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
  1. $125 \mathrm{~m} \mathrm{~s}^{-1}$
  2. $2000 \mathrm{~m} \mathrm{~s}^{-1}$
  3. $8000 \mathrm{~m} \mathrm{~s}^{-1}$
  4. $500 \mathrm{~m} \mathrm{~s}^{-1}$

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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