Question

If the root mean square velocity of the molecules of hydrogen at NTP is $1.84 \,km/s$. Calculate the root mean square velocity of oxygen molecule at NTP molecule weight of hydrogen and oxygen are $2$ and $32$, respectively.

• A. 1.47 km/s .
• B. 0.94 km/s
• C. 1.84 km/s
• D. 0.47 km/s

Answer 1

Answer: (D)

Root mean square velocity $\left(v_{\text {rms }}\right)$ is given by
$v_{ rms }=\sqrt{\frac{3 R T}{M}}$
where $M$ is molecular weight, $R$ the gas constant, and $T$ the absolute temperature.
Given, $v_{ H }=1.84\, km / s$,
$M_{ H }=2, M_{ O }=32$
$ \frac{v_{ H }}{v_{ O }} =\sqrt{\frac{M_{O}}{M_{ H }}} $
$\Rightarrow \frac{v_{ H }}{v_{ O }} =\sqrt{\frac{32}{2}}=4 $
$ \Rightarrow v_{O} =\frac{v_{ H }}{4} $
$=\frac{1.84}{4}=0.47\, km / s $