Question

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

Answer 1

Using Graham's law of effusion, we find that F2 effuses approximately 3.0822 times slower than He. Since it takes He 4.55 minutes to effuse, F2 would take roughly 14 minutes to effuse the same volume, making option (b) the correct answer.

Step-by-step explanation:

To determine how long it would take for 1.5 L of F2 to effuse through a porous membrane under the same conditions as He, we can use Graham's law of effusion. Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. The formula for Graham's law is given by:

rate of effusion of Gas 1 / rate of effusion of Gas 2 = sqrt(molar mass of Gas 2 / molar mass of Gas 1)

Firstly, we need to find the relative rates of effusion for He and F2. The molar mass of He is approximately 4 g/mol, and the molar mass of F2 is approximately 38 g/mol. Plugging these values into the equation, we get:

rate of He / rate of F2 = sqrt(38 / 4)

rate of He / rate of F2 = sqrt(9.5)

rate of He / rate of F2 ≈ 3.0822

This means that helium effuses about 3.0822 times faster than fluorine. Given that it takes 4.55 minutes for helium to effuse, we can find the time for fluorine to effuse by multiplying the helium time by this ratio:

time for F2 = time for He × (rate of He / rate of F2)

time for F2 = 4.55 min × 3.0822

time for F2 ≈ 14.04 min

Therefore, the time it would take for 1.5 L of F2 to effuse under the same conditions is approximately 14 minutes, which corresponds to option (b) 14 min.

Answer 2

b. 14 min

Step-by-step 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