What Is The Numerical Value Of Mole?
Every beginning chemistry textbook includes the mole, and teaching the mole is a recurring topic in chemical education. The mole’s official definition is as follows:
The mole is the amount of substance in a system that includes the same number of elementary entities as atoms in 0.012 kilograms of carbon 12, denoted by the sign “mol.”
The following is a definition from the 2013 draught of the new SI:
The mole, symbol mol, is the SI unit of the substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle, or a specified group of such particles; its magnitude is determined by setting the numerical value of the Avogadro constant to be precisely 6.022 141 29 1023 when expressed in the SI unit mol–1.
Let’s start with the SI Brochure when looking at formal definitions. The current and draught definitions of the mole have already been seen. The mole is defined as an amount of substance in both the recent and draught reports. “The mole… comprises as many elementary entities as [emphasis added]…”, according to the current purpose.
It does not specify what that number is, but it is the same as the number of atoms in a reference mass of a reference substance (12C) (0.012 kg). As a result, the existing definition is implicitly operational: the number of entities in a mole is determined by counting the number of atoms of 12C in 0.012 kg of that substance (which may presumably be done by some form of the experiment).
The draft definition does not use language like “as many” or indicate that it is proportional to the number of entities. It does, however, give the number of elementary entities in a mole in a fashion that no freshman chemistry instructor would employ (that is, by providing the numerical value of the Avogadro constant).
The units are all defined indirectly in the new SI by specifying the value of a physical constant. Thus, the draught SI Brochure does not state (clearly) that a mole contains precisely 6.022 141 29 1023 elementary entities; instead, it states that “… the numerical value of the Avogadro constant [is] exactly 6.022 141 29 1023 when stated in the SI unit mol–1.”
It’s worth noting that these definitions are mainly concerned with formal relationships—the mole’s relationship to a typical mass of standard material (in the current SI), a physical constant (in the new SI), and the physical quantity of substance (in the new SI) (in both).
The finding that instructors tend to use different languages is not a criticism of official definitions or textbook formulations but rather a caution that utilizing a text for one purpose when it was meant for another may not yield optimal outcomes.
The SI Brochure is more concerned with defining base quantities than establishing base units. It does not, for example, specify intuitive concepts like length or more sophisticated ones like thermodynamic temperature. It also doesn’t precisely define the amount of content, yet the following sentence could be interpreted as a definition:
The term “amount of substance” was coined by chemists to describe the number of chemical elements or compounds. The proportionality constant is a universal constant that is the same for all samples. The amount of substance is proportional to the number of specified elementary entities in an instance.
In the second quoted statement, the word “defined” is problematic. Is it supposed to be a definition in that sentence? If that is the case, it is insufficient because establishing a proportionality relationship between two quantities does not provide an adequate formal or pedagogical definition. (Imagine saying that a photon’s energy is proportionate to its frequency.
The proportionality constant is a universal regular—a valid statement, but not a sufficient definition.) Alternatively, the second sentence could relate to a description offered somewhere else—in an unidentified location. And, given the circularity of defining the amount of material with the word “amount,” the first sentence is manifestly insufficient.
Let us look at the IUPAC Gold Book before we leave the topic of official definitions. The Gold Book is useful because, as a Compendium of Chemical Terminology, it contains more terminology and quantities than the SI Brochure.
Its definitions are a little more helpful. However, looking at the entries for a few SI units and quantities reveals that they are meant to illustrate formal relationships rather than teach concepts. Here are the mass and kilogramme entries:
Mass, m: The fundamental quantity in the SI system of measurements.
Kilogramme: The SI mass unit (symbol: kg). The kilogramme is equal to the mass of the kilogram’s international prototype.
This is not the place to learn about the nature of mass.
Do official definitions imply scientific agreement?
The name of the quantity for which the mole is a unit is an example of the claim that SI definitions do not always reflect scientific consensus. Searching ACS journals for the terms “amount of substance” and “number of moles” turned up 400 research papers published since 2000 with the phrase “amount of substance” and 4388 with the words “number of moles.”
This contradicts a statement in the current SI Brochure, which reads, “The quantity used by chemists to define the amount of chemical elements or compounds is now named ‘amount of substance.'”
Whether or not chemists use the term quantity. They rarely refer to it as a substantial amount. In ACS research articles, a similar search of the same database found a marked preference for “Avogadro’s number” over “Avogadro constant.” Since 2000, 1541 research papers published in ACS journals have included the phrase “Avogadro constant” or “Avogadro’s constant,” compared to 5749 that include “Avogadro’s number” or “Avogadro number.”
A unique phrase for the quantity of which a mole is a unit—a term that does not include the word mole—is desirable. However, using the official title for this amount does not reflect the consensus of practicing chemists.
After all, the research articles for this query were published in peer-reviewed ACS publications only a few years ago—more than a generation after adopting the amount of substance as a SI base unit. It is, by any reasonable judgment, expertly written and evaluated work.