Date | May 2019 | Marks available | 1 | Reference code | 19M.2.HL.TZ2.2 |
Level | Higher level | Paper | Paper 2 | Time zone | 2 |
Command term | Calculate | Question number | 2 | Adapted from | N/A |
Question
A container of volume 3.2 × 10-6 m3 is filled with helium gas at a pressure of 5.1 × 105 Pa and temperature 320 K. Assume that this sample of helium gas behaves as an ideal gas.
A helium atom has a volume of 4.9 × 10-31 m3.
The mass of a helium atom is 6.6 × 10-27 kg. Estimate the average speed of the helium atoms in the container.
Show that the number of helium atoms in the container is 4 × 1020.
Calculate the ratio .
Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.
Markscheme
✔
v = 1.4 × 103«ms–1» ✔
OR
✔
✔
«» ✔
«For an ideal gas» the size of the particles is small compared to the distance between them/size of the container/gas
OR
«For an ideal gas» the volume of the particles is negligible/the volume of the particles is small compared to the volume of the container/gas
OR
«For an ideal gas» particles are assumed to be point objects ✔
calculation/ratio/result in (c)(i) shows that volume of helium atoms is negligible compared to/much smaller than volume of helium gas/container «hence assumption is justified» ✔
Examiners report
At HL this was very well answered but at SL many just worked out E=3/2kT and left it as a value for KE.
Again at HL this was very well answered with the most common approach being to calculate the number of moles and then multiply by NA to calculate the number of atoms. At SL many candidates calculated n but stopped there. Also at SL there was some evidence of candidates working backwards and magically producing a value for ‘n’ that gave a result very close to that required after multiplying by NA.
This was well answered with the most common mistake being to use the volume of a single atom rather than the total volume of the atoms.
At HL candidates seemed more able to focus on the key part feature of the question, which was the nature of the volumes involved. Examiners were looking for an assumption of the kinetic theory related to the volume of the atoms/gas and then a link to the ratio calculated in ci). The command terms were slightly different at SL and HL, giving slightly more guidance at SL.