Oxidation state


The oxidation state, sometimes referred to as oxidation number, describes the degree of oxidation of an atom in a chemical compound. Conceptually, the oxidation state, which may be positive, negative or zero, is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic, with no covalent component. This is never exactly true for real bonds.
The term oxidation was first used by Antoine Lavoisier to signify 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 reactions in which electrons are lost, regardless of whether oxygen was involved.
Oxidation states are typically represented by integers which may be positive, zero, or negative. In some cases, the average oxidation state of an element is a fraction, such as for iron in magnetite. The highest known oxidation state is reported to be +9 in the tetroxoiridium cation. It is predicted that even a +10 oxidation state may be achievable by platinum in the tetroxoplatinum cation. The lowest oxidation state is −5, as for boron in Al3BC.
The increase in oxidation state of an atom, through a chemical reaction, is known as an oxidation; a decrease in oxidation state is known as a reduction. Such reactions involve the formal transfer of electrons: a net gain in electrons being a reduction, and a net loss of electrons being an oxidation. For pure elements, the oxidation state is zero.
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, oxidation states of atoms in a given compound may vary depending on 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 compounds. Also, a number of observations pertaining to chemical reactions may be explained at a basic level in terms of oxidation states.
In inorganic nomenclature, the oxidation state is represented by a Roman numeral placed after the element name inside a parenthesis or as a superscript after the element symbol.

IUPAC definition

IUPAC has published a "Comprehensive definition of the term oxidation state ". It is a distillation of an IUPAC technical report "Toward a comprehensive definition of oxidation state" from 2014. The current IUPAC Gold Book definition of oxidation state is:
and the term oxidation number is nearly synonymous.
The underlying principle is that the ionic signs for two atoms that are bonded are deduced from the electron distribution in a LCAO–MO model. In a bond between two different elements, the bond's electrons are assigned to its main atomic contributor; in a bond between two atoms of the same element, the electrons are divided equally. In practical use, the sign of the ionic approximation follows Allen electronegativities:

Determination

While introductory levels of chemistry teaching use postulated oxidation states, the IUPAC recommendation and the Gold Book entry list [|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,
  1. OS = +1 for hydrogen
  2. 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 H2SO4 or H2Cr2O7. Its coverage can be extended either by a list of exceptions or by assigning priority to the postulates. The latter works for 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:
  1. An element in a free form has OS = 0.
  2. In a compound or ion, the sum of the oxidation states equals the total charge of the compound or ion.
  3. Fluorine in compounds has OS = −1; this extends to chlorine and bromine only when not bonded to a lighter halogen, oxygen or nitrogen.
  4. Group 1 and group 2 metals in compounds have OS = +1 and +2, respectively.
  5. Hydrogen has OS = +1, but adopts −1 when bonded as a hydride to metals or metalloids.
  6. Oxygen in compounds has OS = −2.
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, as well as salts of such acids with group 1 and 2 metals. It also covers iodides, sulfides and similar simple salts of these metals.

Algorithm of assigning bonds

This algorithm is performed on a Lewis structure. Oxidation state equals the charge of an atom after each of its heteronuclear bonds has been assigned to the more-electronegative partner of the bond and homonuclear bonds have been divided equally:
where each "—" represents an electron pair, 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 are subtracted from the number N of valence electrons of the neutral atom to yield that atom's oxidation state.
This example shows the importance of describing the bonding. Its summary formula, HNO3, corresponds to two structural isomers; the peroxynitrous acid in the above figure and the more stable nitric acid. With the formula HNO3, the [|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, the two oxygens in the O–O bond each have OS = −1 and the nitrogen has OS = +3, which requires a structure to understand.
Organic compounds are treated in a similar manner; exemplified here on functional groups occurring in between CH4 and CO2:
Analogously for transition-metal compounds; CrO2 on the left has a total of 36 valence electrons, and Cr6 on the right has 66 valence electrons :
A key step is drawing the Lewis structure of the molecule : atom symbols are arranged so that pairs of atoms can be joined by single two-electron bonds as in the molecule, and the remaining valence electrons are distributed such that sp atoms obtain an octet with priority that increases with electronegativity. In some cases, this leads to alternative formulae that differ in bond orders. Consider the sulfate anion. The bond orders to the terminal oxygens have no effect on 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 :
The bond-order formula at 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 to the implied cation and follows the 8 − N rule requiring that the main-group atom's bond order equals 8 minus N valence electrons of the neutral atom, enforced with priority that increases with electronegativity.
This algorithm works equally for molecular cations composed of several atoms. An example is the ammonium cation of 8 valence electrons :
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:

