Balancing Chemical Equations

Balancing Chemical Equations – Complete Study Notes

A chemical equation is a symbolic representation of a chemical reaction showing the reactants and products. A balanced chemical equation has equal numbers of atoms of each element on both sides of the equation, in compliance with the Law of Conservation of Mass.

1. Law of Conservation of Mass

Proposed by Antoine Lavoisier (1774): "Matter can neither be created nor destroyed in a chemical reaction." This means the total mass of reactants equals the total mass of products. Every atom present at the start must be accounted for in the products.

2. Writing and Balancing Equations – Step by Step

A skeletal (unbalanced) equation only shows formulas — it does not have equal atom counts. Balancing requires adjusting stoichiometric coefficients (the numbers in front of formulas).

Rules for Balancing by Inspection (Trial-and-Error Method):

  1. Write the skeletal (word) equation with correct chemical formulas.
  2. Count atoms of each element on both sides.
  3. Add coefficients to balance — start with the most complex compound first.
  4. Never change subscripts within a formula (that would change the substance).
  5. Balance hydrogen and oxygen last (they appear in many compounds).
  6. Ensure the final equation uses the simplest whole-number ratio.

3. Worked Examples

  • Combustion of Methane: CH₄ + O₂ → CO₂ + H₂O
    → Balanced: CH₄ + 2O₂ → CO₂ + 2H₂O
    ✓ C: 1=1, H: 4=4, O: 4=4
  • Haber Process: N₂ + H₂ → NH₃
    → Balanced: N₂ + 3H₂ → 2NH₃
    ✓ N: 2=2, H: 6=6
  • Decomposition of Lead Nitrate: Pb(NO₃)₂ → PbO + NO₂ + O₂
    → Balanced: 2Pb(NO₃)₂ → 2PbO + 4NO₂ + O₂
  • Aluminium + HCl: Al + HCl → AlCl₃ + H₂
    → Balanced: 2Al + 6HCl → 2AlCl₃ + 3H₂
  • Combustion of Propane: C₃H₈ + O₂ → CO₂ + H₂O
    → Balanced: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O

4. Types of Chemical Equations

  • Word Equation: "Hydrogen + Oxygen → Water"
  • Skeletal Equation: H₂ + O₂ → H₂O (unbalanced)
  • Balanced Equation: 2H₂ + O₂ → 2H₂O
  • Ionic Equation: Shows ions separately; spectator ions are removed. Example: Ag⁺ + Cl⁻ → AgCl↓
  • Thermochemical Equation: Includes the enthalpy change. Example: CH₄ + 2O₂ → CO₂ + 2H₂O, ΔH = –890 kJ/mol

5. State Symbols

State symbols tell us the physical state of each substance:

  • (s) = solid | (l) = liquid | (g) = gas | (aq) = aqueous (dissolved in water)
  • The downward arrow ↓ denotes a precipitate (insoluble solid formed in solution).
  • The upward arrow ↑ denotes a gas produced (collected above the solution).

6. Algebraic Method for Complex Equations

For complex reactions, assign letters (a, b, c, d...) as coefficients, then write equations for each element and solve the system of simultaneous equations. This is useful for redox reactions that are hard to balance by inspection.

7. Oxidation Number (Half-Reaction) Method for Redox

For balancing redox reactions, use the change in oxidation number method:

  1. Assign oxidation numbers to all atoms.
  2. Identify which atom is oxidized (oxidation number increases) and which is reduced (decreases).
  3. Calculate the change in oxidation number for both.
  4. Equalize the changes by multiplying appropriately.
  5. Balance remaining atoms and charge with H⁺, OH⁻, or H₂O.

Key Exam Tips

  • Always balance by changing coefficients, never subscripts.
  • C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O: This is balanced cellular respiration.
  • Identify if both sides have the same total number of atoms — that confirms balance.
  • For ionic equations, spectator ions (present on both sides) are cancelled out.