Chemical equations, ion formulae and conservation of mass
What this lesson covers
- A reaction turns reactants into products, and three kinds of equation show it: a general pattern in words, the actual names, or balanced formulae.
- Atoms gain or lose electrons to reach a full outer shell, which sets the charge on each ion.
- In an ionic formula the positive and negative charges add up to zero, with brackets around more than one polyatomic ion.
- Equations are balanced by changing the numbers in front of formulae, never the small numbers inside them.
- Atoms are only rearranged in a reaction, so total mass stays the same unless a gas escapes or joins from the air.
Reactants, products and three kinds of equation
- In a chemical reaction the starting substances (reactants) change into new substances (products), and the arrow means "react to make".
- A generic word equation gives the pattern for a whole family of reactions, such as acid + metal carbonate → salt + water + carbon dioxide.
- A chemical word equation names the actual substances: hydrochloric acid + calcium carbonate → calcium chloride + water + carbon dioxide.
- A balanced symbol equation uses formulae and shows how many of each particle react: 2HCl + CaCO₃ → CaCl₂ + H₂O + CO₂.
- State symbols say what form each substance is in: (s) solid, (l) liquid, (g) gas and (aq) dissolved in water.
- The names link up: hydrochloric acid makes chlorides, sulfuric acid makes sulfates, nitric acid makes nitrates, and the metal in the base gives the first word of the salt.
Reading a formula: subscripts, brackets and coefficients
- A small number after a symbol (a subscript) counts only the atom just before it: H₂O has 2 H and 1 O.
- A subscript after a bracket multiplies everything inside the bracket: Mg(OH)₂ has 1 Mg, 2 O and 2 H.
- A big number in front (a coefficient) multiplies the whole formula: 3H₂O means three water molecules, so 6 H and 3 O.
- Subscripts are fixed by the substance itself, so changing one makes a different substance; coefficients only change how many particles there are.
Example: counting atoms
- Count the atoms of each element in 3Ca(OH)₂ and in 2Al₂(SO₄)₃.
- 3Ca(OH)₂: Ca = 3 × 1 = 3the coefficient multiplies everything
- O = 3 × 2 = 6, H = 3 × 2 = 6the bracket doubles O and H, then × 3
- 2Al₂(SO₄)₃: Al = 2 × 2 = 4subscript 2, coefficient 2
- S = 2 × 3 = 6, O = 2 × 3 × 4 = 24inside the bracket × 3, then × 2
- 3Ca(OH)₂: Ca 3, O 6, H 6; 2Al₂(SO₄)₃: Al 4, S 6, O 24
Why ions have the charges they do
- Atoms are most stable with a full outer (valence) shell of electrons, and they form ions by losing or gaining electrons to get one.
- A metal atom has only a few outer electrons, so it loses them and becomes a positive ion: magnesium (2, 8, 2) loses 2 electrons to become Mg²⁺ (2, 8).
- A non-metal atom has an almost full outer shell, so it gains electrons and becomes a negative ion: oxygen (2, 6) gains 2 to become O²⁻ (2, 8).
- The charge is the number of protons minus the number of electrons: Mg²⁺ has 12 protons and 10 electrons, so 12 − 10 = +2.
- Polyatomic ions are groups of atoms that carry a charge together, such as OH⁻, CO₃²⁻ and SO₄²⁻, and they stay together through most reactions.
| Charge | Positive ions | Negative ions |
|---|---|---|
| 1 | Na⁺, K⁺, H⁺, Ag⁺, NH₄⁺ | Cl⁻, Br⁻, I⁻, OH⁻, NO₃⁻, HCO₃⁻ |
| 2 | Mg²⁺, Ca²⁺, Ba²⁺, Zn²⁺, Cu²⁺, Fe²⁺, Pb²⁺ | O²⁻, S²⁻, CO₃²⁻, SO₄²⁻ |
| 3 | Al³⁺, Fe³⁺ | PO₄³⁻ |
Writing the formula of an ionic compound
- An ionic compound has no overall charge, so take just enough of each ion for the positive and negative charges to cancel.
- Write the positive ion first and the negative ion second, then find the smallest numbers that make the charges add to zero.
- If you need more than one of a polyatomic ion, put it in brackets with the number outside: Mg(OH)₂, not MgOH₂.
- One polyatomic ion needs no brackets: NaOH, CaCO₃.
- A quick check: total positive charge equals total negative charge.
Example: five formulae from their ions
- Write the formulae of calcium chloride, aluminium oxide, magnesium hydroxide, ammonium sulfate and calcium phosphate.
