Chapter 3 of 8

All 8 chapters
  1. 1Chemical formulae, readunderstood
  2. 2Balancing equations, readunderstood
  3. 3The mole, readunderstood
  4. 4Reacting masses and yield, readunderstood
  5. 5Acids, bases and salts, readunderstood
  6. 6The reactivity series, readunderstood
  7. 7Electrolysis, readunderstood
  8. 8Energy changes and rates, readunderstood

S4.7.3 Chapter 3

The mole

How can a chemist count atoms when they are far too small to see?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Calculate relative formula mass
  • Convert between mass and moles
  • Calculate concentration in moles per cubic decimetre

One drop of water holds about a thousand million million million molecules. Nobody can count them one by one. Chemists use a trick: they weigh. This chapter shows how weighing can count.

Every element has a relative atomic mass. It compares the mass of its atoms with one twelfth of a carbon 12 atom. Hydrogen is 1, carbon is 12 and oxygen is 16. It has no unit. It is an average over the isotopes, which is why chlorine is 35.5.

A table with the columns Element, Symbol and Mass. Hydrogen H 1. Carbon C 12. Nitrogen N 14. Oxygen O 16. Sodium Na 23. Magnesium Mg 24. Sulfur S 32. Chlorine Cl 35.5. Calcium Ca 40. Iron Fe 56.ElementSymbolMasshydrogenH1carbonC12nitrogenN14oxygenO16sodiumNa23magnesiumMg24sulfurS32chlorineCl35.5calciumCa40ironFe56
Relative atomic masses used in this book, part 1. The column Mass is the relative atomic mass, so it has no unit. Part 2 follows.
A table with the columns Element, Symbol and Mass. Aluminium Al 27. Potassium K 39. Copper Cu 63.5. Zinc Zn 65. Bromine Br 80. Tin Sn 119. Lead Pb 207.ElementSymbolMassaluminiumAl27potassiumK39copperCu63.5zincZn65bromineBr80tinSn119leadPb207
Relative atomic masses used in this book, part 2. These are the values the questions use when they do not give them.

The relative formula mass, written Mr, is the sum of the relative atomic masses of all the atoms in a formula. For a molecule it is also called the relative molecular mass. Add the atoms one by one, and use a bracket the same way as in chapter 1.

Worked example

What is the relative formula mass of Ca(OH)₂?

  1. The atoms are Ca 1, O 2 and H 2. The bracket multiplies O and H by 2.
  2. The relative atomic masses are Ca 40, O 16 and H 1.
  3. Ca: 1 × 40 = 40. O: 2 × 16 = 32. H: 2 × 1 = 2.
  4. Mr = 40 + 32 + 2 = 74.

Answer: 74

Now the key idea. A mole is an amount of substance. One mole of anything holds 6.02 × 10²³ particles. This is 602 followed by 21 zeros. The particles may be atoms, molecules or the units of an ionic formula.

The mass of one mole, in grams, is the Mr of the substance. So 12 g of carbon is one mole of carbon atoms. 18 g of water is one mole of water molecules. 44 g of carbon dioxide is one mole of CO₂ molecules. Mr has no unit. The mass of one mole is Mr in grams.

A table with the columns Substance, Mr and 1 mol. Carbon, 12, 12 g. Water, 18, 18 g. Carbon dioxide, 44, 44 g. Table salt, 58.5, 58.5 g.SubstanceMr1 molcarbon1212 gwater1818 gcarbon dioxide4444 gtable salt58.558.5 g
The column 1 mol is the mass of one mole. Table salt is sodium chloride, NaCl. Each row holds 6.02 × 10²³ particles. The particles differ in mass, so the masses differ.

Draw it first

The triangle for mass, moles and Mr

  1. A triangle with a line across and a line down. The top reads mass (g). The bottom left reads n (mol). The bottom right reads Mr. In step 2 the n (mol) cell is hatched, covered. In step 3 the mass (g) cell is hatched, covered.mass(g)n (mol)Mr

    1 Write mass on top, and moles and Mr side by side below.

  2. A triangle with a line across and a line down. The top reads mass (g). The bottom left reads n (mol). The bottom right reads Mr. In step 2 the n (mol) cell is hatched, covered. In step 3 the mass (g) cell is hatched, covered.mass(g)Mr

    2 Cover moles. What is left is mass over Mr, so moles = mass ÷ Mr.

  3. A triangle with a line across and a line down. The top reads mass (g). The bottom left reads n (mol). The bottom right reads Mr. In step 2 the n (mol) cell is hatched, covered. In step 3 the mass (g) cell is hatched, covered.n (mol)Mr

    3 Cover mass. What is left is moles beside Mr, so mass = moles × Mr.

A kitchen scale with water on it. The display reads 90 g.water90 g
The scale for the worked example: water, with a mass of 90 g. The scale was set to zero with the empty cup on it, so it shows the water only.

