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

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Discussion Overview

The discussion revolves around the claim that there are more atoms in a cup of water than there are cups of water in the oceans of the world. Participants explore the implications of this statement, considering the calculations involved and the definitions of volume units.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants express belief in the claim, noting the small size of atoms as a factor.
  • One participant suggests using the density of water and the mass of a water molecule to calculate the number of molecules in a cup of water, estimating it to be more than 1 mol.
  • A detailed calculation is presented, estimating the number of cups in the ocean and comparing it to the number of molecules in a cup of water, leading to a conclusion of approximately 350,000 times more molecules than cups.
  • Participants acknowledge that the definition of a "cup" is important for the calculations, with one noting it is a well-defined English unit of volume.
  • There is a light-hearted exchange about the implications of the calculations and the potential for experimental verification.

Areas of Agreement / Disagreement

While some participants agree with the calculations and the claim, there is no consensus on the implications of the results or the definitions involved. The discussion remains open-ended with various viewpoints expressed.

Contextual Notes

Participants note that the calculations depend on the definitions of volume and the assumptions made about the size of the cup and the nature of the water (e.g., ignoring saltwater effects). There are unresolved aspects regarding the accuracy of the estimates and the assumptions behind them.

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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