The Mole

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 1.27 — The mole as the unit for amount of substance
• 1.28 — Calculations involving amount of substance, Ar and Mr

Specification section 1(e) Chemical formulae, equations and calculations — also taught in Reacting Masses and Percentage Yield, Empirical and Molecular Formulae, Concentration and Gas Volumes, Ionic Bonding.

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

Start with the problem, because the mole is a solution and it makes no sense until you feel what it is solving. Reactions happen atom by atom: two hydrogen molecules react with one oxygen molecule, never with 1.7 of one. So chemistry is about COUNTS. But you cannot count atoms. A pinhead of copper contains more atoms than there are grains of sand on every beach on Earth, and no instrument will ever count them one by one. The only thing a chemist can actually do is put a substance on a balance and read a mass. Counts are what matter, masses are what you can get, and the mole is the bridge between them.

Think of it like buying rice by weight

Suppose a recipe needs exactly twice as many grains of rice as lentils. Counting grains is out of the question. But if you know what a fixed number of grains weighs, you can weigh out the right amount instead of counting it — and you will have the right ratio without ever having counted anything. Chemists do exactly this. They fix on a particular number of particles, and then work out what that many of each substance weighs. The number is 6.02 × 10²³ and it is called a mole, and it was not chosen at random: it was chosen so that one mole of any substance weighs, in grams, the same as its relative mass. That is the whole trick, and it is why the arithmetic turns out to be so easy.

What that gives you

1. Carbon has Ar = 12. So one mole of carbon atoms — 6.02 × 10²³ of them — has a mass of 12 g.
2. Water has Mr = 18. So one mole of water molecules has a mass of 18 g.
3. Turn it round: 36 g of water must be two moles, because 36 ÷ 18 = 2.
4. That is the relationship, in general: moles = mass ÷ Mr.
5. And rearranged the two ways you will need it: mass = moles × Mr, and Mr = mass ÷ moles.

A worked pair, in both directions

(a) How many moles are there in 60 g of calcium carbonate, CaCO₃? (b) What is the mass of 0.20 mol of it? (Mr of CaCO₃ = 100.)

1. (a) moles = mass ÷ Mr = 60 ÷ 100 = 0.60 mol.
2. (b) mass = moles × Mr = 0.20 × 100 = 20 g.
3. Check both against common sense: 60 g is a bit over half of 100 g, so a bit over half a mole. And 0.20 mol is a fifth of a mole, so a fifth of 100 g.

Answer: (a) 0.60 mol (b) 20 g

Now the sentence that makes all of this worth learning. The big numbers in a balanced equation are MOLE ratios, not mass ratios. In 2H₂ + O₂ → 2H₂O, that 2 does not mean two grams of hydrogen — it means two moles of hydrogen molecules for every one mole of oxygen molecules. Two moles of hydrogen is only 4 g while one mole of oxygen is 32 g, so by mass the ratio is nothing like 2 : 1. Every quantitative calculation you meet from here on works by converting the masses you can measure into moles, using the equation's ratio on the moles, and then converting back to a mass at the end. The mole is the only place the equation's numbers can be applied.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

Learn this definition · Mole

The unit for amount of substance. One mole contains 6.02 × 10²³ particles, and has a mass in grams equal to the relative atomic or formula mass of that substance.

amount (mol) = mass (g) ÷ Mr

Mr is the relative formula mass, or Ar for an element existing as atoms

Units: mol, g, and Mr has no units. Rearranged: mass = amount × Mr, and Mr = mass ÷ amount.

number of particles = amount (mol) × 6.02 × 10²³

6.02 × 10²³ per mole is the Avogadro constant; the particles may be atoms, molecules or ions depending on the substance

Units: mol, and the answer is a plain count with no unit.

Any mole calculation, in the same three steps

1. Work out the Mr of the substance from the Periodic Table, remembering brackets and subscripts.
2. Identify which two of the three quantities — mass, amount in moles, Mr — you have been given.
3. Rearrange amount = mass ÷ Mr for the one you are missing, and check the answer is a sensible size.

Mole ratio against mass ratio — the distinction that decides every calculation

A. The numbers in a balanced equation are MOLE ratios. In 2H₂ + O₂ → 2H₂O, two moles of hydrogen react with one mole of oxygen.

B. They are NOT mass ratios. Two moles of H₂ is 4 g and one mole of O₂ is 32 g, so by mass the ratio is 1 : 8, nothing like 2 : 1.

