View source for Oxidation state

{{short description|Hypothetical charge of an atom if all its bonds to different atoms were fully ionic}}

In [[chemistry]], the '''oxidation state''', or '''oxidation number''', is the hypothetical [[Electrical charge|charge]] of an atom if all of its [[Chemical bond|bonds]] to other atoms are fully [[Ionic bond|ionic]]. It describes the degree of [[oxidation]] (loss of [[electron]]s) of an [[atom]] in a [[chemical compound]]. Conceptually, the oxidation state may be positive, negative or zero. Beside nearly-pure [[ionic bonding]], many [[covalent bond]]s exhibit a strong ionicity, making oxidation state a useful predictor of charge.

The oxidation state of an atom does not represent the "real" charge on that atom, or any other actual atomic property. This is particularly true of high oxidation states, where the [[ionization energy]] required to produce a multiply positive ion is far greater than the energies available in chemical reactions. Additionally, the oxidation states of atoms in a given compound may vary depending on [[Electronegativities of the elements (data page)|the choice]] of [[electronegativity]] scale used in their calculation. Thus, the oxidation state of an atom in a compound is purely a formalism. It is nevertheless important in understanding the nomenclature conventions of [[inorganic compound]]s. Also, several observations regarding chemical reactions may be explained at a basic level in terms of oxidation states.

Oxidation states are typically represented by [[integer]]s which may be positive, zero, or negative. In some cases, the average oxidation state of an element is a fraction, such as {{sfrac|8|3}} for [[iron]] in [[magnetite]] {{chem2|Fe3O4}} ([[#Fractional oxidation states|see below]]). The highest known oxidation state is reported to be +9, displayed by [[iridium]] in the [[iridium tetroxide|tetroxoiridium(IX)]] cation ({{chem2|IrO4+}}).<ref>{{cite journal|first1=G.|last1=Wang|first2=M.|last2=Zhou|first3=G. T.|last3=Goettel|first4=G. J.|last4=Schrobilgen|first5=J.|last5=Su|first6=J.|last6=Li|first7=T.|last7=Schlöder|first8=S.|last8=Riedel|title=Identification of an iridium-containing compound with a formal oxidation state of IX|journal=Nature|volume=514|issue=7523|date=2014|pages=475–477|doi=10.1038/nature13795|pmid=25341786|bibcode=2014Natur.514..475W|s2cid=4463905}}</ref> It is predicted that even a +10 oxidation state may be achieved by [[platinum]] in tetroxoplatinum(X), {{chem2|PtO4(2+)}}.<ref>{{cite journal |last1=Yu |first1=Haoyu S. |last2=Truhlar |first2=Donald G. |date=2016 |title=Oxidation State 10 Exists |url= |journal=Angewandte Chemie International Edition |volume=55 |issue=31 |pages=9004–9006 |doi=10.1002/anie.201604670 |pmid=27273799 |access-date=|doi-access=free }}</ref> The lowest oxidation state is −5, as for [[boron]] in {{chem2|Al3BC}}<ref>{{citation |last=Schroeder |first=Melanie |title=Eigenschaften von borreichen Boriden und Scandium-Aluminium-Oxid-Carbiden |url=https://d-nb.info/995006210/34 |page=139 |access-date=2020-02-24 |archive-url=https://web.archive.org/web/20200806021428/https://d-nb.info/995006210/34 |url-status=live |language=de |archive-date=2020-08-06}}</ref> and [[gallium]] in [[pentamagnesium digallide]] ({{chem2|Mg5Ga2}}).

In [[Stock nomenclature]], which is commonly used for inorganic compounds, the oxidation state is represented by a [[Roman numeral]] placed after the element name inside parentheses or as a superscript after the element symbol, e.g. [[Iron(III) oxide]]. The term ''oxidation'' was first used by [[Antoine Lavoisier]] to signify the reaction of a substance with [[oxygen]]. Much later, it was realized that the substance, upon being oxidized, loses electrons, and the meaning was extended to include other [[Chemical reaction|reactions]] in which electrons are lost, regardless of whether oxygen was involved.
The increase in the oxidation state of an atom, through a chemical reaction, is known as oxidation; a decrease in oxidation state is known as a [[redox|reduction]]. Such reactions involve the formal transfer of electrons: a net gain in electrons being a reduction, and a net loss of electrons being oxidation. For pure elements, the oxidation state is zero.

