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Given that the soup and rainwater would mix together, the question of how long it would take to get that last molecule of soup out is one of probability. I'm not qualified to give you a calculated answer, but I can tell you the most likely outcome is that it's going to take a lot of spoonfuls. The soup will begin tasting watered down very quickly and will basically be a bowl of >95% water for a long time before you get those last molecules
I get 1132 spoonfuls as a lower bound.
Big assumptions:
There are ~1.666×10^25 molecules of water in 500 ml (source: WolframAlpha). We seek what power of (500-25)/500 [= 19/20] is small enough to counter this number in order to get to the level of single molecules. This is about 1132.
But like you point out, it's going to be tasting watery a long, long time before that happens. It's 50% rainwater after about 14 spoonfuls (Sanity check: That would be 10 if the container was big enough and no spoonfuls were being removed.). ~90% at 45 spoons and ~99% at 90 spoons.
I got 1022 as the expected value, see my top level comment.
Edit: oops, made a big mistake. Will fix it!
Edit: after correcting I got 1144, much closer to your result 1132.