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Publicly Available Published by De Gruyter June 14, 2019

The mole and IUPAC: a brief history

Roberto Marquardt
From the journal Chemistry International


The mole is the unit of amount of substance in the International System of Units (SI). The amount of substance of a system is a measure of the number of specified elementary entities defining that system. As a matter of fact, the mole is the sole unit currently in use for amount of substance.

Its former definition was given in 1971 and reads as follows [1]: “1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kg of carbon-12; its symbol is ’mol.’ 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.” The year 1971 marks the end of a rather long debate that took place in the first half of the 20th century, and in the course of which the need to introduce the quantity amount of substance, an appropriate unit for it, and the differentiation between both were thoroughly discussed. The present text gives a brief account of this history, and sheds light on the role played be the International Union of Pure and Applied Chemistry (IUPAC) in the formation of the concepts underlying this quantity and the definition of its unit.

With the publication of a Technical Report [2] and a Recommendation [3], IUPAC was also quite influential in the new definition of the mole, which was adopted by the 26th General Conference of Weights and Measures on 16 November 2018, and which came into force, together with the definitions of the kilogram, the ampere and the kelvin on 20 May, the “World Metrology Day,” 2019. The new definition of the mole reads [4]: “The mole, symbol mol, is the SI unit of amount of substance. 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 mol-1, and is called the Avogadro number.” We shall return to this more recent evolution of the mole at the end of this very brief historical review.

The history of the mole is closely related to the history of the quantity amount of substance and that of the Avogadro constant. Ref. [2] covers a small portion of this history and the reader is referred to further references cited therein, which are not exhaustive either. Here we mention only a few points, partly from the original literature, that will be of relevance for the aforementioned definitions of the mole.

Wilhelm Ostwald (1853-1932) introduced the “Mol” (mole in German), probably in 1893 [5]. However, he used this term to mean “molecular weight in gram”: “We generally call one mole the weight in grams that is numerically identical with the molecular weight of a given substance” (translated sentence on page 119, ref. [5]). In 1900 Max Planck (1858-1947) determined the value of the Avogadro constant from his famous law on the blackbody radiation [6]. He wrote (on page 244): “To one gram-molecule of a substance correspond 6,175 1023 molecules.” In 1905 Albert Einstein (1879-1955) developed a theory of the Brownian motion, from which he derived a formula that enabled an additional determination of the Avogadro constant (it is the formula on page 560 of ref. [7]). In a subsequent paper [8] he added the precision that “N is the number of real particles in one gram-molecule” (he wrote ’Grammmolekül’).

          E. A. Guggenheim, courtesy of Prof. I. M. Mills, Reading

E. A. Guggenheim, courtesy of Prof. I. M. Mills, Reading

Indeed, scientists in those days were referring to an extensive quantity (N), but meaning an intensive quantity, such as N/m, where m is the mass of N particles. Today we would write N/n. The quantity n is the amount of substance. However, it was neither explicitly mentioned in those days, nor was the need discussed to introduce a special unit for it.

Jean Perrin (1870-1942) verified Einstein’s formula experimentally in 1909 and obtained, in today’s language, N/n ≈ 70 1022 mol-1. But he did not use n! He wrote [9, page 16]: “This invariable number is a universal constant that merits to be called the Avogadro constant.”

Perrin also wrote [9]: “It has become common language to call gram-molecule (’molécule-gramme’) of a body the mass of this body which occupies, in the gaseous state, the same volume as 2 g of hydrogen at the same temperature and pressure. Avogadro’s proposition then reads: ‘Any two gram-molecules contain the same number of molecules.’”

Very clearly a quantity was there that scientists were referring to as the “number of particles occupying a given volume,” without calling it a number density, or the “number of particles contained in a mass that is equivalent to a molecular weight,” without calling it amount of substance. The need to introduce the concept of the amount of substance, hidden so far, was obvious. The name gram-molecule was introduced to serve as a short-cut for a measurement unit of a quantity that was not actually a mass. That name was more than clumsy, because it uses a unit (gram) while referring to a quantity (weight or mass). Rather than being a clarification, it further increased the confusion. Until the 1960s one used to read: “1 mole of water is 18.016 grams.” In an article of 1961 [10] one can read: “The result is a multiplicity of units which does not appeal to the scientific mind.” The mixing up of units and quantities, whether interrelated or not, became a nightmare, in particular in chemistry education.

