Question

A 3.0 L sample of helium gas was placed in a container filled with a porous membrane. Half of the helium gas effused through the membrane in 24 hours. A 3.0 L sample of oxygen gas was placed in an identical container. How many hours will it take for half of the oxygen gas to effuse through the membrane?

Answer 1

Using Graham's Law of Effusion, it takes approximately 67.9 hours for half of the oxygen gas to effuse through a membrane, comparing it to the 24-hour effusion time for helium.

Step-by-step explanation:

The question you are asking relates to the concept of gas effusion, which is covered in high school chemistry courses. To calculate how many hours it will take for half of the oxygen gas to effuse through the membrane, we use Graham's Law of Effusion.

This law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Since it takes 24 hours for helium (with a molar mass of 4 g/mol) to effuse, we can compare the molar mass of oxygen (approximately 32 g/mol) to find the time it will take for half of the oxygen to effuse.

According to Graham's Law:

RateHe / RateO2 = √(Molar mass of O2 / Molar mass of He)

RateHe / RateO2 = √(32 / 4) = √(8)

Since helium effuses in 24 hours, we can set up a proportion:

24 hours / tO2 = 1 / √(8)

tO2 = 24 * √(8)

Thus, it will take approximately 67.9 hours for half of the oxygen to effuse through the membrane.