Answers · The mole

How much solute is in the solution? — answer key

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

1. LQ9 · Practice

Model answer. Concentration is the quantity of solute in each dm³ of solution: grams in each dm³, g/dm³, or moles in each dm³, mol/dm³. g/mol is a molar mass and dm³ a volume.

A full answer includes

I chose g/dm³.
I chose mol/dm³.
I did not choose g/mol, which is a molar mass.
I did not choose dm³, which is only a volume.

Also accept

g/dm³, mol/dm³

Watch for

“g/mol is a concentration.” — g/mol is the mass of one mole: a molar mass. A concentration is a quantity in each dm³ of solution.
“dm³ is a concentration.” — dm³ is a volume: it says how much solution there is, not how much solute is in each part of it.

2. LQ10 · Practice

Model answer. V = 80.0 cm³ ÷ 1000 = 0.0800 dm³. c = n/V = 0.0144 mol ÷ 0.0800 dm³ = 0.180 mol/dm³.

Checked automatically

(a) Volume: 0.0800 dm³ (3 significant figures)
- Common wrong answer 80000 : You multiplied by 1000. A dm³ is bigger than a cm³, so the number gets smaller: divide by 1000.
- Common wrong answer 0.800 : 1 dm³ is 1000 cm³, not 100. Divide by 1000.
(b) Concentration: 0.180 mol/dm³ (3 significant figures)
- Common wrong answer 0.000180 : You divided by 80.0 cm³. Use the volume in dm³, 0.0800.
- Common wrong answer 5.56 : You divided the volume by the amount. c = n/V: amount ÷ volume.

A full answer includes

(a) I worked out 80.0 ÷ 1000.
(a) I got 0.0800 dm³.
(b) I worked out 0.0144 ÷ 0.0800.
(b) I got 0.180 mol/dm³.
(b) I did not divide by 80.0 cm³.

Also accept

0.0800 dm³; 0.180 mol/dm³

Watch for

“Divide by the volume in cm³.” — Concentration is per dm³. Divide the cm³ by 1000 first: 80.0 cm³ is 0.0800 dm³.
“Concentration = volume ÷ amount.” — Concentration is the amount in each dm³: amount ÷ volume.

3. LQ11 · Practice

Model answer. V = 500.0 ÷ 1000 = 0.5000 dm³. In g/dm³: 7.80 g ÷ 0.5000 dm³ = 15.6 g/dm³. MgSO₄ has M = 24 + 32 + 4 × 16 = 120 g/mol, so n = 7.80 ÷ 120 = 0.0650 mol and c = 0.0650 ÷ 0.5000 = 0.130 mol/dm³. Check: 15.6 g/dm³ ÷ 120 g/mol = 0.130 mol/dm³.

Checked automatically

(a) Concentration in g/dm³: 15.6 g/dm³ (3 significant figures)
- Common wrong answer 0.0156 : You divided by 500.0 cm³. Use the volume in dm³, 0.5000.
(b) Amount: 0.0650 mol (3 significant figures)
- Common wrong answer 15.4 : You divided 120 by 7.80. n = m/M: the mass ÷ the molar mass.
(c) Concentration in mol/dm³: 0.130 mol/dm³ (3 significant figures)
- Common wrong answer 15.6 : That is the number in g/dm³. Change the number too: divide by M = 120 g/mol.
- Common wrong answer 0.000130 : You divided by 500.0 cm³. Use the volume in dm³, 0.5000.

A full answer includes

(a) I worked out 500.0 ÷ 1000 = 0.5000 dm³.
(a) I worked out 7.80 ÷ 0.5000.
(a) I got 15.6 g/dm³.
(b) I found M = 24 + 32 + 4 × 16 = 120 g/mol.
(b) I worked out 7.80 ÷ 120.
(b) I got 0.0650 mol.
(c) I worked out 0.0650 ÷ 0.5000.
(c) I got 0.130 mol/dm³.
(c) I did not give the g/dm³ number with the unit mol/dm³.

