Ideal Gas Molecules
5 marks · NormalA balloon filled with helium has a pressure of 105 kPa and a volume of 1.8 litres at 25°C. The balloon is taken outside where the temperature drops to 5°C, but the pressure remains constant.
Explain what happens to the average kinetic energy of the helium molecules as the temperature changes. Your answer should refer to the temperature in Kelvin.
Calculate the new volume of the balloon at 5°C. Give your answer to 2 significant figures.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) The average kinetic energy of the molecules decreases as the temperature drops. Since the Kelvin temperature decreases, the kinetic energy, which is proportional to temperature in Kelvin, also decreases. · must show kinetic energy proportional to Kelvin temperature
(b) 1.7 litres · must show correct Kelvin conversion and substitution
Common mistakes: Forgetting to use Kelvin; Inverting the ratio for final volume
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · States that kinetic energy is proportional to Kelvin temperature.
M1 (a) · 1 mark · States that when temperature drops, average kinetic energy decreases.
M2 (b) · 1 mark · Converts 25°C and 5°C to Kelvin, uses correct gas law for constant pressure (V1/T1 = V2/T2).
A1 (b) · 1 mark · Rearranges for V2; substitutes correctly.
A2 (b) · 1 mark · Evaluates and gives correct final answer (1.7 litres; 2 significant figures).
Worked solution
(a) The average kinetic energy of the molecules is directly proportional to the Kelvin temperature. As the temperature decreases from 298 K (25°C) to 278 K (5°C), the kinetic energy decreases.
(b) Find Kelvin values: T1 = 25 + 273 = 298 K; T2 = 5 + 273 = 278 K.
For constant pressure: V1/T1 = V2/T2
Rounded to two significant figures: V2 = 1.7 litres.