Worked example

How many moles of water are on the scale?

  1. Mr of H₂O = 2 × 1 + 16 = 18.
  2. moles = mass ÷ Mr.
  3. moles = 90 ÷ 18 = 5 mol.

Answer: 5 mol

See it three ways

As a picture

A triangle with a line across and a line down. The top reads mass (g). The bottom left reads n (mol). The bottom right reads Mr.mass(g)n (mol)Mr

In words

Cover the one you want. Mass over Mr gives moles. Moles beside Mr gives mass: multiply.

In symbols

moles = mass ÷ Mr, and mass = moles × Mr.

Reactions in water use solutions. The concentration of a solution is how many moles of the solute are in 1 dm³ of the solution. A dm³ is a cubic decimetre, which is one litre. It is 1 000 cm³.

Concentration is measured in mol/dm³. Say it as "moles per cubic decimetre". The same amount of solute in less water gives a more concentrated solution.

Worked example

2 g of sodium hydroxide, NaOH, is dissolved in water to make 500 cm³ of solution. What is the concentration in mol/dm³?

  1. Mr of NaOH = 23 + 16 + 1 = 40.
  2. moles = 2 ÷ 40 = 0.05 mol.
  3. volume = 500 cm³ ÷ 1 000 = 0.5 dm³.
  4. concentration = moles ÷ volume = 0.05 ÷ 0.5 = 0.1 mol/dm³.

Answer: 0.1 mol/dm³

A beaker with a scale from 100 to 600 cm³. The liquid reaches the mark at 500 cm³. The label under it reads NaOH solution.100200300400500600cm³NaOH solution
The solution for the worked example. It is at the 500 cm³ mark.
A triangle with a line across and a line down. Moles, n (mol), is on top. Concentration, c (mol/dm³), is bottom left. Volume, V (dm³), is bottom right.n (mol)c(mol/dm³)V (dm³)
The same triangle for concentration: c = n ÷ V, n = c × V and V = n ÷ c. Volume must be in dm³.

Try it

Strong tea and weak tea

You need: cold, strong tea, three clear cups or glasses of the same size, water, a spoon and a sheet of white paper.

Be safe: An adult makes the tea and lets it cool completely. Drink none of it, and wash your hands afterwards.

  1. Put the same amount of water in each of two cups, about half full. Add 1 spoon of tea to one and 2 spoons to the other. Stir.
  2. Hold each cup against the white paper. Which looks darker?
  3. Fill the third cup with twice as much water as the others. Add 4 spoons of tea and stir.
  4. Compare this cup with the one that has 2 spoons.

What you will see: The cup with 2 spoons is darker than the cup with 1 spoon: more tea in the same amount of water. The third cup has 4 spoons in twice the water, which is 2 spoons for each cup of water. It looks like the second cup. Concentration is the amount of solute divided by the volume.

If you cannot try it, this is what happens.
A table with the columns Tea, Water and Colour. 1 spoon in 1 cup of water: lightest. 2 spoons in 1 cup of water: darker. 4 spoons in 2 cups of water: as row 2, the same colour as 2 spoons in 1 cup.TeaWaterColour1 spoon1 cuplightest2 spoons1 cupdarker4 spoons2 cupsas row 2

A wrong idea many people have

One mole of every substance has the same mass.

Why it feels right: Every mole has the same number of particles, so it seems it should weigh the same.

The test that breaks it: Look at the table of one mole. 1 mol of carbon is 12 g, but 1 mol of carbon dioxide is 44 g.

What is true: One mole always has the same number of particles, 6.02 × 10²³. The particles have different masses, so a mole of one substance is heavier than a mole of another.

Key words

relative atomic mass
the mass of an atom compared with one twelfth of a carbon 12 atom.
relative formula mass
Mr, the sum of the relative atomic masses in a formula.
mole
an amount of substance: 6.02 × 10²³ particles.
concentration
the moles of solute in 1 dm³ of solution.

