The rms velocity of a gas at a certain temperature is √2 times than that of the oxygen molecules at that temperature. The gas can be

Question

The rms velocity of a gas at a certain temperature is √2 times than that of the oxygen molecules at that temperature. The gas can be (A) H 2 (B) He (C) CH 4 (D) SO 2

Tardigrade Admin · Accepted Answer

v rms propto (1/√MW) ⇒ (v1/v2)=√(MW2/MW1) ⇒ (v/√2 v)=√(MW2/32) ⇒ MW2=16( CH 4)

Q. The rms velocity of a gas at a certain temperature is $2$ times than that of the oxygen molecules at that temperature. The gas can be

$H_{2}$

$He$

$C H_{4}$

$S O_{2}$

$v_{r m s} \propto \frac{1}{M _{W}}$
$\Rightarrow \frac{v _{1}}{v _{2}} = \frac{M _{W_{2}}}{M _{W_{1}}}$
$\Rightarrow \frac{v}{2 v} = \frac{M _{W_{2}}}{32}$
$\Rightarrow M_{W_{2}} = 16 (C H_{4})$

Q. The rms velocity of a gas at a certain temperature is 2​ times than that of the oxygen molecules at that temperature. The gas can be

H2​

He

CH4​

SO2​