More rinses is generally better than less rinses at removing contaminants but there’s no hard rule about the “correct” number of times you should rinse something.
The standard practice in a lab is to rinse three times, but there’s no reason why it has to be exactly three. It’s just standard because it’s a nice number that seems to give satisfactory results in most cases. The justification that you will often hear is that if each rinse is successful in removing 99% of the contamination, then after 3 rinses your contaminant will be diluted to 1 part per million. But that explanation isn’t really based on anything.
In practice you don’t know if your rinsing actually removed 99% of the contamination (could be more or less), and who is to say whether 1 part per million of contamination at the end is good or bad? For some purposes, you might be able to get away with significantly more contamination and be fine. For example, if I’m reusing a coffee cup to hold water, I’ll be willing to accept only a single rinse because if my water ends up tasting a little bit like coffee that’s not the end of the world. But if I’m trying to calibrate an extremely delicate sensor in an experiment I may want to rinse a piece of glassware 10+ times, because even contamination as small as 1 part per million is unacceptable, so I want to be on the safe side.
I think I see what you’re asking. If you rinse three times using a third of the water, vs rinsing once using the full amount of water, why would the former be more effective? After all, you’re diluting with the same amount of water.
While there are various complications caused by the contaminant sticking to the side, let’s ignore those and work this out mathematically.
You have a 300ml bottle, and it has 1ml of soap in it. You rinse it once to the top with 299ml of water, and pour it out. Therefore, any soap left is diluted by 300 times, its 1 part soap to 299 parts water.
You have the same 300ml bottle with 1ml of soap in it. You rinse it once to a third full with 99ml of water, and pour it out. At this point, any soap left is diluted by 100 times, so its 1 part soap to 99 parts water. You then repeat this, adding another 99ml of water to the 1ml of residue (which is itself, as we said, 99% water and 1% soap). At this point, its 99 parts water to 1 part residue, and the residue is 99 parts water to 1 part soap, so its 9999 parts water to 1 part soap. We do it a third time, 99 parts water to 1 part new residue (which is 9999 parts water to 1 part soap), and now we’re at 999,999 parts water to 1 part soap; the soap is 1 part in a million.
We’ve used the same amount of water, but by using it over 3 rinses instead of 1, we’ve gone from it being 1 in 300 soap to 1 in a million soap. For most purposes, this is enough to make it essentially clean.
More water just adds to the dilution, but each rinse is multiplied by the effect of the previous rinses. Multiplication makes the numbers go higher, quicker, than addition.
No matter how “well” you do it, doing it in one rinse can only water it down by the amount of the contaminant that the water in that one rinse can absorb. If there’s 10g of contaminant and 1 litre of water, there is still going to be 10g of contaminant and 1 litre of water at the end. And that ratio – or worse – will also stay on the inside of the bottle with the water that stays behind, and the residue that wasn’t absorbed or poured away.
Doing it in three rinses, means that tiny ratio that’s left after the first rinse is then washed again, and the ratio drops even further, and then the ratio of THAT rinse’s residue is reduced once again with a third rinse. This means that it’s far less likely for any significant amount of contaminant to remain, even if you used the same amount of water, and what does remain would be so watered down it won’t affect the use of the container.
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