== Overview ==
Oxidation numbers are assigned to elements in a molecule such that the overall sum is zero in a neutral molecule. The number indicates the degree of oxidation of each element caused by molecular bonding. In ionic compounds, the oxidation numbers are the same as the element's ionic charge. Thus for KCl, potassium is assigned +1 and chlorine is assigned −1.<ref name=SiebringSchalff1980/> The complete set of rules for assigning oxidation numbers are discussed in the following sections.

Oxidation numbers are fundamental to the [[chemical nomenclature]] of ionic compounds. For example, Cu compounds with Cu oxidation state +2 are called ''cupric'' and those with state +1 are ''cuprous''.<ref name=SiebringSchalff1980>Siebring, B. R., Schaff, M. E. (1980). General Chemistry. United States: Wadsworth Publishing Company.</ref>{{rp|172}}  
The oxidation numbers of elements allow predictions of chemical formula and reactions, especially [[Redox|oxidation-reduction reactions]].
The oxidation numbers of the most stable chemical compounds follow trends in the periodic table.<ref name=GrayHaight1976>Gray, H. B., Haight, G. P. (1967). Basic Principles of Chemistry. Netherlands: W. A. Benjamin.</ref>{{rp|140}}

== IUPAC definition ==

[[International Union of Pure and Applied Chemistry]] (IUPAC) has published a "Comprehensive definition of oxidation state (IUPAC Recommendations 2016)".<ref name="10.1515/pac-2015-1204">{{cite journal|first1=P.|last1=Karen|first2=P.|last2=McArdle|first3=J.|last3=Takats|title=Comprehensive definition of oxidation state (IUPAC Recommendations 2016)|journal=Pure Appl. Chem.|volume=88|issue=8|date=2016|pages=831–839|doi=10.1515/pac-2015-1204|hdl=10852/59520|s2cid=99403810|hdl-access=free}}</ref> It is a distillation of an IUPAC technical report: "Toward a comprehensive definition of oxidation state".<ref name="10.1515/pac-2013-0505">{{cite journal|first1=P.|last1=Karen|first2=P.|last2=McArdle|first3=J.|last3=Takats|title=Toward a comprehensive definition of oxidation state (IUPAC Technical Report)|journal=Pure Appl. Chem.|volume=86|issue=6 |date=2014 |pages=1017–1081|doi=10.1515/pac-2013-0505|doi-access=free}}</ref> According to the IUPAC ''[[Gold Book]]'': "The oxidation state of an atom is the charge of this atom after ionic approximation of its heteronuclear bonds."<ref name=goldbookoxstate>{{GoldBookRef|title=Oxidation state|file=O04365}}</ref> The term ''oxidation number'' is nearly synonymous.<ref name=goldbookoxnumber>{{GoldBookRef|title=Oxidation number|file=O04363}}</ref>

The ionic approximation means extrapolating bonds to ionic. Several criteria<ref name="10.1002/anie.201407561">{{Cite journal|doi = 10.1002/anie.201407561|title = Oxidation State, A Long-Standing Issue!|year = 2015|last = Karen|first = Pavel|journal = Angewandte Chemie International Edition|volume = 54|issue = 16|pages = 4716–4726|pmid = 25757151|pmc = 4506524}}</ref> were considered for the ionic approximation:

# Extrapolation of the bond's polarity; {{ordered list|list_style_type=lower-alpha
| from the electronegativity difference,
| from the dipole moment, and
| from quantum‐chemical calculations of charges.}}
# Assignment of electrons according to the atom's contribution to the bonding [[Molecular Orbital|Molecular orbital]] (MO)<ref name="10.1002/anie.201407561" /><ref>{{cite journal | last=Hooydonk | first=G. Van | title=O n an Ionic Approximation to Chemical Bonding | journal=Zeitschrift für Naturforschung A | volume=29 | issue=5 | date=1974-05-01 | issn=1865-7109 | doi=10.1515/zna-1974-0517 | pages=763–767| bibcode=1974ZNatA..29..763H | doi-access=free }}</ref> or the electron's allegiance in a [[Linear combination of atomic orbitals|LCAO–MO]] model.<ref>{{Cite book|doi=10.1351/goldbook.O04365|chapter=Oxidation state| title=The IUPAC Compendium of Chemical Terminology: The Gold Book|year=2009|isbn=978-0-9678550-9-7}}</ref>