Also accept

15.6 g/dm³; 0.0650 mol; 0.130 mol/dm³

Watch for

“Divide by the volume in cm³.” — Concentration is per dm³. Divide the cm³ by 1000 first: 500.0 cm³ is 0.5000 dm³.
“g/dm³ and mol/dm³ have the same number.” — They describe the same solution with different numbers: g/dm³ = mol/dm³ × M.

4. LQ12 · Practice

Model answer. V = 200.0 ÷ 1000 = 0.2000 dm³, so n = c × V = 0.110 × 0.2000 = 0.0220 mol. M = m/n = 3.12 g ÷ 0.0220 mol = 141.8 g/mol, which is 142 g/mol to three significant figures, so the Mr is 142. NaCl is 58.5, KNO₃ 101, Na₂CO₃ 106 and Na₂SO₄ 2 × 23 + 32 + 4 × 16 = 142: the solid is sodium sulfate.

Checked automatically

(a) Amount: 0.0220 mol (3 significant figures)
- Common wrong answer 22.0 : You used 200.0 cm³ as it is. Convert it to dm³ first: 0.2000 dm³.
(b) Molar mass: 142 g/mol (3 significant figures)
- Common wrong answer 28.4 : You divided the mass by the concentration. Find the amount first: n = c × V.
- Common wrong answer 0.00705 : You divided the amount by the mass. Molar mass is mass ÷ amount.
- Common wrong answer 0.0686 : You multiplied. Molar mass is mass ÷ amount.
(c) Relative formula mass: 142 (exact value)

A full answer includes

(a) I worked out 200.0 ÷ 1000 = 0.2000 dm³.
(a) I worked out 0.110 × 0.2000.
(a) I got 0.0220 mol.
(b) I worked out 3.12 ÷ 0.0220.
(b) I got 142 g/mol.
(c) I wrote 142, with no unit.
(d) I worked out the Mr of each of the four formulae.
(d) I chose sodium sulfate, Na₂SO₄.
(b) I did not divide the mass by the concentration.

Also accept

0.0220 mol; 142 g/mol; Mr 142; Na₂SO₄

Watch for

“Divide by the volume in cm³.” — Concentration is per dm³. Divide the cm³ by 1000 first: 200.0 cm³ is 0.2000 dm³.
“Molar mass = mass ÷ concentration.” — The concentration is moles in each dm³, not the moles you have. Find the amount first: n = c × V.
“Molar mass = amount ÷ mass.” — That gives moles in each gram. Molar mass is mass ÷ amount.

5. LQ13 · Practice

Model answer. (a) H₂SO₄ has M = 2 × 1 + 32 + 4 × 16 = 98 g/mol. Each dm³ holds 4.90 g, which is 4.90 ÷ 98 = 0.0500 mol, so 0.0500 mol/dm³. (b) Each dm³ holds 8.96 g and 0.160 mol, so one mole has a mass of 8.96 ÷ 0.160 = 56.0 g: M = 56.0 g/mol (potassium hydroxide, KOH, has this molar mass).

Checked automatically

(a) Concentration in mol/dm³: 0.0500 mol/dm³ (3 significant figures)
- Common wrong answer 480 : You multiplied by M. From g/dm³ to mol/dm³, divide by M.
- Common wrong answer 0.0510 : You left out the hydrogen. H₂SO₄ has M = 2 × 1 + 32 + 4 × 16 = 98 g/mol.
- Common wrong answer 0.0505 : H₂ means two H atoms, so M = 2 × 1 + 32 + 4 × 16 = 98 g/mol, not 97.
(b) Molar mass: 56.0 g/mol (3 significant figures)
- Common wrong answer 0.0179 : You divided mol/dm³ by g/dm³. Molar mass is grams ÷ moles.
- Common wrong answer 1.43 : You multiplied. Molar mass is grams ÷ moles.

