Accreditation and Quality Assurance

, Volume 21, Issue 3, pp 231–236 | Cite as

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

  • B. P. Leonard
Discussion Forum


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.


Amount of substance Avogadro constant Mole Entity 


  1. 1.
    De Bièvre P (2015) Clarity about the base quantity ‘amount of substance is required before (re)definition of the associated base unit mole is meaningful. Accred Qual Assur 20:441–443CrossRefGoogle Scholar
  2. 2.
    Furio C, Azcona R, Guisasola J (2002) The learning and Teaching of the concepts of amount of substance and mole: a review of the literature. Chem Educ Res Pract 3:277–292CrossRefGoogle Scholar
  3. 3.
    Fang S-C, Hart C, Clarke D (2014) Unpacking the meaning of the mole concept for secondary school teachers and students. J Chem Educ 91:351–356CrossRefGoogle Scholar
  4. 4.
    BIPM, SI Brochure [8th edition, 2006; updated 2014]
  5. 5.
    Leonard BP (2007) The atomic-scale unit, entity: key to a direct and easily understood definition of the SI base unit for amount of substance. Metrologia 44:402–406CrossRefGoogle Scholar
  6. 6.
    Leonard BP (2010) Comments on recent proposals for redefining the mole and kilogram. Metrologia 47:L5–L8CrossRefGoogle Scholar
  7. 7.
    Leonard BP (2010) Why the invariant atomic-scale unit, entity, is essential for understanding stoichiometry without ‘Avogadro anxiety’. Accred Qual Assur 16:133–141CrossRefGoogle Scholar
  8. 8.
    Leonard BP (2011) Alternative interpretations of the mole and the ideal gas equation. Accred Qual Assur 16:577–581CrossRefGoogle Scholar
  9. 9.
    Leonard BP (2012) Why the dalton should be redefined exactly in terms of the kilogram. Metrologia 49:487–491CrossRefGoogle Scholar
  10. 10.
    Leonard BP (2014) The mole is an Avogadro number of entities, the macroscopic unit for chemical amount. Accred Qual Assur 19:213–220CrossRefGoogle Scholar
  11. 11.
    Milton JT (2011) A new definition for the mole based on the Avogadro constant: a journey from physics to chemistry. Philos Trans R Soc A 369:3993–4003CrossRefGoogle Scholar
  12. 12.
    Perrin JB (1909) Mouvement Brownien et réalité moléculaire. Ann Chim Phys 18:5–114 [trans: Soddy F (1910) Brownian movement and molecular reality, Taylor and Francis (London)].
  13. 13.
    International Avogadro Project (2015)
  14. 14.
    Massa E, Nicolau A (2011) International determination of the Avogadro constant. Metrologia 48 (Foreword)Google Scholar
  15. 15.
    Mohr PJ, Newell DB, Taylor BN (2015) CODATA recommended values of the fundamental physical constants 2014. arXiv:1507.07956v1
  16. 16.
    Leonard BP (2011) The avo (Av), gali (G), entity (ent) and exact dalton. Accred Qual Assur 16:173–174CrossRefGoogle Scholar
  17. 17.
    Mills IM, Mohr PJ, Quinn TJ, Taylor BN, Williams ER (2006) Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005). Metrologia 43:227–246CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.The University of AkronAkronUSA

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