In a bond between two different elements, the bond's electrons are assigned to its main atomic contributor typically of higher electronegativity; in a bond between two atoms of the same element, the electrons are divided equally. Most electronegativity scales depend on the atom's bonding state, which makes the assignment of the oxidation state a somewhat circular argument. For example, some scales may turn out unusual oxidation states, such as −6 for [[platinum]] in {{Chem2|PtH4(2-)}}, for [[Electronegativity#Pauling electronegativity|Pauling]] and [[Electronegativity#Mulliken electronegativity|Mulliken]] scales.<ref name="10.1515/pac-2013-0505" /> The dipole moments would sometimes also turn out abnormal oxidation numbers, such as in [[Carbon monoxide|CO]] and [[Nitrogen oxide|NO]], which
are oriented with their positive end towards oxygen. Therefore, this leaves the atom's contribution to the
bonding MO, the atomic-orbital energy, and from quantum-chemical calculations of charges, as the only viable criteria with cogent values for ionic approximation. However, for a simple estimate for the ionic approximation, we can use [[Electronegativity#Allen electronegativity|Allen electronegativities]],<ref name="10.1515/pac-2013-0505" /> as only that electronegativity scale is truly independent of the oxidation state, as it relates to the average valence‐electron energy of the free atom:

{{Periodic table (electronegativity by Allen scale)|style=font-size:80%}}

== Determination ==
While introductory levels of chemistry teaching use [[postulate]]d oxidation states, the IUPAC recommendation<ref name="10.1515/pac-2015-1204" /> and the ''Gold Book'' entry<ref name="goldbookoxstate" /> list [[#Algorithm of assigning bonds|two entirely general algorithms for the calculation of the oxidation states]] of elements in chemical compounds.

=== Simple approach without bonding considerations ===
Introductory chemistry uses postulates: the oxidation state for an element in a chemical formula is calculated from the overall charge and postulated oxidation states for all the other atoms.

A simple example is based on two postulates,

# OS = +1 for [[hydrogen]]
# OS = −2 for [[oxygen]]

where OS stands for oxidation state. This approach yields correct oxidation states in oxides and hydroxides of any single element, and in acids such as [[sulfuric acid]] ({{chem2|H2SO4}}) or [[dichromic acid]] ({{chem2|H2Cr2O7}}). Its coverage can be extended either by a list of exceptions or by assigning priority to the postulates. The latter works for [[hydrogen peroxide]] ({{chem2|H2O2}}) where the priority of rule 1 leaves both oxygens with oxidation state −1.

Additional postulates and their ranking may expand the range of compounds to fit a textbook's scope. As an example, one postulatory algorithm from many possible; in a sequence of decreasing priority:

# An element in a free form has OS = 0.
# In a compound or ion, the sum of the oxidation states equals the total charge of the compound or ion.
# [[Fluorine]] in compounds has OS = −1; this extends to [[chlorine]] and [[bromine]] only when not bonded to a lighter halogen, oxygen or nitrogen.
# [[Group 1 element|Group 1]] and [[Group 2 element|group 2]] metals in compounds have OS = +1 and +2, respectively.
# Hydrogen has OS = +1 but adopts −1 when bonded as a [[hydride]] to metals or metalloids.
# Oxygen in compounds has OS = −2 but only when not bonded to oxygen (e.g. in peroxides) or fluorine.

This set of postulates covers oxidation states of fluorides, chlorides, bromides, oxides, hydroxides, and hydrides of any single element. It covers all [[oxoacids]] of any central atom (and all their fluoro-, chloro-, and bromo-relatives), as well as [[salt (chemistry)|salts]] of such acids with group 1 and 2 metals. It also covers [[iodide]]s, [[sulfide]]s, and similar simple salts of these metals.

=== Algorithm of assigning bonds ===
This algorithm is performed on a [[Lewis structure]] (a diagram that shows all [[valence electron]]s). Oxidation state equals the charge of an atom after each of its [[heteronuclear]] bonds has been assigned to the more [[Electronegativity#Methods of calculation|electronegative]] partner of the bond ([[#The algorithm's caveat|except when that partner is a reversibly bonded Lewis-acid ligand]]) and [[homonuclear]] bonds have been divided equally:

:[[File:1oxstate.svg|frameless|240px]]

where each "—" represents an electron pair (either shared between two atoms or solely on one atom), and "OS" is the oxidation state as a numerical variable.

After the electrons have been assigned according to the vertical red lines on the formula, the total number of valence electrons that now "belong" to each atom is subtracted from the number {{mvar|N}} of valence electrons of the neutral atom (such as 5 for nitrogen in [[Pnictogen|group 15]]) to yield that atom's oxidation state.

