Girsanov theorem: Difference between revisions

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== 「私の右手は、ああ、私の右手は終わった ==
[[File:Autoprotolyse eau.svg|thumb|upright=1.5]]
{{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.


唖然と愚かな、そして継続的な悲鳴はもちろん休暇のタスク、秦ゆうを完了するために、秦Yuの身長がなくなって、二度鳴った。<br><br>「私の右手は、ああ、私の右手は終わった [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_3.php クリスチャンルブタン 値段]。「ゴースト炎片手だけ彼の手で、ホラーが住んでいた [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_3.php クリスチャンルブタン 店舗]<br>秦ゆうはあまりにも速く<br>、彼は太っ頭、そして脂肪の頭を取ったことを、驚くべき速さで、後に彼の唯一の手を切断し、手のナイフ上のわずかな抵抗を持っている心の中のナイフの切断手に指示しませんでした彼らは離れて浮いた [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_3.php クリスチャンルブタン 靴]。<br>最初から最後まで<br>がつかん [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_13.php クリスチャンルブタン サンダル]。<br><br>'次のレベルに完全に、第二のブロック後の強度スカイチャートの成功を練習し、案の定。一緒にダークの腕章、ダークレギンスと、この黒い金のベスト、スピード、推定最大生得ゾクチェンマスターオフと自信を持って笑顔で私はほとんど右。 [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_1.php クリスチャンルブタン 靴 メンズ] '秦ゆう顔。<br>バベル、秦Yuの物理防御力が戻ってブラックマネーに追いついた秦ゆう電力サージ、体が変換され、本体のみの強力な一般的なダークの武器の程度に実際に傷つけない、第二のブロック図を練習<br>
==Equilibrium constant==
相关的主题文章:
Chemically pure water has an electrical [[Conductivity (electrolytic)|conductivity]] of 0.055&nbsp;&micro;[[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
<ul>
:H<sub>2</sub>O + H<sub>2</sub>O {{eqm}} H<sub>3</sub>O<sup>+</sup> + OH<sup></sup>
 
This equilibrium applies to pure water and any aqueous solution.
  <li>[http://api.open.tenunion.com/forum.php?mod=viewthread&tid=884458 http://api.open.tenunion.com/forum.php?mod=viewthread&tid=884458]</li>
 
  <li>[http://www.aikis.or.jp/~masako-t/main/secret/cgi-bin/yybbs.cgi http://www.aikis.or.jp/~masako-t/main/secret/cgi-bin/yybbs.cgi]</li>
 
  <li>[http://www5a.biglobe.ne.jp/~kohei_y/cgi-bin/aska.cgi http://www5a.biglobe.ne.jp/~kohei_y/cgi-bin/aska.cgi]</li>
 
</ul>


== その呼吸の音には色あせた ==
Approximating [[activity (chemistry)|activities]] by concentrations, the chemical [[equilibrium constant]], ''K''<sub>eq</sub>, for this reaction is given by:
:<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>


。その呼吸の音には色あせた。天と地、雷の雲が完全に強盗に吸収される間に、強盗雲が突然フラッターようになった [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_4.php クリスチャンルブタン 店舗]。<br><br>'ブーム!'<br><br>速度は、制限速度は恐怖未満である。<br>雷、トリックのための腕の厚さのような濃い紫色に腕の太さを<br>、それは非常に微細であった [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_14.php クリスチャンルブタン メンズ 靴]。経験豊富な全体強盗を吸収する二度落雷形成の出力は約すべてが恐怖の力を知っていると思う、クラウドトリックに変わった [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_12.php クリスチャンルブタン メンズ]。<br>彼の目の赤インイン、<br>アップ黒クレイジー [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_1.php クリスチャンルブタン 店舗 東京]。完全に開いた翼、血液の体はほぼ23メートルに至るまで、赤色光の外に急増。黒口は再び渦が再び発生したことを、アップ轟音。大きなスケールながら、この渦の緊急性、そしてより [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_13.php クリスチャンルブタン 日本]。<br>その腕の太さを<br>、黒雷の紫はとてもジェットバスを解雇した。<br><br>渦インスタント断片化は、その雷が強すぎる、黒の渦巻きは、単純に余裕があり、赤の地上道路メートルのカップル厚い雷を撮影することはできません、<br><br>は簡単に最終的にはとげのように、厚い雪を貫通する細い針を見えた。
Expressed with activities {{mvar|a}}, instead of concentrations, the thermodynamic equilibrium constant for the water ionization reaction is:
相关的主题文章:
:<math>K_{\rm w} = \frac{a_{\rm{H_3O^+}} \cdot a_{\rm{OH^-}}}{a_{\rm{H_2O}}^2}</math>
<ul>
 
