Balancing equations and using state symbols
Conserve every atom while describing the reactants, products and physical states.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Count atoms in formulas with coefficients and brackets.
- Know that a formula's subscripts identify the substance.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What may be changed when balancing a reaction with already correct formulas?
What you will learn
- Translate a word equation into a balanced symbol equation.
- Use solid, liquid, gas and aqueous state symbols correctly.
Balance by changing whole-particle counts
A reaction equation places reactants before the arrow and products after it. Conservation of atoms requires the same number of each element on both sides. Start with correct substance formulas, count each element, then adjust coefficients until the counts match. Use the smallest whole-number coefficients for a final balanced equation.
Do not change a subscript to balance an equation: changing H₂O to H₂O₂ would change the product's identity. Oxygen and hydrogen elemental gases are O₂ and H₂, not lone O and H atoms. Recount every element after each coefficient change, since one coefficient may affect several counts.
State symbols describe the sample
The symbols (s), (l), (g) and (aq) mean solid, liquid, gas and dissolved in water respectively. Aqueous is not a synonym for liquid: liquid water is H₂O(l), while sodium chloride dissolved in water is NaCl(aq). Assign states from the stated conditions; heating can change them without changing the formula.
For magnesium burning in oxygen at the stated ordinary conditions, the word equation is magnesium + oxygen → magnesium oxide. The balanced symbol equation is 2Mg(s) + O₂(g) → 2MgO(s). An equation should communicate both correct substances and correct conserved counts, rather than just a pattern of numbers.
Sources for this lesson
Pause and explain
What does NaCl(aq) mean?
Worked example
Balance aluminium + oxygen → aluminium oxide using Al, O₂ and Al₂O₃, including states for solid aluminium and oxide and gaseous oxygen.
Show the worked solution
- Two Al₂O₃ units give six oxygen atoms.
- Three O₂ molecules supply those six oxygens.
- The product contains four aluminium atoms, so use 4Al on the reactant side.
Answer 4Al(s) + 3O₂(g) → 2Al₂O₃(s).
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Balance Fe(s) + O₂(g) → Fe₂O₃(s) by listing atom totals.
Give me a hint
Make the oxygen total a multiple of both two and three.
Compare my reasoning
- Two Fe₂O₃ units contain six oxygens.
- Use three O₂ on the left and four Fe to match four product irons.
- Check left and right totals: four Fe and six O.
4Fe(s) + 3O₂(g) → 2Fe₂O₃(s).
Look for these in your work
- Smallest whole-number coefficients are used.
- Both elements are explicitly recounted.
Balance aqueous hydrochloric acid reacting with aqueous sodium hydroxide to make aqueous sodium chloride and liquid water.
Give me a hint
Begin with HCl, NaOH, NaCl and H₂O.
Compare my reasoning
- Write HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l).
- Count one Na and one Cl each side; each side also has two H and one O.
- All coefficients are already one; distinguish aqueous reactants from liquid water.
HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l).
Look for these in your work
- The compound formulas are unchanged.
- Water's state differs from the aqueous solutes.
A student balances Mg + O₂ → MgO by changing the product to MgO₂. Correct the equation and explain the error.
Give me a hint
Keep magnesium oxide's formula fixed.
Compare my reasoning
- MgO₂ is not the stated magnesium oxide formula.
- Use two MgO units to match the two oxygens in O₂.
- Use two magnesium atoms: 2Mg + O₂ → 2MgO.
2Mg + O₂ → 2MgO; a subscript change would alter the product.
Look for these in your work
- The product identity stays fixed.
- Atom conservation is demonstrated.
Common mistakes
- Changing chemical subscripts instead of coefficients.
- Writing (aq) for every liquid, including pure water.
What can you explain now?
Balance hydrogen gas forming liquid water with oxygen gas.
Compare with the explanation
2H₂(g) + O₂(g) → 2H₂O(l)
Both sides contain four hydrogen and two oxygen atoms; water is a liquid, not an aqueous solute.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Balance three unfamiliar equations from correct supplied formulas. For each, check every element and explain one state symbol.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.