This example shows the importance of describing the bonding. Its summary formula, {{chem2|HNO3}}, corresponds to two [[structural isomer]]s; the [[peroxynitrous acid]] in the above figure and the more stable [[nitric acid]]. With the formula {{chem2|HNO3}}, the [[#Simple approach without bonding considerations|simple approach without bonding considerations]] yields −2 for all three oxygens and +5 for nitrogen, which is correct for nitric acid. For the peroxynitrous acid, however, both oxygens in the O–O bond have OS = −1, and the nitrogen has OS = +3, which requires a structure to understand.

[[Organic compound]]s are treated in a similar manner; exemplified here on [[functional group]]s occurring in between [[methane]] ({{chem2|CH4}}) and [[carbon dioxide]] ({{chem2|CO2}}):

:[[File:3oxstate.svg|frameless|500px]]

Analogously for [[transition-metal]] compounds; {{chem2|CrO(O2)2}} on the left has a total of 36 valence electrons (18 pairs to be distributed), and [[hexacarbonylchromium]] ({{chem2|Cr(CO)6}}) on the right has 66 valence electrons (33 pairs):

:[[File:2oxstate.svg|frameless|380px]]

A key step is drawing the Lewis structure of the molecule (neutral, cationic, anionic): Atom symbols are arranged so that pairs of atoms can be joined by single two-electron bonds as in the molecule (a sort of "skeletal" structure), and the remaining valence electrons are distributed such that sp atoms obtain an [[octet rule|octet]] (duet for hydrogen) with a priority that increases in proportion with electronegativity. In some cases, this leads to alternative formulae that differ in bond orders (the full set of which is called the [[Resonance (chemistry)|resonance formulas]]). Consider the [[sulfate]] anion ({{chem2|SO4(2-)}}) with 32 valence electrons; 24 from oxygens, 6 from sulfur, 2 of the anion charge obtained from the implied cation. The [[bond order]]s to the terminal oxygens do not affect the oxidation state so long as the oxygens have octets. Already the skeletal structure, top left, yields the correct oxidation states, as does the Lewis structure, top right (one of the resonance formulas):

:[[File:7oxstate.svg|frameless|450px]]

The bond-order formula at the bottom is closest to the reality of four equivalent oxygens each having a total bond order of 2. That total includes the bond of order {{sfrac|1|2}} to the implied cation and follows the 8&nbsp;−&nbsp;''N'' rule<ref name="10.1515/pac-2013-0505" /> requiring that the main-group atom's bond-order total equals 8&nbsp;−&nbsp;''N'' valence electrons of the neutral atom, enforced with a priority that proportionately increases with electronegativity.

This algorithm works equally for molecular cations composed of several atoms. An example is the [[ammonium]] cation of 8 valence electrons (5 from nitrogen, 4 from hydrogens, minus 1 electron for the cation's positive charge):

:[[File:5oxstate.svg|frameless|240px]]

Drawing Lewis structures with electron pairs as dashes emphasizes the essential equivalence of bond pairs and lone pairs when counting electrons and moving bonds onto atoms. Structures drawn with electron dot pairs are of course identical in every way:

:[[File:4oxstate.svg|frameless|200px]]

==== The algorithm's caveat ====
The algorithm contains a caveat, which concerns rare cases of [[transition-metal]] [[coordination complex|complexes]] with a type of [[ligand]] that is reversibly bonded as a [[Lewis acid]] (as an acceptor of the electron pair from the transition metal); termed a "Z-type" ligand in Green's [[covalent bond classification method]]. The caveat originates from the simplifying use of electronegativity instead of the [[molecular orbital|MO]]-based electron allegiance to decide the ionic sign.<ref name="10.1515/pac-2015-1204" /> One early example is the {{chem2|O2S\sRhCl(CO)([[triphenylphosphine|PPh3]])2}} complex<ref>{{cite journal|first1=K. W.|last1=Muir|first2=J. A.|last2=Ibers|title=The structure of chlorocarbonyl(sulfur dioxide)bis(triphenylphosphine)rhodium, (RhCl(CO)(SO2)(P(C6H5)3 2)|journal=Inorg. Chem.|volume=8|date=1969|issue=9|pages=1921–1928|doi=10.1021/ic50079a024}}</ref> with [[sulfur dioxide]] ({{chem2|SO2}}) as the reversibly-bonded acceptor ligand (released upon heating). The Rh−S bond is therefore extrapolated ionic against Allen electronegativities of [[rhodium]] and sulfur, yielding oxidation state +1 for rhodium:

