Oxidation Numbers- Rules and Practice Problems
What Are Oxidation Numbers?
An oxidation number is a positive or negative number assigned to an atom in a compound. It tells you how many electrons an atom has gained, lost, or shared.
You don't calculate oxidation numbers by counting actual electrons. Instead, you follow a set of rules to assign hypothetical charges as if every bond were ionic.
Why bother? Oxidation numbers help you track electrons in redox reactions. They're also the first step before you can balance redox equations or figure out谁是氧化剂、谁是还原剂。
The Rules for Assigning Oxidation Numbers
These rules exist for a reason. Memorize them. You'll use them every time.
Rule 1: Free Elements
Any element in its free, uncombined state has an oxidation number of zero.
Examples: O₂, Na, Fe, P₄, S₈
Rule 2: Monatomic Ions
A single atom ion has an oxidation number equal to its charge.
Examples: Na⁺ = +1, Ca²⁺ = +2, Cl⁻ = -1
Rule 3: Oxygen
Oxygen is usually -2.
Exceptions:
- In peroxides (like H₂O₂), oxygen is -1
- In OF₂, oxygen is +2 (fluorine is more electronegative)
Rule 4: Hydrogen
Hydrogen is almost always +1.
Exception: When hydrogen bonds to a metal (like NaH), it's -1.
Rule 5: Alkali and Alkaline Earth Metals
Alkali metals (Li, Na, K, Rb, Cs, Fr) are always +1.
Alkaline earth metals (Be, Mg, Ca, Sr, Ba, Ra) are always +2.
Rule 6: Sum of Oxidation Numbers
The sum of all oxidation numbers in a neutral compound equals zero.
The sum of all oxidation numbers in a polyatomic ion equals the ion's charge.
How to Find Oxidation Numbers: Step-by-Step
Here's how to actually do it.
Step 1: Identify known oxidation numbers
Start with elements you know for sure. If oxygen is in the compound and it's not a peroxide, assign it -2. If hydrogen is present, assign it +1 (unless bonded to metal).
Step 2: Handle metals first
Group 1 metals = +1. Group 2 metals = +2. Halogens usually = -1 when they're the most electronegative element (except oxygen).
Step 3: Set up an equation
Use the sum rule. Write out the equation where all oxidation numbers add up to zero (or the ion's charge).
Step 4: Solve for the unknown
Basic algebra. You can handle this.
Practice Problems
Problem 1: Find the oxidation number of sulfur in H₂SO₄
Let's work through this.
Known values:
- H = +1 (2 atoms) = +2 total
- O = -2 (4 atoms) = -8 total
Let x = oxidation number of sulfur.
Equation: (+1 × 2) + x + (-2 × 4) = 0
2 + x - 8 = 0
x - 6 = 0
x = +6
Sulfur in H₂SO₄ is +6.
Problem 2: Find the oxidation number of chromium in Cr₂O₇²⁻
Known values:
- O = -2 (7 atoms) = -14 total
Let x = oxidation number of chromium (2 atoms).
Equation: 2x + (-14) = -2
2x - 14 = -2
2x = 12
x = +6
Each chromium is +6.
Problem 3: Find the oxidation number of nitrogen in NO₃⁻
Known values:
- O = -2 (3 atoms) = -6 total
Let x = oxidation number of nitrogen.
Equation: x + (-6) = -1
x - 6 = -1
x = +5
Nitrogen in NO₃⁻ is +5.
Problem 4: Find the oxidation number of manganese in KMnO₄
Known values:
- K = +1
- O = -2 (4 atoms) = -8 total
Let x = oxidation number of manganese.
Equation: (+1) + x + (-8) = 0
x - 7 = 0
x = +7
Manganese in KMnO₄ is +7.
Common Oxidation States Reference Table
| Element | Common Oxidation States | Notes |
|---|---|---|
| Hydrogen (H) | +1, -1 | +1 with nonmetals, -1 with metals |
| Oxygen (O) | -2, -1 | -1 in peroxides only |
| Sulfur (S) | -2, +4, +6 | Common in sulfites (+4) and sulfates (+6) |
| Nitrogen (N) | -3, +3, +5 | Depends on oxygen bonding |
| Carbon (C) | -4, +4 | Usually organic context |
| Chlorine (Cl) | -1, +1, +3, +5, +7 | With oxygen, varies by compound |
| Iron (Fe) | +2, +3 | Most common in compounds |
| Phosphorus (P) | -3, +3, +5 | Common in fertilizers |
Quick Reference: Rules Checklist
- Free element = 0
- Monatomic ion = its charge
- Oxygen = -2 (except peroxides: -1)
- Hydrogen = +1 (except metal hydrides: -1)
- Alkali metals = +1
- Alkaline earth metals = +2
- Sum in neutral compound = 0
- Sum in ion = ion's charge
Where Students Go Wrong
Forgetting about peroxides. Students see O and immediately write -2. H₂O₂ has oxygen at -1. That's a free point if you remember it.
Not using parentheses. In compounds like Ca(NO₃)₂, you have 2 nitrate ions. The oxygen count is 2 × 3 = 6 atoms.
Ignoring the charge on polyatomic ions. CO₃²⁻ isn't neutral. The sum has to equal -2, not 0.
Overcomplicating simple cases. For NaCl, sodium is +1, chlorine is -1. That's it. No need to overthink it.
Getting Started With Any Problem
- Write down the formula
- Identify elements with fixed oxidation numbers (O, H, Group 1, Group 2)
- Assign those values
- Set up your equation using the sum rule
- Solve for the unknown
- Check your work by plugging it back in
That's the process. It works every time.