One mole of nitrogen gas at 0.8 atm takes 38 s to diffuse through a pinhole, whereas one mole of an unknown compound of xenon with fluorine at 1.6 atm takes 57s to diffuse through the same hole. Calculate the molecular formula of the compound.

Explanation

`"Ratio of diffusion " prop (p)/(sqrtM)`
`"or "(r_(2))/(r_(1))=(p_(2))/(p_(1))sqrt((M_(1))/(M_(2)))`
Since r is `prop (1)/(t)`, we may write,
`(t_(1))/(t_(2))=(p_(2))/(p_(1))sqrt((M_(1))/(M_(2)))`
`"or "(t_(N_(2)))/(t_(g))=(p_(g))/(p_(N_(2)))xxsqrt((M_(N_(2)))/(M_(g)))`
`(38)/(57)=(1.6)/(0.8)xxsqrt((28)/(M_(g)))`
`therefore" "M_(g)=((1.6)/(0.8)xx(57)/(38))^(2)xx28=252`
Let the molecular formula of compound be `XeF_(n)`