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In What is Life? published in 1944, physicist Erwin Schrodinger writes the following:

Why are atoms so small? To begin with, they are very small indeed. Every little piece of matter handled in everyday life contains an enormous number of them. Many examples have been devised to bring this fact home to an audience, none of them more impressive than the one used by Lord Kelvin: Suppose that you could mark the molecules in a glass of water; then pour the contents of the glass into the ocean and stir the latter thoroughly so as to distribute the marked molecules uniformly throughout the seven seas; if then you took a glass of water anywhere out of the ocean, you would find in it about a hundred of your marked molecules.

Given our advances in understanding since then, would we still say that this is the case? Would we truly find molecules of our glass of water in every future glass of water we sampled from the oceans (presuming near perfect distribution)?

I understand that atoms are small, but at the same time the oceans are big and therefore contain many, many, many, atoms of water. Even if one could evenly distribute the atoms of water in a glass evenly throughout the oceans, it seems unlikely to me that one would still be able to find even 1 atom of that original glass in any future samples of water, let alone a hundred atoms.

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    $\begingroup$ Have you considered two things : (a) how many glasses of water are there in the ocean ? and (b) how many atoms are there in a glass of water ? $\endgroup$
    – StephenG - Help Ukraine
    Commented Jul 12, 2020 at 2:50
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    $\begingroup$ I think Avogadro’s number was known in Lord Kelvin’s time. $\endgroup$
    – G. Smith
    Commented Jul 12, 2020 at 3:32

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According to LiveScience, the volume of seawater in the oceans is about $1.33 \times 10^9$ $km^3$, or $1.33 \times 10^{18}$ $m^3$, or $1.33 \times 10^{21}$ liters, or $5.6 \times 10^{21}$ cups.

A mole of water is $18$ $gm$, which is $18$ $cm^3$. A cup is $237$ $cm^3$ or $13.2$ moles.

A mole is also $6 \times 10^{23}$ molecules of water, so a cup is $7.9 \times 10^{24}$ molecules.

If you mix $7.9 \times 10^{24}$ labelled molecules in $5.6 \times 10^{21}$ cups of seawater, each cup will contain about $1400$ labelled molecules.

Unless I have made a silly arithmetic mistake.

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    $\begingroup$ for the same reason, for a well-stirred atmosphere every breath you take would contain molecules previously breathed by Hitler and Julius Caesar. $\endgroup$
    – niels nielsen
    Commented Jul 12, 2020 at 6:18

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