The molecules in a single drop of water diluted evenly throughout the Earth's oceans would result in a density of one molecule per litre of sea water!

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Offline Erik Moeser

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Erik  asked the Naked Scientists:

Dear Dr. Chris:   My brother and I have come to a "conclusion", and
have a high degree of  confidence in the following statement:

"The molecules in a single drop of water, if diluted evenly throughout the "seven seas" (the oceans of the world), would result in a density of one molecule (from the drop) per litre of sea water."

This is astounding!  Please find below our assumptions and maths.  I
hope you can confirm the correctness of the assumptions and the accuracy of the maths!

This is useful in illustrating the mind-boggling tiny size of molecules.

Erik Moeser
Menomonee Falls, WI

Robert Moeser
Boston, MA

One litre = 24,000 drops

The volume of the sea is 1.4 billion cubic kilometres

18g (or cc) of water = one mole

Number of molecules per drop:  1000/18 (6.022X10 to the 23rd)/24000 = 1.39 X 10 to the 21st

Number of litres in the oceans:  1.4  X  10 to the 9th X  10 to the
ninth  =  cubic metres of sea water, X 1000 = litres of sea water = 1.4 X 10 to the 21st

What do you think?


Offline Evie

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Doesn't a liter of water have 20,000 drops?
"There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy."
Act I, scene 5


Offline Erik Moeser

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I have seen the number 20.000 which would result in even more molecules per drop.  However I have also seen the 24,000 number.  I think drops come in different sizes and therefore not a standard precise volume for one.


Offline chris

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24,000 equates to a volume of about 0.03ml, which not unreasonable for a droplet size.

I never forget a face, but in your case I'll make an exception - Groucho Marx