Stupid Math Tricks: Shuffling Water Molecules

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http://www.flickr.com/photos/latitudes/
Image by Johnny Blood, via WikiCommons.

So, I was having some fun today reading through the amazing-but-true thread at Reddit, when I had the idea to mash some crazy things together. Follow me carefully on this (and feel free to correct my math if you notice mistakes):

There are about 7 billion (7×10^9) people on Earth.

If you replaced every person with another Earth full of people (49 billion-billion, or 4.9×10^19), you’d still have fewer people than there are molecules in a drop of water (divide the number of people by Avogadro’s number to get about 8.1368×10^-5 moles; there are 18mL of water in a mole of water, so a we get a little over .0014 mL of water; a drop of water has been defined in some places as 0.05mL).

Extrapolating back out, we can figure out that there are 3.346×10^28 molecules of water in a cubic meter of water (1×10^6 gms of water per m3, 18 grams per mole, Avogadro’s number again; everything is assuming standard temperature and pressure). The recognized volume of our sun is 1.4×10^27 cubic meters. Multiply those together to find out that there would be 4.684×10^55 molecules in a volume of water equal to that of our sun. That’s a big freakin’ number.

But…

It would take enough water to fill 1.7 TRILLION suns to have as many molecules of water as there are ways to shuffle a standard deck of cards (52! = 8.067×10^67). That’s more than 4 times the number of stars in the Milky Way galaxy.

::head asplode::

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