3. A sealed horizontal cylindrical vessel of length $l$ is divided into two parts by a movable partition. On one side of the partition, there is 1 mole of oxygen, and on the other side, there is 1 mole of helium and 1 mole of oxygen, with the partition being in equilibrium. At some point in time, the partition becomes permeable to helium and remains impermeable to oxygen. Find the displacement of the partition. The temperatures of the gases are the same and do not change during the process.
3. From the condition of equilibrium of the partition (equality of pressures to the right and left of it), we find that initially it is located at a distance of $2 l / 3$ and $l/3$ from the ends of the vessel. After helium is uniformly distributed throughout the vessel, its partial pressures to the right and left of the partition (regardless of its position) will be equal. Therefore, the partition will be positioned such that the partial pressures of oxygen to the right and left are the same. Since the amounts of oxygen substance to the right and left of the partition are the same, it will be positioned in the middle. Consequently, the displacement of the partition after the redistribution of helium is

$$
\Delta x=\frac{2 l}{3}-\frac{l}{2}=\frac{l}{6}
$$