:[[File:8oxstate.svg|frameless|450px]]

=== Algorithm of summing bond orders ===
This algorithm works on Lewis structures and bond graphs of extended (non-molecular) solids:
{{blockquote|Oxidation state is obtained by summing the heteronuclear-bond orders at the atom as positive if that atom is the electropositive partner in a particular bond and as negative if not, and the atom’s formal charge (if any) is added to that sum. The same caveat as above applies.}}

==== Applied to a Lewis structure ====
An example of a Lewis structure with no formal charge,
:[[File:9oxstate.svg|frameless|240px]]
illustrates that, in this algorithm, homonuclear bonds are simply ignored (the bond orders are in blue).

Carbon monoxide exemplifies a Lewis structure with [[formal charges]]:

:[[File:10oxstate.svg|frameless|240px]]

To obtain the oxidation states, the formal charges are summed with the bond-order value taken positively at the carbon and negatively at the oxygen.

Applied to molecular ions, this algorithm considers the actual location of the formal (ionic) charge, as drawn in the Lewis structure. As an example, summing bond orders in the [[ammonium]] cation yields −4 at the nitrogen of formal charge +1, with the two numbers adding to the oxidation state of −3:

:[[File:11oxstate.svg|frameless|240px]]

The sum of oxidation states in the ion equals its charge (as it equals zero for a neutral molecule).

Also in anions, the formal (ionic) charges have to be considered when nonzero. For sulfate this is exemplified with the skeletal or Lewis structures (top), compared with the bond-order formula of all oxygens equivalent and fulfilling the octet and 8&nbsp;−&nbsp;''N'' rules (bottom):

:[[File:13oxstate.svg|frameless|450px]]

==== Applied to bond graph ====
A [[bond graph]] in [[solid-state chemistry]] is a chemical formula of an extended structure, in which direct bonding connectivities are shown. An example is the {{chem2|AuORb3}} [[perovskite]], the unit cell of which is drawn on the left and the bond graph (with added numerical values) on the right:

:[[File:14oxstate.svg|frameless|360px]]

We see that the oxygen atom bonds to the six nearest [[rubidium]] cations, each of which has 4 bonds to the [[auride]] anion. The bond graph summarizes these connectivities. The bond orders (also called [[bond valence]]s) sum up to oxidation states according to the attached sign of the bond's ionic approximation (there are no formal charges in bond graphs).

Determination of oxidation states from a bond graph can be illustrated on [[ilmenite]], {{chem2|FeTiO3}}. We may ask whether the mineral contains {{chem2|Fe(2+)}} and {{chem2|Ti(4+)}}, or {{chem2|Fe(3+)}} and {{chem2|Ti(3+)}}. Its crystal structure has each metal atom bonded to six oxygens and each of the equivalent oxygens to two [[iron]]s and two [[titanium]]s, as in the bond graph below. Experimental data show that three metal-oxygen bonds in the octahedron are short and three are long (the metals are off-center). The bond orders (valences), obtained from the bond lengths by the [[bond valence method]], sum up to 2.01 at Fe and 3.99 at Ti; which can be rounded off to oxidation states +2 and +4, respectively:

:[[File:15oxstate.svg|frameless|200px]]

=== Balancing redox ===
Oxidation states can be useful for balancing chemical equations for oxidation-reduction (or [[redox]]) reactions, because the changes in the oxidized atoms have to be balanced by the changes in the reduced atoms. For example, in the reaction of [[acetaldehyde]] with [[Tollens' reagent]] to form [[acetic acid]] (shown below), the [[carbonyl]] carbon atom changes its oxidation state from +1 to +3 (loses two electrons). This oxidation is balanced by reducing two {{chem2|Ag+}} cations to {{chem2|Ag^{0} }} (gaining two electrons in total).

:[[File:Redox eqn 1.svg|600px]]

