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A level: Kinetic Theory Questions

Q14. The pressure inside a bicycle tyre of volume 1.90 × 10–3m3 is 3.20 × 105 Pa when the temperature is 285 K.

(a)

(i) Calculate the number of moles of air in the tyre.

n = pV/RT = 3.2 × 105 × 1.9 × 10–3/(8.31 × 285)
n = 0.257

n = 0.26 mol

(1 mark)

(ii) After the bicycle has been ridden the temperature of the air in the tyre is 295 K. Calculate the new pressure in the tyre assuming the volume is unchanged. Give your answer to an appropriate number of significant figures.

V, n and R are constant so p/T = constant

p1/T1 = p2/T2

p2= p1T2/T1

p2= 3.20 × 105 x 295/285

3.31 × 105 Pa 3 sig figs

sig fig mark stands alone even with incorrect answer

(3 marks)

(b) Describe one way in which the motion of the molecules of air inside the bicycle tyre is similar and one way in which it is different at the two temperatures.

similar:

  • (rapid) random motion of molecules
  • molecules have a range of speeds

different:

  • the mean kinetic energy of the molecules in the hotter tyre is higher - must have 'mean' in there for the mark
  • the root mean square speed of the molecules in the hotter tyre is higher - must have 'mean' in there for the mark
  • frequency of collisions of the molecules in the hotter tyre is higher - can't just say there rae more collisions - must say more in a given time period!

(2 marks)

(Total 6 marks)