A level: Kinetic Theory Questions

Q7.

The number of molecules in one cubic metre of air decreases as altitude increases. The table shows how the pressure and temperature of air compare at sea-level and at an altitude of 10 000 m.

 altitude pressure/Pa temperature/K sea-level 1.0 × 105 300 10 000 m 2.2 × 104 270

(a) Calculate the number of moles of air in a cubic metre of air at:

(i) sea-level,

n = pV/RT

= 1.0 × 105 x 1.0/(8.31 x 300)

= 40 mol

(ii) 10 000 m.

n = pV/RT

= 2.2 × 104 x 1.0/(8.31 x 270)

= 9.8 mol

(3 marks)

(b) In air, 23% of the molecules are oxygen molecules. Calculate the number of extra oxygen molecules there are per cubic metre at sea-level compared with a cubic metre of air at an altitude of 10 000 m.

Number of molecules = number of moles x Avogadro Number

Total difference in molecules = (40 × 6.02 × 1023) − (9.8 × 6.02 × 1023)

= 1.8 × 1025

(allow C.E. for incorrect values of n from (a))

23% of these are oxygen molecules:

difference in oxygen molecules = 0.23 × 1.8 × 1025

= 4.2 × 1024

(2 marks)

(Total 5 marks)