|
|
| (531 intermediate revisions by more than 100 users not shown) |
| Line 1: |
Line 1: |
| [[File:Autoprotolyse eau.svg|thumb|upright=1.5]]
| | This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users. |
| {{Acids and bases}}
| |
| The '''self-ionization of water''' (also '''autoionization of water''', and '''autodissociation of water''') is an [[ionization]] reaction in [[properties of water|pure water]] or an [[aqueous solution]], in which a water molecule, H<sub>2</sub>O, [[deprotonation|loses the nucleus of one of its hydrogen atoms]] to become a [[hydroxide]] ion, OH<sup>−</sup>. The [[hydron (chemistry)|hydrogen nucleus, H<sup>+</sup>]], immediately [[protonation|protonates]] another water molecule to form [[hydronium]], H<sub>3</sub>O<sup>+</sup>. It is an example of [[autoprotolysis]], and exemplifies the [[amphoteric]] nature of water.
| |
|
| |
|
| ==Equilibrium constant==
| | If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]] |
| Chemically pure water has an electrical [[Conductivity (electrolytic)|conductivity]] of 0.055 µ[[Siemens (unit)|S]]∙cm<sup>−1</sup>. According to the theories of [[Svante Arrhenius]], this must be [[ionic conductor|due to the presence of ions]]. The ions are produced by the self-ionization reaction
| | * Only registered users will be able to execute this rendering mode. |
| :H<sub>2</sub>O + H<sub>2</sub>O {{eqm}} H<sub>3</sub>O<sup>+</sup> + OH<sup>−</sup> | | * Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere. |
| This equilibrium applies to pure water and any aqueous solution.
| |
|
| |
|
| Approximating [[activity (chemistry)|activities]] by concentrations, the chemical [[equilibrium constant]], ''K''<sub>eq</sub>, for this reaction is given by:
| | Registered users will be able to choose between the following three rendering modes: |
| :<math>K_{\rm{eq}} = \frac{[{\rm{H_3O^+}}] [{\rm{OH^-}}]}{[{\rm{H_2O}}]^2}</math>
| |
| If the [[concentration (chemistry)|concentration]] of dissolved [[solution|solutes]] is low, the concentration [H<sub>2</sub>O] can be taken as being constant at c. 55.5M.<ref>McMurry, John. (2004) Organic Chemistry, p. 44</ref>
| |
|
| |
|
| Expressed with activities {{mvar|a}}, instead of concentrations, the thermodynamic equilibrium constant for the water ionization reaction is:
| | '''MathML''' |
| :<math>K_{\rm w} = \frac{a_{\rm{H_3O^+}} \cdot a_{\rm{OH^-}}}{a_{\rm{H_2O}}^2}</math> | | :<math forcemathmode="mathml">E=mc^2</math> |
|
| |
|
| which is numerically equal to the more traditional thermodynamic equilibrium constant written as:
| | <!--'''PNG''' (currently default in production) |
| :<math>K_{\rm w} = \frac{a_{\rm{H^+}} \cdot a_{\rm{OH^-}}}{a_{\rm{H_2O}}}</math> | | :<math forcemathmode="png">E=mc^2</math> |
|
| |
|
| under the assumption that the sum of the chemical potentials of H<sup>+</sup> and H<sub>3</sub>O<sup>+</sup> is formally equal to twice the chemical potential of H<sub>2</sub>O at the same temperature and pressure.<ref name="rel">[http://www.iapws.org/relguide/Ionization.pdf "Release on the Ionization Constant of H<sub>2</sub>O"] The International Association for the Properties of Water and Steam, Lucerne, Switzerland, August 2007.</ref>
| | '''source''' |
| | :<math forcemathmode="source">E=mc^2</math> --> |
|
| |
|
| In infinitely dilute aqueous solution, the activity of water solvent is unity.
| | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
|
| |
|
| The '''ionization constant''', '''dissociation constant''', '''self-ionization constant''', or '''ionic product''' of water, symbolized by ''K''<sub>w</sub> may be given by:
| | ==Demos== |
| :<math>K_{\rm w}=[{\rm{H_3O^+}}][{\rm{OH^-}}] = K_{\rm{eq}} \cdot [{\rm{H_2O}}]^2 </math>
| |
| where [H<sub>3</sub>O<sup>+</sup>] is the concentration of hydrogen or [[hydronium ion]], and [OH<sup>−</sup>] is the concentration of [[hydroxide]] ion.
