View source for Self-ionization of water

{{short description|Autoprotolysis or exchange of a proton between two water molecules}}
[[File:Autoprotolyse eau.svg|thumb|upright=1.5]]
{{Acids and bases}}
The '''self-ionization of water''' (also '''autoionization of water''', '''autoprotolysis of water''', '''autodissociation of water''', or simply '''dissociation''' of water) is an [[ionization]] reaction in [[properties of water|pure water]] or in an [[aqueous solution]], in which a water molecule, H<sub>2</sub>O, [[deprotonation|deprotonates]] (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 a [[hydronium]] cation, H<sub>3</sub>O<sup>+</sup>. It is an example of [[autoprotolysis]], and exemplifies the [[amphoterism|amphoteric]] nature of water.

==History and notation==
The self-ionization of water was first proposed in 1884 by [[Svante Arrhenius]] as part of the theory of ionic dissociation which he proposed to explain the [[Conductivity (electrolytic)|conductivity]] of [[electrolyte]]s including water. Arrhenius wrote the self-ionization as <chem>H2O <=>  H+ + OH-</chem>. At that time, nothing was yet known of atomic structure or subatomic particles, so he had no reason to consider the formation of an <chem>H+</chem> ion from a hydrogen atom on electrolysis as any less likely than, say, the formation of a <chem>Na+</chem> ion from a sodium atom.

In 1923 [[Johannes Nicolaus Brønsted]] and [[Martin Lowry]] proposed that the self-ionization of water actually involves two water molecules: <chem>H2O + H2O <=>  H3O+ + OH-</chem>. By this time the electron and the nucleus had been discovered and [[Ernest Rutherford|Rutherford]] had shown that a nucleus is very much smaller than an atom. This would include a bare ion <chem>H+</chem> which would correspond to a proton with zero electrons. Brønsted and Lowry proposed that this ion does not exist free in solution, but always attaches itself to a water (or other solvent) molecule to form the [[hydronium]] ion <chem>H3O+</chem> (or other protonated solvent).

Later spectroscopic evidence has shown that many protons are actually hydrated by more than one water molecule. The most descriptive notation for the hydrated ion is <chem>H+(aq)</chem>, where aq (for aqueous) indicates an indefinite or variable number of water molecules. However the notations <chem>H+</chem> and <chem>H3O+</chem> are still also used extensively because of their historical importance. This article mostly represents the hydrated proton as <chem>H3O+</chem>, corresponding to hydration by a single water molecule.

==Equilibrium constant==
[[File:Autoionizacion-agua.gif|200px|right|thumb|Animation of the self-ionization of water]]
[[Ultrapure water|Chemically pure water]] has an [[electrical]] [[conductivity (electrolytic)|conductivity]] of 0.055&nbsp;μ[[Siemens (unit)|S]]/cm. According to the theories of [[Svante Arrhenius]], this must be [[Conductivity (electrolytic)|due to the presence of ions]]. The ions are produced by the water self-ionization reaction, which applies to pure water and any aqueous solution:

: H<sub>2</sub>O + H<sub>2</sub>O {{eqm}} H<sub>3</sub>O<sup>+</sup> + OH<sup>−</sup>

Expressed with [[Thermodynamic activity|chemical activities]] {{mvar|a}}, instead of concentrations, the thermodynamic [[equilibrium constant]] for the water ionization reaction is:
:<math>K_{\rm eq} = \frac{a_{\rm{H_3O^+}} \cdot a_{\rm{OH^-}}}{a_{\rm{H_2O}}^2}</math>

which is numerically equal to the more traditional thermodynamic equilibrium constant written as:
:<math>K_{\rm eq} = \frac{a_{\rm{H^+}} \cdot a_{\rm{OH^-}}}{a_{\rm{H_2O}}}</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">{{cite web|url=http://www.iapws.org/relguide/Ionization.pdf |title=Release on the Ionization Constant of H<sub>2</sub>O |publisher=The International Association for the Properties of Water and Steam |location=[[Lucerne]]|date=August 2007}}</ref>

