations of Chemical Engineering*. McGraw-Hill. Chapter "Evaporation" (boiling-point elevation and Dühring lines; the Dühring chart for aqueous sodium hydroxide). [^os-af-507]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. §10.4 "Phase Diagrams", pp. 507–508 (a gas above its critical temperature cannot be liquefied by pressure; CO₂ extinguisher contains liquid at 18 °C but not at 35 °C; NH₃ liquefiable at room temperature, O₂ not). Portal Book 051. [^trouton1884]: Trouton, Frederick (1884). "On molecular latent heat." *Philosophical Magazine*, Series 5, 18 (110): 54–57. [^blackstock-imf]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter "Intermolecular Forces and Liquids and Solids", pp. 363–381 (intermolecular forces and their effect on vapour pressure and boiling point; page to pin). Portal Book 054. https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry [^epa-episuite]: United States Environmental Protection Agency. "EPI Suite™ — Estimation Program Interface" (MPBPWIN module: boiling point, melting point and vapour pressure estimated from molecular structure). https://www.epa.gov/tsca-screening-tools/epi-suitetm-estimation-program-interface [^ams-vp]: American Meteorological Society. *Glossary of Meteorology*, entries "vapor pressure" and "saturation vapor pressure". https://glossary.ametsoc.org/ [^ams-dew]: American Meteorological Society. *Glossary of Meteorology*, entries "relative humidity" and "dew point". https://glossary.ametsoc.org/ ## External links - [Chemistry: Atoms First 2e](https://openstax.org/details/books/chemistry-atoms-first-2e), OpenStax — §10.4, the open text behind Portal Book 051 - [NIST Chemistry WebBook](https://webbook.nist.gov/chemistry/) — Antoine parameters and phase-change data by substance - [AMS Glossary of Meteorology](https://glossary.ametsoc.org/) — the meteorological definitions used above - For the pair's other external links, see the Wikipedia article's *External links* section. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Vapor_pressure.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Vapor pressure* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/Vapour_pressure_of_water.html" data-title="Vapor pressure"></div> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Vapor_pressure) : [Wikitube](https://en.wikitube.io/wiki/Vapor_pressure) · pinned revision [1361465036](https://en.wikipedia.org/w/index.php?oldid=1361465036) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K16 · sim live (reused Vapour_pressure_of_water.html; registry row for Vapor_pressure to add).*