Editing Partial pressure

{{short description|Pressure of a component gas in a mixture}}
[[File:Dalton's law of partial pressures.svg|thumb|upright=1.7|The [[atmospheric pressure]] is roughly equal to the sum of partial pressures of constituent gases – oxygen, nitrogen, [[argon]], [[water vapor]], carbon dioxide, etc.]]

In a mixture of [[gas]]es, each constituent gas has a '''partial pressure''' which is the notional [[pressure]] of that constituent gas as  if it alone occupied the entire [[volume]] of the original mixture at the same [[temperature]].<ref>{{cite book|author=Charles Henrickson|title=Chemistry|publisher=Cliffs Notes|year=2005|isbn=978-0-7645-7419-1|url-access=registration|url=https://archive.org/details/chemistry00henr}}</ref> The '''total pressure''' of an [[ideal gas]] mixture is the sum of the partial pressures of the gases in the mixture ([[Dalton's Law]]).

In [[respiratory physiology]], the partial pressure of a dissolved gas in liquid (such as oxygen in arterial blood) is also defined as the partial pressure of that gas as it would be undissolved in gas phase yet in equilibrium with the liquid.<ref>{{cite web | url=https://www.compadre.org/nexusph/course/Partial_pressure_-_liquids | title=Partial pressure - liquids - Nexus Wiki }}</ref><ref>{{cite journal | pmc=4666443 | date=2015 | last1=Collins | first1=J. A. | last2=Rudenski | first2=A. | last3=Gibson | first3=J. | last4=Howard | first4=L. | last5=O'Driscoll | first5=R. | title=Relating oxygen partial pressure, saturation and content: The haemoglobin–oxygen dissociation curve | journal=Breathe (Sheffield, England) | volume=11 | issue=3 | pages=194–201 | doi=10.1183/20734735.001415 | pmid=26632351 }}</ref> This concept is also known as [[blood gas tension]]. In this sense, the diffusion of a gas liquid is said to be driven by differences in partial pressure (not concentration). In [[chemistry]] and [[thermodynamics]], this concept is generalized to non-ideal gases and instead called [[fugacity]]. The partial pressure of a gas is a measure of its [[Thermodynamic activity|thermodynamic activity]]. Gases dissolve, diffuse, and react according to their partial pressures and not according to their [[Concentration|concentrations]] in a gas mixture or as a solute in solution.<ref>Collman, J. P.; Brauman, J. I.; Halbert, T. R.; Suslick, K. S. (1976). “[https://www.pnas.org/doi/abs/10.1073/pnas.73.10.3333 Nature of O2 and CO binding to metalloporphyrins and heme proteins”. ''Proceedings of the National Academy of Sciences'']. '''73''' (10): 3333-3337.</ref> This general property of gases is also true in chemical reactions of gases in biology.

==Symbol==
The symbol for pressure is usually {{math|''p''}} or {{math|''pp''}} which may use a subscript to identify the pressure, and gas species are also referred to by subscript. When combined, these subscripts are applied recursively.<ref name="Elsevier guide">{{cite web|last1=Staff|title=Symbols and Units|url=https://www.elsevier.com/__data/promis_misc/RESPNBsymbolsunits.pdf |archive-url=https://web.archive.org/web/20150723160454/http://www.elsevier.com/__data/promis_misc/RESPNBsymbolsunits.pdf |archive-date=2015-07-23 |url-status=live |website=Respiratory Physiology & Neurobiology : Guide for Authors|publisher=Elsevier|access-date=3 June 2017|page=1|quote=All symbols referring to gas species are in  subscript,}}</ref><ref>{{GoldBookRef |title=pressure,  ''p'' |file=P04819 }}</ref>

Examples:
*<math>P_1</math> or <math>p_1</math> = pressure at time 1
*<math chem>P_\ce{H2}</math> or <math chem>p_\ce{H2}</math> = partial pressure of hydrogen
*<math chem>P_{a_\ce{O2}}</math> or <math chem>p_{a_\ce{O2}}</math> or '''P<sub>a</sub>O<sub>2</sub>''' = arterial partial pressure of oxygen
*<math chem>P_{v_\ce{O2}}</math> or <math chem>p_{v_\ce{O2}}</math> or '''P<sub>v</sub>O<sub>2</sub>''' = venous partial pressure of oxygen

