Editing Oxidation state (section)

== Appearances ==
=== Nominal oxidation states ===
A nominal oxidation state is a general term with two different definitions:
* [[Electrochemistry|Electrochemical]] oxidation state<ref name="10.1515/pac-2013-0505" />{{rp|1060}} represents a molecule or ion in the [[Latimer diagram]] or [[Frost diagram]] for its redox-active element. An example is the Latimer diagram for [[sulfur]] at pH&nbsp;0 where the electrochemical oxidation state +2 for sulfur puts [[thiosulfate|{{chem|HS|2|O|3|−}}]] between S and [[sulfurous acid|H<sub>2</sub>SO<sub>3</sub>]]:

::[[File:16oxstate.svg|frameless|600px]]
* Systematic oxidation state is chosen from close alternatives as a pedagogical description. An example is the oxidation state of phosphorus in [[phosphorous acid|H<sub>3</sub>PO<sub>3</sub>]] (structurally [[diprotic]] HPO(OH)<sub>2</sub>) taken nominally as +3, while [[Electronegativity#Allen electronegativity|Allen electronegativities]] of [[phosphorus]] and [[hydrogen]] suggest +5 by a narrow margin that makes the two alternatives almost equivalent:
::[[File:17oxstate.svg|frameless|450px]]
:Both alternative oxidation numbers for phosphorus make chemical sense, depending on which chemical property or reaction is emphasized. By contrast, a calculated alternative, such as the average (+4) does not.

=== Ambiguous oxidation states ===
[[Lewis formula]]e are rule-based approximations of chemical reality, as are [[Electronegativity#Allen electronegativity|Allen electronegativities]]. Still, oxidation states may seem ambiguous when their determination is not straightforward. If only an experiment can determine the oxidation state, the rule-based determination is ambiguous (insufficient). There are also truly [[dichotomy|dichotomous]] values that are decided arbitrarily.

==== Oxidation-state determination from resonance formulas ====
Seemingly ambiguous oxidation states are derived from a set of [[resonance]] formulas of equal weights for a molecule having heteronuclear bonds where the atom connectivity does not correspond to the number of two-electron bonds dictated by the 8&nbsp;−&nbsp;''N'' rule.<ref name="10.1515/pac-2013-0505" />{{rp|1027}} An example is [[Disulfur dinitride|S<sub>2</sub>N<sub>2</sub>]] where four resonance formulas featuring one S=N double bond have oxidation states +2 and +4 for the two sulfur atoms, which average to +3 because the two sulfur atoms are equivalent in this square-shaped molecule.

==== A physical measurement is needed to determine oxidation state ====
* when a [[non-innocent ligand|non-innocent]] [[ligand]] is present, of hidden or unexpected redox properties that could otherwise be assigned to the central atom. An example is the [[nickel]] [[metal dithiolene complex|dithiolate]] complex, {{chem|Ni(S|2|C|2|H|2|)|2|2−}}.<ref name="10.1515/pac-2013-0505" />{{rp|1056–1057}}
* when the redox ambiguity of a central atom and ligand yields dichotomous oxidation states of close stability, thermally induced [[tautomerism]] may result, as exemplified by [[manganese]] [[catecholate]], {{chem2|Mn(C6H4O2)3}}.<ref name="10.1515/pac-2013-0505" />{{rp|1057–1058}} Assignment of such oxidation states requires spectroscopic,<ref>{{cite book|first=C. K.|last=Jørgensen|contribution=Electric Polarizability, Innocent Ligands and Spectroscopic Oxidation States|title=Structure and Bonding|volume=1|pages=234–248|publisher=Springer-Verlag|location=Berlin|date=1966}}</ref> magnetic or structural data.
* when the bond order has to be ascertained along with an isolated tandem of a heteronuclear and a homonuclear bond. An example is [[thiosulfate]] {{chem|S|2|O|3|2−}} having two possible oxidation states (bond orders are in blue and formal charges in green):

::[[File:21oxstate.svg|frameless|500px]]

:The S–S distance measurement in [[thiosulfate]] is needed to reveal that this bond order is very close to 1, as in the formula on the left.