A full answer includes

(a) I found M = 2 × 1 + 32 + 4 × 16 = 98 g/mol.
(a) I worked out 4.90 ÷ 98.
(a) I got 0.0500 mol/dm³.
(b) I worked out 8.96 ÷ 0.160.
(b) I got 56.0 g/mol.
(a) I did not multiply by the molar mass.

Also accept

0.0500 mol/dm³; 56.0 g/mol

Watch for

“g/dm³ and mol/dm³ have the same number.” — They describe the same solution with different numbers: g/dm³ = mol/dm³ × M.
“Molar mass = mol/dm³ ÷ g/dm³.” — That gives moles in each gram. Molar mass is grams ÷ moles.

6. LQ14 · Practice

Model answer. The flask is filled to the line at the end, so the final volume is 200.0 cm³ however much water was in the flask at the start: the pupil simply adds less water from the wash bottle. All the weighed solute is in the flask, so the amount is as planned, and the concentration is the same as planned. Row C. A volumetric flask need not be dry before you use it.

A full answer includes

I chose row C.
I can say why: the volume is set by the line, so it is 200.0 cm³.
I can say why: all the weighed solute is in the flask, so the amount is as planned.
I did not choose row B: the water already in the flask only means less water is added later.

Also accept

Row C

Watch for

“Row A.” — The water in the flask does not add to the final volume: the volume is fixed when you stop at the line.
“Row B.” — The extra water does not dilute the solution, because you add that much less water before the line. Amount and volume are both as planned.
“Row D.” — The water in the flask does not take up room that the solution needs. The bottom of the meniscus still stops at the line, at 200.0 cm³.

7. LQ15 · Practice

Model answer. The meniscus curves down in the middle, and its bottom should sit on the line. If the edges are on the line, the bottom is below it, so the flask holds less than 100.0 cm³. All the weighed solute is in the flask, so the same amount is in a smaller volume: the concentration is higher than planned. Row A. She can still add drops until the bottom of the meniscus is on the line; had she gone past the line, she would have to make the solution again.

A full answer includes

I chose row A.
I can say why: the bottom of the meniscus is below the line.
I can say why: so the volume is less than 100.0 cm³.
I can say why: the amount of solute is as planned.
I can say why: the same amount in a smaller volume is a higher concentration.
I did not choose row B: the flask holds too little water, not too much.

Also accept

Row A

Watch for

“Row B.” — The bottom of the meniscus is below the line, so the flask holds too little water, not too much.
“Row C.” — No solute was lost: all of it was rinsed into the flask. Only the volume is wrong.
“Row D.” — The bottom of the meniscus, not its edges, marks 100.0 cm³. Here it is below the line.

8. LQ16 · Practice

Model answer. (a) Rearrange c = n/V to n = c × V. 40.0 cm³ = 0.0400 dm³, so n = 0.350 × 0.0400 = 0.0140 mol. (b) Each dm³ holds 6.40 g, so the volume that holds 0.960 g is V = mass ÷ concentration = 0.960 g ÷ 6.40 g/dm³ = 0.150 dm³ (the grams cancel, leaving dm³).

Checked automatically

(a) Amount: 0.0140 mol (3 significant figures)
- Common wrong answer 14.0 : You used 40.0 cm³ as it is. Convert it to dm³ first: 0.0400 dm³.
- Common wrong answer 8.75 : You divided. The amount is concentration × volume.
(b) Volume: 0.150 dm³ (3 significant figures)
- Common wrong answer 6.14 : You multiplied. Divide the mass by the concentration: V = mass ÷ concentration.
- Common wrong answer 6.67 : You divided the concentration by the mass. Divide the mass by the concentration.
- Common wrong answer 0.000150 : The answer is wanted in dm³, and 0.960 ÷ 6.40 already gives dm³. Do not divide by 1000.

