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

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 :)

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Danger
Gold Member
Sounds right to me. Atoms are really small.

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.

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? :)

Pythagorean
Gold Member

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)

Chi Meson
Homework Helper
Woooooooooo HOOOOOOO!

Now That's science, Yeah Baby! Yeah!

ehm

Danger
Gold Member

lisab
Staff Emeritus
Gold Member
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.

Moonbear
Staff Emeritus
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.

Pythagorean
Gold Member
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 -_-