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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
Solution
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
\[t = \frac{\lambda}{v_{avg}}\]
\[ \Rightarrow t = \frac{1 . 38 \times {10}^{- 8}}{1700}\]
\[ \Rightarrow t = 8 \times {10}^{- 12} s\]
\[\text { Number of collisions in 1 s} = \frac{1}{8 . 11 \times {10}^{- 12}} = 1 . 23 \times {10}^{11}\]
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