==== Ambiguous/arbitrary oxidation states ====
* when the electronegativity difference between two bonded atoms is very small (as in [[phosphorous acid|H<sub>3</sub>PO<sub>3</sub>]]). Two almost equivalent pairs of oxidation states, arbitrarily chosen, are obtained for these atoms.
* when an electronegative [[p-block]] atom forms solely homonuclear bonds, the number of which differs from the number of two-electron bonds suggested by [[Octet rule|rules]]. Examples are homonuclear finite chains like [[azide|{{chem|N|3|−}}]] (the central nitrogen connects two atoms with four two-electron bonds while only three two-electron bonds<ref>{{Cite web|url=https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%3A_General_Chemistry_Supplement_(Eames)/Lewis_Bonding_Theory/The_Two-Electron_Bond|title=The Two-Electron Bond|date=June 25, 2016|website=Chemistry LibreTexts|access-date=September 1, 2020|archive-date=February 9, 2021|archive-url=https://web.archive.org/web/20210209034153/https://chem.libretexts.org/Bookshelves/General_Chemistry/Book:_General_Chemistry_Supplement_(Eames)/Lewis_Bonding_Theory/The_Two-Electron_Bond|url-status=live}}</ref> are required by the 8&nbsp;−&nbsp;''N'' rule<ref name="10.1515/pac-2013-0505" />{{rp|1027}}) or [[triiodide|{{chem|I|3|−}}]] (the central iodine connects two atoms with two two-electron bonds while only one two-electron bond fulfills the 8&nbsp;−&nbsp;''N'' rule). A sensible approach is to distribute the ionic charge over the two outer atoms.<ref name="10.1515/pac-2013-0505" /> Such a placement of charges in a [[polysulfide]] {{chem|S|''n''|2−}} (where all inner sulfurs form two bonds, fulfilling the 8&nbsp;−&nbsp;''N'' rule) follows already from its Lewis structure.<ref name="10.1515/pac-2013-0505" />
* when the isolated tandem of a heteronuclear and a homonuclear bond leads to a bonding compromise in between two Lewis structures of limiting bond orders. An example is [[nitrous oxide|N<sub>2</sub>O]]:

::[[File:18oxstate.svg|frameless|420px]]

:The typical oxidation state of nitrogen in N<sub>2</sub>O is +1, which also obtains for both nitrogens by a molecular orbital approach.<ref name="10.1002/anie.201407561" /> The formal charges on the right comply with electronegativities, which implies an added ionic bonding contribution. Indeed, the estimated N−N and N−O bond orders are 2.76 and 1.9, respectively,<ref name="10.1515/pac-2013-0505" /> approaching the formula of integer bond orders that would include the ionic contribution explicitly as a bond (in green):

::[[File:19oxstate.svg|frameless|280px]]

:Conversely, formal charges against electronegativities in a Lewis structure decrease the bond order of the corresponding bond. An example is [[carbon monoxide]] with a bond-order estimate of 2.6.<ref>{{cite journal|first1=R. J.|last1=Martinie|first2=J. J.|last2=Bultema|first3=M. N. V.|last3=Wal|first4=B. J.|last4=Burkhart|first5=D. A. V.|last5=Griend|first6=R. L.|last6=DeCock|title=Bond order and chemical properties of BF, CO, and N<sub>2</sub>|journal=J. Chem. Educ.|volume=88|date=2011|issue=8|pages=1094–1097|doi=10.1021/ed100758t|bibcode=2011JChEd..88.1094M}}</ref>

=== Fractional oxidation states ===
Fractional oxidation states are often used to represent the average oxidation state of several atoms of the same element in a structure. For example, the formula of [[magnetite]] is {{chem|Fe|3|O|4}}, implying an average oxidation state for iron of +{{sfrac|8|3}}.<ref name=Petrucci>{{cite book|first1=R. H.|last1=Petrucci|first2=W. S.|last2=Harwood|first3=F. G.|last3=Herring|title=General Chemistry|url=https://archive.org/details/generalchemistry00hill|url-access=registration|edition=8th|publisher=Prentice-Hall|date=2002|isbn=978-0-13-033445-9}}{{ISBN missing}}</ref>{{rp|81–82}} However, this average value may not be representative if the atoms are not equivalent. In a {{chem|Fe|3|O|4}} crystal below {{cvt|120|K|°C|0}}, two-thirds of the cations are {{chem|Fe|3+}} and one-third are {{chem|Fe|2+}}, and the formula may be more clearly represented as FeO·{{chem|Fe|2|O|3}}.<ref>{{cite journal|first1=M. S.|last1=Senn|first2=J. P.|last2=Wright|first3=J. P.|last3=Attfield|title=Charge order and three-site distortions in the Verwey structure of magnetite|journal=Nature|volume=481|issue=7380|pages=173–6|date=2012|doi=10.1038/nature10704|pmid=22190035|bibcode=2012Natur.481..173S|s2cid=4425300|url=https://www.pure.ed.ac.uk/ws/files/10796489/Charge_order_and_three_site_distortions_in_the_Verwey_structure_of_magnetite.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.pure.ed.ac.uk/ws/files/10796489/Charge_order_and_three_site_distortions_in_the_Verwey_structure_of_magnetite.pdf |archive-date=2022-10-09 |url-status=live|hdl=20.500.11820/1b3bb558-52d5-419f-9944-ab917dc95f5e|hdl-access=free}}</ref>

Likewise, [[propane]], {{chem|C|3|H|8}}, has been described as having a carbon oxidation state of −{{sfrac|8|3}}.<ref>{{cite book|first1=K. W.|last1=Whitten|first2=K. D.|last2=Galley|first3=R. E.|last3=Davis|title=General Chemistry|url=https://archive.org/details/generalchemistry00whit_0|url-access=registration|edition=4th|publisher=Saunders|date=1992|page=[https://archive.org/details/generalchemistry00whit_0/page/147 147]|isbn=978-0-03-075156-1}}{{ISBN missing}}</ref> Again, this is an average value since the structure of the molecule is {{chem|H|3|C−CH|2|−CH|3}}, with the first and third carbon atoms each having an oxidation state of −3 and the central one −2.