| |
|
| |
|
| The ionic product of water can be also expressed on activity basis as:<ref>IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006–) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook. [http://goldbook.iupac.org/A00532.html Entry: autoprotolysis constant].</ref>
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
| :<math>K_{\rm w}=a_{\rm{H_3O^+}} \cdot a_{\rm{OH^-}} </math> | |
|
| |
|
| At 25 °C ''K''<sub>w</sub> is equal to {{val|1.0|e=-14}}.
| |
|
| |
|
| ==Dependence on temperature, pressure and ionic strength==
| | * accessibility: |
| {|
| | ** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]] |
| |[[Image:Temperature dependence water ionization.svg|thumb|240px|Temperature dependence of the water ionization constant at 25 MPa]] | | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)] |
| |[[Image:Pressure dependence water ionization pKw on P.svg|thumb|300px|Pressure dependence of the water ionization constant at 25 °C]] | | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)] |
| |[[File:Kw vs I.png|thumb|270px|Variation of pK<sub>w</sub> with ionic strength of NaCl solutions at 25 °C]]
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)] |
| |}
| | ** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]]. |
| The dependence of the water ionization on temperature and pressure has been investigated thoroughly.<ref>[http://www.iapws.org/ International Association for the Properties of Water and Steam (IAPWS)]</ref> The value of pK<sub>w</sub> decreases as temperature increases from the melting point of ice to a minimum at c. 250 °C, after which it increases up to the [[critical point (thermodynamics)|critical point]] of water c. 374 °C. It decreases with increasing pressure.
| | ** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]]. |
| | ** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode. |
|
| |
|
| {| class="wikitable" style="text-align: center;"
| | ==Test pages == |
| |+pK<sub>w</sub> values for liquid water.<ref>{{cite journal | last1 = Bandura | first1 = Andrei V. | last2 = Lvov | first2 = Serguei N. | year = 2006 | title = The Ionization Constant of Water over Wide Ranges of Temperature and Density | journal = Journal of Physical and Chemical Reference Data | volume = 35 | issue = 1 | pages = 15–30 | doi = 10.1063/1.1928231 | url = http://www.nist.gov/data/PDFfiles/jpcrd696.pdf }}</ref>
| |
| |-
| |
| ! Temperature
| |
| ! Pressure<ref>0.1 MPa for T < 100°C. [[Vapor pressure of water|Saturation pressure]] for T ≥ 100°C.</ref>
| |
| ! pK<sub>w</sub>
| |
| |-
| |
| |0°C
| |
| |0.10 MPa
| |
| |14.95
| |
| |-
| |
| |25°C
| |
| |0.10 MPa
| |
| |13.99
| |
| |-
| |
| |50°C
| |
| |0.10 MPa
| |
| |13.26
| |
| |-
| |
| |75°C
| |
| |0.10 MPa
| |
| |12.70
| |
| |-
| |
| |100°C
| |
| |0.10 MPa
| |
| |12.25
| |
| |-
| |
| |150°C
| |
| |0.47 MPa
| |
| |11.64
| |
| |-
| |
| |200°C
| |
| |1.5 MPa
| |
| |11.31
| |
| |-
| |
| |250°C
| |
| |4.0 MPa
| |
| |11.20
| |
| |-
| |
| |300°C
| |
| |8.7 MPa
| |
| |11.34
| |
| |-
| |
| |350°C
| |
| |17 MPa
| |
| |11.92
| |
| |}
| |
|
| |
|
| With [[electrolyte]] solutions, the value of pK<sub>w</sub> is dependent on [[ionic strength]] of the electrolyte. Values for [[sodium chloride]] are typical for a 1:1 electrolyte. With 1:2 electrolytes, MX<sub>2</sub>, pK<sub>w</sub> decreases with increasing ionic strength.<ref>{{cite book|last1=Harned|first1=H.S. |last2=Owen, |first2=B.B. |title=The Physical Chemistry of Electrolytic Solutions|edition=£rd.|year=1958|publisher=Reinhold Publishing Corp., |location=New York|pages=634–649, 752–754}}</ref>
| | To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages: |
| | *[[Displaystyle]] |
| | *[[MathAxisAlignment]] |
| | *[[Styling]] |
| | *[[Linebreaking]] |
| | *[[Unique Ids]] |
| | *[[Help:Formula]] |
|
| |
|
| The value of ''K''<sub>w</sub> is usually of interest in the [[liquid phase]]. Example values for [[superheated steam]] (gas) and [[supercritical water]] fluid are given in the table.