A full answer includes

(a) I worked out 40.0 ÷ 1000 = 0.0400 dm³.
(a) I worked out 0.350 × 0.0400.
(a) I got 0.0140 mol.
(b) I worked out 0.960 ÷ 6.40.
(b) I got 0.150 dm³.
(b) I did not multiply the mass by the concentration.

Also accept

0.0140 mol; 0.150 dm³

Watch for

“Divide by the volume in cm³.” — Concentration is per dm³. Divide the cm³ by 1000 first: 40.0 cm³ is 0.0400 dm³.
“Amount = concentration ÷ volume.” — The concentration is the moles in each dm³, so multiply by the number of dm³: n = c × V.
“Volume = mass × concentration.” — g × g/dm³ does not give dm³. Divide the mass by the grams in each dm³.

9. LQ17 · Practice

Model answer. Rearrange c = n/V to V = n/c: 0.00450 mol ÷ 0.300 mol/dm³ = 0.0150 dm³ (the moles cancel, leaving dm³). Multiply by 1000 for cm³: 15.0 cm³.

Checked automatically

(a) Volume in dm³: 0.0150 dm³ (3 significant figures)
- Common wrong answer 66.7 : You divided the concentration by the amount. V = n/c.
- Common wrong answer 0.00135 : You multiplied. V = n/c: divide the amount by the concentration.
(b) Volume in cm³: 15.0 cm³ (3 significant figures)
- Common wrong answer 0.0000150 : You divided by 1000. A cm³ is smaller, so the number gets bigger: multiply by 1000.

A full answer includes

(a) I worked out 0.00450 ÷ 0.300.
(a) I got 0.0150 dm³.
(b) I worked out 0.0150 × 1000.
(b) I got 15.0 cm³.
(a) I did not divide the concentration by the amount.

Also accept

0.0150 dm³; 15.0 cm³

Watch for

“Volume = concentration ÷ amount.” — That gives a unit of 1/dm³. Divide the amount by the concentration.
“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.

10. LT2 · Apply

Model answer. (a) V = 500.0 ÷ 1000 = 0.5000 dm³. Each dm³ holds 3.18 g, so the solution holds 3.18 × 0.5000 = 1.59 g of Na₂CO₃. (b) Na₂CO₃ has M = 2 × 23 + 12 + 3 × 16 = 106 g/mol, so n = 1.59 ÷ 106 = 0.0150 mol. (c) Each crystal formula unit has one Na₂CO₃, so she needs 0.0150 mol of crystals. Their M = 106 + 10 × 18 = 286 g/mol, so m = 0.0150 × 286 = 4.29 g. More mass of crystals is needed for the same amount, because part of their mass is water; that water joins the solvent when they dissolve.

Checked automatically

(a) Mass of Na₂CO₃: 1.59 g (3 significant figures)
- Common wrong answer 1590 : You used 500.0 cm³ as it is. Convert it to dm³ first: 0.5000 dm³.
- Common wrong answer 6.36 : You divided by the volume. Mass = concentration × volume.
(b) Amount of Na₂CO₃: 0.0150 mol (3 significant figures)
- Common wrong answer 66.7 : You divided 106 by 1.59. n = m/M: the mass ÷ the molar mass.
- Common wrong answer 0.00556 : The 1.59 g is Na₂CO₃ without water, so use M = 106 g/mol, not 286.
(c) Mass of crystals: 4.29 g (3 significant figures)
- Common wrong answer 1.59 : That is the mass of Na₂CO₃ without water. The crystals have M = 286 g/mol.
- Common wrong answer 1.86 : The 10 means ten water molecules: M = 106 + 10 × 18 = 286 g/mol.
- Common wrong answer 2.70 : That is only the water in the crystals. Use the whole formula: M = 286 g/mol.

A full answer includes

(a) I worked out 500.0 ÷ 1000 = 0.5000 dm³.
(a) I worked out 3.18 × 0.5000.
(a) I got 1.59 g.
(b) I found M = 2 × 23 + 12 + 3 × 16 = 106 g/mol.
(b) I worked out 1.59 ÷ 106.
(b) I got 0.0150 mol.
(c) I found M = 106 + 10 × 18 = 286 g/mol for the crystals.
(c) I worked out 0.0150 × 286.
(c) I got 4.29 g.
(c) I did not weigh out 1.59 g of crystals.