- Ca²⁺ and Cl⁻: +2 needs 2 × (−1), so CaCl₂two chloride ions
- Al³⁺ and O²⁻: 2 × (+3) = +6, 3 × (−2) = −6, so Al₂O₃lowest common multiple is 6
- Mg²⁺ and OH⁻: Mg(OH)₂two hydroxide ions, in brackets
- NH₄⁺ and SO₄²⁻: (NH₄)₂SO₄two ammonium ions, in brackets
- Ca²⁺ and PO₄³⁻: 3 × (+2) = +6, 2 × (−3) = −6, so Ca₃(PO₄)₂phosphate in brackets
- CaCl₂, Al₂O₃, Mg(OH)₂, (NH₄)₂SO₄, Ca₃(PO₄)₂
Balancing an equation
- Write the correct formula of every reactant and product first, and then leave the formulae alone.
- Count the atoms of each element on both sides.
- Put coefficients in front of formulae to even up the counts: metals first, then non-metals, leaving hydrogen and oxygen until last.
- Treat a polyatomic ion that appears unchanged on both sides, such as SO₄²⁻, as one unit.
- Recount everything at the end, and use the smallest whole numbers that work.
Example: balancing natural gas burning
- Natural gas in a gas hob is mostly methane, CH₄. It burns in oxygen to make carbon dioxide and water.
- Balance CH₄ + O₂ → CO₂ + H₂O.
- left: C 1, H 4, O 2 right: C 1, H 2, O 3carbon already balances
- CH₄ + O₂ → CO₂ + 2H₂O2 water molecules give 4 H
- right now has O = 2 + 2 = 42 in CO₂, 1 in each water
- CH₄ + 2O₂ → CO₂ + 2H₂O2 oxygen molecules give 4 O
- both sides: C 1, H 4, O 4
Example: an antacid tablet
- Some antacid tablets contain aluminium hydroxide, which neutralises hydrochloric acid in the stomach.
- Write the chemical word equation and the balanced equation.
- hydrochloric acid + aluminium hydroxide → aluminium chloride + wateracid + base → salt + water
- HCl + Al(OH)₃ → AlCl₃ + H₂Ocorrect formulae, not yet balanced
- 3HCl + Al(OH)₃ → AlCl₃ + H₂O3 Cl on the right needs 3 HCl
- 3HCl + Al(OH)₃ → AlCl₃ + 3H₂Oleft has 3 + 3 = 6 H, so 3 waters
- both sides: Al 1, Cl 3, H 6, O 3
Conservation of mass
- In a reaction no atoms appear or vanish; the same atoms are just joined up in new ways, which is exactly what a balanced equation shows.
- Because the atoms are the same, the total mass of the products equals the total mass of the reactants.
- In a sealed container the reading on a balance therefore stays the same, even when a gas is made.
- In an open container a gas product can escape, so the mass you measure goes down by the mass of that gas.
- If a gas from the air joins in, such as oxygen when magnesium burns or iron rusts, the mass of the solid goes up by the mass of the oxygen added.
- If one reactant runs out first it limits how much product can form, and the extra of the other reactant is left over unchanged.
Example: a sealed bottle, then an open one
- A Year 11 class put vinegar and a parcel of baking soda in a fizzy drink bottle, screwed the cap on and weighed it, then tipped it so the two mixed.
- Vinegar contains ethanoic acid: NaHCO₃ + CH₃COOH → CH₃COONa + H₂O + CO₂.
- Explain each reading.
| Stage | Mass (g) |
|---|---|
| Sealed, before mixing | 182.4 |
| Sealed, after fizzing stopped | 182.4 |
| Cap taken off, after 2 minutes | 181.3 |
- left: Na 1, H 5, C 3, O 5 right: Na 1, H 5, C 3, O 5the equation balances as written
- sealed: 182.4 g → 182.4 gevery atom, including those in the CO₂, stays in the bottle
- opened: 182.4 − 181.3 = 1.1 gthe mass of CO₂ gas that escaped
- mass is conserved; the drop is only the gas leaving
Writing it up for Achieved, Merit and Excellence
- Achieved describes: name the reactants and products, give a word equation and a balanced equation, and say that mass is conserved.
- Merit explains: use the atom counts on each side to say why the mass stays the same, and say why a measured mass rises or falls (a gas joins or leaves).
- Excellence interprets: discuss what conservation of mass means in this situation, linking the equation, the observations and the numbers, and predict what would change if the amounts changed.