| | *[[Inputtypes|Inputtypes (private Wikis only)]] |
| | | *[[Url2Image|Url2Image (private Wikis only)]] |
| :{| class="wikitable" style="text-align:center"
| | ==Bug reporting== |
| |+Comparison of pK<sub>w</sub> values for liquid water, superheated steam, and supercritical water.<ref name="rel"/>
| | If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de . |
| |-
| |
| ! scope="row" |T/°C
| |
| | 350 || 400 || 450 || 500 || 600 || 800
| |
| |-
| |
| ! scope="row" |0.1 MPa
| |
| |11.920 (liquid)<sup>a</sup> || 47.961<sup>b</sup> || 47.873<sup>b</sup> || 47.638 <sup>b</sup> || 46.384 <sup>b</sup> ||40.785 <sup>b</sup>
| |
| |-
| |
| ! scope="row" |25 MPa
| |
| |11.551 (liquid)<sup>c</sup> ||16.566||18.135||18.758||19.425||20.113 | |
| |-
| |
| ! scope="row" |100 MPa
| |
| |10.600 (liquid)<sup>c</sup> ||10.744||11.005||11.381||12.296||13.544
| |
| |-
| |
| ! scope="row" |1000 MPa
| |
| |8.311 (liquid)<sup>c</sup> ||8.178||8.084||8.019||7.952||7.957
| |
| |}
| |
| ''Notes to the Table. The values are for supercritical fluid except those marked: <sup>a</sup> at saturation pressure corresponding to 350 °C. <sup>b</sup> superheated steam. <sup>c</sup> subcooled liquid.''
| |
| | |
| ==Isotope effects==
| |
| [[Heavy water]], D<sub>2</sub>O, self-ionizes less than normal water, H<sub>2</sub>O;
| |
| :D<sub>2</sub>O + D<sub>2</sub>O {{eqm}} D<sub>3</sub>O<sup>+</sup> + OD<sup>−</sup>
| |
| This is attributed to oxygen forming a slightly stronger bond to [[deuterium]] because the larger mass of deuterium difference results in a lower [[zero-point energy]], a quantum mechanical effect.
| |
| | |
| The dissociation constant and the ionic product of heavy water is given by:
| |
| :<math>K_{\rm{eq}} = \frac{[{\rm{D_3O^+}}] [{\rm{OD^-}}]}{[{\rm{D_2O}}]^2}</math>
| |
| :<math>K_{\rm w}=[{\rm{D_3O^+}}][{\rm{OD^-}}] = K_{\rm{eq}} \times [{\rm{D_2O}}]^2 </math>
| |
| The following table compares the values of pK<sub>w</sub> for H<sub>2</sub>O and D<sub>2</sub>O.<ref name=crc>{{cite book | author=Lide, D. R. (Ed.) | title=CRC Handbook of Chemistry and Physics (70th Edn.) | publisher=Boca Raton (FL):CRC Press | year=1990}}</ref>
| |
| :{| class="wikitable" style="text-align:center"
| |
| |+pK<sub>w</sub> values for pure water
| |
| |-
| |
| ! scope="row" |T/°C
| |
| |10||20|| 25||30|| 40 || 50
| |
| |-
| |
| ! scope="row" |H<sub>2</sub>O
| |
| |14.535 || 14.167|| 13.997|| 13.830|| 13.535 ||13.262
| |
| |-
| |
| ! scope="row" |D<sub>2</sub>O
| |
| |15.439||15.049||14.869||14.699||14.385|| 14.103
| |
| |}
| |
| | |
| ===Ionization equilibria in water - heavy water mixtures===
| |
| In water - heavy water mixtures equilibria several species are involved:H<sub>2</sub>O, HDO, D<sub>2</sub>O, H<sub>3</sub>O<sup>+</sup>, D<sub>3</sub>O<sup>+</sup>, H<sub>2</sub>D</sub>O<sup>+</sup>, HD<sub>2</sub>O<sup>+</sup>, HO<sup>-</sup>, DO<sup>-</sup>.
