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How many millilitres of water would it take so that, when they are thoroughly dispersed around the world, it would yield an average of one molecule of the original sample of water in each millilitre of water in the world? For the sake of argument, assume that the H and O atoms do not dissociate, and the water molecules remain intact.

I calculated it once and got something around 40 ml, but I forgot how I made that calculation.

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    $\begingroup$ Well, you need to find out how many mL of water are there in the world, and then take that many molecules. $\endgroup$ Feb 14, 2016 at 19:22
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    $\begingroup$ The answer I calculated is very close to the 40 mL calculated by the OP. Thus I think it is safe to assume that we do know what he asking and that we should reopen this question. $\endgroup$
    – Curt F.
    Feb 15, 2016 at 4:13

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A very quick Googling tells me that the volume of the oceans is 1.3 billion $\mathrm{km}^3 = 1.3\times10^9\;\mathrm{km}^3 = 1.3\times10^{18}\;\mathrm{m}^3 = 1.3\times10^{24}\;\mathrm{cm}^3 = 1.3\times10^{24}\;\mathrm{mL}$.

To get one molecule into each of those mL, we'd need $1.3\times10^{24}$ molecules of water, or $\frac{1.3\times10^{24}}{N_A} = \frac{1.3\times10^{24}}{6.02\times 10^{23}}$ moles of water, about 2.2 mols. Since water is 18 g/mol, that comes out to 39 grams of water or about 39 mL.

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