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Answers · Relative masses

Relative masses — return questions key

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

1. RR1 · Return

Model answer. (a) Each atom has a whole number of protons and neutrons, so every thallium atom has a mass of 203 or 205. Ar is the average mass of the isotopes in a sample, compared to 1/12 of the mass of a carbon-12 atom, so it lies between them. (b) Call the thallium-205 share x %. Of 100 atoms, x have mass 205 and (100 − x) have mass 203, and together they have a mass of 204.4 × 100 = 20 440. So 203 × (100 − x) + 205 × x = 20 440, which gives 20 300 + 2x = 20 440, so 2x = 140 and x = 70. Check: 203 × 30 + 205 × 70 = 6090 + 14 350 = 20 440, and 20 440 ÷ 100 = 204.4. A quicker way: 204.4 is 1.4 of the 2 mass units from 203 towards 205, and 1.4 ÷ 2 = 0.70, so 70 % of the atoms are thallium-205.

Checked automatically

  • (b) Thallium-205: 70 % (within ±0.5 %)
    • Common wrong answer 30 : That is the share of thallium-203. 204.4 is nearer 205, so thallium-205 is the bigger share.
    • Common wrong answer 50 : Equal shares would give 204.0, exactly halfway. 204.4 is above halfway.
    • Common wrong answer 40 : 0.4 is the distance above halfway. Measure from 203 instead: 204.4 is 1.4 of the 2 mass units towards 205.

A full answer includes

  • (a) I explained that every thallium atom is either thallium-203 or thallium-205.
  • (a) I explained that 204.4 is the average mass of the atoms in a mixture of the two.
  • (b) I wrote the total mass of 100 atoms: 204.4 × 100 = 20 440.
  • (b) I called the number of thallium-205 atoms x and wrote 203 × (100 − x) + 205 × x = 20 440.
  • (b) I wrote 70 %.
  • (b) I did not give 30 %, the share of the lighter isotope.

Also accept

  • (a) Thallium is a mixture of thallium-203 and thallium-205 atoms; 204.4 is their average. (b) 70 %

Watch for

  • “The relative atomic mass is the mass number of the atom.” — The mass number counts the protons and neutrons in one atom of one isotope. Ar is the average of all the isotopes, so it need not be a whole number.
  • “The heavier isotope is always the less common one.” — 204.4 is nearer 205, so the average is pulled towards thallium-205: it is the bigger share.
  • “Two isotopes are always equally common.” — Equal shares would give 204.0, exactly halfway. 204.4 is above halfway.
  • “The decimal part of Ar is the share of the heavier isotope.” — Measure from 203, not from the halfway point: 204.4 is 1.4 of the 2 mass units towards 205.

2. RR2 · Return

Model answer. Nitric acid: 1 + 14 + 48 = 63. Ethanol has 2 carbon atoms, 5 + 1 = 6 hydrogen atoms and 1 oxygen atom: 24 + 6 + 16 = 46.

Checked automatically

  • Mr of HNO3: 63 (exact value)
    • Common wrong answer 31 : HNO3 has three oxygen atoms: 1 + 14 + 3 × 16.
  • Mr of C2H5OH: 46 (exact value)
    • Common wrong answer 45 : There is one more hydrogen atom in OH: 6 in all.

A full answer includes

  • I counted three oxygen atoms in HNO3: 3 × 16 = 48.
  • I wrote 63 for HNO3.
  • I counted six hydrogen atoms in C2H5OH.
  • I wrote 46 for C2H5OH.
  • I did not forget the H in OH.

Also accept

  • 63, 46

Watch for

  • “Count only the hydrogen atoms written with a small number.” — C2H5OH has five hydrogen atoms in C2H5 and one more in OH: six in all.

3. RR3 · Return

Model answer. No Mr is needed: the experiment gives the ratio. 5.6 g of iron reacts with 8.8 − 5.6 = 3.2 g of sulfur to make 8.8 g of iron(II) sulfide. 22 g is 8.8 g multiplied by 2.5, so multiply the others by 2.5 too: 5.6 × 2.5 = 14 g of iron and 3.2 × 2.5 = 8.0 g of sulfur. Check: 14 + 8 = 22.

Checked automatically

  • (a) Iron: 14 g (within ±0.05 g)
    • Common wrong answer 34.6 : You scaled the wrong way: the iron is lighter than the iron(II) sulfide it makes.
    • Common wrong answer 18.8 : Multiply by the same number, 2.5; do not subtract a fixed mass.
  • (b) Sulfur: 8.0 g (within ±0.05 g)
    • Common wrong answer 3.2 : That makes only 8.8 g of iron(II) sulfide; you need 2.5 times as much.
    • Common wrong answer 13.2 : Multiply by the same number, 2.5; do not subtract a fixed mass.

A full answer includes

  • I saw that 22 g is 2.5 × 8.8 g.
  • (a) I wrote 14 g of iron.
  • (b) I found the sulfur in the experiment: 8.8 − 5.6 = 3.2 g.
  • (b) I wrote 8.0 g of sulfur.
  • I did not add or subtract a fixed mass instead of multiplying.

Also accept

  • (a) 14 g (b) 8.0 g

Watch for

  • “Scale by adding the same mass to every substance.” — Masses keep the same ratio: multiply every mass by the same number.
  • “You always need the equation and the Mr values.” — A measured pair of masses gives the ratio directly.