==Dalton's law of partial pressures==
{{main|Dalton's law}}
[[File:Schematic Depicting Dalton's Law-en.svg|thumb|Schematic showing the concept of Dalton's Law.]]
Dalton's law expresses the fact that the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the individual gases in the mixture.<ref>[http://www.chm.davidson.edu/vce/gaslaws/daltonslaw.html Dalton's Law of Partial Pressures]</ref> This equality arises from the fact that in an ideal gas, the molecules are so far apart that they do not interact with each other. Most actual real-world gases come very close to this ideal. For example, given an ideal gas mixture of [[nitrogen]] (N<sub>2</sub>), [[hydrogen]] (H<sub>2</sub>) and  [[ammonia]] (NH<sub>3</sub>):

<math chem display="block">p = p_\ce{N2} + p_\ce{H2} + p_\ce{NH3}</math>
where:
*<math>p </math> = total pressure of the gas mixture
*<math chem>p_\ce{N2}</math> = partial pressure of nitrogen (N<sub>2</sub>)
*<math chem>p_\ce{H2}</math> = partial pressure of hydrogen (H<sub>2</sub>)
*<math chem>p_\ce{NH3}</math> = partial pressure of ammonia (NH<sub>3</sub>)

==Ideal gas mixtures==
Ideally the ratio of partial pressures equals the ratio of the number of molecules. That is, the [[mole fraction]] <math>x_{\mathrm{i}}</math> of an individual gas component in an [[ideal gas]] [[mixture]] can be expressed in terms of the component's partial pressure or the [[mole (unit)|moles]] of the component:
<math display="block">x_{\mathrm{i}} = \frac{p_{\mathrm{i}}}{p} = \frac{n_{\mathrm{i}}}{n}</math>

and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression:
<math display="block">p_{\mathrm{i}} = x_{\mathrm{i}} \cdot p</math>

{| border="0" cellpadding="2"
|-
|align=right|where:
|&nbsp;
|-
!align=right|<math>x_{\mathrm{i}}</math>  
|align=left|= mole fraction of any individual gas component in a gas mixture
|-
!align=right|<math>p_{\mathrm{i}}</math>
|align=left|= partial pressure of any individual gas component in a gas mixture
|-
!align=right|<math>n_{\mathrm{i}}</math>
|align=left|= moles of any individual gas component in a gas mixture
|-
!align=right|<math>n</math>
|align=left|= total moles of the gas mixture
|-
!align=right|<math>p</math>
|align=left|= total pressure of the gas mixture
|}

The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.<ref>[http://antoine.frostburg.edu/chem/senese/101/gases/ Frostberg State University's "General Chemistry Online"]</ref>

The ratio of partial pressures relies on the following isotherm relation:
<math display="block">\frac{V_{\rm X}}{V_{\rm tot}} = \frac{p_{\rm X}}{p_{\rm tot}} = \frac{n_{\rm X}}{n_{\rm tot}}</math>
* ''V''<sub>X</sub> is the partial volume of any individual gas component (X)
* ''V''<sub>tot</sub> is the total volume of the gas mixture
* ''p''<sub>X</sub> is the '''partial pressure''' of gas X
* ''p''<sub>tot</sub> is the total pressure of the gas mixture 
* ''n''<sub>X</sub> is the [[amount of substance]] of gas (X)
* ''n''<sub>tot</sub> is the total amount of substance in gas mixture

==Partial volume (Amagat's law of additive volume)==
The partial volume of a particular gas in a mixture is the volume of one component of the gas mixture. It is useful in gas mixtures, e.g. air, to focus on one particular gas component, e.g. oxygen.