- For the bottle, an Excellence line reads: the 1.1 g drop is the CO₂ that left (a little more may still be dissolved in the liquid), and a teaspoon more baking soda (with enough vinegar) would make more CO₂, so the drop would be bigger, while the sealed reading would still not change.
| Grade | What a sentence about the bottle looks like |
|---|---|
| Achieved | Baking soda and vinegar make sodium ethanoate, water and carbon dioxide, and mass is conserved. |
| Merit | There are 1 Na, 5 H, 3 C and 5 O atoms on each side, so the mass in the sealed bottle cannot change; it drops when opened because CO₂ escapes. |
| Excellence | The 1.1 g lost is the CO₂ that left; some may still be dissolved, so at least 1.1 g formed, and more reactant would give a bigger drop. |
Common mistakes
- To balance H₂ + O₂ → H₂O, change the water to H₂O₂.H₂O₂ is hydrogen peroxide, a different substance; change coefficients only: 2H₂ + O₂ → 2H₂O.
- Magnesium hydroxide is MgOH₂.Two hydroxide ions need brackets, Mg(OH)₂, because the 2 applies to both the O and the H.
- The mass went down in the open flask, so mass was not conserved.Mass was conserved, but a gas product escaped into the air, so the balance no longer weighed all the products.
- Aluminium oxide is AlO because aluminium and oxygen combine.Al³⁺ and O²⁻ only cancel as Al₂O₃: 2 × (+3) = +6 and 3 × (−2) = −6.
Weigh a reaction in a sealed bottle
You need: an empty 1.5 L fizzy drink bottle with its cap, kitchen scales, 100 mL white vinegar, 1 teaspoon baking soda, a square of paper towel, a measuring jug
- Pour 100 mL of vinegar into the bottle, then wrap the teaspoon of baking soda in the paper towel and twist it into a parcel thin enough to fit through the neck.
- Hold the bottle upright, push the parcel just into the neck so it sits above the vinegar, screw the cap on tightly and weigh the whole bottle.
- Shake the bottle so the parcel drops into the vinegar, wait until the fizzing stops, and weigh it again with the cap still on.
- Point the bottle away from your face, unscrew the cap slowly over the sink, wait two minutes and weigh it a third time.
- Look for: the two sealed readings match, because no atoms left the bottle, and the opened reading is lower by roughly a gram or two, the mass of the carbon dioxide that escaped.
Safety: The gas makes the bottle firm and vinegar can spray when you open it, so use only a fizzy drink bottle and one teaspoon of baking soda, and open it slowly pointed away from faces.
Your turn
1
Write the formulae of potassium carbonate, iron(III) hydroxide and zinc nitrate.
2
Count the atoms of each element in 3Ca(NO₃)₂.
3
Balance Fe + O₂ → Fe₂O₃, the equation for iron rusting.
4
Hydrogen peroxide breaks down into water and oxygen. Balance H₂O₂ → H₂O + O₂.
5
5.0 g of baking soda is added to 50.0 g of vinegar in an open cup. When the fizzing stops the cup's contents weigh 52.4 g. What mass of carbon dioxide escaped?
6
Steel wool is heated in air and its mass goes up. Explain why, using conservation of mass.
Show answer
1. K⁺ and CO₃²⁻ give K₂CO₃; Fe³⁺ and OH⁻ give Fe(OH)₃; Zn²⁺ and NO₃⁻ give Zn(NO₃)₂. 2. Ca 3, N 6, O 18 (3 × 2 × 3 = 18). 3. 4Fe + 3O₂ → 2Fe₂O₃ (Fe 4 and O 6 on each side). 4. 2H₂O₂ → 2H₂O + O₂ (H 4 and O 4 on each side). 5. 5.0 + 50.0 = 55.0 g at the start, so 55.0 − 52.4 = 2.6 g of CO₂ escaped. 6. Iron atoms combine with oxygen atoms from the air to make iron oxide; no atoms are created, but the oxygen atoms were not weighed at the start, so the solid gains their mass.
Balancing Chemical Equations
Full screen · PhET Interactive Simulations, University of Colorado Boulder, CC BY 4.0
Recap
- Reactants become products; equations can be generic word, chemical word or balanced symbol equations.
- Ion charges come from losing or gaining electrons to fill the outer shell, and an ionic formula has charges that add to zero.
- Balance with coefficients only, then recount every element.
- Atoms are rearranged, never made or destroyed, so mass is conserved; a measured mass changes only when a gas leaves or joins.
| Idea | Example |
|---|---|
| Ionic formula | Ca²⁺ + PO₄³⁻ → Ca₃(PO₄)₂ |
| Balanced equation | CH₄ + 2O₂ → CO₂ + 2H₂O |
| Gas escapes | mass measured goes down |
| Gas from the air joins | mass measured goes up |
The maths behind it
How is NCEA Level 1 maths going?
See the NCEA Level 1 maths guide