# Why is ‘amount of substance’ so poorly understood? The mysterious Avogadro constant is the culprit!

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## Abstract

The base quantity ‘amount of substance’ is poorly understood and the name and symbol usually avoided. This is because of its formal interpretation as the number of entities multiplied by the *reciprocal* of the mysterious Avogadro *constant*, *N* _{A}. If X signifies the kind of entities involved, the number of entities in a sample, *N*(X), is easily comprehended, and if *m* _{av}(X) is the sample-average entity mass, the total mass, *m*(X) = *N*(X)*m* _{av}(X)—an aggregate of *N*(X) average entity masses—is also conceptually straightforward. However, the corresponding amount of substance, *n*(X) = *N*(X)(1/*N* _{A})—an aggregate of *N*(X) ‘reciprocal Avogadro constants’—is incomprehensible unless some physical meaning can be attached to 1/*N* _{A}. By contrast, the base unit, mole, is thought of by chemists as an aggregate of a *particular* number of entities: mol = \( {\mathcal N}_{\rm{Avo}} \) ent, where \( {\mathcal N}_{\rm{Avo}} \) is the Avogadro *number* (equal to g/Da) and ent represents one entity. It makes sense, therefore, to interpret amount of substance as an aggregate of a *general* number of entities: *n*(X) = *N*(X) ent—an easily grasped concept. A ‘reciprocal Avogadro *constant*’ is thus seen to actually be exactly one entity. One mole then corresponds to setting *N*(X) = \( {\mathcal N}_{\rm{Avo}} \), for which the total mass is the relative entity mass in grams—conforming to the original mole concept.

## Keywords

Amount of substance Avogadro constant Mole Entity## References

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