It can be approximated both from partial pressure and molar fraction:<ref name=biophysics200>Page 200 in: Medical biophysics. Flemming Cornelius. 6th Edition, 2008.</ref>
<math display="block">V_{\rm X} = V_{\rm tot} \times \frac{p_{\rm X}}{p_{\rm tot}} = V_{\rm tot} \times \frac{n_{\rm X}}{n_{\rm tot}}</math>
* ''V''<sub>X</sub> is the partial volume of an individual gas component X in the mixture
* ''V''<sub>tot</sub> is the total volume of the gas mixture
* ''p''<sub>X</sub> is the partial pressure of gas X
* ''p''<sub>tot</sub> is the total pressure of the gas mixture
* ''n''<sub>X</sub> is the [[amount of substance]] of gas X
* ''n''<sub>tot</sub> is the total amount of substance in the gas mixture

==Vapor pressure==
{{main|Vapor pressure}}
[[Image:vapor_pressure_chart.svg|thumb|right|A log-lin vapor pressure chart for various liquids]]

[[Vapor pressure]] is the pressure of a [[vapor]] in equilibrium with its non-vapor phases (i.e., liquid or solid). Most often the term is used to describe a [[liquid]]'s tendency to [[evaporate]].  It is a measure of the tendency of [[molecule]]s and [[atom]]s to escape from a liquid or a [[solid]]. A liquid's atmospheric pressure boiling point corresponds to the temperature at which its vapor pressure is equal to the surrounding atmospheric pressure and it is often called the [[normal boiling point]].

The higher the vapor pressure of a liquid at a given temperature, the lower the normal boiling point of the liquid.

The vapor pressure chart displayed has graphs of the vapor pressures versus temperatures for a variety of liquids.<ref>{{cite book |editor1-last=Perry |editor1-first=R.H. |editor2-last=Green |editor2-first=D.W. |title=Perry's Chemical Engineers' Handbook |edition=7th |publisher=McGraw-Hill |year=1997 |isbn= 978-0-07-049841-9 |title-link=Perry's Chemical Engineers' Handbook }}</ref> As can be seen in the chart, the liquids with the highest vapor pressures have the lowest normal boiling points.

For example, at any given temperature, [[methyl chloride]] has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point (−24.2&nbsp;°C), which is where the vapor pressure curve of methyl chloride (the blue line) intersects the horizontal pressure line of one atmosphere ([[Atmosphere (unit)|atm]]) of absolute vapor pressure. At higher altitudes, the atmospheric pressure is less than that at sea level, so boiling points of liquids are reduced. At the top of [[Mount Everest]], the atmospheric pressure is approximately 0.333&nbsp;atm, so by using the graph, the boiling point of [[diethyl ether]] would be approximately 7.5&nbsp;°C versus 34.6&nbsp;°C at sea level (1&nbsp;atm).

==Equilibrium constants of reactions involving gas mixtures==
It is possible to work out the [[equilibrium constant]] for a chemical reaction involving a mixture of gases given the partial pressure of each gas and the overall reaction formula. For a reversible reaction involving gas reactants and gas products, such as:
<chem display="block">{\mathit{a}A} + {\mathit{b}B} <=> {\mathit{c}C} + {\mathit{d}D}</chem>

the equilibrium constant of the reaction would be:
<math display="block">K_\mathrm{p} = \frac{p_C^c\, p_D^d} {p_A^a\, p_B^b}</math>

{| border="0" cellpadding="2"
|-
|align=right|where:
|&nbsp;
|-
!align=right|<math>K_p</math>
|align=left|= &nbsp;the equilibrium constant of the reaction
|-
!align=right|<math>a</math>  
|align=left|= &nbsp;coefficient of reactant <math>A</math>
|-
!align=right|<math>b</math>
|align=left|= &nbsp;coefficient of reactant <math>B</math>
|-
!align=right|<math>c</math>  
|align=left|= &nbsp;coefficient of product <math>C</math>
|-
!align=right|<math>d</math>
|align=left|= &nbsp;coefficient of product <math>D</math>
|-
!align=right|<math>p_C^c</math>
|align=left|= &nbsp;the partial pressure of <math>C</math> raised to the power of <math>c</math>
|-
!align=right|<math>p_D^d</math>
|align=left|= &nbsp;the partial pressure of <math>D</math> raised to the power of <math>d</math>
|-
!align=right|<math>p_A^a</math>
|align=left|= &nbsp;the partial pressure of <math>A</math> raised to the power of <math>a</math>
|-
!align=right|<math>p_B^b</math>
|align=left|= &nbsp;the partial pressure of <math>B</math> raised to the power of <math>b</math>
|}

For reversible reactions, changes in the total pressure, temperature or reactant concentrations will shift the [[Chemical equilibrium|equilibrium]] so as to favor either the right or left side of the reaction in accordance with [[Le Chatelier's Principle]]. However, the [[Chemical kinetics|reaction kinetics]] may either oppose or enhance the equilibrium shift. In some cases, the reaction kinetics may be the overriding factor to consider.

