Ideal Gas Molecules
4 marks · EasyA gas cylinder contains a fixed mass of oxygen at a pressure of 300 kPa and a temperature of 27°C. The gas escapes until the pressure drops to 100 kPa. The temperature does not change throughout the process.
Explain, in terms of the number of particles, why the pressure in the cylinder decreases when gas escapes.
If the initial volume of the gas was 4.5 litres, calculate the final volume of the remaining gas in the cylinder, assuming all other conditions stay the same.
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(a) When gas escapes, there are fewer particles in the cylinder. With fewer particles, there are fewer collisions with the walls per second, so the pressure decreases. · must show fewer particles, fewer collisions with walls, lower pressure
(b) 13.5 litres · must show p1V1 = p2V2, V2 = p1V1/p2= (300 × 4.5)/100
Common mistakes: Using the wrong pressure-volume relationship
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Marking points
B1 (a) · 1 mark · Mentions that the number of particles decreases.
B2 (a) · 1 mark · Mentions that fewer particles means fewer collisions with the wall per second, so lower pressure.
M1 (b) · 1 mark · Uses p1V1 = p2V2 and rearranges for V2.
A1 (b) · 1 mark · Substitutes values correctly: V2 = (300 × 4.5)/100 = 13.5 litres. (follow-through)
Worked solution
a) When gas escapes, there are fewer gas particles inside the cylinder. As a result, there are fewer collisions with the walls per second, so the gas exerts a lower pressure.
b) Use the equation p1V1 = p2V2 (Boyle's law):