At identical temperature and pressure, the rate of diffusion of hydrogen gas is `3sqrt(3)` times that of a hydrocarbon having molecular formula `C_(n)H_(2n-2)`. What is the value of n ?

Explanation

`(gamma_(H_(2)))/(gamma_(C_(n)H_(2 _(n-2))))=sqrt((m_(C_(n)H_(2n-2)))/(m_(H_(2))))`
`3 sqrt(3)=sqrt((m_(C_(n)H_(2n-2)))/(2))`
Sqaring on both sides and rearranging
`27xx2=m_(c_(n)H_(2)n-2)`
`545=n_((12))+(2n-2)(1)`
`54=12+2n-2`
`54=14n-2`
`n=(54+2)//14`
`=(56)/(14)=4`
`:.n=4`