Question

If the root mean square velocity of the molecules of hydrogen at NTP is $1.84km/s$. 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
$v_{rms}=\sqrt{\frac{3RT}{M}}$
where $M$ is molecular weight, $R$ the gas constant, and $T$ the absolute temperature.
Given, $v_H=1.84km/s$,
$M_H=2,M_O=32$
$\frac{v_H}{v_O}=\sqrt{\frac{M_O}{M_H}}$
$\Rightarrow \frac{v_H}{v_O}=\sqrt{\frac{32}{2}}=4$
$\Rightarrow v_O=\frac{v_H}{4}$
$=\frac{1.84}{4}=0.47km/s$