Expert: George Maxwell - 7/14/2007

Question
How many H20 Molecules are in 1 gallon of Evian?

Answer
Hi there, and thank you for your question.

Quick answer:
1 American gallon (3.785 litres) contains about
126650305555555555555555556. water molecules

1 British gallon (4.546 litres) contains about
152088955555555555555555556. water molecules

Long Answer:

This question relies on the fact that 1ml of water weighhs 1 gram.

The periodic table of Elements gives the relative atomic mass of Hydrogen as 1 and Oxygen as 16, so the relative molecular mass of water is 18 (2x1 + 16).

The relative molecular mass of a substance is the weight of that substance that contains a fixed number of moleucles - that number is 6.022 exp.23 (Which is a quick way of writing 6022000,000,000,000,000,000,00 or something like that: *huge number*).

So 18g (or 18 ml) of water always contains that many molecules. Now all you have to do is multipy it up:

1 American gallon = 3.785 litres = 3785ml
How much bigger is 3785 than 18?

3785ml / 18ml = 210.27; that means that the gallon contains 210.27 times more molecules than 18ml does. I multiply 6.023exp.23 by 210.27 to get the answer:

so 1 American gallon contains
126650305555555555555555555.555556 water molecules
(rounded up after the decimal point).
The same is true for the British gallon. Actually, this is only a good guess, because the relative molecular mass of water isn't exactly 18. But it's close enough!
Thanks again for your question. Let me know if you want any more information.
Take Care