Question

One gram mole $N{O}_2$ at ${57}^{\circ }C$ and 2 atm pressure is kept in a vessel. Assuming the molecules to be moving with rms velocity. Find the number of collisions per second which the molecules make with one square meter area of the vessel wall.

Answer 1

The RMS velocity of particles will be

$v_{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\left(8.314\right)330}{46X{10}^{-3}}}=423m/s$

Thus, momentum change per unit area per second will be

$\frac{\Delta p}{A\Delta t}=P$

Assuming collision to be elastic, the molecules will return with the same speed. Hence,

$\frac{N2m{v}_{rms}}{A\Delta t}=P$

$\frac{N}{A\Delta t}=\frac{P}{2m{v}_{rms}}$

$\frac{N}{A\Delta t}=\frac{2X{10}^5\left(6.022X{10}^{23}\right)}{2\left(46X{10}^{-3}\right)\left(423\right)}=3.1X{10}^{27}$

Answer is $3.1X{10}^{27}$