Question

One mole of nitrogen gas at 0.8atm takes 38 seconds to diffuse through a pin hole whereas one mole of an unknown compound of Xenon with Fluorine at 1.6 atm takes 56.26 seconds to diffuse through the same pin hole. The molecular formula of compound is (atomic mass of xenon=131.3 u):

1.XeF2
2.XeF4
3.XeF5
4.XeF6​

Answer 1

from Graham's law of diffusion,

t2/t1 = (P1/P2)√{M2/M1}

given, t1 = 38sec, t2 = 57sec , M1 = 28g/mol, P1 = 0.8atm, P2 = 1.6atm and M2 = ?

now, 57/38 = (0.8/1.6)√{M2/28}

squaring both sides,

57²/38² = (1/4)(M2/28)

or, M2 = (57² × 28 × 4)/38² = 252

hence, molecular weight of compound is 252 g/mol.

compound contains Xenon and Fluorine.

atomic weight of Xenon = 131

and atomic mass of Fluorine = 19

and general formula of Xenon fluoride is XeFx

so, 131 + 19x = 252

or, 19x = 252 - 131 = 121

or, x = 6.36. ≈ 6

hence, molecular formula is XeF6