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A level: Kinetic Theory Questions

Q13.

(a) The air in a room of volume 27.0 m3 is at a temperature of 22 °C and a pressure of 105 kPa. Calculate

(i) the temperature, in K, of the air,

T =273 + 22 = 295 K

(ii) the number of moles of air in the room,

pV = nRT

105 × 103 × 27 = n × 8.31 × 295

n = (105 × 103 × 27)/(8.31 × 295)

n = 1156 (Needed to 4sf to carry forward in calculations)

1160 (moles) (Answers to be quoted finally to 3sf)

(iii) the number of gas molecules in the room.

N = number of moles x Avogadro Number

= 1156 × 6.02 × 1023 

= 7.0 × 1026  

(5 marks)

(b) The temperature of an ideal gas in a sealed container falls. State, with a reason, what happens to the

(i) mean square speed of the gas molecules,

The mean square speed of the gas molecules decreases because the temperature of a gas depends on the mean kinetic energy of the molecules, which in turn depends on the mean square speed.

(ii) pressure of the gas.

The pressure of the gas decreases as the reduced speed makes the number of collisions (per second) fall. This results in making the rate of change of momentum at the container wall decrease.

[OR if using pV = nRT you can say that p decreases as V, n and R are constant, making p proportional to T]

(4 marks)

(Total 9 marks)