I stumbled upon a couple of papers where amounts were expressed in yoctomoles ([ymol], $\pu{10^{-24} mol}$) and I find it somewhat bothersome as 1 ymol would correspond to about 60% of atom/molecule/ion etc., which doesn't make much sense to me:

$$N_\mathrm{A} \times \pu{10^{-24} mol} = \pu{6.022 \times 10^{23} mol-1} \times \pu{10^{-24} mol} \approx \pu{0.6}\,\text{(elementary entities)}$$

Simply put, I'd say that using zeptomoles ([zmol], $\pu{10^{-21} mol}$) is already a stretch as one of the ideas behind a mole concept is to allow to handle large numbers of entities more conveniently, and at this scale there is no reason not to use direct quantities of molecules/atoms/ions.

Should the yoctomoles units really be used, and if so, then how to rationalize fractional elementary entities?

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    I don't follow your conversion, but agree that a yoctomole would correspond to 0.6 molecules. Using the unit seems fine to me. – MaxW Oct 23 '17 at 3:46
  • @MaxW Originally (before edit by @aventurin) it was a result of solving a proportion (1 mol – $N_\mathrm{a}$; $10^{-24}$ mol – $\pu{x mol-1}$), so the units were preserved. – andselisk Oct 23 '17 at 21:48
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    When it comes to homeopathic dilutions even this unit seems a little bit coarse-grained. Oscillococcinum e.g. has one part duck offal in $10^{400}$ parts water. – aventurin Oct 23 '17 at 21:53

Well, the closer you get to atomic detection limits, the less sense bulk units make, that is correct.

However, coming from lab scale units it is much easier to scale down directly with SI prefixes — the exact reason what they were designed for. Therefore, it makes sense that these papers might say ‘Our predecessors could only detect $\pu{10zmol}$, we have lowered the detection limit by a factor of $100$ to $\pu{0.1zmol}= \pu{100ymol}$.’ And that is basically what they say. I note that both abstracts immediately place a molecule count behind the amount in ymol, so they are well aware of the scale of their unit with respect to molecules.

Once you get to the full molecular scale, you will be dealing with a type of quantisation this way or that; whether you are reporting energy, charge, mass or amount. In none of the other cases is anything special described for atomic scales so why should we make an exception for moles? Just make sure that the value itself corresponds to a whole number of molecules within the boundaries of rounding errors.

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