the molar mass of the unknown gas is?

Question

A sample of N₂ gas is observed to effuse through a porous barrier in 7.96 minutes. Under the same conditions, the same number of moles of an unknown gas requires 10.9 minutes to effuse through the same barrier. The molar mass of the unknown gas is  _____g/mol.

Answer 1

Graham's Law of Effusion:

rate gas 1/rate gas 2 = √MW gas 2 / √MW gas 1 ... rate of effusion is inversely related to sqrt MW of the gas

MW N_{2 =} 28 g/mol

rate N₂ = 7.96 min

MW X = ?

rate X =10.9 min

(NOTE: it takes longer for the unknown, so the MW of X must be greater than that for N2)

10.9/7.96 = sqrt x / sqrt 28

1.378 = sqrt x / 5.29

sqrt x = 7.29

x = 53.2 = MW of unknown gas