| |
| | |
| ==Mechanism==
| |
| | |
| The [[reaction rate|rate of reaction]] for the dissociation
| |
| : H<sub>2</sub>O → H<sup>+</sup> + OH<sup>−</sup> | |
| depends on the [[activation energy]], ΔE<sup>‡</sup>. According to the [[Boltzmann distribution]] the proportion of water molecules that have sufficient energy, due to thermal population, is given by
| |
| | |
| :<math>\frac{N}{N_0} = e^{-\frac{\Delta E^\ddagger}{kT}}</math>
| |
| where {{mvar|k}} is the [[Boltzmann constant]]. Thus some dissociation can occur because sufficient thermal energy is available. The following sequence of events has been proposed on the basis of [[electric field]] fluctuations in liquid water.<ref>{{cite journal | author = Geissler, P. L.; Dellago, C.; Chandler, D.; Hutter, J.; Parrinello, M. | year = 2001 | title = Autoionization in liquid water | journal = [[Science (journal)|Science]] | volume = 291 | pages = 2121–2124 | doi = 10.1126/science.1056991 | pmid = 11251111 | issue = 5511|bibcode = 2001Sci...291.2121G }}</ref> Random fluctuations in molecular motions occasionally (about once every 10 hours per water molecule<ref>{{cite journal | author = Eigen, M.; de Maeyer, L. | year = 1955 | title = Untersuchungen über die Kinetik der Neutralisation I | journal = Z. Elektrochem. | volume = 59 | pages = 986}}</ref>) produce an electric field strong enough to break an oxygen–hydrogen [[covalent bond|bond]], resulting in a hydroxide (OH<sup>−</sup>) and hydronium ion (H<sub>3</sub>O<sup>+</sup>); the hydrogen nucleus of the hydronium ion travels along water molecules by the [[Grotthuss mechanism]] and a change in the [[hydrogen bond]] network in the solvent isolates the two ions, which are stabilized by solvation. Within 1 [[picosecond]], however, a second reorganization of the hydrogen bond network allows rapid proton transfer down the electric potential difference and subsequent recombination of the ions. This timescale is consistent with the time it takes for hydrogen bonds to reorientate themselves in water.<ref>{{cite journal | author = Stillinger, F. H. | year = 1975 | journal = Adv. Chem. Phys. | volume = 31 | pages = 1 | doi = 10.1002/9780470143834.ch1 | title = Theory and Molecular Models for Water}}</ref><ref>{{cite journal | author = Rapaport, D. C. | year = 1983 | journal = [[Mol. Phys.]] | volume = 50 | pages = 1151 | doi = 10.1080/00268978300102931 | title = Hydrogen bonds in water | issue = 5|bibcode = 1983MolPh..50.1151R }}</ref><ref>{{cite journal | author = Chen, S.-H. & Teixeira, J. | year = 1986 | journal = Adv. Chem. Phys | volume = 64 | pages = 1 | doi = 10.1002/9780470142882.ch1 | title = Structure and Dynamics of Low-Temperature Water as Studied by Scattering Techniques}}</ref>
| |
| | |
| == Relationship with the neutral point of water ==
| |
| Water molecules dissociate into equal amounts of H<sub>3</sub>O<sup>+</sup> and OH<sup>−</sup>, so their concentrations are equal to {{val|1.00|e=-7|u=mol∙dm<sup>−3</sup>}} at 25 °C. A solution in which the H<sub>3</sub>O<sup>+</sup> and OH<sup>−</sup> concentrations equal each other is considered a '''neutral''' solution. In general, the pH of the neutral point is numerically equal to pK<sub>w</sub>/2.
| |
| | |
| Pure water is neutral, but most water samples contain impurities. If an impurity is an [[acid]] or [[base (chemistry)|base]] this will affect the concentrations of hydronium ion and hydoxide ion. Water samples which are exposed to air will absorb the acid [[carbon dioxide]] and the concentration of H<sub>3</sub>O<sup>+</sup> will increase. The concentration of OH<sup>−</sup> will decrease in such a way that the product [H<sub>3</sub>O<sup>+</sup>][OH<sup>−</sup>] remains constant for fixed temperature and pressure.
| |
| | |
| ==See also==
| |
| {{Portal|Water}}
| |
| *[[Chemical equilibrium]]
| |
| *[[Acid–base reaction]]
| |
| *[[Standard hydrogen electrode]]
| |
| | |
| ==References==
| |
| <references/>
| |
| | |
| ==External links==
| |
| * [http://www.vias.org/genchem/acidbase_equ_12591_04.html General Chemistry] – Autoionization of Water
| |
| | |
| {{Chemical equilibria}}
| |
| | |
| {{DEFAULTSORT:Self-Ionization Of Water}}
| |
| [[Category:Water chemistry]]
| |
| [[Category:Equilibrium chemistry]]
| |
| [[Category:Acid-base chemistry|Water]]
| |
| | |
| [[de:Protolyse#Autoprotolyse]]
| |
