The ratio of speeds of diffusion of two gases A and B is 1:4. If the mass ratio of A to B present in the given mixture is 2:1, then which of the following is the ratio mole-fraction of A to B?

Options

A. `2:3`
B. `1:8`
C. `2:1`
D. `1:2`

Explanation

`(r_(A))/(r_(B))=(1)/(4)=(n_(A))/(n_(B))sqrt((M_(B))/(M_(A)))`
`(1)/(4)=(m_(A)//M_(A))/(m_(B)//M_(B))sqrt((M_(B))/(M_(A)))`
`(1)/(4)=(m_(A))/(m_(B))((M_(B))/(M_(A)))^(3//2)`
`(1)/(4)=(2)/(1)((M_(B))/(M_(A)))^(3//2)`
`((M_(B))/(M_(A)))(8)^(2//3)=(1)/(4)`
`(n_(A))/(n_(B))=(m_(A))/(m_(B))xx(M_(B))/(M_(A))=(2)/(1)xx(1)/(4)`
=1:2