[foota]

Some non-zero remainder is all but inevitable, but even if your refining process yields 1 part pure to 99 parts mixed, after N steps you have 1 - (0.99) ^ N percent pure gas out of the whole, right?

So the ratio is somewhat arbitrarily (up to whatever the limit of your refining process is).

[simcop2387]

Unfortunately that doesn't usually hold out because as things get closer but not quite to the purity you need, you tend to need longer times, larger surfaces areas, higher temps, etc. in order to continue the process. You tend to hit spots during purification where you end up with an Azetrope (or similar for gasses) where you can't do a lot of the same techniques anymore because the impurities and the gas you want end up behaving the same at that concentration. At that point you have to start looking at adding catalysts or other chemical reactions to destroy or transform the impurities so that you can remove the end products from those reactions. But as you have less and less of the impurities it then ends up harder to target them to purify further. It's a nasty cycle that can drive costs up exponentially in terms of reagents, dollars, time and energy needed to do the purification. Ethyl Alcohol is a fun little rabbit hole to look at, at ~95% purity it forms an azetrope with water and you can no longer distill off the water or alcohol separately and have to resort to chemical or other means to get further purity. That's why you usually end up with other alcohols as a byproduct when purifying further (methanol in particular, since it disrupts the azetrope and lets you boil things off) or have to take rather expensive methods that remove the water.

https://en.wikipedia.org/wiki/Azeotrope

[bananaflag]

This assumes that the refining process works the same no matter what the initial concentration is. (Don't know if it's true or not, but it's an unstated assumption.)

[wonnage]

Balloon gas is already 99% helium. There’s not that much of it (one source is apparently as a byproduct of filling pure helium containers) and reprocessing it is not economical.