==Henry's law and the solubility of gases==
{{main|Henry's law}}

Gases will [[solvation|dissolve]] in [[liquid]]s to an extent that is determined by the equilibrium between the undissolved gas and the gas that has dissolved in the liquid (called the ''[[solvent]]'').<ref name=RolfeSander>[http://www.henrys-law.org An extensive list of Henry's law constants, and a conversion tool]</ref> The equilibrium constant for that equilibrium is:
{{NumBlk||<math display="block">k = \frac {p_x}{C_x}</math>|{{EquationRef|1}}}}
where:
*<math>k</math> = &nbsp;the equilibrium constant for the [[solvation]] process
*<math>p_x</math> = &nbsp;partial pressure of gas <math>x</math> in equilibrium with a [[Solution (chemistry)|solution]] containing some of the gas 
*<math>C_x</math> = &nbsp;the concentration of gas <math>x</math> in the liquid solution

The form of the equilibrium constant shows that '''the concentration of a [[solute]] gas in a solution is directly proportional to the partial pressure of that gas above the solution'''. This statement is known as [[Henry's law]] and the equilibrium constant <math>k</math> is quite often referred to as the Henry's law constant.<ref name=RolfeSander/><ref>{{cite journal |author1=Francis L. Smith  |author2=Allan H. Harvey  |name-list-style=amp |date=September 2007 |title=Avoid Common Pitfalls When Using Henry's Law |journal=Chemical Engineering Progress |issn=0360-7275}}</ref><ref>[http://dwb4.unl.edu/Chem/CHEM869J/CHEM869JLinks/www.chem.ualberta.ca/courses/plambeck/p101/p01182.htm Introductory University Chemistry, Henry's Law and the Solubility of Gases] {{webarchive|url=https://web.archive.org/web/20120504234140/http://dwb4.unl.edu/Chem/CHEM869J/CHEM869JLinks/www.chem.ualberta.ca/courses/plambeck/p101/p01182.htm |date=2012-05-04 }}</ref>

Henry's law is sometimes written as:<ref name=UArizona>{{Cite web |url=http://www.chem.arizona.edu/~salzmanr/103a004/nts004/l41/l41.html |title=University of Arizona chemistry class notes |access-date=2006-05-26 |archive-url=https://web.archive.org/web/20120307045555/http://www.chem.arizona.edu/~salzmanr/103a004/nts004/l41/l41.html |archive-date=2012-03-07 |url-status=dead }}</ref>
{{NumBlk||<math display="block">k' = \frac {C_x}{p_x}</math>|{{EquationRef|2}}}}

where <math>k'</math> is also referred to as the Henry's law constant.<ref name=UArizona/> As can be seen by comparing equations ({{EquationNote|1}}) and ({{EquationNote|2}}) above, <math>k'</math> is the reciprocal of <math>k</math>. Since both may be referred to as the Henry's law constant, readers of the technical literature must be quite careful to note which version of the Henry's law equation is being used.

Henry's law is an approximation that only applies for dilute, ideal solutions and for solutions where the liquid solvent does not [[chemical reaction|react chemically]] with the gas being dissolved.