In physics, clarifying steps have been undertaken somewhat earlier. In 1957, the Commission for Symbols, Units and Nomenclature (SUN) of the International Union of Pure and Applied Physics (IUPAP) formulated a recommendation (published in ref. [11]) to consider the unit “mole” as a unit for “quantity of substance”.

In 1961 Edward Guggenheim (1901-1970) wrote [12]: “…it is hoped that the term ’atomic weight’ may fall into disuse so that eventually it may become unnecessary to explain to every novice that ’atomic weight’ does not mean weight of an atom.” Further: “During the past score of years the view has been accepted by a rapidly increasing number of physicists and chemists that there is a third quantity different from mass and weight but proportional to both. This quantity was first named ‘Stoffmenge’ in German and the English translation is ‘amount of substance.’” In the last citation, Guggenheim was referring to a name mentioned by Ulrich Stille (1910-1976) [13].

Finally, Guggenheim wrote [12]: “The mole is the amount of substance containing the same number of molecules (or atoms or radicals or ions or electrons as the case may be) as there are atoms in 12 grams of 12C.” Guggenheim was a member of the SUN Commission of IUPAP and the Commission of Symbols, Terminology and Units (Commission I.1) of of the Physical Chemistry Division (Division I) of IUPAC [14, page 312]. In the minutes of the Council meeting at the 22nd IUPAC Conference in 1963 one can read that Commission I.1 was authorized to revise the Manual on Physico-chemical Symbols and Terminology, and that it was instructed to pay particular attention to the definition of the mole as a unit of the quantity of substance as well as to the adoption of the abbreviation mol proposed by IUPAP. Guggenheim’s recommendation was adopted by the IUPAC Council at Cortina d’Ampezzo in 1969 [15]. The liaison with the IUPAP SUN Commission and the Technical Committee 12 of the International Organization for Standardization (ISO/TC 12) on this recommendation is explicitly mentioned in ref. [15].

Later, in 1971, it was adopted, in a slightly modified wording, as resolution 3 by the 14th General Conference of Weights and Measures, by which the mole was included as a base unit of the SI (see above). Both IUPAP and IUPAC recommendations are explicitly mentioned in ref. [1].

          the cover page of the 1971 resolution from the Bureau International des Poids et Mesures

the cover page of the 1971 resolution from the Bureau International des Poids et Mesures

In the 1980s, the idea came up to redefine the kilogram and with it other units of base quantities of the SI [16], and in 2005 preparative steps towards redefining the kilogram, ampere, kelvin and mole started to be taken [17].

In 2013 IUPAC launched a project with the aim to critically review the then proposed new definitions in the SI of fundamental chemical quantities and their impact on chemical communities (IUPAC project 2013-048-1-100). In this project, published work related to the definition of the quantity amount of substance, and its unit, the mole, was compiled, discussed and critically reviewed, together with the consequences of these definitions on the unit of the quantity mass, the kilogram. All possible aspects were assembled in order to enable IUPAC to judge the adequateness of the existing definitions or new proposals. Compilation and critical review relies on the broadest spectrum of interested IUPAC members.

The Technical Report [2] is one result of this project. The report also covers aspects related to chemical education and one particular result is alarming: only about 2 out of 10 students at High School or initial University level know the physical quantity ’amount of substance,’ and even less know the 1971 definition of its unit, the mole. A replacement of the definition of the mole seemed then to be mandatory alone for educational reasons.

The definition text proposed until September 2017 to replace the current definition was technically correct, but difficult to understand, in particular to less specialized readers [2]. As a result, IUPAC issued a Recommendation [3] which had a positive impact on the aforementioned new definition of the mole. Future generations of chemists will learn this new definition and will finally benefit from the fact that the “Avogadro number” is now properly defined.

The author acknowledges help from Prof. Ian Mills and members of the task group involved in the IUPAC project 2013-048-1-100.


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Online erschienen: 2019-06-14
Erschienen im Druck: 2019-07-01

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