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  <li>[http://bbs.owwan.com/forum.php?mod=viewthread&tid=385420 http://bbs.owwan.com/forum.php?mod=viewthread&tid=385420]</li>
 
</ul>


== 秦ゆうが少し驚い ==
which is numerically equal to the more traditional thermodynamic equilibrium constant written as:
:<math>K_{\rm w} = \frac{a_{\rm{H^+}} \cdot a_{\rm{OH^-}}}{a_{\rm{H_2O}}}</math>


家族の面積が、私は彼を見てみたかった。あなたはそれで何の惑星侯料を知っていますか? '<br><br>は秦ゆう、孟香港に表示されますが、この1三〇から六プラウは、天皇の魔法の牛の指揮下に、多くのことを知っている必要があります [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_4.php クリスチャンルブタン通販]。<br>召喚状が来る前に<br>モンゴルと香港は瞬間があった: '。秦ゆう兄弟は、いくつかの時間前、私は侯飛わからない。どこかの、どこかに思えることを聞いていた」<br>秦ゆうが少し驚い<br> [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_12.php クリスチャンルブタン メンズ]。<br><br>モンゴルと香港ナンセンス言葉は何に等しくない [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_14.php クリスチャンルブタン バッグ]?<br><br>孟香港とコミュニケーションは言った: [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_3.php クリスチャンルブタン ブーツ] 'しかし、秦ゆう兄弟が、私はあなたが、彼は侯料だったとどこに場所を知る限り、あなたは確信しているように、場所に行く示唆している..'<br><br>'どこ [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_14.php クリスチャンルブタン バッグ]?'秦玉里馬は尋ねた。<br><br>「Cuiyunスター!陛下は。皇室王朝牛マジック場所」孟香港すばやく侯料は大きな猿の皇帝によっての世話をしている」と答えた。ちょうど大きな猿の皇帝龍の頭ではなく、尾、それが大規模な見つけることは困難である猿皇帝は、そのように牛を探し魔法陛下が最も簡単な方法を尋ねた。 '<br><br>秦Yuは密かにうなずく。
under the assumption that the sum of the chemical potentials of H<sup>+</sup> and H<sub>3</sup>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</sup>O"] The International Association for the Properties of Water and Steam, Lucerne, Switzerland, August 2007.</ref>
相关的主题文章:
<ul>
 
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  <li>[http://www.beidafuxiao.com/plus/feedback.php?aid=11436 http://www.beidafuxiao.com/plus/feedback.php?aid=11436]</li>
 
</ul>


== 「どのように血の月は、どのように振動 ==
In infinitely dilute aqueous solution, the activity of water solvent is unity.