An inorganic example is the Bettendorf reaction using [[tin dichloride]] ({{chem2|SnCl2}}) to prove the presence of [[arsenite]] ions in a concentrated [[hydrochloric acid|HCl]] extract. When arsenic(III) is present, a brown coloration appears forming a dark precipitate of [[arsenic]], according to the following simplified reaction:
:{{chem2|2 As^{3+} + 3 Sn^{2+} -> 2 As^{0} + 3 Sn^{4+} }}
Here three [[tin]] atoms are oxidized from oxidation state +2 to +4, yielding six electrons that reduce two arsenic atoms from oxidation state +3 to 0. The simple one-line balancing goes as follows: the two redox couples are written down as they react;
:{{chem2|As^{3+} + Sn^{2+} <-> As^{0} + Sn^{4+} }}
One tin is oxidized from oxidation state +2 to +4, a two-electron step, hence 2 is written in front of the two arsenic partners. One arsenic is reduced from +3 to 0, a three-electron step, hence 3 goes in front of the two tin partners. An alternative three-line procedure is to write separately the [[half-reaction]]s for oxidation and reduction, each balanced with electrons, and then to sum them up such that the electrons cross out. In general, these redox balances (the one-line balance or each half-reaction) need to be checked for the ionic and electron charge sums on both sides of the equation being indeed equal. If they are not equal, suitable ions are added to balance the charges and the non-redox elemental balance.

== 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.

== List of oxidation states of the elements ==
This is a list of known oxidation states of the [[chemical element]]s, excluding [[#Fractional oxidation states|nonintegral values]]. The most common states appear in bold. The table is based on that of Greenwood and Earnshaw,<ref>{{Greenwood&Earnshaw|pages=27–28}}</ref> with additions noted. Every element exists in oxidation state 0 when it is the pure non-ionized element in any phase, whether monatomic or polyatomic [[allotrope]]. The column for oxidation state 0 only shows elements known to exist in oxidation state 0 in compounds.
{{List of oxidation states of the elements}}

=== Early forms (octet rule) ===
A figure with a similar format was used by [[Irving Langmuir]] in 1919 in one of the early papers about the [[octet rule]].<ref>{{cite journal |last= Langmuir |first= Irving |year= 1919 |title= The arrangement of electrons in atoms and molecules |url= https://zenodo.org/record/1429026 |journal= J. Am. Chem. Soc. |volume= 41 |issue= 6 |pages= 868–934 |doi= 10.1021/ja02227a002 |bibcode= 1919JAChS..41..868L |access-date= 2019-07-01 |archive-date= 2019-06-21 |archive-url= https://web.archive.org/web/20190621192330/https://zenodo.org/record/1429026 |url-status= live }}</ref> The periodicity of the oxidation states was one of the pieces of evidence that led Langmuir to adopt the rule.

:[[File:Langmuir valence.png|700px]]

== Use in nomenclature ==
The oxidation state in compound naming for [[transition metal]]s and [[lanthanides]] and [[actinides]] is placed either as a right superscript to the element symbol in a chemical formula, such as Fe<sup>III</sup> or in parentheses after the name of the element in chemical names, such as iron(III). For example, {{chem|Fe|2|(SO|4|)|3}} is named [[iron(III) sulfate]] and its formula can be shown as Fe{{su|p=III|b=2}}{{chem|(SO|4|)|3}}. This is because a [[sulfate ion]] has a charge of −2, so each iron atom takes a charge of +3.

== History of the oxidation state concept ==
=== Early days ===
Oxidation itself was first studied by [[Antoine Lavoisier]], who defined it as the result of reactions with [[oxygen]] (hence the name).<ref>{{cite web|url=https://www.acs.org/content/acs/en/education/whatischemistry/landmarks/lavoisier.html|title=Antoine Laurent Lavoisier The Chemical Revolution – Landmark – American Chemical Society|website=American Chemical Society|access-date=14 July 2018|archive-date=5 January 2021|archive-url=https://web.archive.org/web/20210105040544/https://www.acs.org/content/acs/en/education/whatischemistry/landmarks/lavoisier.html|url-status=live}}</ref><ref>{{cite web|url=http://chem125-oyc.webspace.yale.edu/125/history99/2Pre1800/Lavoisier/Nomenclature/Lavoisier_on_Elements.html|title=Lavoisier on Elements|website=Chem125-oyc.webspace.yale.edu|access-date=14 July 2018|archive-date=13 June 2020|archive-url=https://web.archive.org/web/20200613025757/http://chem125-oyc.webspace.yale.edu/125/history99/2Pre1800/Lavoisier/Nomenclature/Lavoisier_on_Elements.html|url-status=live}}</ref> The term has since been generalized to imply a ''formal'' loss of electrons. Oxidation states, called ''oxidation grades'' by [[Friedrich Wöhler]] in 1835,<ref>{{cite book|first=F.|last=Wöhler|title=Grundriss der Chemie: Unorganische Chemie|trans-title=Foundations of Chemistry: Inorganic Chemistry|publisher=Duncker und Humblot|location=Berlin|date=1835|page=4}}</ref> were one of the intellectual stepping stones that [[Dmitri Mendeleev]] used to derive the [[periodic table]].<ref>{{Greenwood&Earnshaw|pages=33}}</ref> [[William B. Jensen]]<ref>{{cite journal|author1-link=William B. Jensen|first=W. B.|last=Jensen|title=the origin of the oxidation-state concept|journal=J. Chem. Educ.|volume=84|issue=9|date=2007|pages=1418–1419|doi=10.1021/ed084p1418|bibcode=2007JChEd..84.1418J}}</ref> gives an overview of the history up to 1938.

