high-resolution terminology - matching measurements at high-resolution

## Description

{Quote} The Avogadro constant NA is a proportionality constant between the quantity amount of substance (with unit mole) and the quantity for counting entities ... One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number {End of Quote: Bureau International des Poids et Mesures 2019 The International System of Units (SI)}.

Thus the Avogadro constant NA has the SI unit 'per mole' [mol-1], but more strictly the unit for counting entities per amount is 'units per mole' [x·mol-1] (compare elementary charge). Therefore, NA is 'count per amount' with units 'counting units per mole'. The Avogadro constant times elementary charge is the Faraday constant.

Abbreviation: NA [x·mol-1]

```Communicated by Gnaiger Erich (2018-10-18) last update 2022-08-16
in: Anastrophe XX Entity X and the elementary unit x of A X-mass Carol
```

## Discussion

In a critical article on dimensionless units in the SI, Mohr and Phillips (2015) comment on the Avogadro constant NA: "Evidently, this constant can be viewed as the conversion factor between entities and moles." The unit mole [mol], however, is the SI base unit for amount of substance, defined by IUPAC (Cohen et al 2008) as: "Amount of substance is proportional to the number of specified elementary entities of that substance". Therefore, NA is not the conversion factor between entities and moles, but NA is the conversion factor between count and amount, expressed in counting units of entities (count) and moles of entities (amount). Thus, the unit 'ent' suggested by Mohr and Phillips (2015) for the quantity count would imply, that they should consider 'mol ent' as the unit for amount of substance. In this case, the unit of NA should be [ent/(mol ent) = mol-1], in line with SI, but contrary to the valid intention of Mohr and Phillips (2015).
NA is the conversion factor between countable entities, expressed in counting units [x], and amount of entities (amount of substance), expressed in moles [mol]. Therefore, the unit of NA is 'counting units per mole' [x·mol-1].