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Balance with coefficients and verify

About 13 minutes · 3 reading + 10 practice and checks
Time includes reading, practice, and questions. Extra videos or further study are optional.
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A reaction-model sheet with atom inventories, balanced symbolic equations, a limiting-count model and an explanation of energy transfer.

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What to include

  • Distinguish coefficient and subscript atom counts.
  • Classify physical, chemical and unresolved records.
  • Audit each element before and after reaction models.
  • Balance both supplied symbolic equations and independently recount atoms.
  • Track complete reaction sets and leftover paper units.
  • Account for energy transfer and include all six changed cases.

Review and revise

Use these criteria to check your work and choose what to improve.

  • Method: applies the course-specific rules to the supplied cases with visible intermediate work.
  • Accuracy: results agree with the stated facts, units, boundaries and independent checks.
  • Reasoning: explains why the result follows and identifies a limitation or unresolved question.
  • Transfer: completes changed cases and revises the final project when a relevant assumption changes.
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Before you begin

The idea in everyday life

Paper equation Fe + O2 → Fe2O3. Smallest positive common oxygen count for groups of two and three is six. Coefficients must represent complete formula units, not pieces of a unit.

The idea

Use whole-number coefficients to match each element. For the supplied iron/oxygen model, first choose a common oxygen count that fits both O2 and Fe2O3; then match iron. Finish by recounting every element and reducing any common coefficient factor. Guessing without a recount can hide a new mismatch.

Follow along

Balance with coefficients and verify — worked practice

Use whole-number coefficients to match each element. For the supplied iron/oxygen model, first choose a common oxygen count that fits both O2 and Fe2O3; then match iron. Finish by recounting every element and reducing any common coefficient factor. Guessing without a recount can hide a new mismatch.

Paper equation Fe + O2 → Fe2O3. Smallest positive common oxygen count for groups of two and three is six. Coefficients must represent complete formula units, not pieces of a unit.

  1. 1. 1. Oxygen

    Use six oxygen atoms on each side.

    You should see: 3O2 supplies six O; 2Fe2O3 contains six O.

  2. 2. 2. Iron

    Count iron in the chosen product amount and match the left.

    You should see: 2Fe2O3 contains four Fe, so use 4Fe.

  3. 3. 3. Verify

    Recount the equation 4Fe + 3O2 → 2Fe2O3.

    You should see: Left Fe=4, O=6; right Fe=4, O=6.

  4. 4. 4. Reduce

    Check for a common whole-number factor across 4,3,2.

    You should see: No factor greater than one is shared, so this is the smallest whole-number ratio.

Now change one thing

For N2 + H2 → NH3, supply product coefficient 2. Enter the H2 coefficient needed to balance hydrogen.

Your work

What to finish

Balanced symbolic equations with element inventories and smallest-ratio checks.

Common mistake

Watch for this

A change can fix one element and disturb another. Recounting each element is the independent check that confirms the final model.

How can I tell I understand it?

Balance a changed hydrogen count and verify nitrogen as well.

Try 3 questions

Quick knowledge check

Answer all 3 questions. Get at least 2 right and the lesson completes automatically.

Not yet passed

You’ll get an explanation for each answer. Signed in? Your results save to your account.

1What O2 coefficient fits the supplied six-oxygen balance?
2Why is 4Fe needed after choosing 2Fe2O3?
3What must happen after choosing coefficients?
0 of 3 answeredApply the lesson to a short question, then review the explanation.
4
Finish this lesson

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Answer all 3 questions above and get at least 2 right. You can review the explanations and try again.

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Sources and further reading

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OpenStax: chemical equation balancing
Source & access notes · checked 2026-10-01

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