Balancing Chemical Equations
Ensuring equal numbers of each atom on both sides of the equation
Law of Conservation of Mass
Atoms In = Atoms Out
Total atoms of each element must be equal on both sides
aA + bB → cC + dD
a, b, c, d are stoichiometric coefficients
Balancing Methods
Method 1: Inspection (Trial & Error)
- Balance atoms that appear in only one reactant and one product first
- Balance polyatomic ions as units (if they remain intact)
- Balance H and O last (most common elements)
- Use fractional coefficients if needed, then multiply all by LCD
- Check: count atoms of each element on both sides
Method 2: Algebraic Method
1. Assign variables to each coefficient
2. Write equations for each element
3. Set one coefficient = 1 (usually most complex molecule)
4. Solve system of equations
5. Convert to whole numbers if needed
Method 3: Half-Reaction (for Redox)
1. Separate into oxidation and reduction half-reactions
2. Balance atoms except O and H
3. Balance O with H₂O, then H with H⁺
4. Balance charge with electrons
5. Multiply to equalize electrons, then combine
Worked Examples
Example 1: Combustion (Inspection)
Unbalanced: C₃H₈ + O₂ → CO₂ + H₂O
Solution:
Step 1: Balance C: 3 C on left → 3 CO₂ on right
C₃H₈ + O₂ → 3CO₂ + H₂O
Step 2: Balance H: 8 H on left → 4 H₂O on right
C₃H₈ + O₂ → 3CO₂ + 4H₂O
Step 3: Balance O: 10 O on right → 5 O₂ on left
C₃H₈ + 5O₂ → 3CO₂ + 4H₂O ✓
Check: C: 3=3, H: 8=8, O: 10=10 ✓
Example 2: Double Replacement
Unbalanced: Al(OH)₃ + H₂SO₄ → Al₂(SO₄)₃ + H₂O
Solution:
Step 1: Balance Al: 2 Al on right → 2 Al(OH)₃
2Al(OH)₃ + H₂SO₄ → Al₂(SO₄)₃ + H₂O
Step 2: Balance SO₄: 3 SO₄ on right → 3 H₂SO₄
2Al(OH)₃ + 3H₂SO₄ → Al₂(SO₄)₃ + H₂O
Step 3: Balance H₂O: 12 H on left → 6 H₂O
2Al(OH)₃ + 3H₂SO₄ → Al₂(SO₄)₃ + 6H₂O ✓
Example 3: Synthesis with Fractions
Unbalanced: N₂ + H₂ → NH₃
Solution:
N₂ + H₂ → 2NH₃ (balance N)
N₂ + 3H₂ → 2NH₃ (balance H: 6 H needed)
N₂ + 3H₂ → 2NH₃ ✓
Common Mistakes
Changing Subscripts Instead of Coefficients
Never change H₂O to H₃O - this changes the compound! Only add coefficients: 2H₂O
Forgetting to Multiply Subscripts
In 2Al₂(SO₄)₃: Al=4, S=6, O=24 (multiply inside and outside parentheses)
Not Simplifying to Lowest Terms
2H₂ + 2Cl₂ → 4HCl should be simplified to H₂ + Cl₂ → 2HCl
Balance Most Complex Molecule First
Start with the molecule containing the most elements
Leave Diatomic Elements (O₂, H₂) for Last
These are easier to balance after other atoms are set