If 100cm3 of oxygen pass through a porous plug is 50 seconds, the time taken for the same volume of hydrogen…

Analyze the question: This is about diffusion (effusion) of gases through a porous plug, so we use Graham's Law. We're given the time for oxygen and asked for the time for the same volume of hydrogen.

Concept: Graham's Law

Rate of diffusion is inversely proportional to the square root of molar mass:

R₁/R₂ = √(M₂/M₁)

For the same volume of gas, rate = V/t, so the volumes cancel and:

t₁/t₂ = √(M₁/M₂)

Solution:

• Molar mass of O₂ = 32
• Molar mass of H₂ = 2
• Time for O₂ = 50 s
• Time for H₂ = t

t(O₂)/t(H₂) = √(32/2)

50/t = √16 = 4

t = 50/4 = 12.5 s

Answer: B (12.5 s)

Tip: Hydrogen is lighter, so it diffuses faster and takes less time. Your answer must be less than 50 s, which already rules out D. Also remember to use the molar masses of the molecules (O₂ = 32, H₂ = 2), not the atomic masses. Using 16 and 1 would give √16 = 4 as well here, but that is a coincidence of the ratio, so don't rely on it in other questions.