Building a formula from ions

A chemical formula shows the ratio of atoms in a substance. For an ionic compound the positive and negative charges must cancel out — so you balance the ion charges (valencies).

Common ions to know: Na⁺, K⁺, Ca²⁺, Mg²⁺, Al³⁺, H⁺ · Cl⁻, O²⁻, OH⁻, NO₃⁻, CO₃²⁻, SO₄²⁻. For a "swap-and-drop" shortcut: the charge of one ion becomes the subscript of the other (then cancel down).

Pick the right formula

Writing & balancing equations

A balanced symbol equation shows what reacts and what forms, with state symbols — (s) solid, (l) liquid, (g) gas, (aq) aqueous. You balance it by adding big numbers in front of formulae until every element has equal atoms on both sides.

Golden rule: you can only change the big numbers in front — never the small subscripts inside a formula. Changing a subscript would change the substance itself.

Is it balanced?

Tap the equation that is correctly balanced in each pair.

What decides the little numbers in a formula?

Atoms are never lost

In a chemical reaction atoms are only rearranged — none are created or destroyed. So the total mass of products = total mass of reactants. This is why a balanced equation must have the same atoms on each side.

Watch out — "the mass changed!": if a reaction looks like it gains or loses mass, a gas has escaped or joined in. Burning magnesium gains mass because O₂ from the air is added; a fizzing acid–carbonate reaction loses mass because CO₂ gas escapes. Seal the container and the mass stays the same.

Where did the mass go?

Relative formula mass, M_r

The relative formula mass (M_r) of a compound is found by adding up the relative atomic masses (A_r) of every atom in its formula.

Watch out: M_r has no units — it is a relative mass compared to carbon-12, so it is just a number. Multiply a subscript (like the 3 in CO₃) through the A_r before you add.

Your turn — relative formula mass

How do you count atoms by weighing?

The mole & Avogadro's constant

Chemists count particles in moles. One mole is simply a fixed number of particles — Avogadro's constant:

Conveniently, the mass of one mole of a substance in grams is numerically equal to its M_r. So 1 mol of water (M_r = 18) weighs 18 g. That gives the key equation:

Your turn — moles from mass

How do you count atoms by weighing?

Reacting masses from equations

The big numbers in a balanced equation give the mole ratio of the substances. Convert a known mass to moles, use the ratio, then convert back to a mass.

Your turn — reacting masses

Balancing from masses / moles

On the Higher tier you can be given the masses that react and asked to deduce the balancing numbers. Convert each mass to moles, then write the moles as the simplest whole-number ratio — that is the equation ratio.

Tip: always simplify the mole ratio to the smallest whole numbers — multiply through to clear any decimals (here ×2).

The limiting reactant

When two reactants are mixed, one usually runs out first — the limiting reactant. It is completely used up, and it controls how much product can form. The other reactant is in excess (some is left over).

Watch out: the limiting reactant is the one that gives the fewest moles of product — not always the one with the smaller mass. Always work in moles, applying the equation ratio, to decide which runs out.

Which one limits?

How can a perfect reaction still waste atoms?

Concentration: g/dm³ and mol/dm³

The concentration of a solution tells you how much solute is dissolved in each dm³ (1 dm³ = 1 litre = 1000 cm³). You can measure it two ways:

Watch out: g/dm³ and mol/dm³ are different units — convert between them with M_r: divide a g/dm³ value by M_r to get mol/dm³ (and ×M_r to go back). Also convert cm³ → dm³ by dividing by 1000.

Your turn — concentration in g/dm³

Your turn — concentration in mol/dm³

Percentage yield

You rarely get every gram a reaction promises — some product is lost, reactions don't fully finish, or side-reactions occur. Percentage yield compares the actual amount you got with the theoretical maximum:

Why less than 100%? Product is lost on filtering/transfer, the reaction may be reversible or incomplete, and reactants may react in unexpected (side) reactions.

Your turn — percentage yield

Atom economy

Atom economy measures how much of the reactant mass ends up as the useful product (rather than waste). A high atom economy means a more sustainable, less wasteful process.

Don't confuse them: percentage yield is about how much you actually made; atom economy is about how much of the reactant mass becomes useful product in theory. A reaction can have 100% yield but poor atom economy.

Your turn — atom economy

How can a perfect reaction still waste atoms?

Why does a mole of any gas fill the same space?

Empirical & molecular formulae from data

The empirical formula is the simplest whole-number ratio of atoms in a compound. From masses or percentages: divide each element's mass by its A_r (to get moles), then divide by the smallest to get the ratio.

Empirical → molecular: the molecular formula is a whole-number multiple of the empirical one. If the empirical M_r is 15 (CH₃) and the true M_r is 30, the multiplier is 30 ÷ 15 = 2, so the molecular formula is C₂H₆.

Titration calculations

A titration finds an unknown concentration by reacting an acid and alkali exactly to the end-point. From the known solution: find its moles, use the equation ratio to find the unknown's moles, then divide by its volume.

Your turn — titration

The molar volume of a gas

At room temperature and pressure (rtp), one mole of any gas occupies the same volume — the molar volume:

Handy reverse: moles = volume ÷ 24. So 48 dm³ of any gas at rtp is 48 ÷ 24 = 2 mol — whatever the gas, because equal volumes contain equal numbers of molecules.

Your turn — gas volume

Why does a mole of any gas fill the same space?

Match each tool to its job

Tap a quantity on the left, then its correct formula on the right.

The equations to know

You've covered Eduqas Topic 3 — formulae & balancing, conservation of mass and M_r, plus the Higher-tier (H) calculations: the mole, reacting masses, limiting reactants, empirical formulae and gas volumes — and, from other topics, concentration and titrations (Topic 7, H) and percentage yield and atom economy (Topic 11). Press Finish to see your score.