Because most acid–base solutions are typically very dilute, the activity of water is generally approximated as being equal to unity, which allows the ionic product of water to be expressed as:<ref>{{GoldBookRef|file=A00532|title=autoprotolysis constant}}</ref>
:<math>K_{\rm eq} \approx a_{\rm{H_3O^+}} \cdot a_{\rm{OH^-}} </math>

In dilute aqueous solutions, the activities of solutes (dissolved species such as ions) are approximately equal to their concentrations. Thus, the ''ionization constant'', ''dissociation constant'', ''self-ionization constant'', ''water ion-product constant'' or ''ionic product'' of water, symbolized by ''K''<sub>w</sub>, may be given by:
:<math>K_{\rm w}=[{\rm{H_3O^+}}][{\rm{OH^-}}] </math>
where [H<sub>3</sub>O<sup>+</sup>] is the [[molarity]] ([[molar concentration]])<ref name="Stumm">{{cite book |first1=Werner |last1=Stumm |first2=James |last2=Morgan |title=Aquatic Chemistry. Chemical Equilibria and Rates in Natural Waters |edition=3rd |publisher=John Wiley & Sons, Inc. |year=1996 |isbn=9780471511847}}</ref> of [[Hydron (chemistry)|hydrogen cation]] or [[hydronium ion]], and [OH<sup>−</sup>] is the concentration of [[hydroxide]] ion. When the equilibrium constant is written as a product of concentrations (as opposed to activities) it is necessary to make corrections to the value of <math>K_{\rm w}</math> depending on [[ionic strength]] and other factors (see below).<ref>{{cite book|last1=Harned|first1=H. S. |last2=Owen |first2=B. B. |title=The Physical Chemistry of Electrolytic Solutions|url=https://archive.org/details/physicalchemistr0003harn|url-access=registration|edition=3rd|year=1958|publisher=Reinhold|location=New York|pages=[https://archive.org/details/physicalchemistr0003harn/page/635 635]}}</ref>

At 24.87&nbsp;°C and zero [[ionic strength]], ''K''<sub>w</sub> is equal to {{val|1.0|e=-14}}. Note that as with all equilibrium constants, the result is dimensionless because the concentration is in fact a concentration relative to the [[standard state]], which for H<sup>+</sup> and OH<sup>−</sup> are both defined to be 1 [[molality|molal]] (= 1 mol/kg) when molality is used or 1 [[molarity|molar]] (= 1 mol/L) when molar concentration is used. For many practical purposes, the molality (mol solute/kg water) and molar (mol solute/L solution) concentrations can be considered as nearly equal at ambient temperature and pressure if the solution density remains close to one (''i.e.'', sufficiently diluted solutions and negligible effect of temperature changes). The main advantage of the molal concentration unit (mol/kg water) is to result in stable and robust concentration values which are independent of the solution density and volume changes (density depending on the water salinity ([[ionic strength]]), temperature and pressure); therefore, [[molality]] is the preferred unit used in [[thermodynamics|thermodynamic calculations]] or in precise or less-usual conditions, e.g., for [[seawater]] with a density significantly different from that of pure water,<ref name="Stumm"/> or at elevated temperatures, like those prevailing in thermal power plants.

We can also define p''K''<sub>w</sub> <math>\equiv</math> −log<sub>10</sub>&nbsp;''K''<sub>w</sub> (which is approximately 14 at 25&nbsp;°C). This is analogous to the notations pH and p''K''<sub>a</sub> for an [[acid dissociation constant]], where the symbol p denotes a [[cologarithm]]. The logarithmic form of the equilibrium constant equation is p''K''<sub>w</sub>&nbsp;=&nbsp;pH&nbsp;+&nbsp;pOH.

