What a balanced equation tells you
In Topic 4.1 you learned to recognise a chemical change. A chemical equation is the symbolic record of that change. Because a reaction only rearranges atoms into new combinations, a correct equation must have:
- the same number of atoms of each element on both sides, which is why mass is conserved; and
- the same total charge on both sides, which is why charge is conserved.
Coefficients (the large numbers in front of formulas) tell you how many of each particle take part. Subscripts are part of the formula and you must never change them to balance an equation: changing H₂O to H₂O₂ makes a different substance.
State symbols show the physical form of each species: (s) solid, (l) liquid, (g) gas and (aq) dissolved in water. They are not decoration. As you will see, they decide whether a substance is written as ions or kept together.
Equations for physical changes
Physical changes can be written as equations too. The formula does not change, because the composition does not change; only the state symbol does.
| Physical change | Equation |
|---|---|
| Water boils | H₂O(l) → H₂O(g) |
| Iodine sublimes | I₂(s) → I₂(g) |
| Glucose dissolves | C₆H₁₂O₆(s) → C₆H₁₂O₆(aq) |
| Potassium nitrate dissolves | KNO₃(s) → K⁺(aq) + NO₃⁻(aq) |
| Calcium chloride dissolves | CaCl₂(s) → Ca²⁺(aq) + 2Cl⁻(aq) |
Notice the difference between the last three rows. Molecular solutes such as glucose dissolve as whole molecules. Ionic solutes separate into their ions, and the coefficients show how many of each ion one formula unit gives. These equations still conserve atoms and charge: CaCl₂ gives one +2 ion and two −1 ions, a total charge of zero, like the solid.
Balancing an equation from a description
When a question describes a reaction in words, work in this order.
- Write the correct formula for every reactant and product, with state symbols.
- Tally the atoms of each element on each side.
- Change coefficients only, one element at a time. Leave elements that appear in several substances, and O and H, until last.
- Re-tally every element. Use the smallest whole-number coefficients.
Worked example 1: balancing from a description
Question. When solid sodium hydrogen carbonate is heated, it breaks down into solid sodium carbonate, water vapour and carbon dioxide gas. Write the balanced equation.
-
Formulas: NaHCO₃(s) → Na₂CO₃(s) + H₂O(g) + CO₂(g).
-
Tally (unbalanced):
Element Left Right Na 1 2 H 1 2 C 1 1 + 1 = 2 O 3 3 + 1 + 2 = 6 -
Every element on the right is double the left, so put 2 in front of NaHCO₃.
-
Re-tally: Na 2 = 2; H 2 = 2; C 2 = 2; O 6 = 6.
Answer. 2NaHCO₃(s) → Na₂CO₃(s) + H₂O(g) + CO₂(g)
Check with masses. Left: 2 × 84.01 = 168.02 g. Right: 105.99 + 18.02 + 44.01 = 168.02 g. The masses agree, as they must when atoms are conserved.
Three ways to write a reaction in solution
Many reactions happen between ions in water. Then there are three useful forms of the same equation.
- The molecular equation writes every substance as a complete formula, as if it were a whole unit: what you would read on the reagent bottles.
- The complete ionic equation shows every species as it actually exists in the solution. Strong electrolytes are split into their ions.
- The net ionic equation removes the spectator ions, the ions that are present but unchanged, and shows only the particles that react.
What to split into ions and what to keep together:
| Write as separate ions | Keep as one formula |
|---|---|
| Soluble ionic compounds, (aq) | Solids, including precipitates, (s) |
| Strong acids: HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄ | Liquids, including water, (l) |
| Soluble strong bases such as NaOH and KOH | Gases, (g) |
| Weak acids such as CH₃COOH, and other molecular substances, even when (aq) |
How do you know whether an ionic product is soluble? In this course you are expected to know that all sodium, potassium, ammonium and nitrate salts are soluble in water. Any other solubility information will be given to you, or you can read it from the observation: a solid forming when two solutions mix is an insoluble product.
Figure 1 shows the idea at the particle level for magnesium chloride solution mixed with sodium hydroxide solution.
Worked example 2: a precipitation reaction
Question. Aqueous potassium phosphate is mixed with aqueous calcium nitrate. A white precipitate of calcium phosphate forms. Write the molecular, complete ionic and net ionic equations.
- Formulas and states. K₃PO₄(aq) + Ca(NO₃)₂(aq) → Ca₃(PO₄)₂(s) + KNO₃(aq). Potassium nitrate is soluble (all potassium and all nitrate salts are), and the precipitate is the calcium phosphate.
