Worked example 1
Balance: C₃H₈ + O₂ → CO₂ + H₂O
Try it first: Which element should you leave until last, and why?
0 of 5 steps revealed.
Balancing Chemical EquationsCourse level: FoundationsCourse level: AP Chemistry
Balancing Chemical Equations
What you'll be able to do: Balance a chemical equation with the smallest whole-number coefficients and explain why the atom counts must match.
Best after: The Mole and Molar Mass
Introduction
A chemical equation is a statement about conservation. Atoms are rearranged in a reaction, never created or destroyed, so every element must appear in equal numbers on both sides. Balancing is the bookkeeping that makes an equation usable for every calculation that follows in this unit.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- State the law of conservation of mass and explain what it requires of an equation.
- Balance equations by adjusting coefficients without altering formulas.
- Choose a productive order in which to balance elements.
- Reduce a balanced equation to the smallest whole-number coefficients and interpret state symbols.
Coefficients versus subscripts
A coefficient sits in front of a formula and multiplies the whole formula unit: 2 H₂O means two water molecules, four H atoms and two O atoms. A subscript is part of the substance's identity.
Changing H₂O to H₂O₂ does not balance an equation, it replaces water with hydrogen peroxide.
Only coefficients may be changed. Touching a subscript changes the chemistry.
A reliable order of attack
- Count every atom on both sides. 2. Balance elements that appear in exactly one substance on each side. 3. Balance polyatomic ions as whole groups when they survive the reaction intact. 4. Leave free elements such as O₂, H₂ or Na for last, since their coefficient can absorb whatever is left over. 5. Recount everything.
Start with a ledger rather than changing several coefficients at once. For Fe + O₂ → Fe₂O₃, oxygen occurs in groups of two on the left and three on the right. Their least common multiple is six: choose 3 O₂ and 2 Fe₂O₃, then balance iron with 4 Fe.
| Element | Reactant count | Product count |
|---|---|---|
| Fe | 4 × 1 = 4 | 2 × 2 = 4 |
| O | 3 × 2 = 6 | 2 × 3 = 6 |
The answer is 4 Fe + 3 O₂ → 2 Fe₂O₃. An unprinted coefficient is one. Replacing the product by FeO would be changing the chemistry, even if it made the arithmetic easier.
Keep a running atom tally in two columns. Mental counting is where most errors enter.
Fractions are a legal intermediate
When a free diatomic element blocks you, a fractional coefficient such as 3/2 O₂ is a perfectly valid intermediate. Multiply the entire equation by the denominator at the end to clear it. For combustion of C₂H₆ this gives 2 C₂H₆ + 7 O₂ → 4 CO₂ + 6 H₂O.
For C₂H₆ combustion, begin C₂H₆ + O₂ → 2 CO₂ + 3 H₂O. The products contain seven O atoms, requiring 7/2 O₂. Multiply every coefficient, including the implied one before C₂H₆, by two. A fractional intermediate is bookkeeping for amounts of substance; a final smallest-integer equation is convenient for particle counts.
C₂H₆ + 7/2 O₂ → 2 CO₂ + 3 H₂O
Smallest whole numbers
An equation such as 4 H₂ + 2 O₂ → 4 H₂O is atom-balanced but not in lowest terms. Divide through by the greatest common divisor to get 2 H₂ + O₂ → 2 H₂O.
Grading systems, including the equation checker in the Question Bank, expect the reduced set.
Balanced but not reduced is still marked incomplete.
State symbols
(s), (l), (g) and (aq) describe the physical state under the stated conditions. They do not affect atom balancing, but they carry chemical information, especially for precipitation and gas-forming reactions later in the course. Include them when the question supplies them.
Why this matters downstream
Every mole ratio in the rest of this unit is read off the coefficients of a balanced equation. An unbalanced equation silently corrupts limiting reactant and yield calculations, and the error usually shows up as an answer that is off by a small whole-number factor.
Balancing establishes conservation, not whether the proposed reaction actually occurs. Product identities must come from the stated reaction or chemical evidence. Nor must the total number of molecules match: 2 H₂ + O₂ → 2 H₂O converts three molecules into two while preserving every atom. For ionic equations, conserved electric charge supplies another independent check; balancing atoms alone cannot repair an incorrect electron-transfer equation.
