The mole and molar mass

A chemist's dozen

A mole is the amount of a substance that contains Avogadro's number of particles, 6.022 × 10²³. Like a dozen means 12 oranges, a mole means 6.022 × 10²³ particles.

Always say which particles you mean. A mole of carbon is 6.022 × 10²³ atoms (12 g). A mole of O₂ is that many molecules (32 g), and a mole of NaCl that many formula units (58.5 g).

The mass of one mole is the molar mass, in g mol⁻¹. A mole of hydrogen atoms is 1.008 g, but a mole of H₂ molecules is 2.016 g.

To find a molar mass, add the contribution of each atom. H₂SO₄: 2(1) + 32 + 4(16) = 98 g mol⁻¹.

Now 2C + O₂ → 2CO also reads as 2 moles + 1 mole → 2 moles: 24 g + 32 g → 56 g.

Key terms

Mole

Counting particles by weighing.

Molar mass

Turning moles into grams.

Formula unit

Counting moles of ionic compounds.

g mol⁻¹

The unit of molar mass.

Short questions with model answers

1. Q1. Find the molar mass of glucose, C₆H₁₂O₆ (C 12, H 1, O 16). (p. 59)

   • 6(12) = 72
   • 12(1) = 12
   • 6(16) = 96
   • 72 + 12 + 96 = 180

   180 g mol⁻¹

2. Q2. Find the molar mass of MgCO₃ (Mg 24, C 12, O 16). (exercise, p. 59)

   • 24 + 12 + 3(16)
   • 24 + 12 + 48 = 84

   84 g mol⁻¹

Common mistakes

• ✗ A mole of hydrogen always weighs 1 g.

  ✓ 1.008 g for H atoms, 2.016 g for H₂ molecules: say which particles.

• ✗ H₂SO₄ = 1 + 32 + 16 = 49.

  ✓ Multiply each atomic mass by its subscript: 2(1) + 32 + 4(16) = 98.

• ✗ A mole is a fixed mass, like 1 kg.

  ✓ A mole is a number of particles; its mass depends on the substance.

MCQs

1. 1. Molar mass of H₂SO₄:

   1. (a) 49 g mol⁻¹
   2. (b) 96 g mol⁻¹
   3. (c) 98 g mol⁻¹
   4. (d) 100 g mol⁻¹
   Show answer

   (c) 2(1) + 32 + 4(16) = 98 (p. 59).

2. 2. One mole of NaCl contains 6.022 × 10²³:

   1. (a) Atoms
   2. (b) Molecules
   3. (c) Formula units
   4. (d) Electrons
   Show answer

   (c) p. 59: NaCl is ionic, counted as formula units.

3. 3. Molar mass of hydrogen molecules (H₂):

   1. (a) 1.008 g
   2. (b) 2.016 g
   3. (c) 0.504 g
   4. (d) 6.022 g
   Show answer

   (b) p. 59: two atoms per molecule.

4. 4. Molar mass of SiO₂ (Si 28, O 16):

   1. (a) 44 g mol⁻¹
   2. (b) 60 g mol⁻¹
   3. (c) 56 g mol⁻¹
   4. (d) 76 g mol⁻¹
   Show answer

   (b) 28 + 2(16) = 60 (exercise, p. 59).

5. 5. A mole is most like:

   1. (a) A kilogram
   2. (b) A litre
   3. (c) A dozen
   4. (d) A metre
   Show answer

   (c) p. 58: a mole is a number, like a dozen or a gross.

Quick revision

• 1 mole = 6.022 × 10²³ particles; always name the particles.
• Molar mass = mass of one mole, found by adding each atom's contribution.
• Equations can be read in moles and grams: 2 mol C + 1 mol O₂ → 2 mol CO.