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

Rate of diffusion,
`r=(K.p)/(sqrtM)`
`r_(N_(2))=(1)/(38)"mol s"^(-1)`,
`r_(x)=(1)/(57)"mols s"^(-1)`
For `N_(2)," "(1)/(38)=(Kxx0.8)/(sqrt(28))" ….(i)"`
For unknown gas, `(1)/(57)=(Kxx16)/(sqrt(M_(x)))" ....(ii)"`
Dividing (i) by (ii)
`(1)/(38)xx(57)/(1)=(0.8)/(16)xxsqrt((M_(x))/(28))`
`(3)/(2)=(1)/(2)xx((M_(x))/(28))^((1)/(2))`
`"or "M_(x)=9xx28="252 g mol"^(-1)`
Molecular mass of compound of Xe and F = 252. Let the formula be `MF_(x)` so that
`131+x xx19=252`
`19x=252-131=121`
`x=(121)/(19)=6.36or ~~6`
`therefore" Molecular formula"=XeF_(6)`.