# Oxidation number

Oxidation numbers or oxidation states (also oxidation state , electrochemical valence ) are the result of a formalistic model of the structure of the molecules. Oxidation numbers indicate the ionic charges of the atoms in a chemical compound or in a polyatomic ion if the compound or the polyatomic ion were made up of monatomic ions. It follows that the sum of the oxidation numbers of all atoms of a compound or a polyatomic ion must be equal to the charge of the compound or ion. Because of its simplicity, its high predictive power, and its broad applicability, this approach is of great importance to chemists.

The easy-to-determine oxidation numbers are important in inorganic and organic chemistry for understanding redox reactions and are very helpful when formulating redox equations. An atom in a compound or in an ion would have reached the highest possible or the lowest possible oxidation number if it had given up or absorbed so many electrons that it would have reached the next noble gas configuration . An overview of the possible oxidation numbers of chemical elements can be found in the list of oxidation states of the chemical elements . The determination of the oxidation numbers of atoms in compounds and ions follows a few simple rules.

## Specification of oxidation numbers: examples and reaction equations

While actual ion charges in formulas are written as charge numbers followed by + or - and placed after the formula, when oxidation numbers are specified in formulas, the + or - as a sign is placed in front of the value and placed above the atomic symbols. In texts and names, oxidation numbers can be specified with both Arabic and Roman numerals . In the case of the oxidation number zero, ± 0 is written.

The indication of the oxidation number is important in the nomenclature of inorganic salts , e.g. B. in the case of iron (III) chloride and iron (II) chloride , and when naming metal complexes in which the oxidation number always indicates the oxidation number of the central atom, z. B. in the case of potassium hexacyanidoferrate (II) and potassium hexacyanidoferrate (III) . Only whole-number oxidation numbers are used which, apart from the number 0, are always given as Roman numerals. When displaying oxidation numbers in formulas, they are usually given as Arabic numerals and are usually whole numbers .

Examples
 ${\ displaystyle \ mathrm {{\ overset {+1} {K}} {\ overset {+7} {Mn}} {\ overset {-2} {O_ {4}}}}}$ ${\ displaystyle \ mathrm {{\ overset {+4} {Mn}} {\ overset {-2} {O_ {2}}}}}$ ${\ displaystyle \ mathrm {{\ overset {+6} {S}} {\ overset {-2} {O_ {4} ^ {2-}}}}}$ ${\ displaystyle \ mathrm {{\ overset {+4} {S}} {\ overset {-2} {O_ {3} ^ {2-}}}}}$ ${\ displaystyle \ mathrm {{\ overset {-3} {N}} {\ overset {+1} {H_ {3}}}}}$ ${\ displaystyle \ mathrm {{\ overset {-3} {N}} {\ overset {+1} {H_ {4} ^ {+}}}}}$ ${\ displaystyle \ mathrm {{\ overset {+1} {H_ {2}}} {\ overset {-2} {S}}}}$ ${\ displaystyle \ mathrm {{\ overset {0} {O}} {\ mathord {=}} {\ mathord {\ overset {0} {O}}}}}$ ${\ displaystyle \ mathrm {\ overset {+2} {Fe ^ {2+}}}}$ potassium permanganate permanganate Manganese dioxide Sulfate ion Sulfite ion ammonia Ammonium ion sulfur hydrogen oxygen Iron (II) ion

When formulating redox equations , usually only the oxidation numbers of the atoms are given that are oxidized or reduced because the oxidation numbers of the other atoms do not change. The number of electrons exchanged must be taken into account when checking the charge balance of a redox equation. It must be exactly as large as the difference between the two oxidation numbers. The atomic balances must be balanced by the accompanying substances present in the reaction medium, such as. B. water H 2 O and acid (hydroxonium ions H 3 O + ) or base (hydroxyl ions OH - ). As a final check, the charge balance of the reaction equation must then also be correct.

