Table of Contents
Purpose of Oxidation Numbers
Oxidation numbers (also called oxidation states) are bookkeeping numbers assigned to atoms in molecules or ions to keep track of electron transfer in redox reactions. They do not necessarily describe real charges on atoms, but they allow you to:
- Decide which species is oxidized and which is reduced.
- Identify oxidizing and reducing agents.
- Systematically balance redox equations.
In this chapter we focus on how to assign oxidation numbers and how to use them, not yet on how to balance full redox equations in detail (that is treated elsewhere).
Basic Idea
- Oxidation numbers indicate how many electrons an atom has “lost” or “gained” relative to its elemental form.
- By convention:
- A more positive oxidation number means relative loss of electrons (oxidation).
- A more negative oxidation number means relative gain of electrons (reduction).
For a single atom or ion, the oxidation number is written as a signed integer, often as a superscript with the sign first, e.g. $+2$, $-1$.
General Rules for Assigning Oxidation Numbers
Oxidation numbers are assigned according to a set of rules that are applied in a standard order. These rules are conventions; they are chosen to be self-consistent and to match common chemical behavior.
Below, Ox stands for oxidation number.
1. Elementary substances
For an element in its standard form (not combined with other elements, only with itself):
- $ \text{Ox} = 0 $
Examples:
- $ \text{H}_2,\ \text{O}_2,\ \text{N}_2,\ \text{Cl}_2,\ \text{P}_4,\ \text{S}_8,\ \text{Fe} $ all have oxidation numbers:
- H in $ \text{H}_2$: $0$
- O in $ \text{O}_2$: $0$
- Fe in metallic iron: $0$
This includes allotropes such as graphite and diamond (both C with $ \text{Ox} = 0$).
2. Monatomic ions
For a simple ion containing only one atom, the oxidation number equals the ion charge:
- $ \text{Ox}(\text{Na}^+) = +1 $
- $ \text{Ox}(\text{Mg}^{2+}) = +2 $
- $ \text{Ox}(\text{Cl}^-) = -1 $
- $ \text{Ox}(\text{Fe}^{3+}) = +3 $
3. Sum of oxidation numbers
- In a neutral compound, the sum of all oxidation numbers is $0$.
- In a polyatomic ion, the sum of all oxidation numbers equals the net charge of the ion.
Examples:
- In $\text{H}_2\text{O}$ (neutral): sum of oxidation numbers $= 0$.
- In $\text{SO}_4^{2-}$: sum of oxidation numbers $= -2$.
This rule is the main tool to determine unknown oxidation numbers once a few are known from other rules.
4. Oxidation number of oxygen
Typical rule:
- Oxygen usually has $ \text{Ox} = -2 $.
Exceptions (to remember specifically):
- Peroxides (e.g. $\text{H}_2\text{O}_2$):
- Here, oxygen has $ \text{Ox} = -1 $.
- Superoxides (e.g. $\text{KO}_2$):
- Here, oxygen has $ \text{Ox} = -\frac{1}{2} $ on average.
- Some compounds of oxygen with fluorine, e.g. $\text{OF}_2$:
- Here, fluorine is more electronegative, so oxygen is forced into a positive oxidation state:
- In $\text{OF}_2$, O has $ \text{Ox} = +2 $, F has $-1$ (usual for F).
5. Oxidation number of hydrogen
Typical rule:
- Hydrogen usually has $ \text{Ox} = +1 $ when bonded to nonmetals.
Important exception:
- In metal hydrides (such as $\text{NaH}$, $\text{CaH}_2$), hydrogen has $ \text{Ox} = -1 $.
Examples:
- $\text{H}_2\text{O}$: H is $+1$, O is $-2$.
- $\text{CH}_4$: H is $+1$, so C must be $-4$.
- $\text{NaH}$: Na is $+1$ (alkali metal), so H is $-1$.
6. Oxidation numbers of halogens
- Fluorine (F) always has $ \text{Ox} = -1 $ in its compounds (no exceptions in simple inorganic chemistry).
- Other halogens (Cl, Br, I) usually have $ \text{Ox} = -1 $ in binary compounds with less electronegative elements.
However, when bonded to oxygen or to more electronegative halogens, they can have positive oxidation numbers:
- In $\text{ClO}^-$: O is $-2$, the ion has charge $-1$. So Cl must be $+1$.
- In $\text{ClO}_4^-$: O is $-2$, total $4 \times (-2)=-8$. Charge is $-1$; therefore Cl is $+7$.
7. Oxidation numbers of s-block metals
- Group 1 (alkali metals) in their compounds: $ \text{Ox} = +1$.
