Graham's Law of gaseous diffusion

Problem 1

Question: A mixture of helium (He) and argon (Ar) gases is placed in a container with a small pinhole. If the rate of effusion of helium is 3.16 times faster than that of argon, calculate the molar mass ratio of the two gases and determine the time it takes for 50% of the helium to effuse if 25% of the argon effuses in 10 minutes.

Problem 2

Question: Two gases, X and Y, effuse through a porous barrier. Gas X has a molar mass of 16 g/mol and effuses at a rate of 0.25 mol/s. If gas Y takes 4 times longer to effuse the same amount under identical conditions, what is the molar mass of gas Y, and how does the temperature affect this relationship if the experiment is repeated at 500 K instead of 300 K?

Problem 3

Question: Hydrogen gas (H₂) and an unknown gas Z diffuse through a narrow tube. If 100 mL of H₂ diffuses in 2.5 minutes, while 100 mL of gas Z takes 10 minutes under the same conditions, calculate the molar mass of gas Z. Additionally, predict the change in diffusion rates if the pressure is doubled for both gases.

Problem 4

Question: Oxygen gas (O₂) effuses at 0.0312 mol/min. A second gas, with a molar mass four times that of oxygen, is introduced. Determine the effusion rate of the second gas and explain how a third gas with an intermediate molar mass alters the dynamics.

Problem 5

Question: Neon (Ne) effuses at 0.1 mol/s, and an unknown gas at 0.05 mol/s. Calculate the molar mass of the unknown gas and the percentage change in the effusion rate ratio between 25°C and 100°C.