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

  1. Nov 29, 2008 #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. Nov 29, 2008 #2

    Danger

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    Sounds right to me. Atoms are really small.
     
  4. Nov 29, 2008 #3
    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. Nov 29, 2008 #4
    Well, that doesn't really tell you how many cups are in the ocean, though, does it? :)
     
  6. Nov 29, 2008 #5

    Pythagorean

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    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

    ----------------------------------------------------------------------------------
    CONCLUSION

    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. Nov 29, 2008 #6

    Chi Meson

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    Woooooooooo HOOOOOOO!

    Now That's science, Yeah Baby! Yeah!




    ehm :redface:
     
  8. Nov 29, 2008 #7

    Danger

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    Great answer, Pythagorean.
     
  9. Nov 29, 2008 #8

    lisab

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    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. Nov 29, 2008 #9

    Moonbear

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    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. Nov 29, 2008 #10

    Pythagorean

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