Oxidation Numbers

Keeping track of electrons

In lesson 1.5.2 you met valence: Mn is +7 in KMnO₄ and S is +6 in H₂SO₄. Lesson 2.7.2 described zinc reacting with copper(II) sulfate: Zn loses electrons to become Zn²⁺, and Cu²⁺ gains electrons to become Cu. This chapter is about such oxidation–reduction (redox) reactions, where electrons move from one atom to another. To see where the electrons go, we first need to keep a ledger for every atom: in this compound, does it count as having gained electrons or lost them?

The oxidation number氧化数 (or oxidation state) of an atom is the charge it would have if every shared electron pair in the compound belonged completely to the more electronegative atom (lesson 2.3.5).

Take H₂O. O is more electronegative than H, so both shared pairs are counted toward O. O started with 6 valence electrons and now counts 8, two extra, so its oxidation number is −2. Each H counts one electron fewer than it started with, so each is +1. In an ionic compound, atoms really have gained or lost electrons, and the oxidation number is just the ion’s charge.

Oxidation numbers are bookkeeping, so they can even be fractions: the average oxidation number of Fe in Fe₃O₄ is +8/3.

Rules for assigning oxidation numbers

The rules are listed in order of priority. When two rules conflict, the one higher on the list wins:

An atom in an element is 0: Cl₂, Fe, O₂.
A monatomic ion equals its charge: Fe³⁺ is +3, Cl⁻ is −1.
The oxidation numbers in a compound add up to 0; in a polyatomic ion they add up to the ion’s charge.
F is always −1 in compounds.
Group 1 metals are always +1, Group 2 metals are always +2, and Al is always +3.
H is +1 when bonded to nonmetals and −1 when bonded to metals (metal hydrides such as NaH and CaH₂).
O is usually −2. It is −1 in peroxides (H₂O₂, Na₂O₂) and +2 in OF₂.
Cl, Br, and I are usually −1, but positive when bonded to O: Cl is +1 in ClO⁻.

Use the rules to settle what you can, then find the last element from the sum. In KMnO₄, K is +1 and O is −2; letting Mn be x:

(+1) + x + 4 \times (-2) = 0, \quad x = +7

Oxidation numbers are often written above the symbols:

\ce{K}\overset{+7}{\ce{Mn}}\ce{O4}

Pick a molecule or ion below and use + and − to give each element an oxidation number. Watch whether the sum matches the charge. The last three are the “exceptions” for H and O:

Try it: assign an oxidation number to each element

One element, many oxidation numbers

Many elements have different oxidation numbers in different substances. Nitrogen is a good example:

Substance	NH₃	N₂	NO	NO₂	HNO₃
Oxidation number of N	−3	0	+2	+4	+5

For main-group elements, the highest positive oxidation number usually equals the group’s A-group number (N is in group 5A, so +5 at most), and for nonmetals the most negative equals the group number minus 8 (N is −3 at least). O and F are exceptions. An element at its highest oxidation number can only go down, one at its lowest can only go up, and one in between can do either. Lesson 2.13.2 uses this.

How Chinese textbooks differ

Chinese high school textbooks talk about 化合价 (valence) rising and falling rather than oxidation numbers. For almost every substance at this level the numbers are the same.
The Chinese convention writes valence directly above the symbol with the sign first (+7). It also keeps valence a whole number: Fe₃O₄ is described as containing both +2 and +3 iron rather than +8/3.
Roman numerals in names such as iron(III) chloride (lesson 2.5.1) are oxidation numbers; Chinese names use 亚铁 and 铁 instead.

Example 1: oxidation numbers in an ion

Find the oxidation number of Cr in the dichromate ion, Cr₂O₇²⁻.

Step-by-step solution

The rules. In a neutral compound the oxidation numbers add up to 0; in an ion they add up to the ion’s charge. O is usually −2.
What the rules settle. O is −2; seven O atoms give 7 × (−2) = −14.
Set up the equation. Let Cr be x; two Cr atoms give 2x, and the sum must equal the ion’s charge, −2:
$\begin{aligned} 2x + (-14) &= -2 \\ 2x &= +12 \\ x &= \boxed{+6} \end{aligned}$
Check. 2(+6) + 7(−2) = +12 − 14 = −2, the ion’s charge.
A common mistake. Setting the sum to 0 and getting +7. The ion has a charge, so the sum is −2.

Example 2: two unusual oxidation numbers

(a) Find the oxidation number of O in H₂O₂. (b) Find the average oxidation number of Fe in Fe₃O₄, and check it by treating Fe₃O₄ as FeO·Fe₂O₃.

Step-by-step solution

H₂O₂: start with H. H is bonded to a nonmetal, so it is +1, giving +2 in total. Let O be x:
$\begin{aligned} 2(+1) + 2x &= 0 \\ x &= \boxed{-1} \end{aligned}$
Why not −2? The two O atoms share an O–O bond equally, so each O counts only one extra electron. Forcing O to be −2 would make H +2, which is impossible.
Fe₃O₄ average. Four O atoms give −8. Let the average for Fe be x:
$\begin{aligned} 3x + 4(-2) &= 0 \\ x &= \boxed{+\tfrac{8}{3}} \end{aligned}$
Check. As FeO·Fe₂O₃, one Fe is +2 and two are +3: (+2) + 2(+3) = +8, again an average of +8/3. Chinese textbooks describe it this way, as two valences.
Think about it. An average oxidation number can be a fraction, but each atom’s actual oxidation number is a whole number. A fraction means the element is present in more than one oxidation state.
A common mistake. Writing −2 for O automatically. In peroxides such as H₂O₂ and Na₂O₂, O is −1.

Practice: what is the oxidation number of the element asked about?

N in NH₃
O in H₂O₂
H in CaH₂
S in S₈
C in CO
N in NO₂
N in HNO₃
S in SO₄²⁻
Cl in HClO₄

Common mistakes

Mistake 1: “O is always −2 in compounds.” O is −1 in peroxides (H₂O₂, Na₂O₂) and +2 in OF₂. The rules have a priority order, and the rules for F and H come before the rule for O.

Mistake 2: “The oxidation numbers in a polyatomic ion add up to 0.” They add up to the ion’s charge. For SO₄²⁻, x + 4 × (−2) = −2, not 0; setting it to 0 would give S an impossible +8.

Mistake 3: “An oxidation number is the real charge on the atom.” In an ionic compound it is. In a covalent compound it is only bookkeeping, as if one atom took all the shared electrons. C in CH₄ has oxidation number −4, but the carbon atom does not actually carry a 4− charge.

Quick check

What is the oxidation number of Cr in K₂Cr₂O₇?

In which substance is the oxidation number of O not −2?

Summary

An oxidation number is the charge an atom would have if shared electrons all went to the more electronegative atom. It can be a fraction.
Apply the rules in order: elements 0; monatomic ions equal their charge; F −1; Group 1 and 2 metals +1 and +2; H usually +1 (−1 in metal hydrides); O usually −2 (−1 in peroxides). The sum equals the charge on the species.
One element can have several oxidation numbers; for main-group elements the highest usually equals the group number.

On to AP (for later)

AP topic 4.9 uses oxidation numbers to decide whether a reaction is redox and which element is oxidized or reduced. A free-response answer such as “the oxidation number of Mn changes from +7 to +2” is the kind of evidence AP expects.

Oxidation Numbers氧化数

Learning goals

Before you start

Keeping track of electrons