それはまたはない魔法のデバイスに属し、魔法皇帝マスターの一般的なレベルは、金製品の魔法を使用している、魔法のデバイス「ブラッド·ムーン」、最高の魔法のデバイス '血染めの月」である悪魔が必要です。だから、他の武器は、ウクライナの空の血液を放棄したすべての努力は、特別なGorefiendマジック精製法の一部である精錬ブラッドムーン、来た。<br><br>Xuexingチーロール [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_2.php クリスチャンルブタン バッグ] - [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_4.php クリスチャンルブタン通販] <br><br>ウクライナの空の血液や血液毎月、ますます緊密な関係。<br>突然<br> [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_11.php クリスチャンルブタン 取扱店] - <br><br>「どのように血の月は、どのように振動? '黒い空の心は血jingchanバースト。<br><br>血液デビルなくGorefiend魔法の武器の非常に有名な作品は、殺害の数が恐ろしいの底に到達し、さらにいくつかの精神性を持っています。<br><br>「パフ」<br><br>線システムだけでゴードン建チー、pixia簡単に高さから、もし、すべての2年半のような全宮殿豆腐 [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_14.php クリスチャンルブタン 銀座]。<br><br>'?'<br>同時に<br>ボイスシャウトは、いくつかの考え、さらには血が空いた排出量の空の黒い血を保持している [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_13.php クリスチャンルブタン 日本]<br><br>「空の黒い血、することができます
The '''ionization constant''', '''dissociation constant''', '''self-ionization constant''', or '''ionic product''' of water, symbolized by ''K''<sub>w</sub> may be given by:
相关的主题文章:
:<math>K_{\rm w}=[{\rm{H_3O^+}}][{\rm{OH^-}}] = K_{\rm{eq}} \cdot [{\rm{H_2O}}]^2 </math>
<ul>
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.
 
 
  <li>[http://cgi.www5f.biglobe.ne.jp/~undemand-place/bbs/yybbs.cgi http://cgi.www5f.biglobe.ne.jp/~undemand-place/bbs/yybbs.cgi]</li>
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>
 
:<math>K_{\rm w}=a_{\rm{H_3O^+}} \cdot a_{\rm{OH^-}} </math>
  <li>[http://www.adonim.com/comments/guestbook.cgi http://www.adonim.com/comments/guestbook.cgi]</li>
 
 
At 25&nbsp;°C ''K''<sub>w</sub> is equal to {{val|1.0|e=-14}}.
  <li>[http://bbs.x5ds.net/forum.php?mod=viewthread&tid=206031 http://bbs.x5ds.net/forum.php?mod=viewthread&tid=206031]</li>
 
 
==Dependence on temperature, pressure and ionic strength==
</ul>
{|
|[[Image:Temperature dependence water ionization.svg|thumb|240px|Temperature dependence of the water ionization constant at 25 MPa]]
|[[Image: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|270px|Variation of pK<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 pK<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;"
|+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 &lt; 100°C.  [[Vapor_pressure_of_water|Saturation pressure]] for T &ge; 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>
 
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 pK<sub>w</sub> values for liquid water, superheated steam, and  supercritical water.<ref name="rel"/>
|-
! 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&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 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. &amp; 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]&nbsp;– Autoionization of Water
 
{{Chemical equilibria}}
 
{{DEFAULTSORT:Self-Ionization Of Water}}
[[Category:Water chemistry]]
[[Category:Equilibrium chemistry]]
[[Category:Acid-base chemistry|Water]]
 
[[de:Protolyse#Autoprotolyse]]

Revision as of 16:08, 22 November 2013

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my blog post ipad repair hanover park The self-ionization of water (also autoionization of water, and autodissociation of water) is an ionization reaction in pure water or an aqueous solution, in which a water molecule, H2O, loses the nucleus of one of its hydrogen atoms to become a hydroxide ion, OH. The hydrogen nucleus, H+, immediately protonates another water molecule to form hydronium, H3O+. It is an example of autoprotolysis, and exemplifies the amphoteric nature of water.

Equilibrium constant

Chemically pure water has an electrical conductivity of 0.055 µS∙cm−1. According to the theories of Svante Arrhenius, this must be due to the presence of ions. The ions are produced by the self-ionization reaction

H2O + H2O Template:Eqm H3O+ + OH

This equilibrium applies to pure water and any aqueous solution.

Approximating activities by concentrations, the chemical equilibrium constant, Keq, for this reaction is given by:

If the concentration of dissolved solutes is low, the concentration [H2O] can be taken as being constant at c. 55.5M.[1]

Expressed with activities Template:Mvar, instead of concentrations, the thermodynamic equilibrium constant for the water ionization reaction is:

which is numerically equal to the more traditional thermodynamic equilibrium constant written as:

under the assumption that the sum of the chemical potentials of H+ and H3O+ is formally equal to twice the chemical potential of H2O at the same temperature and pressure.[2]

In infinitely dilute aqueous solution, the activity of water solvent is unity.

