Question

A gas bulb of capacity 1 litre contains $9.0\times {10}^{21}$ molecules of nitrogen exerting a pressure of $3.5\times {10}^{4}N/m^2$. Calculate the root mean square speed of the gas molecules.
Take $R=\frac{25}{3}J/molK,N_A=6\times {10}^{23}$

• A. 300 $m/s$
• B. 400 $m/s$
• C. 500 $m/s$
• D. 600 $m/s$

Answer 1

The correct option is C 500 $m/s$

For nitrogen gas
$V=1LP=3.5\times {10}^{4}Pan=\frac{9.0\times {10}^{21}}{6\times {10}^{23}}PV=nRT$
We can compute T
$T=\frac{PV}{nR}T=\frac{3.5\times {10}^4\times 1\times {10}^{-3}\times 6\times {10}^{23}}{9.0\times {10}^{21}\times 25/3}T=280K{C}_{RMS}=\sqrt{\frac{3RT}{M}}{C}_{RMS}=\sqrt{\frac{(3\times 25/3\times 280)}{28\times {10}^{-3}}}{C}_{RMS}=500m/s$