Question

Calculate the rms speed of $O_2$ at $273\text{K}$ and $1\times {10}^4\text{Pa}$ pressure. The density of $O_2$ under these conditions is $1.50{\text{kg m}}^{-3}$.

• A. $2\times {10}^4{\text{m s}}^{-1}$
• B. $5\times {10}^2{\text{m s}}^{-1}$
• C. $141.42{\text{m s}}^{-1}$
• D. $943.6{\text{m s}}^{-1}$

Answer 1

The correct option is C $141.42{\text{m s}}^{-1}$

As $u_{rms}=\sqrt{\frac{3RT}{M}}$
using $PV=nRT$
$u_{rms}=\sqrt{\frac{3PV}{nM}}$
$u_{rms}=\sqrt{\frac{3PV\times M}{w\times M}}$
$u_{rms}=\sqrt{\frac{3PV}{w}}$
$u_{rms}=\sqrt{\frac{3P}{d}}$
​​​​​​where, density $d=\frac{w}{V}$
therefore,
​​$u_{rms}=\sqrt{\frac{3P}{d}}=\sqrt{\frac{3\times {10}^4}{1.50}}=141.42{\text{m s}}^{-1}$