The ionization constant, dissociation constant, self-ionization constant, or ionic product of water, symbolized by Kw may be given by:

where [H3O+] is the concentration of hydrogen or hydronium ion, and [OH] is the concentration of hydroxide ion.

The ionic product of water can be also expressed on activity basis as:[3]

At 25 °C Kw is equal to Template:Val.

Dependence on temperature, pressure and ionic strength

Temperature dependence of the water ionization constant at 25 MPa
Pressure dependence of the water ionization constant at 25 °C
Variation of pKw with ionic strength of NaCl solutions at 25 °C

The dependence of the water ionization on temperature and pressure has been investigated thoroughly.[4] The value of pKw 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 of water c. 374 °C. It decreases with increasing pressure.

pKw values for liquid water.[5]
Temperature Pressure[6] pKw
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 pKw is dependent on ionic strength of the electrolyte. Values for sodium chloride are typical for a 1:1 electrolyte. With 1:2 electrolytes, MX2, pKw decreases with increasing ionic strength.[7]

The value of Kw is usually of interest in the liquid phase. Example values for superheated steam (gas) and supercritical water fluid are given in the table.

Comparison of pKw values for liquid water, superheated steam, and supercritical water.[2]
T/°C 350 400 450 500 600 800
0.1 MPa 11.920 (liquid)a 47.961b 47.873b 47.638 b 46.384 b 40.785 b
25 MPa 11.551 (liquid)c 16.566 18.135 18.758 19.425 20.113
100 MPa 10.600 (liquid)c 10.744 11.005 11.381 12.296 13.544
1000 MPa 8.311 (liquid)c 8.178 8.084 8.019 7.952 7.957

Notes to the Table. The values are for supercritical fluid except those marked: a at saturation pressure corresponding to 350 °C. b superheated steam. c subcooled liquid.

Isotope effects

Heavy water, D2O, self-ionizes less than normal water, H2O;

D2O + D2O Template:Eqm D3O+ + OD

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:

The following table compares the values of pKw for H2O and D2O.[8]

pKw values for pure water
T/°C 10 20 25 30 40 50
H2O 14.535 14.167 13.997 13.830 13.535 13.262
D2O 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:H2O, HDO, D2O, H3O+, D3O+, H2DO+, HD2O+, HO-, DO-.

Mechanism

The rate of reaction for the dissociation

H2O → H+ + OH

depends on the activation energy, ΔE. According to the Boltzmann distribution the proportion of water molecules that have sufficient energy, due to thermal population, is given by

where Template:Mvar 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.[9] Random fluctuations in molecular motions occasionally (about once every 10 hours per water molecule[10]) produce an electric field strong enough to break an oxygen–hydrogen bond, resulting in a hydroxide (OH) and hydronium ion (H3O+); 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.[11][12][13]

Relationship with the neutral point of water

Water molecules dissociate into equal amounts of H3O+ and OH, so their concentrations are equal to Template:Val at 25 °C. A solution in which the H3O+ and OH concentrations equal each other is considered a neutral solution. In general, the pH of the neutral point is numerically equal to pKw/2.

Pure water is neutral, but most water samples contain impurities. If an impurity is an acid or 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 H3O+ will increase. The concentration of OH will decrease in such a way that the product [H3O+][OH] remains constant for fixed temperature and pressure.

See also

Sportspersons Hyslop from Nicolet, usually spends time with pastimes for example martial arts, property developers condominium in singapore singapore and hot rods. Maintains a trip site and has lots to write about after touring Gulf of Porto: Calanche of Piana.

References

  1. McMurry, John. (2004) Organic Chemistry, p. 44
  2. 2.0 2.1 "Release on the Ionization Constant of H2O" The International Association for the Properties of Water and Steam, Lucerne, Switzerland, August 2007.
  3. 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. Entry: autoprotolysis constant.
  4. International Association for the Properties of Water and Steam (IAPWS)
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  6. 0.1 MPa for T < 100°C. Saturation pressure for T ≥ 100°C.
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    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  11. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  12. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  13. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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