Numeracy Higher June 2023 Unit 1 Q8
8. The mass of an atom of hydrogen is about \(1{\cdot}7 \times 10^{-24}\) g.
The mass of an atom of oxygen is about \(2{\cdot}7 \times 10^{-23}\) g.
(a) Using a suitable approximation, estimate how many atoms of hydrogen there are in 1000 g of hydrogen.
Give your answer in standard form. [3]
Give your answer in standard form. [3]
(b) A molecule of water consists of two atoms of hydrogen and one atom of oxygen.
Calculate the mass of a molecule of water.
Give your answer in standard form. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{1000}{2\times10^{-24}}\) OR \(\dfrac{1000}{1.5\times10^{-24}}\) OR \(\dfrac{1000}{1.6\times10^{-24}}\) | M1 | Or equivalents |
| = \(5 \times 10^{26}\) OR \(6.6(66\ldots) \times 10^{26}\) OR \(6.25 \times 10^{26}\) or \(6.7 \times 10^{26}\) or \(6.3 \times 10^{26}\) or \(7 \times 10^{26}\) or \(6 \times 10^{26}\) | A2 | A1 for equivalent values but not in standard form e.g. \(500 \times 10^{24}\) or \(0.5 \times 10^{27}\) or their equivalent ordinary numbers |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{1020}{1.7\times10^{-24}}\) | M1 | Allow M1 for 1000/\(1.7\times10^{-24}\) provided their answer has a leading digit of 6 |
| = \(6 \times 10^{26}\) | A2 | A1 for equivalent value but not in standard form e.g. \(600 \times 10^{24}\) or \(0.6 \times 10^{27}\) or the equivalent ordinary number If M0A0, award SC1 for an answer of \(5.8(\ldots)\times 10^{26}\) or \(5.9 \times 10^{26}\) from 1000/\(1.7\times10^{-24}\) |
| Scheme | Marks | Comments |
|---|---|---|
| 2×(\(1.7 \times 10^{-24}\)) + (\(2.7 \times 10^{-23}\)) or equivalent = \(3.04 \times 10^{-23}\) (g) | M1 A2 | If a candidate adds the mass of 2 atoms of oxygen and 1 atom of hydrogen, treat as a misread (Answer will be \(5.57\times 10^{-23}\)) A1 for the equivalent of \(3.04 \times 10^{-23}\) but not in standard form e.g. \(30.4 \times 10^{-24}\) or the equivalent ordinary number, OR A1 for \(3 \times 10^{-23}\) If no marks, award SC1 for an answer of \(2.87 \times 10^{-23}\) (using one atom of hydrogen) |