Concepts Of Physics MCQ Edition [Volume 2]PhysicsKinetic Theory of Gases
Determine the approximate number of collisions per second experienced by a molecule within a hydrogen sample at STP. The mean free path (the average distance a molecule travels between successive collisions) is given as 1.38 10⁻⁵ cm .
Options
- A1.09 10¹⁰
- B1.23 10¹⁰
- C1.23 10⁸
- D1.34 10¹⁰
Correct answer
B. 1.23 10¹⁰
Step-by-step solution
The number of collisions per second (collision frequency) experienced by a molecule is given by the ratio of the average speed of the molecules to their mean free path. Z = v_ avg For hydrogen gas at STP, the temperature is T = 273 K and the molar mass is M = 2 10⁻³ kg/mol . The average speed v_ avg is given by: v_ avg = 8RT M Substituting the standard values ( R = 8.314 J/(mol K) ): v_ avg = 8 8.314 273 2 10⁻³ v_ avg 1700 m/s = 1.7 10^5 cm/s Given the mean free path = 1.38 10⁻⁵ cm , the number of collisions per se