The algorithm's caveat

The algorithm contains a caveat, which concerns rare cases of transition-metal complexes with a type of ligand that is reversibly bonded as a Lewis acid ; termed a "Z-type" ligand in Green's covalent bond classification method. The caveat originates from the simplifying use of electronegativity instead of the MO-based electron allegiance to decide the ionic sign. One early example is the O2S−RhCl2 complex with SO2 as the reversibly-bonded acceptor ligand. The Rh−S bond is therefore extrapolated ionic against Allen electronegativities of rhodium and sulfur, yielding oxidation state +1 for rhodium:

Algorithm of summing bond orders

This algorithm works on Lewis structures and on bond graphs of extended solids:

Applied to a Lewis structure

An example of a Lewis structure with no formal charge,
illustrates that, in this algorithm, homonuclear bonds are simply ignored.
Carbon monoxide exemplifies a Lewis structure with formal charges:
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 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:
The sum of oxidation states in the ion equals its charge.
Also in anions, the formal charges have to be considered when nonzero. For sulfate this is exemplified with the skeletal or Lewis structures, compared with the bond-order formula of all oxygens equivalent and fulfilling the octet and 8 − N rules :

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 AuORb3 perovskite, the unit cell of which is drawn on the left and the bond graph on the right:
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 sum up to oxidation states according to the attached sign of the bond's ionic approximation.
Determination of oxidation states from a bond graph can be illustrated on ilmenite, FeTiO3. We may ask whether the mineral contains Fe2+ and Ti4+, or Fe3+ and Ti3+. Its crystal structure has each metal atom bonded to six oxygens and each of the equivalent oxygens to two irons and two titaniums, as in the bond graph below. Experimental data show that three metal–oxygen bonds in the octahedron are short and three are long. The bond orders, 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:

Balancing redox

Oxidation states can be useful for balancing chemical equations for oxidation–reduction 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, the carbonyl carbon atom changes its oxidation state from +1 to +3. This oxidation is balanced by reducing two Ag+ cations to Ag0.
An inorganic example is the Bettendorf reaction using SnCl2 to prove the presence of arsenite ions in a concentrated HCl extract. When arsenic is present, a brown coloration appears forming a dark precipitate of arsenic, according to the following simplified reaction:
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;
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-reactions for oxidation and for reduction, each balanced with electrons, and then to sum them up such that the electrons cross out. In general, these redox balances 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 for two specific purpose-oriented values:
  • Electrochemical oxidation state; it 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 0 where the electrochemical oxidation state +2 for sulfur puts thiosulfate| between S and H2SO3:
  • Systematic oxidation state; it is chosen from close alternatives for pedagogical reasons of descriptive chemistry. An example is the oxidation state of phosphorus in H3PO3 taken nominally as +3, while Allen electronegativities of phosphorus and hydrogen suggest +5 by a narrow margin that makes the two alternatives almost equivalent:
Both alternative oxidation states of phosphorus make chemical sense, depending on the chemical property or reaction we wish to emphasize. In contrast, their average does not.

Ambiguous oxidation states

e are fine rule-based approximations of chemical reality, as indeed are Allen electronegativities. Still, oxidation states may seem ambiguous when their determination is not straightforward. Rule-based oxidation states feel ambiguous when only experiment can decide. There are also truly dichotomous values to be decided by mere convenience.

Oxidation-state determination from resonance formulas is not straightforward

Seemingly ambiguous oxidation states are obtained on a set of resonance formulas of equal weights for a molecule of heteronuclear bonds where the atom connectivity does not correspond to the number of two-electron bonds dictated by the 8 − N rule. An example is S2N2 where four resonance formulas featuring one S=N double bond have oxidation states +2 and +4 on the two sulfur atoms, to be averaged to +3 because the two sulfur atoms are equivalent in this square-shaped molecule.

