This question can only be answered very approximately. You need the cross sectional area of the pipe (A), the volume of the vessel (V), the atomic mass of the gas (M), and the final temperature (T)
The momentum flux of the gas at the outlet of the pipe is P*A. If you divide out the atomic mass, you can get the particle flux.
So, calculate how many particles are in the vessel at temperature T, pressure P using the ideal gas law, and then you know how long it will take (roughly).
In reality, the particle flux will slow down as the vessel fills up, and the vessel won't necessarily mix fast enough to have a well defined pressure or temperature for a bit. I would multiply the result by a factor of e just for the hell of it.