- Group 2 (alkaline earth metals) in their compounds: $ \text{Ox} = +2$.
These are very reliable rules and widely used for quick assignments.
8. Using electronegativity as a last resort
If none of the special rules apply, the more electronegative element in a bond is formally assigned the negative oxidation number, and the less electronegative one the corresponding positive value so that the total fits the overall charge.
This is mostly needed for unusual or advanced compounds.
Worked Examples of Oxidation Number Assignments
In practice, you apply the rules in combination. The following examples illustrate common patterns and also highlight exceptions.
Example 1: $\text{H}_2\text{O}$
- H usually $+1$.
- Sum of oxidation numbers in a neutral molecule is $0$.
Let $ \text{Ox}(\text{O}) = x$.
Then:
$$ 2 \cdot (+1) + x = 0 $$
$$ 2 + x = 0 \Rightarrow x = -2 $$
Result: $ \text{Ox}(\text{H}) = +1,\ \text{Ox}(\text{O}) = -2$.
Example 2: $\text{CO}_2$
- O is usually $-2$.
- Sum of oxidation numbers in a neutral molecule is $0$.
Let $ \text{Ox}(\text{C}) = x$.
Then:
$$ x + 2 \cdot (-2) = 0 $$
$$ x - 4 = 0 \Rightarrow x = +4 $$
Result: C is $+4$, each O is $-2$.
Example 3: $\text{NH}_3$
- H is $+1$.
- Sum of oxidation numbers is $0$.
Let $ \text{Ox}(\text{N}) = x$.
Then:
$$ x + 3 \cdot (+1) = 0 $$
$$ x + 3 = 0 \Rightarrow x = -3 $$
Result: N is $-3$, each H is $+1$.
Example 4: $\text{H}_2\text{O}_2$ (a peroxide)
- H is $+1$.
- The compound is neutral: sum is $0$.
- Recognize this is a peroxide, so O is $-1$ by special rule.
Check:
$$ 2 \cdot (+1) + 2 \cdot (-1) = 2 - 2 = 0 $$
Result: H is $+1$, O is $-1$.
Example 5: $\text{SO}_4^{2-}$ (sulfate ion)
- O is $-2$.
- Total charge is $-2$.
Let $ \text{Ox}(\text{S}) = x$.
Then:
$$ x + 4 \cdot (-2) = -2 $$
$$ x - 8 = -2 \Rightarrow x = +6 $$
Result: S is $+6$, each O is $-2$.
Example 6: $\text{NO}_3^-$ (nitrate ion)
- O is $-2$.
- Total charge is $-1$.
Let $ \text{Ox}(\text{N}) = x$.
Then:
$$ x + 3 \cdot (-2) = -1 $$
$$ x - 6 = -1 \Rightarrow x = +5 $$
Result: N is $+5$, each O is $-2$.
Example 7: $\text{NaH}$ (a metal hydride)
- Na is an alkali metal: $+1$.
- Sum of oxidation numbers in a neutral compound is $0$.
Let $ \text{Ox}(\text{H}) = x$.
Then:
$$ (+1) + x = 0 \Rightarrow x = -1 $$
Result: Na is $+1$, H is $-1$.
Example 8: $\text{KMnO}_4$ (potassium permanganate)
- K is an alkali metal: $+1$.
- O is $-2$.
- The compound is neutral.
Let $ \text{Ox}(\text{Mn}) = x$.
Then:
$$ (+1) + x + 4 \cdot (-2) = 0 $$
$$ 1 + x - 8 = 0 $$
$$ x - 7 = 0 \Rightarrow x = +7 $$
Result: Mn is $+7$, each O is $-2$, K is $+1$.
Example 9: $\text{Fe}_2\text{O}_3$
- O is $-2$.
- Total sum is $0$ for neutral compound.
Let $ \text{Ox}(\text{Fe}) = x$.
Then:
$$ 2x + 3 \cdot (-2) = 0 $$
$$ 2x - 6 = 0 \Rightarrow x = +3 $$
Result: Fe is $+3$, O is $-2$.
Note: This is iron(III) oxide; the Roman numeral matches the oxidation number of Fe.
Example 10: $\text{ClO}_3^-$ (chlorate ion)
- O is $-2$.
- The ion charge is $-1$.
Let $ \text{Ox}(\text{Cl}) = x$.
Then:
$$ x + 3 \cdot (-2) = -1 $$
$$ x - 6 = -1 \Rightarrow x = +5 $$
Result: Cl is $+5$, each O is $-2$.
Oxidation Numbers vs. Formal Charges
Oxidation numbers are formal electron bookkeeping tools based on fully ionic bond splitting (electrons go entirely to the more electronegative partner in the accounting).
