Temperature of helium = ${27}^0 \mathrm{C}=300 \mathrm{K}$

The root-mean-square velocity of helium ${\mathrm{\mu }}_{\mathrm{rms}}$ = $\sqrt{\frac{3\mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{3\mathrm{R}\times 300}{4}}$

The most probable speed ${\mathrm{\mu }}_{\mathrm{mp}}$= $\sqrt{\frac{2\mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{2\mathrm{R}\times 7200}{\mathrm{M}}}$

Put the ${\mathrm{\mu }}_{\mathrm{rms}}=$${\mathrm{\mu }}_{\mathrm{mp}}$

$$\begin{gathered} \sqrt{\frac{3\mathrm{R}\times 300}{4}}=\sqrt{\frac{2\mathrm{R}\times 7200}{\mathrm{M}}} \\ \frac{3\mathrm{R}\times 300}{4}=\frac{2\mathrm{R}\times 7200}{\mathrm{M}} \\ 900\times \mathrm{M} =7200\times 8 \\ \mathrm{M} =\frac{7200\times 8}{900}=64 \end{gathered}$$

So, the molar mass of gas is $64$. The sulphur dioxide has the molar mass of $64 \mathrm{g}/\mathrm{mol}$.

Hence, the gas is ${\mathrm{SO}}_2$.