The mole and reacting masses – GCSE Combined Science Chemistry

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Atoms are far too small to count or weigh one at a time. But chemists need to know how many atoms react. The mole is the tool that solves this problem.

This matters because every reacting mass calculation uses it. If you can use moles, you can predict how much of a product you will make. You can also work out how much of a reactant you need.

By the end you will be able to convert between mass and moles. You will use a balanced equation to find a reacting mass. You will also work out a formula from masses.

Course note: the mole, reacting masses and balancing numbers from masses are Higher tier in Combined Science. Concentration in g/dm³ comes in the next lesson and is for both tiers.

What is a mole?

Atoms and molecules are too small to count one at a time. Chemists count them in moles instead. A mole is a very large number of particles, just as a dozen is 12.

One mole of any substance contains 6.02 × 10²³ particles. This is the Avogadro constant.

The mass of one mole in grams equals the Ar or Mr. One mole of carbon atoms has a mass of 12 g. One mole of water molecules has a mass of 18 g. This is called the molar mass.

From mass to moles

To find moles, use this equation: number of moles = mass in g ÷ Mr. For atoms, use the Ar instead.

Take 8.0 g of sodium hydroxide, NaOH, with Mr = 40. Moles = 8.0 ÷ 40 = 0.20 mol.

Check that your answer is sensible. One mole of NaOH has a mass of 40 g, and you only have 8.0 g. So the answer must be less than 1. It is like asking how many 40 g bags you can fill from 8 g of sweets.

From moles to mass, and counting particles

Rearrange the same equation: mass = moles × Mr. The mass of 0.50 mol of carbon dioxide is 0.50 × 44 = 22 g. A triangle can help. Put mass at the top, and moles and Mr at the bottom. Cover what you want to find.

To count particles, use number of particles = moles × 6.02 × 10²³. In 0.50 mol of carbon atoms there are 0.50 × 6.02 × 10²³ = 3.01 × 10²³ atoms.

Say which particle you are counting. One water molecule, H₂O, has three atoms.

Reacting masses

The big numbers in a balanced equation give the ratio of moles. In 2Mg + O₂ → 2MgO, two moles of magnesium make two moles of magnesium oxide. They react with one mole of oxygen. Think of a recipe: two eggs for every cup of flour.

To find a reacting mass, follow four steps. One, write the balanced equation. Two, turn the known mass into moles. Three, use the ratio to find the moles of the other substance. Four, turn those moles into a mass.

A worked reacting mass calculation

What mass of magnesium oxide forms when 12 g of magnesium burns? Moles of Mg = 12 ÷ 24 = 0.50 mol. The ratio of Mg to MgO is 2 : 2, so 0.50 mol of MgO forms. Mass = 0.50 × 40 = 20 g.

Now take 4Al + 3O₂ → 2Al₂O₃. The ratio of Al to Al₂O₃ is 4 : 2. So the moles of Al₂O₃ are half the moles of Al. 5.4 g of Al is 0.20 mol, which makes 0.10 mol of Al₂O₃. Mass = 0.10 × 102 = 10.2 g.

Formulae and balancing numbers from masses

You can work out a formula from masses. Divide each mass by its Mr to get moles. Then divide by the smallest number of moles to find the simplest ratio.

Say 2.4 g of magnesium reacts with 1.6 g of oxygen. Moles of Mg = 2.4 ÷ 24 = 0.10. Moles of O = 1.6 ÷ 16 = 0.10. The ratio is 1 : 1, so the formula is MgO.

Now try 4.2 g of iron and 1.8 g of oxygen. That is 0.075 mol of Fe and 0.1125 mol of O. The ratio is 1 : 1.5, which is 2 : 3. So the formula is Fe₂O₃.

The same method gives the balancing numbers of an equation. Higher tier: convert each reacting mass to moles, then divide every answer by the smallest. The simplest whole-number ratio gives the numbers in front of each formula.

Example: 4.8 g of magnesium reacts with 3.2 g of oxygen to make 8.0 g of magnesium oxide. Moles: Mg 4.8 ÷ 24 = 0.20, O₂ 3.2 ÷ 32 = 0.10, MgO 8.0 ÷ 40 = 0.20. The ratio is 2 : 1 : 2, so the equation is 2Mg + O₂ → 2MgO. Notice that the masses add up: 4.8 + 3.2 = 8.0.

Recap

Moles = mass ÷ Mr. Mass = moles × Mr. One mole has 6.02 × 10²³ particles.

The big numbers in a balanced equation give the ratio of moles.

Write each step on its own line and give the answer with a unit.

Check for sense. A product cannot weigh more than all the reactants together.