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

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SUMMARY

The discussion confirms the assertion that there are more atoms in a cup of water than there are cups of water in the oceans. A standard cup of water, approximately 236.6 grams, contains about 7.8 x 1024 molecules of water, calculated using the molecular mass of water (18 g/mol) and Avogadro's number. In contrast, the total volume of Earth's oceans translates to roughly 2.2 x 1019 cups of water. This results in a factor of approximately 350,000, indicating that there are over a quarter million times more molecules in a cup than cups in the ocean.

PREREQUISITES
  • Understanding of molecular mass and Avogadro's number
  • Basic knowledge of water density (1 g/cm3)
  • Familiarity with volume conversions (e.g., cups to liters)
  • Ability to perform basic scientific calculations
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  • Research the concept of Avogadro's number and its applications in chemistry
  • Learn about the molecular structure of water and its properties
  • Explore the methods for calculating volumes of large bodies of water
  • Investigate the implications of atomic scale comparisons in scientific discussions
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Students, educators, and science enthusiasts interested in molecular chemistry, water properties, and comparative scientific calculations will benefit from this discussion.

bchandler
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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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Sounds right to me. Atoms are really small.
 
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.
 
WarPhalange said:
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? :)
 
according to yahoo answers:

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

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)
 
Woooooooooo HOOOOOOO!

Now That's science, Yeah Baby! Yeah!

ehm :redface:
 
Great answer, Pythagorean.
 
bchandler said:
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.
 
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:
 
  • #10
Chi Meson said:
Woooooooooo HOOOOOOO!

Now That's science, Yeah Baby! Yeah!

ehm :redface:

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

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