IMAT Chemistry · Redox Reactions

Oxidation Numbers: Rules and Calculation

An oxidation number is the charge an atom would carry if every bond were fully ionic; a few fixed rules and the total charge let you find it for any atom.

All Redox Reactions notes

Why this matters

Oxidation numbers are the most tested idea in this chapter. The 2025 paper asked which compound gives chlorine +3 and what kind of number an oxidation number cannot be; the older papers asked for the states of nitrogen, chlorine and vanadium across a list of species, and for a general formula for an oxoacid.

Concept 1 of 3: The rules for assigning oxidation numbers

Oxidation numbers are bookkeeping. Pretend every bond is broken so that the more electronegative atom takes all the shared electrons, then read off the charge each atom would have. A handful of atoms almost always behave the same way, so start with them and let the total charge decide the rest.

Definition

The oxidation number (oxidation state) of an atom is the charge it would have if all its bonds were ionic.

Work in this order: elements, then fixed atoms (F, Group 1, Group 2, Al, H, O), then the unknown atom from the total.
The sum of oxidation numbers is 0 in a neutral compound and equals the charge in an ion.
When rules clash, the higher one in the table wins: in $\mathrm{OF_2}$ , F is −1, so O must be +2.
The naming side (Stock numbers such as iron(III), and the -ite and -ate endings) is covered in the Inorganic Compounds and Nomenclature chapter.

Atom or situation	Oxidation number	Exception or example
An uncombined element	0	$\mathrm{Na}$ , $\mathrm{O_2}$ , $\mathrm{Cl_2}$ , $\mathrm{P_4}$ , $\mathrm{S_8}$ are all 0
A simple (monatomic) ion	Equal to its charge	$\mathrm{Mg^{2+}}$ is +2, $\mathrm{Cl^-}$ is −1
Fluorine in a compound	−1 always	The most electronegative element, no exceptions
Group 1, Group 2, aluminium	+1, +2, +3	Almost no exceptions in IMAT
Hydrogen	+1	−1 in metal hydrides: $\mathrm{NaH}$ , $\mathrm{LiH}$ , $\mathrm{CaH_2}$
Oxygen	−2	−1 in peroxides ( $\mathrm{H_2O_2}$ , $\mathrm{Na_2O_2}$ ); +2 in $\mathrm{OF_2}$ Peroxides are the exception IMAT likes most: in hydrogen peroxide each O is −1.
Cl, Br, I	−1 in halides	Positive when bonded to O: +1 in $\mathrm{HClO}$ , +7 in $\mathrm{HClO_4}$

Practice this conceptself-check · 4 quick reps

Oxygen is not always −2, and hydrogen is not always +1

In peroxides each oxygen is −1, and in

\mathrm{OF_2}

oxygen is +2. In metal hydrides such as NaH, hydrogen is −1. Applying the usual values blindly to these compounds gives a wrong oxidation number for every other atom.

Concept 2 of 3: Working out an oxidation number from a formula

Once the fixed atoms are assigned, the unknown atom must make the total come out right. Write one equation, with the unknown multiplied by how many of those atoms there are, and solve it. For oxoacids and oxoanions this gives a quick general formula.

Definition

Write: (count × unknown) + (sum of the known oxidation numbers) = overall charge.
For an oxoacid $\mathrm{H_mXO_n}$ : $x + m - 2n = 0$ , so $x = 2n - m$ .
For an oxoanion $\mathrm{XO_n^{c-}}$ : $x - 2n = -c$ , so $x = 2n - c$ .
In a polyatomic ion, remember the charge: in $\mathrm{NH_4^+}$ the sum is +1, not 0.

