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

by bchandler
Tags: atoms, cups, ocean, water
 P: 16 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 :)
 PF Gold P: 8,964 Sounds right to me. Atoms are really small.
 P: 343 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.
P: 16
More atoms in a cup of water, than cups in an ocean?

 Quote by WarPhalange 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.
Well, that doesn't really tell you how many cups are in the ocean, though, does it? :)
PF Gold
P: 4,287

 The volume of Earths oceans is 1.37 billion cubic kilometers. Translating this into measuring cups (standard 8 ounce cup), you get 22,617,336,000,000,000,000 cups of water - 22.6 million trillon, give or take a little. This would be over 3.2 billion cups (200 million gallons) for each and every person on the planet.
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

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)
 Sci Advisor HW Helper P: 1,772 Woooooooooo HOOOOOOO! Now That's science, Yeah Baby! Yeah! ehm
 PF Gold P: 8,964 Great answer, Pythagorean.
Mentor
P: 2,985
 Quote by bchandler I know it would depend on the size of the cup, etc. Let's not be too logical about it :)
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.
 Emeritus Sci Advisor PF Gold P: 12,270 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.
PF Gold
P: 4,287
 Quote by Chi Meson Woooooooooo HOOOOOOO! Now That's science, Yeah Baby! Yeah! ehm
well, that's the theoretical half. Sounds like Moonbear has an experimentalist lined up for us -_-

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