Question

Estimate the number of collision 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) $=1.38\times {10}^{-5}cm$.

Answer 1

The mean free path of the molecule is $1.38\times {10}^{-5}cm$.

The average velocity of the molecules of hydrogen is given as:

$V_{mean}=\sqrt{\frac{8RT}{\pi M}}$

$=\sqrt{\frac{8\times 8.3\times 273}{3.14\times 2\times {10}^{-3}}}=1698.96$

Total Distance covered by molecule in 1 second is:

$d=1698.96m$

The No. of Collisions made by the molecules per second is:

$n=\frac{d}{meanfreepath}$

$=\frac{1698.96}{1.38\times {10}^{-7}}=1.23\times {10}^{10}$