Question

It requires 24 hours for a sample of helium gas to effuse through a porous membrane. How long will it take for the same amount of oxygen gas to effuse through the same membrane? Assume both gases are at the same temperature. A. 12 hours B. 68 hours C. 48 hours D. 8.5 hours E. 32 hours

Answer 1

B. 68 hours

Step-by-step explanation:

The effusion is the escape of gas molecules through a tiny hole. Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. So, for gas A and B:

rate of A/ rate of B = (√MB)/(√MA)]

Where M is the molar mass. The rate is the amount divided by time. So, calling A of helium gas (MA = 4 g/mol), and B as oxygen gas (MB = 32 g/mol), the amounts as A and B, and the times tA and tB:

(A/tA)/(B/tB) = (√32)/(√4)

Because they have the same amount, A = B

tB/tA = 5.657/2

tB/24 = 2.828

tB = 68 hours