Question

$6\times {10}^{22}$ gas molecules each of mass ${10}^{-24}$ kg are taken in a vessel of 10 litres. What is the pressure exerted by gas molecules?

[The average velocity of the gas molecules is 92.62 m/sec.]

• A. $2\times {10}^5$ Pa
• B. 20 Pa
• C. $2\times {10}^6$ Pa
• D. $2\times {10}^4$ Pa

Answer 1

Answer: (A)

$2\times {10}^5$ Pa

Root mean square velocity: $V_{rms}=\sqrt{\frac{3RT}{M}}$

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

$\frac{V_{rms}}{V_{avg}}$=$\frac{\sqrt{3}}{\sqrt{\frac{8}{\pi }}}$

mass of gas molecules taken = ${10}^{-24}\times A_o$(avagadro no.)

=0.6023=0.6023 Kg/mole

The kinetic energy of the gas

$\frac{1}{2}M{V}_{rms}^2=\frac{3}{2}PV$

$\Rightarrow \frac{1}{2}\times 0.6023\times \frac{3\pi }{8}\times (92.62{)}^2$

$=\frac{3}{2}P\times \frac{10}{100}$

P=100×0.6023×$\frac{\pi }{8}\times (92.62{)}^2$

P=202900

P$\approx 2\times {10}^5$Pa

Hence, the correct option is $\text{A}$