Sum of oxidation numbers

\sum (\text{number of atoms} \times \text{oxidation number}) = \text{overall charge}

overall charge0 for a neutral compound; the ion's charge for an ion

Worked example

Find the oxidation number of chromium in

\mathrm{Cr_2O_7^{2-}}

and of nitrogen in

\mathrm{NH_4^+}

Practice this conceptself-check · 4 quick reps

Divide by the number of atoms of the unknown element

\mathrm{Cr_2O_7^{2-}}

the oxygens contribute −14 and the ion is −2, so the two chromium atoms together are +12 and EACH is +6. Forgetting to divide gives +12, an impossible value that IMAT sometimes offers.

Concept 3 of 3: The range of oxidation numbers, and fractional averages

A main-group atom can lose at most all its outer electrons and gain at most enough to fill its octet. That fixes the highest and lowest oxidation number it can show. Inside that range many values are possible, and when atoms of the same element in one formula sit in different states, the calculation gives their average, which may be a fraction.

Definition

For a main-group element: highest oxidation number = the number of outer electrons (the group number in the 1 to 8 numbering); lowest = that number minus 8.
Nitrogen: −3 to +5. Sulfur: −2 to +6. Chlorine: −1 to +7. Carbon: −4 to +4.
Transition metals show many states: manganese from +2 to +7, chromium +3 and +6, iron +2 and +3, vanadium +2 to +5.
An oxidation number can be positive, negative, zero, or a fraction (an average over several atoms). Being a ratio of whole numbers, it is always rational, never an irrational number.

Limits for a main-group element

\text{lowest} = \text{outer electrons} - 8 \qquad \text{highest} = \text{outer electrons}

outer electronsvalence electrons: 5 for N and P, 6 for O and S, 7 for the halogens

Worked example

Find the oxidation number of iron in magnetite,

\mathrm{Fe_3O_4}

, and explain the result.

Practice this conceptself-check · 4 quick reps

Oxidation numbers can be fractions, but not irrational

An average such as

+8/3

\mathrm{Fe_3O_4}

or +2.5 in

\mathrm{S_4O_6^{2-}}

is a genuine result. Every oxidation number is a whole-number total shared among whole numbers of atoms, so it is always a ratio of integers: never irrational.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Working out an oxidation number from a formula
Sum of oxidation numbers
$\sum (\text{number of atoms} \times \text{oxidation number}) = \text{overall charge}$
The range of oxidation numbers, and fractional averages
Limits for a main-group element
$\text{lowest} = \text{outer electrons} - 8 \qquad \text{highest} = \text{outer electrons}$

Reference tables (1)

The rules for assigning oxidation numbers7 rows

Atom or situation	Oxidation number	Exception or example
An uncombined element	0	$\mathrm{Na}$ , $\mathrm{O_2}$ , $\mathrm{Cl_2}$ , $\mathrm{P_4}$ , $\mathrm{S_8}$ are all 0
A simple (monatomic) ion	Equal to its charge	$\mathrm{Mg^{2+}}$ is +2, $\mathrm{Cl^-}$ is −1
Fluorine in a compound	−1 always	The most electronegative element, no exceptions
Group 1, Group 2, aluminium	+1, +2, +3	Almost no exceptions in IMAT
Hydrogen	+1	−1 in metal hydrides: $\mathrm{NaH}$ , $\mathrm{LiH}$ , $\mathrm{CaH_2}$
Oxygen	−2	−1 in peroxides ( $\mathrm{H_2O_2}$ , $\mathrm{Na_2O_2}$ ); +2 in $\mathrm{OF_2}$ Peroxides are the exception IMAT likes most: in hydrogen peroxide each O is −1.
Cl, Br, I	−1 in halides	Positive when bonded to O: +1 in $\mathrm{HClO}$ , +7 in $\mathrm{HClO_4}$

Watch out for (3)

Oxygen is not always −2, and hydrogen is not always +1
→ The rules for assigning oxidation numbers
Divide by the number of atoms of the unknown element
→ Working out an oxidation number from a formula
Oxidation numbers can be fractions, but not irrational
→ The range of oxidation numbers, and fractional averages

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