Question

At 27 c temp 500ml of helium diffuse in 30 minutes . what is the time (in hours) taken for 100 ml of sulphur dioxide to diffuse under same experimental conditions

Answer 1

From Graham's law of diffusion , the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

⇒ r ∞ 1/ √M
⇒ r = k/√M        where , k is a constant

Also r = V/t  i/e rate of diffusion of volume of gas

Now ,

Molar mass of He = M₁ = 4 gm
Volume = V₁ = 500 ml
t₁ = 30 mins
Molar mass of SO₂ = M₂ = 64 gm
Volume = V₂ = 100 ml
t₂ = ?
rate of diffusion of Helium = r₁  = V₁/t₁  = 500/30 ml/mins
r₂ = 100/t₂
r₁ = k/√M₁        and      r₂ = k/√M₂

r₁ / r₂ = k/√M₁ / k /√M₂ = 500/30/100/t₂

t₂ = 24 mins

Hope my answer is correct.