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How to Assign Oxidation Numbers

The oxidation number is the positive or negative number of an atom that indicates the electrical charge the atom has if its compound consists of ions. In other words, the oxidation number gives the degree of oxidation (loss of electrons) or reduction (gain of electrons) of the atom in a compound. Because they track the number of electrons lost or gained, oxidation numbers are a sort of shorthand for balancing charge in chemical formulas.

This is a list of rules for assigning oxidation numbers, with examples showing the numbers for elements, compounds, and ions.

Rules for Assigning Oxidation Numbers

Various texts contain different numbers of rules and may change their order. Here is a list of oxidation number rules:

• Write the cation first in a chemical formula, followed by the anion. The cation is the more electropositive atom or ion, while the anion is the more electronegative atom or ion. Some atoms may be either the cation or anion, depending on the other elements in the compound. For example, in HCl, the H is H + , but in NaH, the H is H – .
• Write the oxidation number with the sign of the charge followed by its value. For example, write +1 and -3 rather than 1+ and 3-. The latter form is used to indicate oxidation state .
• The oxidation number of a free element or neutral molecule is 0. For example, the oxidation number of C, Ne, O 3 , N 2 , and Cl 2 is 0.
• The sum of all the oxidation numbers of the atoms in a neutral compound is 0. For example, in NaCl, the oxidation number of Na is +1, while the oxidation of Cl is -1. Added together, +1 + (-1) = 0.
• The oxidation number of a monatomic ion is the charge of the ion. For example, the oxidation number of Na + is +1, the oxidation number of Cl – is -1, and the oxidation number of N 3- is -3.
• The sum of the oxidation numbers of a polyatomic ion is the charge of the ion. For example, the sum of the oxidation numbers for SO 4 2-  is -2.
• The oxidation number of a group 1 (alkali metal) element in a compound is +1.
• The oxidation number of a group 2 (alkaline earth) element in a compound is +2.
• The oxidation number of a group 7 (halogen) element in a compound is -1. The exception is when the halogen combines with an element with higher electronegativity (e.g., oxidation number of Cl is +1 in HOCl).
• The oxidation number of hydrogen in a compound is usually +1. The exception is when hydrogen bonds with metals forming the hydride anion (e.g., LiH, CaH 2 ), giving hydrogen an oxidation number of -1.
• The oxidation number of oxygen in a compound is usually -2. Exceptions include OF 2 and BaO 2 .

Examples of Assigning Oxidation Numbers

Example 1: Find the oxidation number of iron in Fe 2 O 3 .

The compound has no electrical charge, so the oxidation numbers of iron and oxygen balance each other out. From the rules, you know the oxidation number of oxygen is usually -2. So, find the iron charge that balances the oxygen charge. Remember, the total charge of each atom is its subscript multiplied by its oxidation number. O is -2 There are 3 O atoms in the compound so the total charge is 3 x -2 = -6 The net charge is zero (neutral), so: 2 Fe + 3(-2) = 0 2 Fe = 6 Fe = 3

Example 2: Find the oxidation number for Cl in NaClO3.

Usually, a halogen like Cl has an oxidation number of -1. But, if you assume Na (an alkali metal) has an oxidation number of +1 and O has an oxidation number of -2, the charges don’t balance out to give a neutral compound. It turns out all of the halogens, except for fluorine, have more than one oxidation number. Na = +1 O = -2 1 + Cl + 3(-2) = 0 1 + Cl -6 = 0 Cl -5 = 0 Cl = -5

• IUPAC (1997) “Oxidation Number”. Compendium of Chemical Terminology (the “Gold Book”) (2nd ed.). Blackwell Scientific Publications. doi: 10.1351/goldbook
• Karen, P.; McArdle, P.; Takats, J. (2016). “Comprehensive definition of oxidation state (IUPAC Recommendations 2016)”.  Pure Appl. Chem .  88  (8): 831–839. doi: 10.1515/pac-2015-1204
• Whitten, K. W.; Galley, K. D.; Davis, R. E. (1992).  General Chemistry  (4th ed.). Saunders.

Related Posts

What Are the Rules for Assigning Oxidation Numbers?

Redox Reactions and Electrochemistry

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Electrochemical reactions involve the transfer of electrons . Mass and charge are conserved when balancing these reactions, but you need to know which atoms are oxidized and which atoms are reduced during the reaction. Oxidation numbers are used to keep track of how many electrons are lost or gained by each atom. These oxidation numbers are assigned using the following rules.

