Worked example 1
Balance: C₃H₈ + O₂ → CO₂ + H₂O
Try it first: Which element should you leave until last, and why?
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StoichiometryBalancing Chemical EquationsContent level: Core 20 min
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.
Lesson
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
1. 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.
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.
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.
Next: Mole Ratios and Mass-to-Mass StoichiometryUse 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
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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.
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Common mistakes
Balancing by editing a subscript, for example writing H₂O₂ instead of H₂O.
Why it's wrong: That changes the substance rather than the amount, so the equation now describes a different reaction.
Check instead: Only place numbers in front of formulas.
Leaving coefficients such as 4 H₂ + 2 O₂ → 4 H₂O.
Why it's wrong: The atom counts match but the set is not the smallest whole-number solution that graders expect.
Check instead: Divide every coefficient by their greatest common divisor as the final step.
Setting the O₂ coefficient before the carbon and hydrogen are settled.
Why it's wrong: Later changes to CO₂ or H₂O keep altering the oxygen total, so the work has to be redone repeatedly.
Check instead: Balance elements that appear in one compound on each side first, free elements last.
Breaking up a spectator polyatomic ion into separate atoms.
Why it's wrong: It is not wrong chemically, but it multiplies the bookkeeping and invites arithmetic slips.
Check instead: If a polyatomic ion appears unchanged on both sides, balance it as one group.
Stopping as soon as the last element looks right.
Why it's wrong: Adjusting a late coefficient often unbalances an element that was correct earlier.
Check instead: Recount every element on both sides before you commit to the answer.
After the lesson · Question bank
Independent practice
Work through new problems on this topic on your own. The lesson's quick checks and worked examples stay above if you need to review a step.
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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.
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
Chemistry 2e, OpenStax, Rice University, licensed CC BY 4.0. License