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

`(gammaH_(2))/(gammaC_(n)H_(2n-2))=sqrt((m_(C_(n)H_(2n-2)))/(m_(H_(2))))`
`3sqrt(3)=sqrt((m_(C_(n)H_(2n-2)))/(2))`
Squaring on both sides and rearranging
`27xx2-m_(C_(n)H_(2n-2))`
`54=n_(12)+(2n-2)(1)`
`54=12n+2n-2`
`n=(54+2)//14`
`=56/14=4`
`:.n=4`