=== Use in nomenclature ===
When it was realized that some metals form two different binary compounds with the same nonmetal, the two compounds were often distinguished by using the ending ''-ic'' for the higher metal oxidation state and the ending ''-ous'' for the lower. For example, FeCl<sub>3</sub> is [[ferric chloride]] and FeCl<sub>2</sub> is [[ferrous chloride]]. This system is not very satisfactory (although sometimes still used) because different metals have different oxidation states which have to be learned: ferric and ferrous are +3 and +2 respectively, but cupric and cuprous are +2 and +1, and stannic and stannous are +4 and +2. Also, there was no allowance for metals with more than two oxidation states, such as [[vanadium]] with oxidation states +2, +3, +4, and +5.<ref name=Petrucci />{{rp|84}}

This system has been largely replaced by one suggested by [[Alfred Stock]] in 1919<ref>{{cite journal|first=A.|last=Stock|title=Einige Nomenklaturfragen der anorganischen Chemie|trans-title=Some nomenclature issues of inorganic chemistry|journal=Angew. Chem.|volume=32|issue=98|date=1919|pages=373–374|doi=10.1002/ange.19190329802|bibcode=1919AngCh..32..373S|url=https://zenodo.org/record/1424478|access-date=2019-07-01|archive-date=2020-08-06|archive-url=https://web.archive.org/web/20200806044615/https://zenodo.org/record/1424478|url-status=live}}</ref> and adopted<ref name="1940IUPACinorgnom">{{cite journal|first1=W. P.|last1=Jorissen|first2=H.|last2=Bassett|first3=A.|last3=Damiens|first4=F.|last4=Fichter|first5=H.|last5=Rémy|title=Rules for naming inorganic compounds|journal=J. Am. Chem. Soc.|volume=63|date=1941|pages=889–897|doi=10.1021/ja01849a001}}</ref> by [[IUPAC]] in 1940. Thus, FeCl<sub>2</sub> was written as [[iron(II) chloride]] rather than ferrous chloride. The Roman numeral II at the central atom came to be called the "[[Stock nomenclature|Stock number]]" (now an obsolete term), and its value was obtained as a charge at the central atom after removing its ligands along with the [[electron pair]]s they shared with it.<ref name="RedBook2005" />{{rp|147}}

