Stoichiometry

Cambridge IGCSE Co-ordinated Sciences 0654 and Combined Science 0653 · Core and Extended

Syllabus points

• Write the formulae of ionic and covalent compounds, using brackets where needed.
• Write and balance symbol equations, and include state symbols.
• Write ionic equations, leaving out spectator ions.
• Define relative atomic mass and relative molecular mass, and calculate relative formula mass.
• Use the mole, the Avogadro constant and the molar gas volume in calculations.

Writing formulae

An ionic formula shows the ratio in which the ions combine, and the ratio is whatever makes the total charge zero.

The positive ion is always written first.

Brackets are the detail that is examined. When a compound needs more than one copy of a group of atoms that acts as a single ion, that group goes in brackets with the number outside. Copper hydroxide has one Cu²⁺ balanced by two OH⁻ ions, so it is written Cu(OH)₂.

Writing it as CuH₂O₂ counts the atoms correctly, one copper, two hydrogens and two oxygens, and is still wrong. The brackets say that each oxygen stays with its own hydrogen as a hydroxide unit, and without them the grouping is lost. The same applies to Ca(OH)₂, Mg(NO₃)₂ and Al₂(SO₄)₃.

Balancing equations

Only the big numbers in front may be changed. The formulae themselves must never be altered.

That rule decides more marks than any other in the topic. An equation such as H₂ + O → H₂O has the same number of each atom on both sides, and it is still wrong, because it has rewritten oxygen as single atoms. Oxygen exists as O₂ molecules, so an equation using O describes a substance that was not there.

The correct version is:

$$2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$$

with four hydrogen atoms and two oxygen atoms on each side.

A method that works every time. Balance carbon first, then hydrogen, then oxygen last, because oxygen usually appears in more than one product and is easiest to fix at the end.

Worked example. Pentane, C₅H₁₂, burns in a limited air supply to give some carbon dioxide and some carbon monoxide.

• Carbon: the five carbon atoms appear as 3CO₂ and 2CO, which accounts for all five.
• Hydrogen: twelve hydrogen atoms give 6H₂O.
• Oxygen: count the right-hand side. 3CO₂ holds 6, 2CO holds 2, and 6H₂O holds 6, making 14 oxygen atoms. Oxygen comes as O₂, so 14 / 2 = 7 molecules are needed.

$\mathrmC_5H_12 + 7O₂ arrow 3CO₂ + 2CO + 6H_2O$

How to check an equation quickly. Count one element at a time across both sides. For Fe₃O₄ + 2H₂ → 3Fe + 2H₂O, the left has 4 oxygen atoms and the right has only 2, so it is not balanced. It needs 4H₂ and 4H₂O.

State symbols are (s) solid, (l) liquid, (g) gas and (aq) dissolved in water. They are not decoration: an equation claiming a precipitate is (aq) contradicts the observation the question is about.

Ionic equations

An ionic equation shows only the particles that change. Any ion that appears in the same form on both sides is a spectator ion and is left out.

Worked example. Sodium hydroxide solution is added to iron(II) sulfate solution, giving a precipitate of iron(II) hydroxide.

The full equation is FeSO₄(aq) + 2NaOH(aq) → Fe(OH)₂(s) + Na₂SO₄(aq).

The sodium ions and the sulfate ions are dissolved before and dissolved afterwards, so they are spectators. What actually changes is:

$\mathrmFe^2+(aq) + 2OH^-(aq) arrow Fe(OH)_2(s)$

Two traps live here. Writing every ion out on both sides gives a balanced equation that is not an ionic equation, since stripping out the spectators is the entire point. And the state symbol on the product must be (s), because the precipitate is what makes the reaction worth writing.

The precipitation test for sulfate ions works the same way: Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s).

Relative masses

Relative atomic mass (Ar) is the average mass of an atom of an element compared with 1/12 of the mass of a carbon-12 atom. It has no units, because it is a ratio.

Relative molecular mass (Mr) is the sum of the relative atomic masses in a molecule. For an ionic compound the same sum is called the relative formula mass.

Worked example. Mr of Ca(OH)₂, with Ar values Ca 40, O 16, H 1.

Mr = 40 + 2 × (16 + 1) = 74

Multiply everything inside the brackets by the number outside. Forgetting to include the hydrogen in that doubling is the standard slip.

The mole

One mole is the amount of substance containing 6 × 10²³ particles, the Avogadro constant. The mass of one mole of a substance in grams is numerically equal to its Ar or Mr.

$moles = (mass in g) ÷ (M_r)$

Worked example. 1 g of hydrogen contains 6 × 10²³ atoms. How many atoms are in 1 g of helium, whose Ar is 4?

Hydrogen has Ar 1, so 1 g is one mole and contains 6 × 10²³ atoms. Helium has Ar 4, so

moles of helium = 1 / 4 = 0.25 mol

number of atoms = 0.25 × 6 × 10²³ = 1.5 × 10²³

The heavier the atom, the fewer of them there are in a fixed mass. That is the sense check to apply to any answer here.

Gas volumes

One mole of any gas occupies 24 dm³ at room temperature and pressure, which is 24 000 cm³. It does not matter which gas, because gas particles are so far apart that their own size is irrelevant to the volume.

$moles of gas = (volume in dm^3) ÷ (24)$

Worked example. Carbon dioxide is collected in a gas syringe. The reading goes from 7 cm³ to 43 cm³. What mass of carbon dioxide was produced? Ar values: C 12, O 16.

Volume produced = 43 − 7 = 36 cm³

moles = 36 / 24000 = 0.0015 mol

Mr of CO₂ = 12 + 2 × 16 = 44

mass = 0.0015 × 44 = 0.066 g

Two habits protect this calculation. Subtract the initial reading, since the syringe did not start at zero. And divide by 24 000 when the volume is in cm³, or by 24 when it is in dm³; mixing the two is out by a factor of a thousand and is the commonest source of a wrong answer that still looks tidy.

Common mistakes

• Leaving out the brackets in Cu(OH)₂ or Mg(NO₃)₂.
• Writing the negative ion first in an ionic formula.
• Balancing an equation by changing a formula, for instance writing O instead of O₂ or H₂O₂ instead of H₂O.
• Counting only one element and declaring an equation balanced.
• Writing every ion on both sides of an "ionic" equation instead of cancelling the spectators.
• Giving a precipitate the state symbol (aq).
• Forgetting to multiply the contents of brackets when calculating an Mr.
• Giving relative atomic mass a unit.
• Using 24 instead of 24 000 for a volume measured in cm³.
• Forgetting to subtract the initial gas syringe reading.