==Dependence on temperature, pressure and ionic strength==
{|
|[[File:Temperature dependence water ionization.svg|thumb|350px|Temperature dependence of the water ionization constant at 25&nbsp;MPa]]
|[[File:Pressure dependence water ionization pKw on P.svg|thumb|300px|Pressure dependence of the water ionization constant at 25&nbsp;°C]]
|[[File:Kw vs I.png|thumb|300px|Variation of p''K''<sub>w</sub> with ionic strength of NaCl solutions at 25&nbsp;°C]]
|}
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 p''K''<sub>w</sub> decreases as temperature increases from the melting point of ice to a minimum at c.&nbsp;250&nbsp;°C, after which it increases up to the [[critical point (thermodynamics)|critical point]] of water c.&nbsp;374&nbsp;°C. It decreases with increasing pressure

{| class="wikitable" style="text-align: center;"
|+p''K''<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 = https://www.nist.gov/data/PDFfiles/jpcrd696.pdf |bibcode = 2006JPCRD..35...15B }}</ref>
|-
! Temperature
! Pressure<ref>0.1&nbsp;MPa for {{nowrap|''T'' < 100 °C}}. [[Vapor pressure of water|Saturation pressure]] for {{nowrap|''T'' > 100 °C}}.</ref>
! p''K''<sub>w</sub>
|-
|0&nbsp;°C
|0.10 MPa
|14.95
|-
|25&nbsp;°C
|0.10 MPa
|13.99
|-
|50&nbsp;°C
|0.10 MPa
|13.26
|-
|75&nbsp;°C
|0.10 MPa
|12.70
|-
|100&nbsp;°C
|0.10 MPa
|12.25
|-
|150&nbsp;°C
|0.47 MPa
|11.64
|-
|200&nbsp;°C
|1.5 MPa
|11.31
|-
|250&nbsp;°C
|4.0 MPa
|11.20
|-
|300&nbsp;°C
|8.7 MPa
|11.34
|-
|350&nbsp;°C
|17 MPa
|11.92
|}

With [[electrolyte]] solutions, the value of p''K''<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>, p''K''<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|url=https://archive.org/details/physicalchemistr0003harn|url-access=registration|edition=3rd|year=1958|publisher=Reinhold|location=New York|pages=[https://archive.org/details/physicalchemistr0003harn/page/634 634]–649, 752–754}}</ref>

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.

:{| class="wikitable" style="text-align:center"
|+Comparison of p''K''<sub>w</sub> values for liquid water, superheated steam, and supercritical water.<ref name="rel"/>
|-
!{{diagonal split header|Pressure|Temp.}} !! 350&nbsp;°C !! 400&nbsp;°C !! 450&nbsp;°C !! 500&nbsp;°C !! 600&nbsp;°C !! 800&nbsp;°C
|-
! scope="row" |0.1 MPa
||| 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" |17 MPa
|11.920 (liquid)<sup>a</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> [[compressed fluid|compressed or 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 due to the [[Equilibrium constant#Effect of isotopic substitution|equilibrium isotope effect]], a quantum mechanical effect attributed to oxygen forming a slightly stronger bond to [[deuterium]] because the larger mass of deuterium results in a lower [[zero-point energy]].

Expressed with activities ''a'', instead of concentrations, the thermodynamic equilibrium constant for the heavy water ionization reaction is:
:<math>K_{\rm eq} = \frac{a_{\rm{D_3O^+}} \cdot a_{\rm{OD^-}}}{a_{\rm{D_2O}}^2}</math>

Assuming the activity of the D<sub>2</sub>O to be 1, and assuming that the activities of the D<sub>3</sub>O<sup>+</sup> and OD<sup>−</sup> are closely approximated by their concentrations
:<math>K_{\rm w}=[{\rm{D_3O^+}}][{\rm{OD^-}}] </math>
The following table compares the values of p''K''<sub>w</sub> for H<sub>2</sub>O and D<sub>2</sub>O.<ref name=crc>{{cite book |editor-last=Lide|editor-first= D. R.|title=CRC Handbook of Chemistry and Physics |url=https://archive.org/details/handbookofchemis00crcp|url-access=registration|edition=70th  |publisher=Boca Raton (FL):CRC Press |year=1990|isbn= 978-0-8493-0471-2}}</ref>
:{| class="wikitable" style="text-align:center"
|+p''K''<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>DO<sup>+</sup>, HD<sub>2</sub>O<sup>+</sup>, HO<sup>−</sup>, DO<sup>−</sup>.

