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General Chemistry I · Stoichiometry

Balancing Chemical Equations

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On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Key takeaway
  6. Study tools
  7. Sources & references

In 30 seconds

A balanced chemical equation has the same number of each type of atom on both sides, expressing the law of conservation of mass: atoms are neither created nor destroyed in a chemical reaction. Balancing means adjusting the coefficients (the numbers in front of formulas) until every element has an equal count on both sides. Subscripts inside formulas must never be changed, because altering a subscript changes the substance itself.

Why this matters

A balanced equation is the quantitative blueprint of a reaction — the coefficients are the mole ratios used in every stoichiometry calculation. An unbalanced or wrongly balanced equation gives wrong reactant amounts, wrong yields, and, in industrial and pharmaceutical settings, unsafe or failed reactions. Getting coefficients right is the gate to all the math that follows.

The college version

Key Ideas

The law of conservation of mass

  • In any chemical reaction, the total mass of reactants equals the total mass of products.
  • Matter is rearranged, not created or destroyed — so atom counts must balance.

Coefficients vs. subscripts

  • Coefficients (in front) multiply an entire formula and may be changed when balancing.
  • Subscripts (within a formula) define the compound's identity and must never be changed to balance.

Interpreting coefficients

  • 2 H₂ + O₂ → 2 H₂O means two molecules of H₂ react with one of O₂ to make two of H₂O.
  • Coefficients also scale to moles: 2 mol H₂ + 1 mol O₂ → 2 mol H₂O.

Equations and Variables

  • Conservation statement: (mass of reactants) = (mass of products)
  • Balancing goal: for every element E, (atoms of E on left) = (atoms of E on right).

How It Works (Problem-Solving Method)

  1. Write the correct formulas for every reactant and product (never change them).
  2. Count atoms of each element on both sides.
  3. Balance one element at a time by placing coefficients, starting with the element appearing in the fewest formulas.
  4. Re-count after each change; balance polyatomic ions as a unit when they appear unchanged on both sides.
  5. Balance H and O last (they often appear in several formulas), especially in combustion.
  6. Clear fractions by multiplying the whole equation by the denominator if a fractional coefficient appears.
  7. Final check: every element equal on both sides, and all coefficients in the lowest whole-number ratio.

Worked Example

Balance the combustion of propane: C₃H₈ + O₂ → CO₂ + H₂O

  1. Count: C = 3 → 1, H = 8 → 2, O = 2 → 3.
  2. Balance C: put a 3 before CO₂ → C₃H₈ + O₂ → 3 CO₂ + H₂O.
  3. Balance H: put a 4 before H₂O → C₃H₈ + O₂ → 3 CO₂ + 4 H₂O.
  4. Now count O on the right: 3(2) + 4(1) = 10 O atoms. Need 10 on the left, so put a 5 before O₂: C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O
  5. Check: C 3 = 3, H 8 = 8, O 10 = 10. Balanced.

Common Confusions

  • "Change the subscript to balance." — Never. Changing H₂O to H₂O₂ to get more oxygen changes the substance; only coefficients may change.
  • "A balanced equation must have the same total number of molecules on both sides." — Wrong. 2 H₂ + O₂ → 2 H₂O has 3 molecules on the left but 2 on the right; only atoms must match.
  • "Balance by trial and error without recounting." — Recounting after every change is the reliable method; skipping it causes double-counted atoms.
  • "Oxygen is best balanced first." — Often it is easiest to balance H and O last because they appear in multiple formulas.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Balancing an equation is like making sure both sides of a LEGO wall use the same bricks. If the left has 3 red bricks, 8 white, and some blue, the right must end with exactly 3 red, 8 white, and the same blues — you can snap bricks together differently, but you can't make a brick vanish. Chemists change how many groups of bricks they use (the big numbers in front), but they never break a brick in half to cheat — that would be like changing a subscript and turning water (H₂O) into hydrogen peroxide (H₂O₂), which is a completely different chemical.

Key takeaways

  • Balance by changing coefficients, never subscripts.
  • Atoms of each element must be equal on both sides (conservation of mass).
  • Change one coefficient at a time and recount.
  • Balance H and O last in combustion reactions.
  • Coefficients give mole ratios used in stoichiometry.
  • Fractions in coefficients are cleared by multiplying the whole equation.
  • Conservation of mass → equal atom counts on both sides.
  • Change coefficients only, never subscripts.
  • Balance one element at a time; H and O last.
  • Final check: every element equal, lowest whole-number coefficients.

Keep learning

Ready to build on this? Continue to the next lesson.

Practice General Chemistry I

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • State the law of conservation of mass and its role in balancing equations.
  • Balance chemical equations by adjusting coefficients, not subscripts.
  • Use a systematic atom-inventory method for equations of any size.
  • Interpret the meaning of a balanced equation's coefficients.

Sources & references

  1. OpenStax, "4.1 Writing and Balancing Chemical Equations." *Chemistry 2e*.
  2. Chemistry LibreTexts, "7.4: How to Write Balanced Chemical Equations."
  3. OpenStax, "4.3 Reaction Stoichiometry." *Chemistry 2e*.

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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