- Balance the molecular equation. Ca₃(PO₄)₂ needs 3 Ca and 2 PO₄, so use 3Ca(NO₃)₂ and 2K₃PO₄. That supplies 6 K and 6 NO₃, so use 6KNO₃: 2K₃PO₄(aq) + 3Ca(NO₃)₂(aq) → Ca₃(PO₄)₂(s) + 6KNO₃(aq)
- Complete ionic equation. Split every (aq) ionic compound. Keep the solid together. 6K⁺(aq) + 2PO₄³⁻(aq) + 3Ca²⁺(aq) + 6NO₃⁻(aq) → Ca₃(PO₄)₂(s) + 6K⁺(aq) + 6NO₃⁻(aq)
- Cancel spectators. 6K⁺ and 6NO₃⁻ appear unchanged on both sides.
- Net ionic equation. 3Ca²⁺(aq) + 2PO₄³⁻(aq) → Ca₃(PO₄)₂(s)
Check. Atoms: 3 Ca, 2 P and 8 O on each side. Charge: left 3(+2) + 2(−3) = 0; right 0 (a neutral solid). Both conserved.
Worked example 3: a solid reacting with an acid
Question. Chalk (solid calcium carbonate) is added to hydrochloric acid. It fizzes, giving carbon dioxide, and a solution of calcium chloride forms. Write the net ionic equation.
- Molecular equation. CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g)
- Complete ionic equation. HCl is a strong acid, so split it. CaCl₂ is soluble (it dissolves, as the question says), so split it. CaCO₃ is a solid, H₂O is a liquid and CO₂ is a gas, so keep them together. CaCO₃(s) + 2H⁺(aq) + 2Cl⁻(aq) → Ca²⁺(aq) + 2Cl⁻(aq) + H₂O(l) + CO₂(g)
- Cancel the spectator ion 2Cl⁻.
- Net ionic equation. CaCO₃(s) + 2H⁺(aq) → Ca²⁺(aq) + H₂O(l) + CO₂(g)
Check. Atoms: 1 Ca, 1 C, 3 O and 2 H on each side. Charge: +2 on the left (2 × +1) and +2 on the right. Note that Ca²⁺ appears only on the right: it was locked in the solid at the start, so it is not a spectator.
Atoms balanced is not enough: check the charge
Copper metal placed in silver nitrate solution forms silver metal and a blue solution of copper(II) ions. A first attempt might be:
Cu(s) + Ag⁺(aq) → Cu²⁺(aq) + Ag(s)
The atoms balance (1 Cu, 1 Ag each side), but the charge does not: +1 on the left, +2 on the right. Charge is not conserved, so the equation is wrong. Doubling the silver fixes both:
Cu(s) + 2Ag⁺(aq) → Cu²⁺(aq) + 2Ag(s) charge: +2 = +2
Always add up the charges on each side as your last step. It catches errors that an atom tally misses.
Which form should you use?
All three forms are correct; they answer different questions.
- Molecular equation: best when you are planning amounts, because it names the compounds you actually weigh out or measure from a bottle.
- Complete ionic equation: best for showing every species present in the solution, for example to explain why a solution conducts electricity or to find the spectator ions.
- Net ionic equation: best for showing what really happens. It also shows that different pairs of reagents can give the same reaction. Mixing BaCl₂(aq) with Na₂SO₄(aq), or Ba(NO₃)₂(aq) with K₂SO₄(aq), gives the same net ionic equation, Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s), because the other ions are spectators in both.
If a question asks for “a balanced net ionic equation”, give only that form, with state symbols, and do not leave spectator ions in it.
Common misconceptions
- Changing subscripts to balance. This changes the substance. Change coefficients only.
- Splitting a solid into ions. A precipitate, or a solid reactant such as CaCO₃(s), is written as one formula in every form of the equation.
- Splitting a weak acid or a molecular substance. CH₃COOH(aq) and C₆H₁₂O₆(aq) stay as molecules.
- Breaking up polyatomic ions. NO₃⁻, SO₄²⁻ and PO₄³⁻ stay intact when a salt dissolves.
- Dropping the coefficient when splitting. 3Ca(NO₃)₂ gives 3Ca²⁺ and 6NO₃⁻.
- Cancelling an ion that changes state. An ion is a spectator only if it is in the same form, (aq), on both sides.
- Checking atoms but not charge. An equation can have equal atoms and still be wrong.
- Leaving spectators in the net ionic equation, or cancelling them from only one side.
Where this leads
This topic builds on Topic 4.1, Introduction for Reactions, where you learned to spot a reaction. Next, Topic 4.3, Representations of Reactions, links these equations to particle diagrams like Figure 1. You will use balanced equations for amounts in Topic 4.5 (stoichiometry) and to classify precipitation, acid–base and redox reactions in Topics 4.7 to 4.9. Try the practice questions now, then use the revision notes and the checklist to consolidate.
Quick questions
Should I write H⁺(aq) or H₃O⁺(aq)?
Either is accepted in this course. H₃O⁺ (hydronium) is the preferred form, but H⁺ makes equations shorter and is the same thing in water. Be consistent within one answer.
Do I need to memorise a full table of solubility rules?
No. You need to know that all sodium, potassium, ammonium and nitrate salts are soluble. Anything else will be given to you, or you can deduce it from an observation such as a precipitate forming.