Example: Two partial reactions of redox reactions with the permanganate anion as the oxidizing agent, which is reduced differently, either in an acidic solution or in a basic solution.
${\ displaystyle \ mathrm {{\ overset {+7} {Mn}} O_ {4} ^ {-} \ + \ 8 \ H_ {3} O ^ {+} + 5 \ e ^ {-} \ longrightarrow { \ overset {+2} {Mn ^ {2 +}}} + 12 \ H_ {2} O}}$
${\ displaystyle \ mathrm {{\ overset {+7} {Mn}} O_ {4} ^ {-} \ + \ 2 \ H_ {2} O + 3 \ e ^ {-} \ longrightarrow {\ overset {+ 4} {MnO_ {2} {}}} + 4 \ OH ^ {-}}}$

A stoichiometric redox reaction is z. B. the Tollensprobe , in which acetaldehyde is oxidized with Ag + to acetic acid and elemental Ag is formed.

${\ displaystyle \ mathrm {CH_ {3} {\ mathord {-}} {\ overset {+1} {C}} HO \ + \ 2 \ {\ overset {+1} {Ag ^ {+}}} + 2 \ OH ^ {-} \ longrightarrow \ CH_ {3} {\ mathord {-}} {\ overset {+3} {C}} OOH \ + \ 2 \ {\ overset {0} {Ag}} \ + \ \ H_ {2} O}}$

In redox reactions that are stoichiometrically correct, the sum of the oxidation numbers of the starting materials is equal to the sum of the oxidation numbers of the products.

## Importance and use

The oxidation number of an atom can be used to formally describe the electron density of an atom, with a positive oxidation number indicating a reduced electron density (compared to the state in the element) and a negative oxidation number indicating an increased electron density. As a purely formal parameter , the oxidation number correlates only poorly with the actual electron density or charge distribution.

Oxidation numbers are of great importance in the proper formulation and determination of the stoichiometry of redox reactions . They serve to show the different oxidation states and their changes during redox reactions and to determine the number of exchanged electrons. A lowering of the oxidation number of an atomic type in a redox reaction means that this atomic type has been reduced; analogously, an increase in the oxidation number of an atomic type means that this atomic type has been oxidized.

According to IUPAC , the terms oxidation state and oxidation number can be used. The term oxidation state corresponds in its meaning to the oxidation number and is often used in organic chemistry to compare different substance classes with regard to their oxidation state, e.g. B. with the following statements: Carboxylic acids are in the same oxidation state as carboxylic acid esters and other structurally comparable derivatives of carboxylic acids such. B. also carboxylic acid chlorides . However, carboxylic acids and their derivatives are in a higher oxidation state than aldehydes and alcohols and in a lower oxidation state than carbon dioxide .

By comparing oxidation numbers, you can quickly see that the conversion of a primary alcohol to an aldehyde and also the conversion of an aldehyde to a carboxylic acid are both oxidations .
 ${\ displaystyle \ mathrm {{\ overset {-3} {C}} H_ {3} {\ mathord {-}} {\ overset {-1} {C}} H_ {2} OH}}$ ${\ displaystyle \ mathrm {{\ overset {-3} {C}} H_ {3} {\ mathord {-}} {\ overset {+1} {C}} HO}}$ ${\ displaystyle \ mathrm {{\ overset {-3} {C}} H_ {3} {\ mathord {-}} {\ overset {+3} {C}} OOH}}$ Ethanol acetaldehyde acetic acid
With different hydrocarbons, the different oxidation states of the carbon atoms become clear.
 ${\ displaystyle \ mathrm {{\ overset {-4} {C}} H_ {4}}}$ ${\ displaystyle \ mathrm {{\ overset {-3} {C}} H_ {3} {\ mathord {-}} {\ overset {-3} {C}} H_ {3}}}$ ${\ displaystyle \ mathrm {{\ overset {-3} {C}} H_ {3} {\ mathord {-}} {\ overset {-2} {C}} H_ {2} {\ mathord {-}} {\ overset {-3} {C}} H_ {3}}}$ ${\ displaystyle \ mathrm {{\ overset {-3} {C}} H_ {3} {\ mathord {-}} {\ overset {-1} {C}} H {\ mathord {=}} {\ overset {-2} {C}} H_ {2}}}$ methane Ethane propane Propene

## Special oxidation numbers

Oxidation numbers can also assume fractional values. So have z. B. in hyperoxide KO 2 ( potassium hyperoxide ) both oxygen atoms have an oxidation number of −0.5. Their oxidation state differs from the oxidation state of the oxygen atoms in normal peroxides , which contain the peroxide anion O 2 2− or the peroxy group –O – O–, with oxygen in the oxidation state −1.

