Answers · The mole

The mole — final check key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. LK1 · Final check

Model answer. A mole is the unit of amount of substance, and one mole of anything contains 6.02 × 10²³ particles: the Avogadro constant. O₂ has M = 2 × 16 = 32 g/mol and sodium 23 g/mol, so 32 g of oxygen and 23 g of sodium are each one mole: 6.02 × 10²³ O₂ molecules and 6.02 × 10²³ Na atoms. The oxygen holds twice as many atoms.

A full answer includes

(a) I wrote that the mole is the unit of amount of substance.
(a) I wrote that one mole contains 6.02 × 10²³ particles.
(a) I did not write 6.02 × 10²³ grams.
(b) I wrote that O₂ has M = 2 × 16 = 32 g/mol.
(b) I wrote that 32 g of oxygen is one mole.
(b) I wrote that Na has M = 23 g/mol.
(b) I wrote that 23 g of sodium is one mole.
(b) I wrote that one mole of each holds 6.02 × 10²³ particles.
(b) I did not write that both hold 6.02 × 10²³ atoms: the oxygen holds that many molecules.

Also accept

(a) the unit of amount of substance, 6.02 × 10²³ particles (b) each is one mole

Watch for

“One mole of every substance has the same mass.” — One mole always holds the same number of particles, 6.02 × 10²³, but the particles have different masses, so a mole of each substance has its own mass: its molar mass.
“A mole is 6.02 × 10²³ grams.” — 6.02 × 10²³ is a number of particles, not grams.

2. LK2 · Final check

Model answer. (a) K₂CO₃ has M = 2 × 39 + 12 + 3 × 16 = 138 g/mol, so n = m/M = 13.8 ÷ 138 = 0.100 mol. (b) n = 1.505 × 10²² ÷ 6.02 × 10²³ = 0.0250 mol of CO₂. CO₂ has M = 44 g/mol, so m = n × M = 0.0250 × 44 = 1.10 g.

Checked automatically

(a) Amount of potassium carbonate: 0.100 mol (3 significant figures)
- Common wrong answer 0.139 : K₂ means two potassium atoms: M = 2 × 39 + 12 + 3 × 16 = 138 g/mol.
(b) Mass of carbon dioxide: 1.10 g (3 significant figures)

A full answer includes

(a) I found M = 2 × 39 + 12 + 3 × 16 = 138 g/mol.
(a) I worked out 13.8 ÷ 138.
(a) I got 0.100 mol.
(a) I did not count only one potassium atom.
(b) I worked out 1.505 × 10²² ÷ 6.02 × 10²³ = 0.0250 mol.
(b) I worked out 0.0250 × 44.
(b) I got 1.10 g.

Also accept

0.100 mol; 1.10 g

Watch for

“Amount = molar mass ÷ mass.” — Divide the mass by the molar mass, n = m/M. The units show it: g ÷ g/mol leaves mol.
“Particles → moles: multiply by the Avogadro constant.” — Divide the number of particles by 6.02 × 10²³.

3. LK3 · Final check

Model answer. (a) n = 1.204 × 10²² ÷ 6.02 × 10²³ = 0.0200 mol. (b) M = m/n = 1.28 g ÷ 0.0200 mol = 64.0 g/mol. (c) The Mr is the same number with no unit: 64. (d) CO₂ is 44, H₂S 34, SO₂ 32 + 2 × 16 = 64 and Cl₂ 71, so the gas is sulfur dioxide.

Checked automatically

(a) Amount of gas: 0.0200 mol (3 significant figures)
- Common wrong answer 7.25e45 : You multiplied by the Avogadro constant. To go from molecules to moles, divide.
- Common wrong answer 0.200 : Check the powers of ten: 10²² ÷ 10²³ is 10⁻¹, so 1.204 ÷ 6.02 × 0.1 = 0.0200.
(b) Molar mass: 64.0 g/mol (3 significant figures)
- Common wrong answer 0.0156 : You divided the amount by the mass. Molar mass is mass ÷ amount.
- Common wrong answer 6.40 : Your amount is ten times too big. 1.204 × 10²² ÷ 6.02 × 10²³ is 0.0200 mol.
(c) Relative molecular mass: 64 (exact value)

A full answer includes

(a) I worked out 1.204 × 10²² ÷ 6.02 × 10²³.
(a) I got 0.0200 mol.
(a) I did not multiply by the Avogadro constant.
(b) I worked out 1.28 ÷ 0.0200.
(b) I got 64.0 g/mol.
(c) I wrote 64, with no unit.
(d) I worked out the Mr of each of the four gases.
(d) I chose sulfur dioxide, SO₂.

