# Amount of substance expressed in yoctomole units

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?

• 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
• 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

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.