Question

Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen at STP. The mean free path (average distance covered by a molecule between successive collisions) = 1.38 × 10⁻⁵ cm.

Use R = 8.31 JK⁻¹ mol⁻¹

Answer 1

Here,

\[\lambda = 1 . 38 \times  {10}^{- 8}   \text { m }\]

T = 273 K
M = \[2 \times  {10}^{- 3}  \text{ kg }\]

Average speed of the H molecules is given  by 

\[v_{avg}  = \sqrt{\frac{8RT}{\pi M}}\] 

\[ = \sqrt{\frac{8 \times 8 . 31 \times 273}{3 . 14 \times 2 \times {10}^{- 3}}}\] 

\[ = 1700  \text { ms }^{- 1} \]

The time between two collisions is given by

\[t = \frac{\lambda}{v_{avg}}\] 

\[ \Rightarrow t = \frac{1 . 38 \times {10}^{- 8}}{1700}\] 

\[ \Rightarrow t = 8 \times  {10}^{- 12}   s\] 

\[\text { Number  of  collisions  in  1  s}   =   \frac{1}{8 . 11 \times {10}^{- 12}} = 1 . 23 \times  {10}^{11}\]