In the Fe 3 O 4 ( iron (II, III) oxide ), iron has an average oxidation number of + 8 / 3 . The oxidation states listed in Roman numerals in the name indicate that iron atoms are present in this compound in the oxidation states +2 and +3. Fe II Fe 2 III O 4 has an inverse spinel structure (simplified: FeO · Fe 2 O 3 ) and formal Fe 2+ and Fe 3+ ions can be localized.

The sum formula of the thiosulfate anion (S 2 O 3 2− ,) gives an average oxidation number of + 2 for sulfur. However, the structure of the anion shows that there are two sulfur atoms in completely different bonding ratios, with the different oxidation states +5 and −1, as can be deduced from the structure. The middle and the two discrete oxidation states are suitable for stoichiometric calculations and for formulating redox reactions. The thiosulfate anion must not be confused with the disulfate anion , in which the S atoms are present in the highest possible oxidation state +6, as in the normal sulfate anion .

 ${\ displaystyle \ mathrm {{\ overset {+1} {K_ {2}}} {\ overset {-1} {O_ {2}}}}}$ ${\ displaystyle \ mathrm {{\ overset {+1} {K}} {\ overset {-0.5} {O_ {2}}}}}$ ${\ displaystyle \ mathrm {{\ overset {+2} {Fe}} (II) {\ overset {+3} {Fe_ {2}}} (III) {\ overset {-2} {O_ {4}} }}}$ ${\ displaystyle \ mathrm {{\ overset {+ {\ frac {8} {3}}} {Fe_ {3}}} {\ overset {-2} {O_ {4}}}}}$ ${\ displaystyle \ mathrm {{\ overset {+2} {S_ {2}}} {\ overset {-2} {O_ {3} ^ {2-}}}}}$ ${\ displaystyle \ mathrm {({\ overset {-2} {O_ {3}}} {\ overset {+5} {S}} {\ mathord {-}} {{\ overset {-1} {S} }) ^ {2-}}}}$ Potassium peroxide Potassium hyperoxide Iron (II, III) oxide with discrete oxidation states Iron (II, III) oxide with a medium oxidation state Thiosulfate ion with a medium oxidation state Thiosulfate ion with discrete oxidation states

The lowest known oxidation state of an atom in a molecule is −4 (for elements of the carbon group ), the highest +9 (in [IrO 4 ] + for iridium ).

## Determination of oxidation numbers

### Main rules

Oxidation numbers in elements, inorganic and organic, neutral or ionic compounds can be determined with the help of the following rules or checked after determination:

1. The sum of the oxidation numbers of all atoms of a neutral or charged compound must be exactly as large as the charge of the compound. This already results in the following rules.
2. Atoms in atomic and molecular elements always have the oxidation number 0. Examples: Li, Mg, B, C, O 2 , P 4 , S 8 , I 2 , Ar. The oxidation number 0 can also result from the determination for atoms in compounds with other elements (example for C see below).
3. In the case of an atomic ion , the oxidation number corresponds to the ion charge . For example, in the Cu 2+ cation, copper has an oxidation number of +2. In the anion Cl - the chlorine has the oxidation number −1).
4. The sum of the oxidation numbers of all atoms of a polyatomic neutral compound is equal to 0.
5. The sum of the oxidation numbers of all atoms in a polyatomic ion must be equal to the total charge of the ion.
6. In the case of organic compounds formulated with covalent bonds, in the valence line formulas (Lewis formulas), the compound can be formally divided into ions based on the electronegativity so that the oxidation numbers of all atoms can be determined. The formal division assumes that the electrons involved in a bond are completely taken over by the more electronegative atom (see example below)

1. Most elements can occur in several oxidation states.
2. The highest possible oxidation number of an element corresponds to the main or subgroup number in the periodic table (PSE).
3. The fluorine atom (F) as an element with the highest electronegativity has in all connections always the oxidation number -1.
4. Oxygen, as an element of very high electronegativity, has an oxidation number of −2 in almost all compounds. However, there are three important exceptions: In peroxides the O atoms have the oxidation number −1 and in hyperoxides the oxidation number −0.5. In connection with fluorine ( oxygen difluoride ), oxygen has an oxidation number of +2.
5. Apart from fluorine, the other halogen atoms chlorine , bromine and iodine always have an oxidation number of −1 in organic compounds and mostly in inorganic compounds. There are, however, many exceptions, such as compounds with oxygen ( halogen oxides ) or compounds with one another, interhalogen compounds with a halogen that is higher in the periodic table .
6. Metal atoms in ionic compounds always have a positive oxidation number.
7. Alkali metals always have the oxidation number +1 and alkaline earth metals always the oxidation number +2.
8. Hydrogen atoms always have the oxidation number +1, except when hydrogen with "electropositive" atoms such as the metals ( hydrides ) is connected.

