IGCSE Chemistry Stoichiometry notes

Every substance can be described by a chemical formula that shows which elements it contains and in what ratio. In a molecule the formula gives the exact number of atoms — this is the molecular formula. In an ionic compound there are no separate molecules, so the formula simply gives the simplest whole-number ratio of ions.

Supplement: you can deduce the formula of an ionic compound from the charges on its ions. The total positive charge must equal the total negative charge, so aluminium ions (Al³⁺) and oxide ions (O²⁻) combine as Al₂O₃ — two lots of three positive charges balance three lots of two negative charges.

1. 1Write the correct formulae

   Sort out the formula of each substance first, using the ions or the combining ratios to get it right.

2. 2Balance the atoms

   Count the atoms of each element on both sides and put large numbers in front of formulae until they match. Never change a subscript to balance an equation.

3. 3Add state symbols

   Write (s), (l), (g) or (aq) after each formula to show whether the substance is a solid, liquid, gas or in aqueous solution.

Supplement: an ionic equation shows only the ions that actually change during a reaction. In the neutralisation of an acid by an alkali, the sodium and chloride ions are spectator ions that stay unchanged, so the ionic equation is H⁺(aq) + OH⁻(aq) → H₂O(l).

Atoms are far too small to weigh individually, so we compare their masses with a standard. The relative atomic mass, Aᵣ, of an element is the average mass of its isotopes compared with 1/12 the mass of one atom of carbon-12. Because it is a comparison, Aᵣ has no units. Many Aᵣ values are not whole numbers because they are weighted averages of the masses of an element’s isotopes.

The relative molecular mass, Mᵣ, of a molecule is found by adding up the Aᵣ values of all the atoms in it. For an ionic compound the same kind of total is called the relative formula mass. Water, H₂O, has Mᵣ = (2 × 1) + 16 = 18, and sodium chloride, NaCl, has a relative formula mass of 23 + 35.5 = 58.5.

1. 1Write the formula

   Note how many atoms of each element the formula contains.

2. 2Look up or recall the Aᵣ values

   Use the Aᵣ values given in the question, or the common ones you have learned.

3. 3Add the totals

   Multiply each Aᵣ by the number of atoms of that element, then add the values together.

A balanced equation gives the ratio in which substances react and are produced. Atoms are only rearranged in a chemical change, so the total mass of the reactants equals the total mass of the products. You can use the ratio in the equation to work out how much of one substance is needed to make a given mass of another.

At Core level these calculations use simple proportions, without the mole. If an equation shows that 4 g of a reactant gives 11 g of a product, then doubling the reactant doubles the product, and taking a quarter of it gives a quarter of the product.

1. 1Balance the equation

   Start from the correct balanced equation for the reaction.

2. 2Find the proportion

   Compare the mass given in the question with the mass in the equation to find the multiple or fraction you are using.

3. 3Scale to the unknown

   Apply exactly the same multiple or fraction to the substance you are asked about, keeping the ratio the same.

• The equation 2Mg + O₂ → 2MgO shows that 48 g of magnesium reacts with 32 g of oxygen to give 80 g of magnesium oxide.
• Mass is conserved, so the masses on the reactant side always add up to the masses on the product side.
• If a question starts from a different mass, scale everything in the same equation by the same factor.

Supplement: chemists count particles in moles rather than one at a time. The mole is the unit of amount of substance and always contains the same number of particles — the Avogadro constant, 6.02 × 10²³. The number is enormous because particles are so tiny, which makes one mole a convenient, weighable amount.

The molar mass of a substance is its relative formula mass expressed in grams per mole. Carbon has Aᵣ 12, so its molar mass is 12 g/mol and one mole of carbon weighs 12 g. Water has Mᵣ 18, so 36 g of water is 36 ÷ 18 = 2 mol. The equation can be rearranged to find any of the three quantities, including an unknown relative atomic mass.

Rearranging the equation also lets you find a relative atomic mass. If 0.20 mol of a metal has a mass of 13 g, its molar mass is 13 ÷ 0.20 = 65 g/mol, so its Aᵣ is 65 — zinc.

Supplement: once you can change between mass and moles, most exam calculations follow the same pattern — change what you are given into moles, use the ratio in the balanced equation, then change back into the quantity the question asks for.

1. 1Balance the equation

   Write or check the balanced equation for the reaction.

2. 2Convert the known quantity to moles

   Turn the given mass, volume or concentration into an amount in moles.

3. 3Use the mole ratio

   Use the ratio in the equation to find the moles of the substance you need.

4. 4Convert back

   Turn those moles into a mass, gas volume or concentration as required.

5. 5Check the units

   Give the correct unit, converting cm³ to dm³ where necessary.

Gas volumes at r.t.p. At room temperature and pressure, one mole of any gas occupies 24 dm³. So amount of gas = volume ÷ 24 dm³, and volume = amount × 24 dm³. This works for every gas because equal volumes of gases under the same conditions contain equal numbers of molecules.

Percentage yield, purity and composition. The percentage yield compares the mass you actually obtain with the mass the equation predicts; a value below 100% is normal because a reaction may be reversible, incomplete, or lose some product during separation. Percentage purity compares the mass of pure substance with the mass of the impure sample, and percentage composition by mass states the mass of one element as a percentage of the whole compound.