Two flasks `A` and `B` have equal volumes. Flask `A` containing `H_(2)` gas is maintained at `27^(@)C` while `B` containing an equal mass of `C_(2)H_(6)` gas is maintained at `627^(@)C`. In which flask and by how many times are molecules moving faster, assuming ideal behaviour for both the gases?

Explanation

Calculate the relative velocities of molecules
Average velocity of a gas
`mu=sqrt((8RT)/(pi M))`
`mu_(H_(2))=sqrt((8RT_(1))/(pi M_(1)))`, `mu_(C_(2)H_(6))=sqrt((8RT_(2))/(pi M_(2)))`
`(mu_(H_(2)))/(mu_(C_(2)H_(6)))=sqrt((T_(1)M_(2))/(T_(2)M_(1)))` [`T_(1)=300K`, `T_(2)=900 K`]
`M_(1)=2g mol^(-1)`
`M_(2)=30 g mol^(-1)`
`(mu_(H_(2)))/(mu_(C_(2)H_(6)))=sqrt((300xx30)/(900xx2))=sqrt((5))/(1)=2.237:1`
Thus, `H_(2)` molecules in flask `A` will be moving `2.237` times faster than `C_(2)H_(6)` molecules in `B`.