Rules for Assigning Oxidation Numbers

• The convention is that the cation is written first in a formula, followed by the anion . For example, in NaH, the H is H-; in HCl, the H is H+.
• The oxidation number of a free element is always 0. The atoms in He and N 2 , for example, have oxidation numbers of 0.
• The oxidation number of a monatomic ion equals the charge of the ion. For example, the oxidation number of Na + is +1; the oxidation number of N 3- is -3.
• The usual oxidation number of hydrogen is +1. The oxidation number of hydrogen is -1 in compounds containing elements that are less ​ electronegative than hydrogen, as in CaH 2 .
• The oxidation number of oxygen in compounds is usually -2. Exceptions include OF 2 because F is more electronegative than O, and BaO 2 , due to the structure of the peroxide ion, which is [O-O] 2- .
• The oxidation number of a Group IA element in a compound is +1.
• The oxidation number of a Group IIA element in a compound is +2.
• The oxidation number of a Group VIIA element in a compound is -1, except when that element is combined with one having a higher electronegativity. The oxidation number of Cl is -1 in HCl, but the oxidation number of Cl is +1 in HOCl.
• The sum of the oxidation numbers of all of the atoms in a neutral compound is 0.
• The sum of the oxidation numbers in a polyatomic ion is equal to the charge of the ion. For example, the sum of the oxidation numbers for SO 4 2- is -2.
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8.5: Redox Reactions

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The oxidation number  (O.N.) of an element represents the total number of electrons which have been removed (a positive oxidation state) or added (a negative oxidation state) to get the element into its present state. The term oxidation describes the loss of electrons by an element and an increase in oxidation state; the term reduction describes the gain of electrons and a decrease in oxidation state. Oxidation numbers for elements in compounds can be calculated using a simple set of rules, which are reproduced below in Table 5.3.

In many chemical reactions, the oxidation number of elements change. Consider the synthesis reaction shown below. In the reactants, carbon and oxygen are both elements and their oxidation numbers are zero (Rule 1). In the product, oxygen will have an oxidation number of –2 (Rule 4), therefore, carbon in CO 2 must have an oxidation number of +4 in order to balance the four negative charges on the oxygens. During this reaction, the oxidation number of carbon has changed from zero in the reactants to +4 in the products and the oxidation number of oxygen has changed from zero to –2. This is an example of a redox reaction ; a chemical reaction in which the oxidation numbers of elements change on going from reactants to products.

C (s) + O 2 (g) → CO 2 (g)

In a redox reaction, the element that “ loses electrons ” is said to be oxidized and will have an increase in its oxidation number . In the example above, the oxidation number of carbon increases from zero to +4; it has “lost electrons” and has been oxidized . The element that “ gains electrons ” in a redox reaction is said to be reduced and will have a decrease in its oxidation number . In the reaction above, the oxidation number of oxygen has decreased from zero to –2; it has “gained electrons” and has been reduced .

An examination of the rules for assigning oxidation numbers reveals that there are many elements for which there are no specific rules, such as nitrogen, sulfur, and chlorine. These elements, as well as some others, can have variable oxidation numbers depending on the other atoms to which they are covalently bonded in a molecular compound. It is useful to analyze a few molecules in order to see the strategy to follow in assigning oxidation numbers to other atoms.

Oxidation numbers for the atoms in a binary ionic compound are easy to assign because they are equal to the charge of the ion (rule 2). In CuCl 2 , the oxidation number of copper is +2, while the oxidation number of chlorine is −1. This is because CuCl 2 is  an ionic compound that is actually composed of these ions.

Assigning oxidation numbers for molecular compounds is trickier. The key is to remember rule 6: that the sum of all the oxidation numbers for any neutral species must be zero. Make sure to account for any subscripts which appear in the formula. As an example, consider the compound nitric acid, HNO 3 . According to rule 3, the oxidation number of hydrogen is +1. According to rule 4, the oxidation number of oxygen is −2. There is no rule regarding nitrogen, but its oxidation number can be calculated as follows.

1(+1)+x+3(−2)=0, where x is the oxidation number of nitrogen.

Solving for x, we obtain x=+5

The oxidation number of the nitrogen atom in HNO 3  is +5

Examples \(\PageIndex{1}\)

For each of the reactions given below, calculate the oxidation number of each of the elements in the reactants and the products and determine if the reaction involves oxidation-reduction. If it is a redox reaction, identify the elements that have been oxidized and reduced.

• Cu 2 S → 2 Cu + S Reactants: Cu O.N.= +1     S  O.N. = -2 Products: Cu O.N.= 0       S   O.N.= 0 Element oxidized: sulfur  Element Reduced: copper. This is a redox reaction.
• CaCO 3 → CaO + CO 2 Reactants: Ca O.N.= +2   C  O.N.= +4    O O.N.= -2 Products: Ca O.N.= +2   C  O.N.= +4     O O.N.= -2 Element oxidized: none. Element Reduced: none. This is non-redox reaction.
• Fe 2 O 3 + 3 H 2 → 2 Fe + 3 H 2 O Reactants: Fe O.N.=+3  O   O.N.=-2   H    O.N.=0 Products: Fe O.N.=0  O  O.N.=-2  H  O.N.=+1 Element oxidized: hydrogen. Element Reduced: iron. This is a redox reaction
• AgNO 3 + NaCl → AgCl (s) + NaNO 3 Reactants: Ag O.N.=+1 (cation) N O.N.=+5 (rule 6)  O O.N.=-2   Na O.N.=+1   Cl O.N.=-1 Ag O.N.=+1 (cation) N O.N.=+5 (rule 6)  O O.N.=-2   Na O.N.=+1   Cl O.N.=-1 Element oxidized: none. Element Reduced: none. This is a non-redox reaction

Contributors

•   Oxidation numbers . Contributed by  Allison Soult  , Senior Lecturer (Chemistry) at  University of Kentucky