A physical measurement is needed to decide the oxidation state

  • This happens when a 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 dithiolate complex,.
  • 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, Mn3. Assignment of such oxidation states in general requires spectroscopic, magnetic or structural data.
  • When the bond order has to be ascertained along an isolated tandem of a heteronuclear and a homonuclear bond. An example is thiosulfate| with two oxidation-state alternatives :

    Truly ambiguous oxidation states occur

  • When the electronegativity difference between two bonded atoms is very small. Two almost equivalent pairs of oxidation states, open for a choice, 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 rules. Examples are homonuclear finite chains like azide| or triiodide|. A sensible approach is to distribute the ionic charge over the two outer atoms. Such a placement of charges in a polysulfide follows already from its Lewis structure.
  • 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 here is N2O:

    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, implying an average oxidation state for iron of +. However, this average value may not be representative if the atoms are not equivalent. In a crystal below, two-thirds of the cations are and one-third are, and the formula may be more specifically represented as FeO·.
Likewise, propane,, has been described as having a carbon oxidation state of −. Again, this is an average value since the structure of the molecule is, 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,. The diatomic superoxide ion has an overall charge of −1, so each of its two equivalent oxygen atoms is assigned an oxidation state of −. This ion can be described as a resonance hybrid of two Lewis structures, where each oxygen has oxidation state 0 in one structure and −1 in the other.
For the cyclopentadienyl anion, the oxidation state of C is −1 + − = −. The −1 occurs because each carbon is bonded to one hydrogen atom, and the − 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.

Elements with multiple oxidation states

Most elements have more than one possible oxidation state. For example, carbon has nine possible integer oxidation states from −4 to +4:

Oxidation state in metals

Many compounds with luster and electrical conductivity maintain a simple stoichiometric formula; such as the golden TiO, blue-black RuO2 or coppery ReO3, all of obvious oxidation state. Ultimately, however, the assignment of the free metallic electrons to one of the bonded atoms has its limits and leads to unusual oxidation states. Simple examples are the LiPb and Cu3Au ordered alloys, the composition and structure of which are largely determined by atomic size and 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 elements, excluding nonintegral values. The most common states appear in bold. The table is based on that of Greenwood and Earnshaw, 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.

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. The periodicity of the oxidation states was one of the pieces of evidence that led Langmuir to adopt the rule.

Use in nomenclature

The oxidation state in compound naming is placed either as a right superscript to the element symbol in a chemical formula, such as FeIII, or in parentheses after the name of the element in chemical names, such as iron. For example, is named iron sulfate and its formula can be shown as Fe. This is because a sulfate ion has a charge of −2, so each iron atom takes a charge of +3. Fractional oxidation numbers should not be used in naming. Red lead,, is represented as lead oxide, showing the actual two oxidation states of the nonequivalent lead atoms.

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. The term has since been generalized to imply a formal loss of electrons. Oxidation states, called oxidation grades by Friedrich Wöhler in 1835, were one of the intellectual stepping stones that Dmitri Mendeleev used to derive the periodic table. Jensen 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, FeCl3 is ferric chloride and FeCl2 is ferrous chloride. This system is not very satisfactory 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.
This system has been largely replaced by one suggested by Alfred Stock in 1919 and adopted by IUPAC in 1940. Thus, FeCl2 was written as iron chloride rather than ferrous chloride. The Roman numeral II at the central atom came to be called the "Stock number", and its value was obtained as a charge at the central atom after removing its ligands along with the electron pairs they shared with it.

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. He used it for the value previously termed "valence", "polar valence" or "polar number" in English, or "oxidation stage" or indeed the "state of oxidation". Since 1938, the term "oxidation state" has been connected with electrochemical potentials and electrons exchanged in redox couples participating in redox reactions. By 1948, IUPAC used the 1940 nomenclature rules with the term "oxidation state", instead of the original valency. In 1948 Linus Pauling proposed that oxidation number could be determined by extrapolating bonds to being completely ionic in the direction of electronegativity. A full acceptance of this suggestion was complicated by the fact that the 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 method to determine the oxidation state. 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" gave the impression that oxidation number might be something specific to coordination complexes. 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 was started in 2008 on the "Comprehensive Definition of Oxidation State", and was concluded by two reports and by the revised entries "Oxidation State" and "Oxidation Number" 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 Allen electronegativities that are independent of oxidation state.