How are there are more atoms in a cup of water than there are cups of water in the oceans of the world ?
In: Chemistry
So a cup of water is about 236.588237 milliliters, using “cup” as its standard definition as a unit of measurement.
The [NOAA estimates](https://oceanservice.noaa.gov/facts/oceanwater.html) the world’s oceans contain 321 million cubic miles of water. Converted to milliliters, that’s
1,338,000,000,000,000,000,000,000 milliliters.
So, that means there are
5,655,395,280,000,000,000,000 cups of water in the world’s oceans.
One mole (a chemistry measurement) of water contains 6.02 x 10^23 molecules of water. Each water molecule contains 3 atoms, so that’s 1.806 x 10^24 atoms in a mole of water. A mole is equal to 18 milliliters, so in one cup of water there are 13.1437909 moles, which is equal to
23,737,686,400,000,000,000,000,000 atoms in one cup of water.
So
23,737,686,400,000,000,000,000,000 atoms, vs
5,655,395,280,000,000,000,000 cups of water.
You can see which number is bigger: there are almost 4,200 times more atoms in a cup of water then there are cups of water in the world’s oceans.
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