An example with true fractional oxidation states for equivalent atoms is potassium [[superoxide]], {{chem|KO|2}}. The diatomic superoxide ion {{chem|O|2|−}} has an overall charge of −1, so each of its two equivalent oxygen atoms is assigned an oxidation state of −{{sfrac|1|2}}. This ion can be described as a [[resonance (chemistry)|resonance]] hybrid of two Lewis structures, where each oxygen has an oxidation state of 0 in one structure and −1 in the other.

For the [[cyclopentadienyl anion]] {{chem|C|5|H|5|−}}, the oxidation state of C is −1 + −{{sfrac|1|5}} = −{{sfrac|6|5}}. The −1 occurs because each carbon is bonded to one hydrogen atom (a less electronegative element), and the −{{sfrac|1|5}} because the total ionic charge of −1 is divided among five equivalent carbons. Again this can be described as a resonance hybrid of five equivalent structures, each having four carbons with oxidation state −1 and one with −2.

:{| class="wikitable"
|+ Examples of fractional oxidation states for carbon
|-
! Oxidation state !! Example species
|-
| −{{sfrac|6|5}} || [[Cyclopentadienyl anion|{{chem|C|5|H|5|−}}]]
|-
| −{{sfrac|6|7}} || [[tropylium|{{chem|C|7|H|7|+}}]]
|-
| +{{sfrac|3|2}} || [[Squarate ion|{{chem|C|4|O|4|2−}}]]
|}

Finally, fractional oxidation numbers '''are not  used''' in the chemical nomenclature.<ref name="RedBook2005">{{cite book|first1=N. G.|last1=Connelly|first2=T.|last2=Damhus|first3=R. M.|last3=Hartshorn|first4=A. T.|last4=Hutton|title=Nomenclature of Inorganic Chemistry (IUPAC Recommendations 2005)|publisher=RSC Publishing|url=http://www.old.iupac.org/publications/books/rbook/Red_Book_2005.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.old.iupac.org/publications/books/rbook/Red_Book_2005.pdf |archive-date=2022-10-09 |url-status=live}}</ref>{{rp|66}} For example the red lead [[Lead(II,IV) oxide|{{chem|Pb|3|O|4}}]] is represented as lead(II,IV) oxide, showing the oxidation states of the two nonequivalent [[lead (metal)|lead]] atoms.

=== Elements with multiple oxidation states ===
{{hatnote|See also {{Section link||List of oxidation states of the elements}}}}
Most elements have more than one possible oxidation state. For example, carbon has nine possible integer oxidation states from −4 to +4:
:{| class="wikitable"
|+ Integer oxidation states of carbon
|-
! Oxidation state !! Example compound
|-
| −4 || [[methane|{{chem|CH|4}}]]
|-
| −3 || [[ethane|{{chem|C|2|H|6}}]]
|-
| −2 || [[ethylene|{{chem|C|2|H|4}}]], [[chloromethane|{{chem|CH|3|Cl}}]]
|-
| −1 || [[acetylene|{{chem|C|2|H|2}}]], [[benzene|{{chem|C|6|H|6}}]], [[ethylene glycol|{{chem|(CH|2|OH)|2}}]]
|-
| 0 || [[formaldehyde|{{chem|HCHO}}]], [[dichloromethane|{{chem|CH|2|Cl|2}}]]
|-
| +1 || [[glyoxal|{{chem|OCHCHO}}]], [[1,1,2,2-Tetrachloroethane|{{chem|CHCl|2|CHCl|2|}}]]
|-
| +2 || [[formic acid|{{chem|HCOOH}}]], [[chloroform|{{chem|CHCl|3}}]]
|-
| +3 || [[oxalic acid|{{chem|HOOCCOOH}}]], [[hexachloroethane|{{chem|C|2|Cl|6}}]]
|-
| +4 || [[carbon tetrachloride|{{chem|CCl|4}}]], [[carbon dioxide|{{chem|CO|2}}]]
|}

=== Oxidation state in metals ===
Many compounds with [[Lustre (mineralogy)|luster]] and [[electrical conductivity]] maintain a simple [[stoichiometric]] formula, such as the golden [[titanium monoxide|TiO]], blue-black [[ruthenium dioxide|RuO<sub>2</sub>]] or coppery [[rhenium trioxide|ReO<sub>3</sub>]], all of obvious oxidation state. Ultimately, assigning the free metallic electrons to one of the bonded atoms is not comprehensive and can yield unusual oxidation states. Examples are the LiPb and {{chem|Cu|3|Au}} ordered [[alloy]]s, the composition and structure of which are largely determined by [[Atomic radius|atomic size]] and [[Atomic packing factor|packing factors]]. Should oxidation state be needed for redox balancing, it is best set to 0 for all atoms of such an alloy.