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

In summary, there are more atoms in a cup of water than there are cups of water in the oceans of the world.
  • #1
bchandler
16
0
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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  • #2
Sounds right to me. Atoms are really small.
 
  • #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.
 
  • #4
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? :)
 
  • #5
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)
 
  • #6
Woooooooooo HOOOOOOO!

Now That's science, Yeah Baby! Yeah!

ehm :redface:
 
  • #7
Great answer, Pythagorean.
 
  • #8
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.
 
  • #9
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 -_-
 

1. How is it possible for there to be more atoms in a cup of water than cups in an ocean?

This statement is based on the fact that a cup of water contains approximately 1024 (1,000,000,000,000,000,000,000,000) atoms, while the estimated number of cups in the ocean is around 3.5 x 1020 (350,000,000,000,000,000,000). The key factor here is the size of the atoms compared to the size of a cup. Atoms are incredibly small, with a diameter of about 0.1 nanometers, while a cup has a much larger volume. Therefore, even though there are a greater number of cups in the ocean, the number of atoms in a cup of water is much larger due to their tiny size.

2. How do scientists know the number of atoms in a cup of water?

Scientists use a method called Avogadro's number to determine the number of atoms in a given substance. This number, which is approximately 6.02 x 1023, represents the number of atoms in one mole of a substance. By measuring the mass of a sample of water and using its molecular weight, scientists can then calculate the number of moles and therefore the number of atoms in that sample.

3. Does the number of atoms in a cup of water vary?

Yes, the number of atoms in a cup of water can vary depending on factors such as temperature and the presence of impurities. The number of atoms in a cup of water also depends on the size of the cup. A smaller cup will contain fewer atoms than a larger cup, even though they both contain the same volume of water.

4. Are there more atoms in other substances compared to water?

The number of atoms in a substance depends on its molecular weight and the size of its atoms. Therefore, it is possible for other substances to have more or fewer atoms compared to water. For example, a cup of saltwater may contain more atoms than a cup of pure water due to the presence of the salt molecules.

5. How does the number of atoms in a cup of water relate to the concept of density?

Density is defined as the mass of a substance per unit volume. Since the number of atoms in a substance is directly related to its mass, the number of atoms in a cup of water affects its density. This is why different substances, even if they have the same volume, can have different densities based on the number and arrangement of atoms in their molecular structure.

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