The rms speed of oxygen and room temperature is about $500 \mathrm{~ms}^{-1}$. The rms speed of hydrogen at…
The rms speed of oxygen and room temperature is about $500 \mathrm{~ms}^{-1}$. The rms speed of hydrogen at the same temperature is about
- $125 \mathrm{~m} \mathrm{~s}^{-1}$
- $2000 \mathrm{~m} \mathrm{~s}^{-1}$
- $8000 \mathrm{~m} \mathrm{~s}^{-1}$
- $500 \mathrm{~m} \mathrm{~s}^{-1}$
Solution
We have
$\begin{aligned} & \mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}_0}}, \text { where } \mathrm{M}_0=\text { molecular mass } \\ & \mathrm{V}_{\mathrm{rms}} \propto \frac{1}{\sqrt{\mathrm{M}_0}}\end{aligned}$
$\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{H}_2}=\left(\mathrm{V}_{\mathrm{rms}}\right)_{0.2} \times\left(\frac{2}{32}\right)^{1 / 2}=500 \times 4=2000 \mathrm{~m} / \mathrm{s}$
Asked in: AP EAMCET 2022 (05 Jul Shift 2)
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