# Ratio of rates of diffusion of gases

I stumbled upon a question, A mixture of 50 mL of Hydrogen gas and 50mL of Oxygen gas is allowed to effuse through an effusimeter. After some time it is observed that the residual gas occupies 90mL. Find the composition of (1) Effused gas and (2) Residual gas. Since there was no information given about the pressure, I took it to be constant.

Acccording to the Graham's Law of Diffusion, $$\frac {R1}{R2}$$ = $$\frac{P1}{P2} \sqrt{\frac{M2}{M1}}$$ , where M1 and M2 are the molar masses of the gases, P1 and P2 are the partial pressures of the gases and R1 and R2 are the rates of diffusion of the gases.

Now, some of my friends took the ratio of the Partial pressures $$\frac{P1}{P2}$$ as a constant and calculated the ratio of rates of diffusion of Hydrogen to Oxygen to be 4 and reached the result composition as: Effused gas- H2=8mL, O2=2mL, Residual gas- H2=42mL, O2=48mL. I personally think that the ratio of partial pressures will change as the gases effuse out, but I'm not sure how to approach the problem and get the answer with the lowest approximation possible. Please help me out. Is there any way we can solve this problem by not taking the difference in partial pressure as zero?

• It is rather mathematical than chemical problem.You have to solve a differential equation. – Poutnik Oct 8 '20 at 10:38
• As @Poutnik indicated, this will be a differential equation problem. This is a high school problem and what your friends actually calculated was the initial rate of diffusion. – Eyy boss Oct 8 '20 at 11:11
• Should I post it on the Maths Stack Exchange then? – Aryan Verma Oct 8 '20 at 11:22