|
|
| Line 1: |
Line 1: |
| In a mixture of [[gas]]es, each gas has a '''partial pressure''' which is the hypothetical [[pressure]] of that gas if it alone occupied the [[volume]] of the mixture at the same [[temperature]].<ref>{{cite book|author=Charles Henrickson|title=Chemistry|edition=|publisher=Cliffs Notes|year=2005|isbn=0-7645-7419-1}}</ref> The total pressure of an [[ideal gas]] mixture is the sum of the partial pressures of each individual gas in the mixture.
| | Hello! <br>I'm Japanese male :D. <br>I really like Petal collecting and pressing!<br><br>Also visit my web page ... [http://www.amazon.com/Marathon-Classic-Silver-Crystal-Bracelet/dp/B00JLM1RXW/ marathon bracelet] |
| | |
| It relies on the following isotherm relation:
| |
| :<math>V_x \times p_{tot} = V_{tot} \times p_x</math>
| |
| :* ''V<sub>x</sub>'' is the partial volume of any individual gas component (X)
| |
| :* ''V<sub>tot</sub>'' is the total volume in gas mixture
| |
| :* ''p<sub>x</sub>'' is the partial pressure of gas X
| |
| :* ''p<sub>tot</sub>'' is the total pressure of gas mixture
| |
| :* ''n<sub>x</sub>'' is the [[amount of substance]] of a gas (X)
| |
| :* ''n<sub>tot</sub>'' is the total amount of substance in gas mixture
| |
| | |
| The partial pressure of a gas is a measure of thermodynamic activity of the gas's [[molecule]]s. Gases dissolve, diffuse, and react according to their partial pressures, and not according to their [[concentration]]s in gas mixtures or liquids.
| |
| | |
| This general property of gases is also true of chemical reactions of gases in biology. For example, the necessary amount of oxygen for human respiration, and the amount that is toxic, is set by the partial pressure of oxygen alone. This is true across a very wide range of different concentrations of oxygen present in various inhaled breathing gases, or dissolved in blood.
| |
| | |
| ==Dalton's law of partial pressures==
| |
| {{main|Dalton's law}}
| |
| | |
| 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 as stated by [[Dalton's law]].<ref>[http://www.chm.davidson.edu/vce/gaslaws/daltonslaw.html Dalton's Law of Partial Pressures]</ref> This is because ideal gas molecules are so far apart that they don't 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>p = p_{{\mathrm{N}}_2} + p_{{\mathrm{H}}_2} + p_{{\mathrm{NH}}_3}</math>
| |
| | |
| {| border="0" cellpadding="2"
| |
| |-
| |
| |align=right|where:
| |
| |
| |
| |-
| |
| !align=right|<math>p \,</math> | |
| |align=left|= total pressure of the gas mixture
| |
| |-
| |
| !align=right|<math>p_{{\mathrm{N}}_2}</math>
| |
| |align=left|= partial pressure of nitrogen (N<sub>2</sub>)
| |
| |-
| |
| !align=right|<math>p_{{\mathrm{H}}_2}</math>
| |
| |align=left|= partial pressure of hydrogen (H<sub>2</sub>)
| |
| |-
| |
| !align=right|<math>p_{{\mathrm{NH}}_3}</math>
| |
| |align=left|= 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]] 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>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>p_{\mathrm{i}} = x_{\mathrm{i}} \cdot p</math>
| |
| | |
| {| border="0" cellpadding="2"
| |
| |-
| |
| |align=right|where:
| |
| |
| |
| |-
| |
| !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>
| |
| | |
| ==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>V_x = V_{tot} \times \frac{p_x}{p_{tot}} = V_{tot} \times \frac{n_x}{n_{tot}}</math>
| |
| :* ''V<sub>x</sub>'' is the partial volume of any individual gas component (X)
| |
| :* ''V<sub>tot</sub>'' is the total volume in gas mixture
| |
| :* ''p<sub>x</sub>'' is the partial pressure of gas X
| |
| :* ''p<sub>tot</sub>'' is the total pressure of gas mixture
| |
| :* ''n<sub>x</sub>'' is the [[amount of substance]] of a gas (X)
| |
| :* ''n<sub>tot</sub>'' is the total amount of substance in gas mixture
| |
| | |
| ==Vapour pressure==
| |
| {{main|Vapor pressure}}
| |
| [[Image:Vapor Pressure Chart.png|thumb|right|301 px|A typical vapour pressure chart for various liquids]]
| |
| | |
| [[Vapour 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 vapour 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 vapour pressure chart to the right has graphs of the vapor pressures versus temperatures for a variety of liquids.<ref>{{cite book|author=Perry, R.H. and Green, D.W. (Editors)|title=[[Perry's Chemical Engineers' Handbook]]|edition=7th|publisher=McGraw-Hill|year=1997|isbn= 0-07-049841-5}}</ref> As can be seen in the chart, the liquids with the highest vapour pressures have the lowest normal boiling points.
| |
| | |
| For example, at any given temperature, [[methyl chloride]] has the highest vapour pressure of any of the liquids in the chart. It also has the lowest normal boiling point (-24.2 °C), which is where the vapour pressure curve of methyl chloride (the blue line) intersects the horizontal pressure line of one atmosphere ([[Atmosphere (unit)|atm]]) of absolute vapour pressure.
