One male of nitrogen gas at `0.8` atm takes 38 seconds on diffuse through a pinhole, whereas one mole of a compound of xenon with fluorine at 1.6 atm takes 57 secondes to diffuse through the same hole. Calculate molecular weight of the compound.

Explanation

`(r_(N_(2)))/(r_(XeF_(n))) = (P_(N_(2)))/(P_(XeF_(n))) sqrt((M_(XeF_(n)))/(M_(N_(2))))`
`(r_(N_(2)))/(r_(XeF_(n))) = (("Molar volume")/(t_(N_(2))))/(("Molar volume")/(t_(XeF_(n)))) = (t_(XeF_(n)))/(t_(N_(2))) = (57)/(38)`
`(57)/(38) = (0.8)/(1.6) sqrt((M_(XeF_(n)))/(28))`
`M_(XeF_(n)) = ((57)/(38))^(2) xx ((1.6)/(8.0))^(2) xx 28`
`= 252`
`Xe + nF = 252`
`131 + n xx 19 = 252`
`n = 6`
Molecular formula `= XeF_(6)`