Hydrogen gas diffuses four times as rapidly as a mixture of `C_(2)H_(4)` and `CO_(2)`. The molar ration of `._(2)H_(4)` to `CO_(2)` in the mixture is

Options

A. `1:1`
B. `2:1`
C. `3:1`
D. `3:2`

Answer

C

Explanation

Effective molar mass of `C_(2)H_(2)` and `CO_(2)` is given by
`(r_(H_(2)))/(r_(mix))=sqrt((M_(eff))/(M_(H_(2)))), 4=sqrt((M_(eff))/(2))impliesM_(eff)= 32`
`M_(eff)=X_(C_(2)H_(4))M_(C_(2)H_(4))+X_(C_(O_(2)))M_(C_(O_(2)))`
`=(1-X_(CO_(2)))M_(C_(2)H_(4))+X_(CO_(2))M_(CO_(2))`
`32=M_(C_(2)H_(4))+(M_(CO_(2))-M_(C_(2)H_(4)))X_(CO_(2))`
`28+(44-28)X_(CO_(2))`
`X_(CO_(2))=(1)/(4)`
`:. X_(C_(2)H_(4))=(3)/(4)`
`implies (X_(C_(2)H_(4)))/(X_(CO_(2)))=(3)/(1)`