Concepts Of Physics MCQ Edition [Volume 2]PhysicsKinetic Theory of Gases
For an oxygen sample at 300 K , determine the average time required for a molecule to cover a distance equal to the diameter of the earth.
Options
- A16 hours
- B4 hours
- C8 hours
- D12 hours
Correct answer
C. 8 hours
Step-by-step solution
The average speed of a gas molecule is given by: v_ avg = 8RT M For an oxygen ( O₂ ) molecule at 300 K : R = 8.314 J K ⁻¹ mol ⁻¹ T = 300 K M = 32 10⁻³ kg mol ⁻¹ Substituting the values: v_ avg = 8 8.314 300 32 10⁻³ 445.5 m s ⁻¹ The diameter of the earth is D = 2 6400 km = 12800 km = 12.8 10^6 m . The average time required to cover this distance is: t = D v_ avg = 12.8 10^6 445.5 28731 s Converting the time into hours: t = 28731 3600 hours 7.98 hours 8 hours