Model answer [3 marks]

Calculate the amount, in moles, of sodium hydroxide in 10.0 g of NaOH. Ar: Na = 23, O = 16, H = 1. [3]

Mr of NaOH = 23 + 16 + 1 = 40. Amount = mass ÷ Mr = 10.0 ÷ 40 = 0.250 mol.

Model answer [3 marks]

Explain why 1 g of hydrogen contains far more molecules than 1 g of oxygen. [3]

The number of molecules depends on the amount in moles, and amount = mass ÷ Mr. Hydrogen has a much smaller Mr than oxygen, 2 against 32, so the same mass of hydrogen is a much larger amount in moles. A larger amount in moles means proportionally more molecules, because every mole contains the same 6.02 × 10²³ particles.

Mark-losing trap. The numbers in an equation are mole ratios, never mass ratios. Convert masses to moles before using them.

Mark-losing trap. Use Mr for a compound and Ar for an element that exists as atoms — but oxygen gas is O₂, so its Mr is 32, not 16.

Mark-losing trap. Check the size of a mole answer. Grams divided by Mr is usually well under 10 mol; an answer in the hundreds means the division went the wrong way.

Mark-losing trap. One mole of any substance holds the same number of particles. It does not hold the same mass — that is the entire point.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · Calculate [1 mark] — Calculate the amount, in moles, in 36 g of water, H₂O. The Mr of water is 18.
2. Grade 7 · Calculate [3 marks] — Calculate the mass of 0.25 mol of calcium carbonate, CaCO₃. Ar: Ca = 40, C = 12, O = 16.
3. Grade 8 · Explain [4 marks] — A student says: 'The equation 2H₂ + O₂ → 2H₂O shows that 2 g of hydrogen react with 1 g of oxygen.' Select every statement that belongs in a full-mark explanation of why this is wrong.
4. Grade 9 · Calculate [3 marks] — 0.150 mol of a compound has a mass of 12.6 g. Calculate the relative formula mass of the compound.
5. 9+ · Analyse [5 marks] — A student has 10.0 g of helium (Ar = 4) and 10.0 g of argon (Ar = 40). She says the two samples must contain the same number of atoms, because they have the same mass. Select every statement that belongs in a full-mark response.

The people behind this science

Two ways into the same idea — the one who worked out how many particles there really are, and the one who determined an atomic mass by hand. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Albert Einstein — the one who worked out how many particles there really are

The number 6.02 × 10²³ looks like something you must simply accept. It is not: Einstein's 1905 analysis of the random jiggling of particles suspended in a liquid produced a way of calculating it from measurements anyone could make with a microscope, and the experiments that followed pinned it down. It is one of the few places where a number this large was genuinely measured rather than assumed.

• “How can anyone measure the number of atoms in a gram of a substance?”
• “Why did it matter so much to know that number precisely?”
• “What convinced people that atoms were real things and not just a useful idea?”
• “Why is the number the same for every substance there is?”

Marie Curie — the one who determined an atomic mass by hand

To convince chemists that radium was a genuine new element, Curie had to produce a relative atomic mass for it — which meant purifying a measurable quantity from tonnes of ore and weighing it with extraordinary care. The Ar values this lesson takes off the Periodic Table are the end product of exactly that kind of work, and hers was among the hardest ever attempted.

• “Why was measuring an atomic mass the proof that radium was a new element?”
• “How much material did you need before a mass could be measured at all?”
• “What was the hardest source of error in weighing something so precious?”
• “How would you know if your measured value was slightly wrong?”

Carry on through the course

• Previous lesson: Formulae and Balanced Equations
• Next lesson: Reacting Masses and Percentage Yield
• The Three States of Matter — What the particles are doing in a solid, a liquid and a gas — and what really changes when ice melts.
• Pure Substances, Mixtures and How to Separate Them — Why a pure substance melts at one temperature, and which separation technique to reach for when.
• Inside the Atom — Protons, neutrons and electrons — where they are, what they weigh, what they carry, and how isotopes give an element a decimal mass.
• Electronic Configurations and the Periodic Table — Why the table has the shape it has: the group number IS the outer-shell electron count, and everything follows from that.
• Solubility and Solubility Curves — Why a solution can be full, why hot water holds more, and how one curve tells you exactly how many crystals you will get back.
• All of Chemistry · Chemistry key terms · required practicals · equations · Incandio Science · The 4CH1 specification