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 Hâ‚‚O, then H with Hâº
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 (Oâ‚‚, Hâ‚‚) for Last
These are easier to balance after other atoms are set