Also accept

0.0200 mol; 64.0 g/mol; Mr 64; SO₂

Watch for

“Particles → moles: multiply by the Avogadro constant.” — Divide the number of particles by 6.02 × 10²³.
“Molar mass = amount ÷ mass.” — That gives moles in each gram. Molar mass is mass ÷ amount.
“Molar mass has no unit, like Mr.” — Mr compares masses and has no unit, but molar mass is the mass of one mole, so it is in g/mol.

4. LK4 · Final check

Model answer. (a) V = 65.0 ÷ 1000 = 0.0650 dm³. Each dm³ holds 32.0 g, so m = 32.0 g/dm³ × 0.0650 dm³ = 2.08 g. (b) V = mass ÷ concentration = 4.00 g ÷ 32.0 g/dm³ = 0.125 dm³, which is 0.125 × 1000 = 125 cm³.

Checked automatically

(a) Mass of potassium sulfate: 2.08 g (3 significant figures)
- Common wrong answer 2080 : You used 65.0 cm³ as it is. Convert to dm³ first: 0.0650 dm³.
- Common wrong answer 492 : You divided the concentration by the volume. The grams in each dm³ times the number of dm³ gives the mass.
- Common wrong answer 0.00203 : You divided the volume by the concentration. Mass = concentration × volume.
(b) Volume in cm³: 125 cm³ (3 significant figures)
- Common wrong answer 0.125 : That is the volume in dm³. The question asks for cm³: multiply by 1000.
- Common wrong answer 0.000125 : A cm³ is smaller than a dm³, so the number gets bigger. Multiply by 1000.
- Common wrong answer 8.00 : You divided the concentration by the mass. Volume = mass ÷ concentration.
- Common wrong answer 128 : You multiplied. g ÷ g/dm³ leaves dm³, so divide the mass by the concentration.

A full answer includes

(a) I worked out 65.0 ÷ 1000 = 0.0650 dm³.
(a) I worked out 32.0 × 0.0650.
(a) I got 2.08 g.
(b) I worked out 4.00 ÷ 32.0 = 0.125 dm³.
(b) I worked out 0.125 × 1000.
(b) I got 125 cm³.
(b) I did not leave the answer in dm³.

Also accept

2.08 g; 125 cm³

Watch for

“Divide by the volume in cm³.” — Concentration is per dm³. Divide the cm³ by 1000 first: 65.0 cm³ is 0.0650 dm³.
“Mass = concentration ÷ volume.” — The concentration is the grams in each dm³, so multiply by the number of dm³.
“To change dm³ to cm³, divide by 1000.” — A cm³ is smaller than a dm³, so the number of cm³ is bigger: multiply by 1000.

5. LK5 · Final check

Model answer. (a) V = 75.0 ÷ 1000 = 0.0750 dm³, so c = n/V = 0.0105 ÷ 0.0750 = 0.140 mol/dm³. (b) V = n/c = 0.0180 ÷ 0.600 = 0.0300 dm³, which is 30.0 cm³.

Checked automatically

(a) Concentration: 0.140 mol/dm³ (3 significant figures)
(b) Volume: 30.0 cm³ (3 significant figures)

A full answer includes

(a) I worked out 75.0 ÷ 1000 = 0.0750 dm³.
(a) I worked out 0.0105 ÷ 0.0750.
(a) I got 0.140 mol/dm³.
(b) I worked out 0.0180 ÷ 0.600 = 0.0300 dm³.
(b) I worked out 0.0300 × 1000.
(b) I got 30.0 cm³.

Also accept

0.140 mol/dm³; 30.0 cm³

Watch for

“Divide by the volume in cm³.” — Concentration is per dm³. Divide the cm³ by 1000 first: 75.0 cm³ is 0.0750 dm³.

6. LK6 · Final check

Model answer. g/dm³ is a concentration: 20.2 g of potassium nitrate in every dm³ of solution. A concentration can also be measured in mol/dm³, the amount of solute in moles in each dm³.

A full answer includes

(a) I wrote that each dm³ of the solution contains 20.2 g of potassium nitrate.
(a) I wrote that the dm³ is the volume of the whole solution.
(a) I did not write 20.2 g of water in each dm³.
(b) I wrote mol/dm³.
(b) I did not write g/mol.

Also accept

(a) 20.2 g of potassium nitrate in each dm³ of solution (b) mol/dm³

Watch for

“20.2 g/dm³ means 20.2 g of water.” — The grams are the solute, potassium nitrate; the dm³ is the whole solution.
“g/mol is the other unit.” — g/mol is a molar mass. The other unit of concentration is mol/dm³.