Question

Hydrogen gas is contained in a closed vessel at 1 atm (100 kPa) and 300 K. (a) Calculate the mean speed of the molecules (b) Suppose the molecules strike the wall with this speed making an average angle of ${45}^{\circ }$ with it. How many molecules strikes each square meter of the wall per second?

Answer 1

$P=1atm={10}^5$ pascal $T=300k$ $M=2g=2\times {10}^{-3}kg$

(a)

The average velocity of the gas molecules is:

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

$=\sqrt{\frac{8\times 8.3\times 300}{3.14\times 2\times {10}^{-3}}}=1781.004\Rightarrow 1780m/s$

(b)

When molecule strike at angle ${45}^{\circ }$

No of molecules striking per unit area

$=\frac{force}{\sqrt{2}mv\times Area}=\frac{Pressure}{\sqrt{2}mv}$

$=\frac{\frac{{10}^5}{\sqrt{2}\times 2\times {10}^{-3}\times 1780}}{6\times {10}^{23}}=\frac{3}{\sqrt{2}\times 1780}\times {10}^{31}$

$=1.19\times {10}^{-3}\times {10}^{31}=1.19\times {10}^{28}\cong 1.2\times {10}^{28}$