Note: This was based on insufficient information. I had no idea what this was for, and based on the initial information I came up with a way to effectively fill an empty box (with a balloon as a liner) with argon. Since the actual use is for storage of items within that box, as opposed to some scientific experiment involving small items placed into the box through an airtight hole or similar usage, the balloon method is not too practical as placing the items inside an uninflated balloon would not be easy. But since the answer still has some potential use, I am leaving it on the page.
I think you are going to have problems doing that. I will assume for the moment that it is really airtight - many times things are "basically" airtight but not 100%.
Start off by a common similar situation - filling a balloon with helium.
Do you start with a balloon full of air and push out the air with helium? No, because that would be very hard to do. In fact, if you tried to do that, you would actually end up with either the helium going in but no air going out - and end up with a 2x pressure mix of helium and air, or you would have to figure out a way to get the helium (which is lighter than air) in while getting air - and only air - to go out. Despite the difference in weight, that would not be an easy thing to do.
What do you do instead? You take an empty balloon and fill it with helium. There is no air to push out, so this works just fine.
With a hard plastic container (like a typical storage box), that just won't work - trying to push in argon would be similar to pushing helium into an air-filled balloon.
But that gave me an idea:
- Get a LARGE latex balloon or similar airtight very flexible material. Large enough that filled/expanded it can fill the entire box but that initially it is empty.
- Cut a hole in the lid of the box. Put a valve in the hole (bicycle tire valve?) and seal around it well.
- Attach the empty balloon to the inside of the lid.
- Put the lid on the box and make sure it is not sealed well. This is to allow the gas outside the balloon to escape as the balloon expands.
- Attach your argon supply (tank?) to the valve and fill 'er up.
- Seal the lid well. The balloon will be the primary airtight enclosure but the box, provided it is truly airtight, will be a secondary enclosure.
If you want to have a mixture - e.g., argon + air, or argon + helium or hydrogen + oxygen (not recommended!), use the same setup and fill up first with one gas and then the other.