### Determination by division based on electronegativity

To determine the oxidation number in a compound, binding electron pairs are assigned to the more electronegative binding partner (formal heterolytic cleavage ). Bonding electron pairs between the same atoms are shared (formal homolytic cleavage ). The atoms in modifications of the elements thus have an oxidation number of zero.

Determination of the oxidation
numbers using 5-hydroxycytosine as an example

If the molecule has a Lewis formula , oxidation numbers in organic compounds can be determined from the electronegativity of the elements involved in the bonds. The following rule applies to the atoms involved in a bond: the bond electrons are assigned to the atom with the greater electronegativity. If the electronegativity is the same, division takes place.

The graphic on the right shows an example of the procedure for determining the oxidation numbers of the atoms of the 5-hydroxycytosine molecule. The procedure on the carbon atom with the oxidation number ± 0 is explained as an example. This carbon atom forms three bonds to neighboring atoms, single bonds to nitrogen and hydrogen and a double bond to the neighboring carbon atom. The comparison of the electronegativities of the elements involved in the bonds gives:

• Carbon has an electronegativity of 2.55. Nitrogen has a higher electronegativity of 3.04 and therefore both binding electrons are assigned to nitrogen.
• Hydrogen with an electronegativity of 2.2 has a lower electronegativity than carbon. Therefore both binding electrons are assigned to carbon.
• The upper carbon atom has the same electronegativity as the lower carbon atom and therefore the two carbon atoms share the bonding electrons involved in the bond. Since it is a double bond, both carbon atoms received two electrons.
• If the electrons assigned to the lower carbon atom are added, this carbon atom has four binding electrons . Since carbon as an element also has four binding electrons, its charge has not changed due to the imaginary assignment. Its oxidation number is therefore: 0.

In comparison, the lowest nitrogen atom gets six bonding electrons in the imaginary assignment (two each from the two carbon atoms and two from the hydrogen atom). However, nitrogen as an element has only three binding electrons. Since electrons are negatively charged, the nitrogen atom would therefore have the charge −3 according to the imaginary assignment and this is also its oxidation number.

To check this, all oxidation numbers determined in this way must be added. Their sum must be zero if the entire molecule is uncharged or must match the charge if the entire molecule is a charged ion.

## Remarks

1. The statement can only be checked with great difficulty using redox equations, which do not show oxidation numbers for every atom, because the stoichiometric coefficients also have to be taken into account. The statement, however, corresponds to the basic rule, which is easy to check, that a stoichiometrically correct redox reaction equation must have a balanced landing balance

## Individual evidence

1. a b Entry on Oxidation state . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.O04365 Version: 2.3 ..
2. Hans-Dieter Jakubke, Ruth Karcher (Ed.): Lexicon of Chemistry , Spectrum Academic Publishing House, Heidelberg, 2001.
3. Brown, Le May: Chemistry, a textbook for all natural scientists . VCH Verlagsgesellschaft, Weinheim 1988, ISBN 3-527-26241-5 , pp. 781 ff .
4. ^ Karl-Heinz Lautenschläger, Werner Schröter, Joachim Teschner, Hildegard Bibrack, Taschenbuch der Chemie , 18th edition, Harri Deutsch, Frankfurt (Main), 2001.
5. Entry on Oxidation number . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.O04363 Version: 2.3 ..
6. ^ Clayden, Greeves Warren, Wothers: Organic Chemistry . Oxford University Press Inc, New York 2001, ISBN 978-0-19-850346-0 , pp. 35 f .
7. Guanjun Wang, Mingfei Zhou, James T. Goettel, Gary G. Schrobilgen, Jing Su, Jun Li, Tobias Schlöder, Sebastian Riedel: Identification of an iridium-containing compound with a formal oxidation state of IX . In: Nature . 514, August 21, 2014, pp. 475-477. doi : 10.1038 / nature13795 .