Calculate the ratio of the rate of effusion of oxygen gas to that of H2 both at 27.0 Celsius

Question

Mixtures of different gases can be separated by effusion, because the effusion rate of gases depends on the molecular mass of the gas. This process was implemented in Oak Ridge during World WarII to separate different isotopes of uranium prepared in gaseous from as uranium hexafluoride. Calculate the ratio of the rate of effusion of oxygen gas to that of H2 both at 27.0 Celsius

Answer 1

So, the rate of effusion of any ideal gas is inversely proportional to the square root of the molar mass of that gas. This relationship is described by Graham's Law of Effusion which states that ...

 

rate gas1/rate gas2 = sqrt MW gas2/sqrt MW gas1

Oxygen is O2 and molar mass is 32 g/mol

Hydrogen is H2 and molar mass is 2

 

Hydrogen being lighter will diffuse faster.

√32 = 5.66

√2 = 1.41

 

5.66/1.41 = 4.0

 

So, H2 will diffuse 4 times faster than will O2, or O2 will diffuse at 1/4 the rate of H2 (to answer the question as asked)