Use unchanged polyatomic ions as bookkeeping units
If the same polyatomic ion appears intact on both sides, temporarily count it as one group. For Fe₂(SO₄)₃ + KOH → Fe(OH)₃ + K₂SO₄, the three sulfate groups require three K₂SO₄; that fixes six KOH, which supplies six OH groups for two Fe(OH)₃.
Then check Fe, K, S, O and H atom by atom. This shortcut is valid only while the group's identity stays the same. If a sulfate group reacts to form a different sulfur species, expand it into individual atoms instead.
For an ionic equation, check total electric charge as well as atoms.
Key ideas
Rule
Conservation of mass
The number of atoms of each element is the same on both sides of an equation, because atoms are only rearranged.
Rule
Coefficients only
Balance by changing coefficients. Subscripts define the substance and are fixed.
Rule
Charge balances too
In an ionic equation the total charge must also match on both sides, not just the atoms.
Definition
Reduced coefficients
A balanced equation written with the smallest possible set of whole-number coefficients.
Assumption
The formulas are correct
Balancing cannot fix a wrong formula. Check ionic charges before you start counting atoms.
Equation
Atom balance condition
sum(coefficient x subscript)reactants = sum(coefficient x subscript)products, for every element
- coefficient = the number in front of a formula, what you are allowed to change
- subscript = the number inside a formula, fixed by the identity of the substance
- use when = checking any equation before using it for stoichiometry
- limits = for ionic equations the total charge must balance as well
Worked examples
Worked example 2
Balance: Al + CuSO₄ → Al₂(SO₄)₃ + Cu
0 of 5 steps revealed.
Worked example 3
Balance Fe₂(SO₄)₃ + KOH → Fe(OH)₃ + K₂SO₄ with the smallest whole-number coefficients.
Try it first: Treat SO₄ and OH as intact groups while setting coefficients.
0 of 3 steps revealed.
Common mistakes
| Mistake | Why it's wrong | Check instead |
|---|---|---|
| Balancing by editing a subscript, for example writing H₂O₂ instead of H₂O. | That changes the substance rather than the amount, so the equation now describes a different reaction. | Only place numbers in front of formulas. |
| Leaving coefficients such as 4 H₂ + 2 O₂ → 4 H₂O. | The atom counts match but the set is not the smallest whole-number solution that graders expect. | Divide every coefficient by their greatest common divisor as the final step. |
| Setting the O₂ coefficient before the carbon and hydrogen are settled. | Later changes to CO₂ or H₂O keep altering the oxygen total, so the work has to be redone repeatedly. | Balance elements that appear in one compound on each side first, free elements last. |
| Breaking up a spectator polyatomic ion into separate atoms. | It is not wrong chemically, but it multiplies the bookkeeping and invites arithmetic slips. | If a polyatomic ion appears unchanged on both sides, balance it as one group. |
| Stopping as soon as the last element looks right. | Adjusting a late coefficient often unbalances an element that was correct earlier. | Recount every element on both sides before you commit to the answer. |
Scroll horizontally if needed to read all columns.
After the lesson · Question bank
Independent practice
Work through new problems on your own. The lesson's quick checks and worked examples stay above if you need to review a step.
18 topic questions across 3 difficulty levels.
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What you should now know
Balance by adjusting coefficients only, never subscripts. Work through elements that appear in one compound on each side first, leave free elements such as O₂ for last, and finish by reducing the coefficients to their smallest whole-number set.
- Atoms are conserved, so every element must have equal counts on both sides.
- Change coefficients only, never subscripts.
- Balance single-compound elements first and free elements last; fractions are a legal intermediate.
- Finish by reducing to the smallest whole-number coefficients and recounting.
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Sources and further reading
- Chemistry 2e, Section 4.1: Writing and Balancing Chemical EquationsPaul Flowers, Klaus Theopold, Richard Langley, William R. Robinson · OpenStax, Rice University · Chapter 4.1View source
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The current online Chemistry 2e edition lists CC BY-NC-SA 4.0. The source version used for this lesson and its applicable rights remain unverified.
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Recorded attribution / license claim (applicability unverified): Chemistry 2e, OpenStax, Rice University, licensed CC BY 4.0.
Source rights and review status - General Chemistry bookshelf (LibreTexts)LibreTexts, University of California, DavisView source
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