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due to the inerrant structure of alcohol, the water molecules tend to fit into the spaces in the alcohol molecules,thus resulting in some extra space having been left by the absorption of the water molecules by the alcohol molecules this results in a volumetric deficit in the total sum of both liquids.The proof of the alcohol would then be exactly 1/2 of the original value assuming that at 100% pure alcohol and 100 % pure water ,after mixing the two ,the alcohol is now at 50% of its original strength or 100 proof after starting out as 200 proof ,therefore proof is 2 times the amount of alcohol (200 proof alcohol diluted with an equal amount of water yields slightly less than 2 liters of 100 proof or 50 % alcohol.

here ends chemistry 101.

surprising that all the big time answerer s could not come up with an answer,so much for credibility

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Q: Why when you mix exactly one liter each of pure ethanol and pure water do you end up with less than exactly two liters of liquid?
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