By contrast, formal charges use a different set of rules (equal sharing of bond electrons) and are often used in drawing Lewis structures. For many simple ions, oxidation number and formal charge may coincide, but in general they are not the same concept and may give different values for the same atom.
In redox chemistry we usually work with oxidation numbers, not formal charges.
Using Oxidation Numbers to Identify Oxidation and Reduction
Once you can assign oxidation numbers, you can analyze redox reactions:
- Oxidation: increase in oxidation number of an atom.
- Reduction: decrease in oxidation number of an atom.
The oxidizing agent is reduced (its oxidation number decreases), and the reducing agent is oxidized (its oxidation number increases).
Example: Reaction of Mg with HCl
Reaction:
$$ \text{Mg} + 2\text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2 $$
Assign oxidation numbers:
- Left side:
- Mg (element): $0$.
- In HCl: H is $+1$, Cl is $-1$.
- Right side:
- In $\text{MgCl}_2$: Cl is $-1$, so Mg must be $+2$.
- In $\text{H}_2$: H (element) is $0$.
Changes:
- Mg: $0 \rightarrow +2$ (increase) → Mg is oxidized, Mg is the reducing agent.
- H: $+1 \rightarrow 0$ (decrease) → H is reduced, $\text{H}^+$ (from HCl) is the oxidizing agent.
Oxidation numbers make these changes obvious.
Example: Combustion of Carbon
Reaction:
$$ \text{C} + \text{O}_2 \rightarrow \text{CO}_2 $$
- C: $0 \rightarrow +4$ (oxidation).
- O: $0 \rightarrow -2$ (reduction for each O atom).
Here, C is oxidized, O is reduced.
Average Oxidation Numbers
In species where an element occurs in equivalent positions, a single oxidation number may apply to all atoms of that element.
Sometimes an element has an average oxidation number that is not an integer because different atoms of the same element in the same species have different environments. In such cases, we still talk about a mean oxidation state.
Example: $\text{Fe}_3\text{O}_4$
- O is $-2$.
- The compound is neutral.
Let the average oxidation number of Fe be $x$:
$$ 3x + 4 \cdot (-2) = 0 $$
$$ 3x - 8 = 0 \Rightarrow x = \frac{8}{3} \approx +2.67 $$
This indicates that in $\text{Fe}_3\text{O}_4$ there are Fe atoms in more than one oxidation state (specifically, Fe(II) and Fe(III)), and the composition is often written as $\text{FeO} \cdot \text{Fe}_2\text{O}_3$.
Typical Oxidation Number Ranges for Selected Elements
You do not need to memorize all possibilities, but some ranges recur frequently and help you recognize redox changes:
- Carbon: $-4$ (e.g. $\text{CH}_4$) to $+4$ (e.g. $\text{CO}_2$).
- Nitrogen: $-3$ (e.g. $\text{NH}_3$) to $+5$ (e.g. $\text{NO}_3^-$).
- Sulfur: $-2$ (e.g. $\text{H}_2\text{S}$) to $+6$ (e.g. $\text{SO}_4^{2-}$).
- Chlorine: $-1$ (e.g. $\text{Cl}^-$) to $+7$ (e.g. $\text{ClO}_4^-$).
- Manganese: from $+2$ (e.g. $\text{Mn}^{2+}$) up to $+7$ (e.g. $\text{MnO}_4^-$).
- Iron: commonly $+2$ and $+3$.
Recognizing these helps you quickly see if a reaction involves oxidation or reduction.
Common Pitfalls and How to Avoid Them
- Confusing charge with oxidation number
- A neutral atom in a compound can have a nonzero oxidation number.
- Example: C in CO$_2$ has $+4$, but the molecule is neutral.
- Forgetting exceptions for O and H
- Always check: Is this a peroxide? Is this a metal hydride?
- Do not automatically assign O $-2$ and H $+1$ in these special cases.
- Misusing average oxidation numbers
- A fractional oxidation number is an average, not the state of an individual atom.
- This occurs in compounds with mixed oxidation states.
- Ignoring the sum rule
- Always check: Does the sum of all oxidation numbers equal the overall charge?
- This is a straightforward consistency check.
Summary
- Oxidation numbers are a formal tool to keep track of electron transfer in redox reactions.
- They are assigned according to clear rules: elements ($0$), monatomic ions (equal to ion charge), fixed patterns for O, H, halogens, and s-block metals, plus the requirement that their sum matches the total charge of the species.
- Correctly assigned oxidation numbers allow you to:
- Identify which elements are oxidized and which are reduced.
- Recognize oxidizing and reducing agents.
- Prepare for systematic balancing of redox equations.