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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.
If you ignore the fact that soup consists of discrete molecules, the answer is infinite.
In real life though, you have to get probabilities involved. Haven’t done the math yet, but my intuition tells me that it’s going to take a lot of spoons. Quick LLM solution suggests it’s only 14 spoons, but I’m not convinced. Need to do it properly later today.
Edit: That first intuition was very wrong. Also, the LLM was wrong too. It was just counting milliliters, not molecules.
Well 14 spoonfuls wouldn't finish the soup even if it wasn't raining so that's definitely wrong.
Ok, Now I've got some sort of estimate. Still didn't do it "the proper way", because writing a simulation was more fun than reading a few Wikipedia articles about mathematics, which would have taken.... probably only a fraction of the time I spent on writing some horrible R code that produces suspicious results.
My simulation is based on keeping track of different kinds of molecules. First, I calculated how many water and soup molecules there are. I assumed that they both have the same molar mass. I also assumed that 500 ml = 500 g, which is close enough IRL. The number of each molecule type doesn't have to be a whole number, so fractions are allowed. When the soup molecule count drops to 0.5, it means that there's a 50% chance of 1 soup molecule being present. I'm not entirely satisfied with this implementation, but it felt reasonable at the time. Anyway, I set the threshold of my while loop to 0.5 soup molecules.
Anyway, here are the results!
It took only 1146 spoons to scoop out the final molecule with 50% certainty. If you used a smaller 5 ml spoon, it would take 5848 spoons, which is still way smaller than I expected. I really thought it would be something totally absurd like the the number of atoms in the observable universe. I feel kinda skeptical about my code until I see a proper mathematical proof about this.
Close enough, somebody mathed it out to 1144 in the comments