==Mechanism==
The [[reaction rate|rate of reaction]] for the ionization reaction
:2&nbsp;H<sub>2</sub>O → H<sub>3</sub>O<sup>+</sup> + OH<sup>−</sup>
depends on the [[activation energy]], Δ''E''<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 ''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 |last1= Geissler|first1= P. L.|last2= Dellago|first2= C.|author2-link=Christoph Dellago|last3=Chandler|first3= D.|last4=Hutter|first4= J.|last5=Parrinello|first5= 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 |citeseerx= 10.1.1.6.4964}}</ref> Random fluctuations in molecular motions occasionally (about once every 10 hours per water molecule<ref>{{cite journal |last1= Eigen|first1= M. |last2=De Maeyer|first2= L. |year = 1955|trans-title=Investigations on the kinetics of neutralization I |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&nbsp;[[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 book |last= Stillinger|first= F. H. |title= Advances in Chemical Physics |year = 1975 |journal = Adv. Chem. Phys. |volume = 31 |pages = 1–101 |doi = 10.1002/9780470143834.ch1 |chapter = Theory and Molecular Models for Water|isbn= 9780470143834 }}</ref><ref>{{cite journal |last= Rapaport|first= D. C. |year = 1983 |journal = [[Mol. Phys.]] |volume = 50 |pages = 1151–1162 |doi = 10.1080/00268978300102931 |title = Hydrogen bonds in water |issue = 5|bibcode = 1983MolPh..50.1151R }}</ref><ref>{{cite book |last1= Chen|first1= S.-H. |last2=Teixeira|first2= J. |year = 1986 |journal = Adv. Chem. Phys. |volume = 64 |pages = 1–45 |doi = 10.1002/9780470142882.ch1 |title = Structure and Dynamics of Low-Temperature Water as Studied by Scattering Techniques|series= Advances in Chemical Physics |isbn= 9780470142882 }}</ref>

The inverse recombination reaction
:H<sub>3</sub>O<sup>+</sup> + OH<sup>−</sup> → 2&nbsp;H<sub>2</sub>O
is among the fastest chemical reactions known, with a [[reaction rate constant]] of {{val|1.3|e=11|u=M<sup>−1</sup>&nbsp;s<sup>−1</sup>}} at room temperature. Such a rapid rate is characteristic of a [[diffusion-controlled reaction]], in which the rate is limited by the speed of molecular [[diffusion]].<ref>{{cite book|last1=Tinoco|first1= I.|last2= Sauer |first2=K. |last3=Wang |first3=J. C. |title=Physical Chemistry: Principles and Applications in Biological Sciences|url=https://archive.org/details/solutionsmanualp00tino|url-access=registration|edition=3rd |publisher=Prentice-Hall |date=1995| page=386|isbn= 978-0-13-435850-5}}</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 almost exactly {{val|1.00|e=-7|u=mol&nbsp;dm<sup>−3</sup>}} at 25&nbsp;°C and 0.1&nbsp;MPa. 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 {{sfrac|2}}p''K''<sub>w</sub>.

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 hydroxide ion. Water samples that are exposed to air will absorb some [[carbon dioxide]] to form carbonic acid (H<sub>2</sub>CO<sub>3</sub>) and the concentration of H<sub>3</sub>O<sup>+</sup> will increase due to the reaction H<sub>2</sub>CO<sub>3</sub> + H<sub>2</sub>O = HCO<sub>3</sub><sup>−</sup> + H<sub>3</sub>O<sup>+</sup>. 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. Thus these water samples will be slightly acidic.  If a pH of exactly 7.0 is required, it must be maintained with an appropriate [[buffer solution]].

==See also==
{{Portal|Water}}
*[[Acid–base reaction]]
*[[Chemical equilibrium]]
*[[Molecular autoionization]] (of various solvents)
*[[Standard hydrogen electrode]]

==References==
<references/>

==External links==
*[http://www.vias.org/genchem/acidbase_equ_12591_04.html General Chemistry]&nbsp;– Autoionization of Water

{{Chemical equilibria}}

{{DEFAULTSORT:Self-Ionization Of Water}}
[[Category:Ionization]]
[[Category:Water chemistry]]
[[Category:Equilibrium chemistry]]
[[Category:Acid–base chemistry|Water]]

[[de:Protolyse#Autoprotolyse]]