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Two adiabatic cylinders are divided internally into two equal parts by a semi-permeable membrane. The membrane only lets hydrogen pass through it. The first cylinder has one half filled with hydrogen (P=1atm) and other half is vacuum initially. The second cylinder has the first part filled with hydrogen(P=1atm) and the second part with oxygen (P=2atm) initially.

When both systems achieve equilibrium, what is the ratio of hydrogen gas (moles) present on either sides of the partition in both cases.

I can see that the first cylinder will have hydrogen in ratio 1:1, but I have a problem with the second part. I think there shouldn't be any diffusion because the pressure on the other side is already greater. But as it turns out, the answer given for second part is also 1:1. Can someone tell me why this is so?

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The unidirectional flow of hydrogen through the membrane is proportional to the frequency of collisions of hydrogen molecules with the membrane. This frequency depends on the partial pressure of the hydrogen. So we must conclude that partial pressures of hydrogen in both halves are the same, which gives us the answer for the ratio 1:1.

To get an intuition, why only partial pressure is important, consider the following. In left half you have mixed gas at $2.5~\text{atm}$: $4$ parts oxygen and $1$ part hydrogen. In the right half only $0.5~\text{atm}$ hydrogen. The molecules bombard the membrane from the left $5$ times more frequently than from the right. But at the same time, only $1/5$ of those molecules are actually hydrogen, which gives us the frequency of hydrogen molecules colliding with membrane the same.

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  • $\begingroup$ A 1:1 ratio in the second cylinder occurs when the pressure of hydrogen in the left and the partial pressure of hydrogen on the right are both 0.5 atm, not 1 atm. $\endgroup$ Feb 12, 2020 at 16:18
  • $\begingroup$ Although it's not important for the intuitive explanation, I corrected the answer for consistency. Thanks. $\endgroup$ Feb 12, 2020 at 16:20

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