The gas having average speed four times as that of \(\mathrm{SO}_{2}\) (molecular mass 64) is

Average speed \(\left(v_{\mathrm{av}}\right)\) of gas molecules is inversely proportional to the square root of the absolute temperature \((T)\) of the gas
\(
v_{\mathrm{av}}=\sqrt{\frac{8 R T}{\pi M}}
\)
where \(R\) is gas constant and \(M\) the molecular weight. Given, \(v_{1}=v, M_{1}=64, v_{2}=4 v\)
\(
\begin{array}{l}
\frac{v_{1}}{v_{2}}=\sqrt{\frac{M_{2}}{M_{1}}} \\
\frac{v}{4 v}=\sqrt{\frac{M_{2}}{64}}
\end{array}
\)
\(
M_{2}=\frac{64}{16}=4
\)
Hence, the gas is helium (molecular mass 4).
Note On the basis of the concept that speed is inversely proportional to molecular weight, one can separate two gases from the mixture. If we enclose the mixture in a porous pot and place it in vacuum, then the lighter gas due to its larger molecular velocity, will diffuse more rapidly from the walls of the vessel than the heavier gas. This method is used to separate the fissionable uranium \(\left(\mathrm{U}^{235}\right)\) from the natural uranium.