Question 4: The pressure in a gas cylinder containing hydrogen will leak more quickly than if it is containing oxygen. Why?
Answer
Leakage of H and O under same conditions
Hydrogen molecule is very small as compared to Oxygen molecule. Molecular mass of Hydrogen is 2 amu, while that of Oxygen is 32 amu. Therefore, at same temperature, the average velocity of Hydrogen molecules will be 4 times greater than Oxygen molecules. Therefore, Hydrogen molecules will leak more quickly as compared to Oxygen molecules due to its high speed. This is in accordance with the Graham’s law of diffusion, “rate of diffusion of a gas is inversely proportional to the square root of its molecular mass”.
Mathematical Proof: Since the temperature of a gas is proportional to the average K.E of the gas molecules. Both the gases are at the same temperature in their cylinders, therefore, the average K.E of the H molecules will be equal to the average K.E of the O molecules.
Let mH and vH are the mass and velocity of H molecules and mO and vO are the mass and velocity of O molecules, then
Put values of their molecular masses,
Thus the velocity of hydrogen molecule will be 4 times greater than the velocity of oxygen molecules if they at the same temperature. Therefore, the hydrogen molecules will leak more speedily than oxygen.