Back to your guess

The answer is C: By weighing them, because the mass of a pile tells how many atoms it holds.

Chemists weigh. Each kind of atom has its own mass, so a known mass of a substance holds a known number of particles. The mole is the name for that number.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. What is the relative formula mass of CO₂? Use C 12 and O 16.

    Tap your answer.

    1. Not this one. That is 12 + 16, for CO with one oxygen. CO₂ has two oxygen atoms. Try another.

    2. Not this one. That is 2 × 16, the two oxygen atoms. The carbon atom must be added too. Try another.

    3. Yes, that is right. CO₂ has 1 carbon and 2 oxygen atoms. 12 + 2 × 16 = 12 + 32 = 44.

    See the answer

    44

    CO₂ has 1 carbon and 2 oxygen atoms. 12 + 2 × 16 = 12 + 32 = 44.

    • If you chose A: That is 12 + 16, for CO with one oxygen. CO₂ has two oxygen atoms.
    • If you chose B: That is 2 × 16, the two oxygen atoms. The carbon atom must be added too.

  2. The scale shows 36 g of water. It was set to zero with the empty cup on it. Mr of water is 18. How many moles of water is that?

    A kitchen scale with water on it. The display reads 36 g.water36 g
    Tap your answer.

    1. Yes, that is right. moles = mass ÷ Mr = 36 ÷ 18 = 2 mol.

    2. Not this one. That is 18 ÷ 36, the wrong way round. Moles are mass divided by Mr. Try another.

    3. Not this one. That is the Mr itself. Divide the mass by it: moles = mass ÷ Mr. Try another.

    See the answer

    2 mol

    moles = mass ÷ Mr = 36 ÷ 18 = 2 mol.

    • If you chose B: That is 18 ÷ 36, the wrong way round. Moles are mass divided by Mr.
    • If you chose C: That is the Mr itself. Divide the mass by it: moles = mass ÷ Mr.

  3. What is the mass of 2 mol of calcium carbonate, CaCO₃?

    Tap your answer.

    1. Not this one. That is 100 ÷ 2. To go from moles to mass, multiply by Mr. Try another.

    2. Yes, that is right. Mr of CaCO₃ = 40 + 12 + 3 × 16 = 100. mass = moles × Mr = 2 × 100 = 200 g.

    3. Not this one. That is the mass of 1 mol. There are 2 mol, so multiply by 2. Try another.

    See the answer

    200 g

    Mr of CaCO₃ = 40 + 12 + 3 × 16 = 100. mass = moles × Mr = 2 × 100 = 200 g.

    • If you chose A: That is 100 ÷ 2. To go from moles to mass, multiply by Mr.
    • If you chose C: That is the mass of 1 mol. There are 2 mol, so multiply by 2.

  4. A 100 cm³ sample of solution holds 0.2 mol of sodium chloride. What is its concentration?

    Tap your answer.

    1. Not this one. That divides by 100 as if the volume were in dm³. 100 cm³ is 0.1 dm³ first. Try another.

    2. Not this one. That multiplies by 100. To change cm³ into dm³ divide by 1 000, which gives 0.1 dm³. Try another.

    3. Yes, that is right. 100 cm³ = 0.1 dm³. concentration = moles ÷ volume = 0.2 ÷ 0.1 = 2 mol/dm³.

    See the answer

    2 mol/dm³

    100 cm³ = 0.1 dm³. concentration = moles ÷ volume = 0.2 ÷ 0.1 = 2 mol/dm³.

    • If you chose A: That divides by 100 as if the volume were in dm³. 100 cm³ is 0.1 dm³ first.
    • If you chose B: That multiplies by 100. To change cm³ into dm³ divide by 1 000, which gives 0.1 dm³.

  5. Which sample holds the most particles: 12 g of carbon, 18 g of water or 44 g of carbon dioxide?

    Tap your answer.

    1. Not this one. More mass does not mean more particles. Each particle of carbon dioxide has more mass than a carbon atom. Try another.

    2. Yes, that is right. Each sample is one mole, because its mass in grams equals its Mr: 12, 18 and 44. One mole always has the same number of particles.

    3. Not this one. The size of a particle does not decide it. Count the moles instead: 12 g of carbon is one mole. Try another.

    See the answer

    All three hold the same number of particles.

    Each sample is one mole, because its mass in grams equals its Mr: 12, 18 and 44. One mole always has the same number of particles.

