Sulphur (IV) oxide travels a given distance in \(10 sec\). How long will it take equal volume of helium to travel the same distance under the same conditions? \([ S =32, O =16, He\) \(=4\) ]
A. \(1.6 sec\) B. \(40 sec\) C. \(5.0 sec\) D. \(2.5 sec\)
Correct Answer: D
Explanation
\(T_{ SO _{2}}=10 sec , T_{l l e}=\) ? \(MMSO _{2}=64 g / mol\) \(R \alpha \frac{1}{\sqrt{M M}} \Rightarrow \frac{R SO _{2}}{R_{\text {He }}}=\sqrt{\frac{M M H e}{M M S O_{2}}}\) Rate \(=\frac{\text { distance }}{\text { time }}\) or \(\frac{\text { vol }}{\text { time }}\); \(\frac{d_{ SO _{3}}}{T_{ SO _{2}}} \div \frac{d_{H e}}{T_{H e}}=\sqrt{\frac{4}{64}}\) \(=\frac{d_{ SO _{1}}}{T_{ SO _{2}}} \times \frac{T_{ He }}{d_{ He }}=\sqrt{\frac{1}{16}} ;\) \(d_{ SO _{2}}=d_{ He }\) ? \(\frac{T_{\text {He }}}{10}=\frac{1}{4}, T_{H e}=\frac{10}{4}=2.5 sec\)