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InkFlaskCambridge IGCSE
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Answers · Relative masses

Relative masses — final check key

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

1. RK1 · Final check

Model answer. (a) Ar is the average mass of the isotopes of an element compared to 1/12 of the mass of an atom of carbon-12. (b) Think of 100 atoms: 93 have a mass of 39 and 7 have a mass of 41. 39 × 93 = 3627 and 41 × 7 = 287, so the 100 atoms total 3914. One atom on average: 3914 ÷ 100 = 39.14, which is 39.1 to one decimal place. Check: 39.1 is between 39 and 41 and very near 39, because most atoms are potassium-39.

A full answer includes

  • (a) I wrote that Ar is the average mass of the isotopes.
  • (a) I wrote that it is compared to 1/12 of the mass of a carbon-12 atom.
  • (a) I did not write that Ar is the mass number.
  • (a) I did not give it a unit such as grams.
  • (b) I multiplied each mass by its percentage and added: 39 × 93 + 41 × 7 = 3914.
  • (b) I divided the total by 100.
  • (b) I wrote 39.1.
  • (b) I did not take the plain average of 39 and 41, which is 40.

Also accept

  • (a) The average mass of the isotopes compared to 1/12 of a carbon-12 atom. (b) 39.1

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.
  • “Relative masses are in grams.” — Ar and Mr compare masses with 1/12 of the mass of a carbon-12 atom, so they have no unit.
  • “Ar is the plain average of the isotope masses.” — Each isotope counts as often as its percentage, so the most common isotope pulls the average towards its own mass.

2. RK2 · Final check

Model answer. K2CO3: 78 + 12 + 48 = 138. (NH4)3PO4: NH4 is 14 + 4 = 18, and the 3 triples it: 54. PO4 is 31 + 64 = 95. Total: 54 + 95 = 149.

Checked automatically

  • Mr of K2CO3: 138 (exact value)
    • Common wrong answer 99 : K2 is two potassium atoms: 2 × 39.
  • Mr of (NH4)3PO4: 149 (exact value)
    • Common wrong answer 113 : The 3 after the bracket multiplies the whole NH4 group: 3 × 18.
    • Common wrong answer 141 : The 3 multiplies the hydrogen atoms in the bracket too: 3 × (14 + 4).

A full answer includes

  • I counted two potassium atoms in K2CO3: 2 × 39 = 78.
  • I wrote 138 for K2CO3.
  • I worked out NH4 as 18 and multiplied it by 3: 54.
  • I wrote 149 for (NH4)3PO4.
  • I did not multiply only the N in the bracket.

Also accept

  • 138, 149

Watch for

  • “The number after a bracket multiplies only the last symbol.” — The number after a bracket multiplies everything inside the bracket.

3. RK3 · Final check

Model answer. Mr: N2 28, H2 2, NH3 17. With the big numbers, 28 g of nitrogen reacts with 3 × 2 = 6 g of hydrogen to make 2 × 17 = 34 g of ammonia (28 + 6 = 34). (a) 7 g is a quarter of 28 g, so it makes 34 ÷ 4 = 8.5 g of ammonia. (b) It reacts with 6 ÷ 4 = 1.5 g of hydrogen. (c) 17 g of ammonia is half of 34 g, so it needs 28 ÷ 2 = 14 g of nitrogen.

Checked automatically

  • (a) Ammonia from 7 g of N2: 8.5 g (within ±0.05 g)
    • Common wrong answer 4.25 : The equation makes 2NH3: 28 g of nitrogen makes 2 × 17 = 34 g of ammonia.
  • (b) Hydrogen that reacts with 7 g of N2: 1.5 g (within ±0.05 g)
    • Common wrong answer 0.5 : The equation has 3H2: 28 g of nitrogen reacts with 3 × 2 = 6 g of hydrogen.
  • (c) Nitrogen needed for 17 g of NH3: 14 g (within ±0.05 g)
    • Common wrong answer 28 : 28 g of nitrogen makes 34 g of ammonia; 17 g is only half of that.

A full answer includes

  • I found the equation masses: 28 g of N2 and 3 × 2 = 6 g of H2 make 2 × 17 = 34 g of NH3.
  • (a) I divided by 4, because 7 g is 28 g ÷ 4.
  • (a) I wrote 8.5 g.
  • (b) I wrote 1.5 g.
  • (c) I saw that 17 g is half of 34 g.
  • (c) I wrote 14 g.
  • I did not use 17 for the ammonia in the equation: it makes 2NH3.

Also accept

  • (a) 8.5 g (b) 1.5 g (c) 14 g

Watch for

  • “Use each Mr as it is and ignore the numbers in front of the formulae.” — Multiply each Mr by its big number in the balanced equation before you compare the masses.

4. RK4 · Final check

Model answer. MgSO4 is 24 + 32 + 64 = 120 and seven water molecules are 7 × 18 = 126, so the crystal is 246. 24.6 g is a tenth of 246 g, so 12.0 g of magnesium sulfate is left and 12.6 g of water is lost. Check: 12.0 + 12.6 = 24.6.

Checked automatically

  • (a) Mr of MgSO4·7H2O: 246 (exact value)
    • Common wrong answer 138 : There are seven water molecules, not one: 120 + 7 × 18.
  • (b) Magnesium sulfate left: 12.0 g (3 significant figures)
    • Common wrong answer 12.6 : That is the water lost. The magnesium sulfate is 120 of every 246.
  • (c) Water lost: 12.6 g (3 significant figures)
    • Common wrong answer 12.0 : That is the magnesium sulfate left. The water is 126 of every 246.

A full answer includes

  • (a) I added MgSO4, 120, and seven water molecules, 7 × 18 = 126.
  • (a) I wrote 246.
  • (a) I did not multiply across the dot.
  • (b) I saw that 24.6 g is 246 g ÷ 10.
  • (b) I wrote 12.0 g.
  • (c) I wrote 12.6 g.
  • I checked that 12.0 + 12.6 = 24.6.

Also accept

  • (a) 246 (b) 12.0 g (c) 12.6 g

Watch for

  • “The dot in a hydrate formula means multiply.” — The dot means "together with": add the mass of the water molecules to the rest.