Answer
The root mean square velocity of $CH_4$: $=651.54 m/s$
The root mean square velocity of $Ar$: $=583.92 m/s$
Work Step by Step
The root mean square velocity of a gas is $=\sqrt{3RT/M}$
The molar mass of $CH_4=(16.04 × 10^{-3} kg/mol)$
The molar mass of $Ar=(39.94 × 10^{-3} kg/mol)$
So the root mean square velocity of $CH_4$ is $=\sqrt{(3×8.314 ×273/16.04 × 10^{-3})}m/s$
$=651.54 m/s$
And the root mean square velocity of $Ar$ is $=\sqrt{(3×8.314 ×546/39.94 × 10^{-3})}m/s$
$=583.92 m/s$