=== Development towards the current concept ===
The term "oxidation state" in English chemical literature was popularized by [[Wendell Mitchell Latimer]] in his 1938 book about electrochemical potentials.<ref>{{cite book|first=W. M.|last=Latimer|title=The Oxidation States of the Elements and their Potentials in Aqueous Solutions|edition=1st|publisher=Prentice-Hall|date=1938}}</ref> He used it for the value (synonymous with the German term ''Wertigkeit'') previously termed "valence", "polar valence" or "polar number"<ref>{{cite journal|first1=W. C.|last1=Bray|first2=G. E. K.|last2=Branch|title=Valence and tautomerism|journal=J. Am. Chem. Soc.|volume=35|issue=10|date=1913|pages=1440–1447|doi=10.1021/ja02199a003|bibcode=1913JAChS..35.1440B |url=https://zenodo.org/record/1428999|access-date=2019-09-16|archive-date=2021-02-09|archive-url=https://web.archive.org/web/20210209031533/https://zenodo.org/record/1428999|url-status=live}}</ref> in English, or "oxidation stage" or indeed<ref>{{cite journal|first1=A. A.|last1=Noyes|first2=K. S.|last2=Pitzer|first3=C. L.|last3=Dunn|title=Argentic salts in acid solution, I. The oxidation and reduction reactions|journal=J. Am. Chem. Soc.|volume=57|issue=7|date=1935|pages=1221–1229|doi=10.1021/ja01310a018|bibcode=1935JAChS..57.1221N }}</ref><ref>{{cite journal|first1=A. A.|last1=Noyes|first2=K. S.|last2=Pitzer|first3=C. L.|last3=Dunn|title=Argentic salts in acid solution, II. The oxidation state of argentic salts|journal=J. Am. Chem. Soc.|volume=57|issue=7|date=1935|pages=1229–1237|doi=10.1021/ja01310a019|bibcode=1935JAChS..57.1229N }}</ref> the "state of oxidation". Since 1938, the term "oxidation state" has been connected with [[electrochemical potential]]s and electrons exchanged in [[redox couple]]s participating in redox reactions. By 1948, IUPAC used the 1940 nomenclature rules with the term "oxidation state",<ref>{{cite journal|first=W. C.|last=Fernelius|title=Some problems of inorganic nomenclature|journal=Chem. Eng. News|volume=26|date=1948|pages=161–163|doi=10.1021/cen-v026n003.p161}}</ref><ref>{{cite journal|first1=W. C.|last1=Fernelius|first2=E. M.|last2=Larsen|first3=L. E.|last3=Marchi|first4=C. L.|last4=Rollinson|title=Nomenclature of coördination compounds|journal=Chem. Eng. News|volume=26|issue=8|date=1948|pages=520–523|doi=10.1021/cen-v026n008.p520}}</ref> instead of the original<ref name="1940IUPACinorgnom" /> ''valency''. In 1948 [[Linus Pauling]] proposed that oxidation number could be determined by extrapolating bonds to being completely ionic in the direction of [[electronegativity]].<ref>{{cite journal|first=L.|last=Pauling|title=The modern theory of valency|journal=J. Chem. Soc.|volume=1948|date=1948|pages=1461–1467|doi=10.1039/JR9480001461|pmid=18893624|url=https://authors.library.caltech.edu/59671/|access-date=2021-11-22|archive-date=2021-12-07|archive-url=https://web.archive.org/web/20211207153730/https://authors.library.caltech.edu/59671/|url-status=live}}</ref> A full acceptance of this suggestion was complicated by the fact that the [[Electronegativity#Pauling electronegativity|Pauling electronegativities]] as such depend on the oxidation state and that they may lead to unusual values of oxidation states for some transition metals. In 1990 IUPAC resorted to a postulatory (rule-based) method to determine the oxidation state.<ref>{{cite journal|first=J. G.|last=Calvert|title=IUPAC Recommendation 1990|journal=Pure Appl. Chem.|volume=62|date=1990|page=2204|doi=10.1351/pac199062112167|doi-access=free}}</ref> This was complemented by the synonymous term oxidation number as a descendant of the Stock number introduced in 1940 into the nomenclature. However, the terminology using "[[ligands]]"<ref name="RedBook2005" />{{rp|147}} gave the impression that oxidation number might be something specific to [[coordination complex]]es. This situation and the lack of a real single definition generated numerous debates about the meaning of oxidation state, suggestions about methods to obtain it and definitions of it. To resolve the issue, an IUPAC project (2008-040-1-200) was started in 2008 on the "Comprehensive Definition of Oxidation State", and was concluded by two reports<ref name="10.1515/pac-2013-0505" /><ref name="10.1515/pac-2015-1204" /> and by the revised entries "Oxidation State"<ref name="goldbookoxstate" /> and "Oxidation Number"<ref name="goldbookoxnumber" /> in the [[IUPAC Gold Book]]. The outcomes were a single definition of oxidation state and two algorithms to calculate it in molecular and extended-solid compounds, guided by [[Electronegativity#Allen electronegativity|Allen electronegativities]] that are independent of oxidation state.

== See also ==
* [[Electronegativity]]
* [[Electrochemistry]]
* [[Atomic orbital]]
* [[Atomic shell]]
* [[Quantum numbers]]
** [[Azimuthal quantum number]]
** [[Principal quantum number]]
** [[Magnetic quantum number]]
** [[Spin quantum number]]
* [[Aufbau principle]]
** [[Wiswesser's rule]]
* [[Ionization energy]]
* [[Electron affinity]]
* [[Ionic potential]]
* [[Ions]]
** [[Cations]] and [[Anions]]
** [[Polyatomic ions]]
* [[Covalent bonding]]
* [[Metallic bonding]]
* [[Orbital hybridisation|Hybridization]]

==References==
{{Reflist}}

{{sfn whitelist|CITEREFPetersonHobart1984}}

{{Oxide}}
{{Authority control}}

[[Category:Chemical nomenclature]]
[[Category:Chemical properties]]
[[Category:Coordination chemistry]]
[[Category:Dimensionless numbers of chemistry]]
[[Category:Redox]]