| |
| | |
| ==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:
| |
| :<math>a\,A + b\,B \leftrightarrow c\,C + d\,D</math>
| |
| | |
| the equilibrium constant of the reaction would be:
| |
| :<math>K_p = \frac{p_C^c\, p_D^d} {p_A^a\, p_B^b}</math>
| |
| | |
| {| border="0" cellpadding="2"
| |
| |-
| |
| |align=right|where:
| |
| |
| |
| |-
| |
| !align=right|<math>K_p</math> | |
| |align=left|= the equilibrium constant of the reaction
| |
| |-
| |
| !align=right|<math>a</math>
| |
| |align=left|= coefficient of reactant <math>A</math>
| |
| |-
| |
| !align=right|<math>b</math>
| |
| |align=left|= coefficient of reactant <math>B</math>
| |
| |-
| |
| !align=right|<math>c</math>
| |
| |align=left|= coefficient of product <math>C</math>
| |
| |-
| |
| !align=right|<math>d</math>
| |
| |align=left|= coefficient of product <math>D</math>
| |
| |-
| |
| !align=right|<math>p_C^c</math>
| |
| |align=left|= the partial pressure of <math>C</math> raised to the power of <math>c</math>
| |
| |-
| |
| !align=right|<math>p_D^d</math>
| |
| |align=left|= the partial pressure of <math>D</math> raised to the power of <math>d</math>
| |
| |-
| |
| !align=right|<math>p_A^a</math>
| |
| |align=left|= the partial pressure of <math>A</math> raised to the power of <math>a</math>
| |
| |-
| |
| !align=right|<math>p_B^b</math>
| |
| |align=left|= 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 over-riding 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:
| |
| | |
| :(1) <math>k = \frac {p_x}{C_x}</math>
| |
| | |
| :{| border="0" cellpadding="2"
| |
| |-
| |
| |align=right|where:
| |
| |
| |
| |-
| |
| !align=right|<math>k</math>
| |
| |align=left|= the equilibrium constant for the [[solvation]] process
| |
| |-
| |
| !align=right|<math>p_x</math>
| |
| |align=left|= partial pressure of gas <math>x</math> in equilibrium with a [[solution]] containing some of the gas
| |
| |-
| |
| !align=right|<math>C_x</math>
| |
| |align=left|= the concentration of gas <math>x</math> in the liquid solution
| |
| |}
| |
| | |
| The form of the equilibrium constant shows that '''the concentration of a [[solution|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|author=Francis L. Smith and Allan H. Harvey |date=September 2007 |title=Avoid Common Pitfalls When Using Henry's Law |journal=CEP (Chemical Engineering Progress) |volume= |issue= |pages= |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]</ref>
| |
| | |
| Henry's Law is sometimes written as:<ref name=UArizona>[http://www.chem.arizona.edu/~salzmanr/103a004/nts004/l41/l41.html University of Arizona chemistry class notes]</ref>
| |
| :(2) <math>k' = \frac {C_x}{p_x}</math>
| |
| | |
| where <math>k'</math> is also referred to as the Henry's Law constant.<ref name=UArizona/> As can be seen by comparing equations (1) and (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.
| |
| | |
| ==Partial pressure in diving breathing gases==
| |
| In [[recreational diving]] and [[professional diving]] the richness of individual component gases of [[breathing gas]]es is expressed by partial pressure.
| |
| | |
| Using diving terms, partial pressure is calculated as:
| |
| :'''partial pressure = (total absolute pressure) × (volume fraction of gas component)'''
| |
| | |
| For the component gas "i":
| |
| :'''ppi = P × Fi'''
| |
| | |
| For example, at 50 metres (165 feet), the total absolute pressure is 6 bar (600 kPa) (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]] 79% by volume are:
| |
| :'''ppN2''' = 6 bar × 0.79 = 4.7 bar absolute
| |
| :'''ppO2''' = 6 bar × 0.21 = 1.3 bar absolute
| |
| | |
| {| border="0" cellpadding="2"
| |
| |-
| |
| |align=right|where:
| |
| |
| |
| |-
| |
| !align=right|ppi
| |
| |align=left|= partial pressure of gas component i = <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|Fi
| |
| |align=left|= volume fraction of gas component i = mole fraction, <math>x_{\mathrm{i}}</math>, in the terms used in this article
| |
| |-
| |
| !align=right|ppN2
| |
| |align=left|= partial pressure of nitrogen = <math>P_{{\mathrm{N}}_2}</math> in the terms used in this article
| |
| |-
| |
| !align=right|ppO2
| |
| |align=left|= partial pressure of oxygen = <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 gas mixture is 0.16 bar (16 kPa) absolute. [[Hypoxia (medical)|Hypoxia]] and sudden unconsciousness becomes a problem with an oxygen partial pressure of less than 0.16 bar absolute. [[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 determines the [[maximum operating depth]] of a gas mixture.
| |
| | |
| [[Nitrogen 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]] is 4.5 bar absolute, based on an [[equivalent narcotic depth]] of {{convert|35|m|ft}}.
| |
| | |
| ==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]].
| |
| | |
| {| 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] 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>] at the Department of Pathology and Laboratory Medicine at the University of British Columbia. By Dr. G.P. Bondy. Retrieved November 2011</ref> || 36
| |
| |}
| |
| | |
| ==See also==
| |
| {{portal|Underwater diving}}
| |
| *[[Breathing gas]]
| |
| *[[Henry's law]]
| |
| *[[Ideal gas]] and [[Ideal gas law]]
| |
| *[[Mole fraction]] and [[Mole (unit)]]
| |
| *[[Vapor]]
| |
| | |
| ==References==
| |
| {{Reflist}}
| |
| | |
| {{Diving medicine, physiology and physics}}
| |
| | |
| [[Category:Chemical engineering]]
| |
| [[Category:Equilibrium chemistry]]
| |
| [[Category:Gas laws]]
| |
| [[Category:Gases]]
| |
| [[Category:Physical chemistry]]
| |
| [[Category:Pressure]]
| |
| [[Category:Underwater diving physics]]
| |