Question

The rms speed of oxygen at room temperature is about $500 \, m \, s^{- 1}.$ The rms speed of hydrogen at the same temperature is about

• A. $125ms^{- 1}$
• B. $2000ms^{- 1}$
• C. $8000ms^{- 1}$
• D. $31ms^{- 1}$

Answer 1

Answer: (B)

RMS speed of gas is given by
$v_{r m s}=\sqrt{\frac{3 R T}{M}}$
Where, $R=$ gas constant
$T=$ absolute temperature in Kelvin
$M=$ molecular mass of the gas
$\therefore \, \, \, \frac{\left(V_{r m s}\right) o x y g e n}{\left(V_{r m s}\right) h y d r o g e n}=\sqrt{\frac{M_{H_{2}}}{M_{O_{2}}}}=\sqrt{\frac{2}{32}}$
$=\sqrt{\frac{1}{16}}=\frac{1}{4}$
$\Rightarrow \, \, \frac{500}{\left(\right. V_{r m s} \left.\right) \, h y d r o g e n}=\frac{1}{4}$
$\Rightarrow \, \, \left(V_{r m s}\right)$ hydrogen $=2000ms^{- 1}$