At a particular temp and pressure it takes 4.55 min for a 1.5 L sample of He to effuse through a porous membrane. how long would it take for 1.5 L of F2 to effuse under the same conditions?

a. 18 min

b. 14 min

c. 10 min

d. 5 min

e. 1.5 min

b. 14 min

Explanation:

At the diffusion the momentum is conserved, so

qHe = qF₂

mHe * (vHe) ² = mF₂ * (vF₂) ²

Because it's the same volume and the same temperature and pressure, the gases will have the same number of moles. So, let's calculated based on 1 mol of the gases. The mass then will be the molar mass multiplied by 1:

mHe = 4 g

mF₂ = 38 g

4 * (vHe) ² = 38 * (vF₂) ²

(vHe/vF₂) ² = 38/4

(vHe/vF₂) ² = 9.5

vHe/vF₂ = √9.5

vHe/vF₂ = 3.0822

The velocity is the volume divided by the time, so:

vHe/vF₂ = (1.5/4.55) / (1.5/t)

vHe/vF₂ = t/4.55

t/4.55 = 3.0822

t = 14.02 min ≅ 14 min