==In diving breathing gases==
In [[underwater diving]] the physiological effects of individual component gases of [[breathing gas]]es are a function of partial pressure.<ref name="NOAA Diving Manual 1979" > {{cite book |title=NOAA Diving Manual, Diving for Science and Technology |author=NOAA Diving Program (U.S.) |edition=2nd |editor-first=James W. |editor-last=Miller |date=December 1979 |publisher=US Department of Commerce: National Oceanic and Atmospheric Administration, Office of Ocean Engineering |location=Silver Spring, Maryland |isbn= }}</ref>

Using diving terms, partial pressure is calculated as:
:'''partial pressure = (total absolute pressure) × (volume fraction of gas component)'''<ref name="NOAA Diving Manual 1979" />

For the component gas "i":
:'''p<sub>i</sub> = P × F<sub>i</sub>'''<ref name="NOAA Diving Manual 1979" />

For example, at {{convert|50|m|ft|0}} underwater, the total absolute pressure is {{convert|6|bar|kPa|abbr=on}} (i.e., 1 bar of [[atmospheric pressure]] + 5 bar of water pressure) and the partial pressures of the main components of [[Earth's atmosphere|air]], [[oxygen]] 21% by volume and [[nitrogen]] approximately 79% by volume are:
:'''pN<sub>2</sub>''' = 6 bar × 0.79 = 4.7 bar absolute
:'''pO<sub>2</sub>''' = 6 bar × 0.21 = 1.3 bar absolute

{| border="0" cellpadding="2"
|-
|align=right|where:
|&nbsp;
|-
!align=right|p<sub>i</sub>  
|align=left|= partial pressure of gas component i &nbsp;= <math>P_{\mathrm{i}}</math> in the terms used in this article
|-
!align=right|P
|align=left|= total pressure = <math>P</math> in the terms used in this article
|-
!align=right|F<sub>i</sub> 
|align=left|= volume fraction of gas component i &nbsp;= &nbsp;mole fraction, <math>x_{\mathrm{i}}</math>, in the terms used in this article
|-
!align=right|pN<sub>2</sub>
|align=left|= partial pressure of nitrogen&nbsp; = <math>P_\mathrm{N_2}</math> in the terms used in this article
|-
!align=right|pO<sub>2</sub> 
|align=left|= partial pressure of oxygen&nbsp; = <math>P_\mathrm{O_2}</math> in the terms used in this article
|}

The minimum safe lower limit for the partial pressures of oxygen in a breathing gas mixture for diving is {{convert|0.16|bar|kPa}}<!-- (The correct figure is <= 9.5 KPa or .095 bars. People living in Colorado have a partial pressure of oxygen of only 13.9 KPa. Working on a proper citation) This is recommendations for breathing gases for underwater diving, see section header. Please make sure your reference is relevant to this application. Divers are not usually acclimatised to high altitute, may have to exert themselves somewhat, and if they lose consciousness underwater they tend to drown.--> absolute. [[Hypoxia (medical)|Hypoxia]] and sudden unconsciousness can become a problem with an oxygen partial pressure of less than 0.16 bar absolute.<ref name="Sawatzky 2008">{{cite book |last=Sawatzky |first=David |editor-last=Mount |editor-first=Tom|editor2-last=Dituri |editor2-first=Joseph |title=Exploration and Mixed Gas Diving Encyclopedia |edition=1st |date=August 2008 |publisher=International Association of Nitrox Divers |location=Miami Shores, Florida |isbn=978-0-915539-10-9|pages=41–50|chapter=3: Oxygen and its affect on the diver }}</ref>   [[Oxygen toxicity]], involving convulsions, becomes a problem when oxygen partial pressure is too high.  The [[NOAA]] Diving Manual recommends a maximum single exposure of 45 minutes at 1.6 bar absolute, of 120 minutes at 1.5 bar absolute, of 150 minutes at 1.4 bar absolute, of 180 minutes at 1.3 bar absolute and of 210 minutes at 1.2 bar absolute. Oxygen toxicity becomes a risk when these oxygen partial pressures and exposures are exceeded. The partial pressure of oxygen also determines the [[maximum operating depth]] of a gas mixture.<ref name="NOAA Diving Manual 1979" />

[[Nitrogen narcosis|Narcosis]] is a problem when breathing gases at high pressure. Typically, the maximum total partial pressure of narcotic gases used when planning for [[technical diving]] may be around 4.5&nbsp;bar absolute, based on an [[equivalent narcotic depth]] of {{convert|35|m|ft}}.

