The molar mass of the unknown gas is____g/mol.

Question

A sample of O₃ gas is observed to effuse through a porous barrier in 9.33 minutes. Under the same conditions, the same number of moles of an unknown gas requires 5.08 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 = sqrt MW gas 2 / sqrt MW gas 1

let gas 1 = 1 mol of O3

rate gas 1 = 1 mol / 9.33 min = 0.1072 mol/min

MW gas 1 = 48 g/mol

gas 2 = 1 mol of unknown

rate gas 2 = 1 mol / 5.08 min = 0.1969 mol/min

MW gas 2 = ?

0.1072 / 0.1969 min = sqrt x / sqrt 48

0.5444 = √x/48

0.2964 = x/48

x = 14.2 g/mol = molar mass of unknown gas