More atoms in a cup of water, than cups in an ocean?

  1. I've heard this before, and am just wondering if you guys think it's true. The saying is "There are more atoms in a cup of water than there are cups of water in the oceans of the world." I am pretty sure I heard this on some Science Channel show about atoms.

    I know it would depend on the size of the cup, etc. Let's not be too logical about it :)
  2. jcsd
  3. Danger

    Danger 9,663
    Gold Member

    Sounds right to me. Atoms are really small.
  4. The density of water is 1g/cm^3 or 1kg/m^3, right? So just use the mass of one water molecule to calculate how many there are per cm^3, and however many cm^3 there are in an average cup of water.

    I'd say it's definitely more than 1 mol.
  5. Well, that doesn't really tell you how many cups are in the ocean, though, does it? :)
  6. Pythagorean

    Pythagorean 4,471
    Gold Member

    according to yahoo answers:

    1 cup water = 235.6 cm^3 = .2366 liters = .2366 kg = 236.6 g

    molecular mass of water is 18 g/mol, so:

    (236.6 g) / (18g/mol) = 13 mols

    Avagadro's number gives us

    13*6*10^23 =


    7.8*10^24 molecules of water in a cup of water

    compared to

    2.2*10^19 cups of water in the ocean


    that's a factor of about 3.5*10^5 = 350000

    so there's over a quarter million times more molecules than cups!

    (notice, I ignored that it was saltwater, but I don't think you can overcome that factor of a quarter million with the adjustments)
  7. Chi Meson

    Chi Meson 1,767
    Science Advisor
    Homework Helper

    Woooooooooo HOOOOOOO!

    Now That's science, Yeah Baby! Yeah!

    ehm :redface:
  8. Danger

    Danger 9,663
    Gold Member

    Great answer, Pythagorean.
  9. lisab

    Staff: Mentor

    I think your confusion is based on the word "cup." It's an English unit of volume, and is well-defined (as seen in Pythagorean's calcuation) as 0.2366 L.
  10. Moonbear

    Moonbear 11,955
    Staff Emeritus
    Science Advisor
    Gold Member

    Excellent answer, Pythagorean! Though, you spoiled all my fun of planning to hand bchandler a measuring cup and telling him to go to the beach and find out. :biggrin: :devil:
  11. Pythagorean

    Pythagorean 4,471
    Gold Member

    well, that's the theoretical half. Sounds like Moonbear has an experimentalist lined up for us -_-
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