The effect of a toxic contaminant such as [[carbon monoxide]] in breathing gas is also related to the partial pressure when breathed. A mixture which may be relatively safe at the surface could be dangerously toxic at the maximum depth of a dive, or a tolerable level of [[carbon dioxide]] in the breathing loop of a [[diving rebreather]] may become intolerable within seconds during descent when the partial pressure rapidly increases, and could lead to panic or incapacitation of the diver.<ref name="NOAA Diving Manual 1979" />

==In medicine==
The partial pressures of particularly oxygen (<math>p_\mathrm{O_2}</math>) and carbon dioxide (<math>p_\mathrm{CO_2}</math>) are important parameters in tests of [[arterial blood gas]]es, but can also be measured in, for example, [[cerebrospinal fluid]]. {{why?|date=October 2018}}

{| class="wikitable" width=700px
|+[[Reference range]]s for <math>p_\mathrm{O_2}</math> and <math>p_\mathrm{CO_2}</math>
!  !! Unit !! [[Arterial blood gas]] !! [[vein|Venous]] blood gas !! [[Cerebrospinal fluid]] !! Alveolar [[pulmonary gas pressures|pulmonary<br /> gas pressures]]
|- align="center"
|rowspan=2| [[oxygen partial pressure|<math>p_\mathrm{O_2}</math>]] || [[kPa]] || 11–13<ref name=mmHg/> || 4.0–5.3<ref name=mmHg/> || 5.3–5.9<ref name=mmHg/> || 14.2
|- align="center"
| [[mmHg]] || 75–100<ref name=southwest>[http://pathcuric1.swmed.edu/PathDemo/nrrt.htm Normal Reference Range Table] {{webarchive|url=https://web.archive.org/web/20111225185659/http://pathcuric1.swmed.edu/pathdemo/nrrt.htm |date=2011-12-25 }} from The University of Texas Southwestern Medical Center at Dallas. Used in Interactive Case Study Companion to Pathologic basis of disease.</ref> || 30–40<ref name=brookside>[http://www.brooksidepress.org/Products/OperationalMedicine/DATA/operationalmed/Lab/ABG_ArterialBloodGas.htm The Medical Education Division of the Brookside Associates--> ABG (Arterial Blood Gas)] Retrieved on Dec 6, 2009</ref> || 40–44<ref name=UBC/> || 107
|- align="center"
|rowspan=2| [[carbon dioxide partial pressure|<math>p_\mathrm{CO_2}</math>]] || kPa || 4.7–6.0<ref name=mmHg>Derived from mmHg values using 0.133322 kPa/mmHg</ref> || 5.5–6.8<ref name=mmHg/> || 5.9–6.7<ref name=mmHg/> || 4.8
|- align="center"
| mmHg || 35–45<ref name=southwest/> || 41–51<ref name=brookside/> || 44–50<ref name=UBC>[http://www.pathology.ubc.ca/path425/SystemicPathology/Neuropathology/CerebrospinalFluidCSFDrGPBondy.rtf Pathology 425 Cerebrospinal Fluid <nowiki>[</nowiki>CSF<nowiki>]</nowiki>] {{webarchive|url=https://web.archive.org/web/20120222145250/http://www.pathology.ubc.ca/path425/SystemicPathology/Neuropathology/CerebrospinalFluidCSFDrGPBondy.rtf |date=2012-02-22 }} at the Department of Pathology and Laboratory Medicine at the University of British Columbia. By G.P. Bondy. Retrieved November 2011</ref> || 36
|}

==See also==

*{{annotated link|Blood gas tension}}
*{{annotated link|Breathing gas}}
*{{annotated link|Henry's law}}
*{{annotated link|Ideal gas}}
**{{annotated link|Ideal gas law}}
*{{annotated link|Mole fraction}}
**{{annotated link|Mole (unit)}}
*{{annotated link|Vapor}}

==References==
{{Reflist}}

{{authority control}}

[[Category:Engineering thermodynamics]]
[[Category:Equilibrium chemistry]]
[[Category:Gas laws]]
[[Category:Gases]]
[[Category:Physical chemistry]]
[[Category:Pressure]]
[[Category:Underwater diving physics]]
[[Category:Distillation]]