    • If you chose A: More mass does not mean more particles. Each particle of carbon dioxide has more mass than a carbon atom.
    • If you chose C: The size of a particle does not decide it. Count the moles instead: 12 g of carbon is one mole.

  6. One mole holds 6.02 × 10²³ particles. How many carbon atoms are in 0.5 mol of carbon?

    Tap your answer.

    1. Yes, that is right. Half a mole holds half the particles. 0.5 × 6.02 × 10²³ = 3.01 × 10²³ atoms.

    2. Not this one. That is the number in a whole mole. Here there is only half a mole, so half as many atoms. Try another.

    3. Not this one. Half of 6.02 is 3.01, but the power of ten stays at 23. A power of 22 would be ten times too small. Try another.

    See the answer

    3.01 × 10²³ atoms

    Half a mole holds half the particles. 0.5 × 6.02 × 10²³ = 3.01 × 10²³ atoms.

    • If you chose B: That is the number in a whole mole. Here there is only half a mole, so half as many atoms.
    • If you chose C: Half of 6.02 is 3.01, but the power of ten stays at 23. A power of 22 would be ten times too small.

  7. Why is the relative atomic mass of chlorine 35.5, and not a whole number?

    Tap your answer.

    1. Not this one. Protons are never split. Every chlorine atom has 17 whole protons. Go to S4.6.1. Try another.

    2. Not this one. It is measured carefully. The value is 35.45, which school tables round to 35.5. It is not whole because chlorine is a mixture of two isotopes with different masses, and 35.5 is their average. Go to S4.6.3. Try another.

    3. Yes, that is right. Chlorine atoms with 18 neutrons are about three times as common as those with 20. The average mass lies between 35 and 37, closer to 35, at 35.5.

    See the answer

    It is the average of the masses of its isotopes, weighted by how common each is.

    Chlorine atoms with 18 neutrons are about three times as common as those with 20. The average mass lies between 35 and 37, closer to 35, at 35.5.

    • If you chose A: Protons are never split. Every chlorine atom has 17 whole protons. Go to S4.6.1.
    • If you chose B: It is measured carefully. The value is 35.45, which school tables round to 35.5. It is not whole because chlorine is a mixture of two isotopes with different masses, and 35.5 is their average. Go to S4.6.3.

  8. From an earlier chapter

    Calcium burns in oxygen to make calcium oxide, CaO. Which is the balanced equation for this?

    Tap your answer.

    1. Yes, that is right. Two CaO have 2 Ca and 2 O. So 2 Ca on the left, and one O₂ for 2 O.

    2. Not this one. This is balanced, but CaO₂ is not calcium oxide. The formula of the product must stay CaO. Only the number in front may change. Go to S4.7.2. Try another.

    3. Not this one. The left has 2 O atoms and the right has 1. The oxygen is not equal. Go to S4.7.2. Try another.

    See the answer

    2Ca + O₂ → 2CaO

    Two CaO have 2 Ca and 2 O. So 2 Ca on the left, and one O₂ for 2 O.

    • If you chose B: This is balanced, but CaO₂ is not calcium oxide. The formula of the product must stay CaO. Only the number in front may change. Go to S4.7.2.
    • If you chose C: The left has 2 O atoms and the right has 1. The oxygen is not equal. Go to S4.7.2.

  9. What is the relative formula mass of Na₂CO₃?

    See the answer

    106

    Na₂CO₃ has 2 Na, 1 C and 3 O. 2 × 23 + 12 + 3 × 16 = 46 + 12 + 48 = 106.

  10. How many moles are in 22 g of carbon dioxide?

    See the answer

    0.5 mol

    Mr of CO₂ is 44. moles = mass ÷ Mr = 22 ÷ 44 = 0.5 mol.

  11. A solution of volume 250 cm³ holds 0.5 mol of solute. What is its concentration in mol/dm³?

    See the answer

    2 mol/dm³

    250 cm³ ÷ 1 000 = 0.25 dm³. concentration = 0.5 ÷ 0.25 = 2 mol/dm³.

Keep it

Copy this into your exercise book.

Mr is the sum of the relative atomic masses. One mole is Mr grams and 6.02 × 10²³ particles. moles = mass ÷ Mr. concentration = moles ÷ volume in dm³.

Draw: The triangle with mass on top and moles and Mr below. Add a second triangle for n, c and V.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

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