Also accept

1.59 g; 0.0150 mol; 4.29 g

Watch for

“Divide by the volume in cm³.” — Concentration is per dm³. Divide the cm³ by 1000 first: 500.0 cm³ is 0.5000 dm³.
“The crystals and the anhydrous solid need the same mass.” — The same amount, yes, but each crystal formula unit carries ten water molecules, so its mass is greater.
“·10H₂O adds one water molecule.” — The 10 means ten water molecules in each formula unit: add 10 × 18 = 180.

11. LT3 · Apply

Model answer. (a) V = 5.00 ÷ 1000 = 0.00500 dm³, so n = c × V = 0.0800 × 0.00500 = 4.00 × 10⁻⁴ mol of CaCl₂. (b) Each CaCl₂ gives one Ca²⁺ and two Cl⁻ ions, so there are 3 × 4.00 × 10⁻⁴ = 1.20 × 10⁻³ mol of ions: 1.20 × 10⁻³ × 6.02 × 10²³ = 7.22 × 10²⁰ ions. (c) CaCl₂ has M = 40 + 2 × 35.5 = 111 g/mol. Each dm³ holds 0.0800 mol, which is 0.0800 × 111 = 8.88 g, so the concentration is 8.88 g/dm³. It is the same for any sample of the solution, however small.

Checked automatically

(a) Amount of calcium chloride: 0.000400 mol (3 significant figures)
- Common wrong answer 0.400 : You used 5.00 cm³ as it is. Convert it to dm³: 0.00500 dm³.
- Common wrong answer 0.0160 : You divided. The amount is concentration × volume.
(b) Ions: 7.22×10^20 (3 significant figures)
- Common wrong answer 2.41e20 : That counts formula units. Each CaCl₂ gives three ions.
- Common wrong answer 4.82e20 : CaCl₂ gives one Ca²⁺ and two Cl⁻: three ions, not two.
(c) Concentration in g/dm³: 8.88 g/dm³ (3 significant figures)
- Common wrong answer 0.0444 : That is the mass in the 5.00 cm³ sample. A concentration is the mass in each dm³.
- Common wrong answer 0.000721 : You divided by M. From mol/dm³ to g/dm³, multiply by M.
- Common wrong answer 6.04 : CaCl₂ has two chlorine atoms: M = 40 + 2 × 35.5 = 111 g/mol.

A full answer includes

(a) I worked out 5.00 ÷ 1000 = 0.00500 dm³.
(a) I worked out 0.0800 × 0.00500.
(a) I got 4.00 × 10⁻⁴ mol.
(b) I counted three ions in each CaCl₂: one Ca²⁺ and two Cl⁻.
(b) I worked out 3 × 4.00 × 10⁻⁴ × 6.02 × 10²³.
(b) I got 7.22 × 10²⁰ ions.
(b) I did not count two ions in each CaCl₂.
(c) I found M = 40 + 2 × 35.5 = 111 g/mol.
(c) I worked out 0.0800 × 111.
(c) I got 8.88 g/dm³.
(c) I did not give the mass in the 5.00 cm³ as the concentration.

Also accept

4.00 × 10⁻⁴ mol; 7.22 × 10²⁰ ions; 8.88 g/dm³

Watch for

“Each CaCl₂ gives two ions.” — The 2 belongs to the chloride: one Ca²⁺ and two separate Cl⁻ ions, three in all.
“Divide by the volume in cm³.” — Concentration is per dm³. Divide the cm³ by 1000 first: 5.00 cm³ is 0.00500 dm³.
“A smaller sample has a lower concentration.” — Every part of a mixed solution has the same concentration. Only the amount depends on the volume.