3a Formulae, equations and relative masses | IGCSE Chemistry 0620

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🎯What you need to be able to do

State the formulae of the elements and compounds in the syllabus, and deduce a formula from a model or diagram.
Define molecular formula; define empirical formula EXTENDED.
Deduce the formula of an ionic compound from the charges on its ions EXTENDED.
Write word equations and balanced symbol equations with state symbols; ionic equations EXTENDED.
Describe relative atomic mass A_r and define relative molecular (formula) mass M_r.
Calculate reacting masses in simple proportions (without moles).

📚The chemistry

Formulae

The molecular formula gives the number and type of each atom in one molecule: ethene is C₂H₄. EXTENDED The empirical formula is the simplest whole-number ratio of the atoms or ions: CH₂ for ethene. Ionic compounds are always written as their empirical formula (NaCl, not Na₆Cl₆). To deduce a formula from a model, count each kind of atom.

A ball-and-stick model of a propane molecule: three carbon atoms in a chain, with three hydrogen atoms on each end carbon and two on the middle carbon, eight hydrogens in total. Beneath it: C3H8. — Counting atoms in a model: 3 carbon, 8 hydrogen, so the molecular formula is C₃H₈ (propane).

Useful ions to know: Na⁺, K⁺, NH₄⁺, Mg²⁺, Ca²⁺, Cu²⁺, Zn²⁺, Fe²⁺, Fe³⁺, Al³⁺; Cl⁻, OH⁻, NO₃⁻, O²⁻, SO₄²⁻, CO₃²⁻. Balance the charges and use brackets when more than one compound ion is needed: calcium hydroxide is Ca(OH)₂, ammonium sulfate (NH₄)₂SO₄.

Equations

A balanced symbol equation has the same number of each type of atom on both sides. Balance by changing the big numbers in front of the formulae, never the small subscripts. Add state symbols: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water).

A particle picture of 2H2 + O2 giving 2H2O. On the left, two hydrogen molecules and one oxygen molecule: four hydrogen atoms and two oxygen atoms. On the right, two water molecules: also four hydrogen atoms and two oxygen atoms. — \( \mathrm{2H_2(g) + O_2(g) \rightarrow 2H_2O(l)} \): 4 H and 2 O atoms on each side — atoms are rearranged, never created or destroyed.

EXTENDED An ionic equation shows only the particles that change. Write the full equation with state symbols, split every aqueous ionic compound into its ions, and cross out the spectator ions that appear unchanged on both sides:

\[ \mathrm{AgNO_3(aq) + NaCl(aq) \rightarrow AgCl(s) + NaNO_3(aq)} \]

\[ \mathrm{Ag^{+}(aq) + Cl^{-}(aq) \rightarrow AgCl(s)} \]

Relative masses

The relative atomic mass, A_r, is the average mass of the isotopes of an element compared with \( \tfrac{1}{12} \) of the mass of a ¹²C atom (topic 2a). The relative molecular mass, M_r, is the sum of the relative atomic masses of all the atoms in the formula (for ionic compounds it is called the relative formula mass). For CaCO₃: \( 40 + 12 + 3 \times 16 = 100 \).

Reacting masses in proportion. The balanced equation, with M_r values, gives a mass ratio that you can scale up or down. In \( \mathrm{CaCO_3 \rightarrow CaO + CO_2} \), 100 g of calcium carbonate gives 56 g of calcium oxide, so 25 g gives \( \tfrac{25}{100} \times 56 = 14 \) g.

✏️Worked example

(a) Balance: \( \mathrm{Fe_2O_3 + CO \rightarrow Fe + CO_2} \). [1] (b) Calculate the M_r of ammonium sulfate, (NH₄)₂SO₄. [1] (c) Calculate the mass of calcium oxide made by heating 25 g of calcium carbonate. [2] (d) EXTENDED Write the ionic equation, with state symbols, for zinc reacting with aqueous copper(II) sulfate. [2]

(a) \( \mathrm{Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2} \): 2 Fe, 6 O and 3 C on each side.

(b) \( 2(14 + 4) + 32 + 4(16) = 36 + 32 + 64 = 132 \).

(c) M_r CaCO₃ \( = 100 \), M_r CaO \( = 56 \): 100 g gives 56 g, so 25 g gives 14 g.

(d) \( \mathrm{Zn(s) + CuSO_4(aq) \rightarrow ZnSO_4(aq) + Cu(s)} \); the sulfate ion is a spectator:

\[ \mathrm{Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)} \]

Check it. In (c), mass is conserved overall: 25 g of CaCO₃ gives 14 g of CaO plus \( 25 - 14 = 11 \) g of CO₂, and \( \tfrac{25}{100} \times 44 = 11 \) ✓. An ionic equation must balance in charge too: \( +2 \) on each side in (d) ✓.

Changing a formula to balance. Writing Fe₂O₃ + CO → Fe₂ + CO₄ “balances” but invents substances. Only the numbers in front may change.

📝Practise

In the style of the multiple-choice and theory papers. Use A_r: H 1, C 12, N 14, O 16, Mg 24, Al 27, S 32, Ca 40. EXTENDED marks Supplement content.

1. (Multiple choice.) What is the relative formula mass of magnesium nitrate, Mg(NO₃)₂? A: 86. B: 110. C: 148. D: 172.

C. \( 24 + 2(14 + 3 \times 16) = 24 + 2 \times 62 = 148 \). (A and B forget the bracket.)

2. (Theory.) Balance \( \mathrm{Al + O_2 \rightarrow Al_2O_3} \). [1]

\( \mathrm{4Al + 3O_2 \rightarrow 2Al_2O_3} \) (4 Al and 6 O each side).

3. (Theory.) Write the balanced symbol equation, with state symbols, for the complete combustion of propane, C₃H₈, to carbon dioxide and water (a liquid). [3]

\( \mathrm{C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(l)} \).

4. (Theory.) In \( \mathrm{2Mg + O_2 \rightarrow 2MgO} \), 48 g of magnesium makes 80 g of magnesium oxide. Calculate the mass of magnesium oxide made from 6 g of magnesium. [2]

\( \tfrac{6}{48} \times 80 = 10 \) g.

5. (Theory.) EXTENDED State the empirical formula of (a) ethene, C₂H₄, (b) glucose, C₆H₁₂O₆. [2]

(a) CH₂. (b) CH₂O (divide by 6).

6. (Theory.) EXTENDED Write the ionic equation for the neutralisation of any acid by any alkali, with state symbols. [2]

\( \mathrm{H^{+}(aq) + OH^{-}(aq) \rightarrow H_2O(l)} \).

7. (Theory.) EXTENDED Write the formulae of iron(III) sulfate and ammonium carbonate. [2]

Fe³⁺ and SO₄²⁻: Fe₂(SO₄)₃ (charges +6 and −6). NH₄⁺ and CO₃²⁻: (NH₄)₂CO₃.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

PhET “Balancing Chemical Equations” — balance equations by adjusting coefficients and watch the atoms
Royal Society of Chemistry — ionic equations and spectator ions