Understanding the Mole

Like many chemical terms, the mole has a long and complex history, disguised by the simplicity of its modern definition.

mole [abridged]

One mole contains exactly 6.02214076 \times 10^{23} elementary entities.

IUPAC, 20/05/19

Initially a unit of mass, like the gram-equivalent, the mole was the mass of substance with a specific potential to react with other substances.

The mole morphed into the unit for an ‘amount of substance’, based on the number of particles in a mass of reference substance (hydrogen, oxygen, oxygen-16, and eventually carbon-12).

The redefinition of the mole that came into force on the 20th of May 2019 divorced the mole from any physical measurement entirely. Prior to that, the mole was described in reference to carbon-12:

mole [abridged]

One mole contains the same number of elementary entities as there are atoms in 12 grams of carbon-12.

IUPAC, 1967-2019

While the new definition is based on the results of the superb Avogadro Project, it bears no memory of that; aptly put by Bob Bucat, the number 6.02214076 \times 10^{23} “happens to be our best estimate of the number of carbon-12 atoms in 0.012 kilogram of carbon-12”. However the number was determined, the new definition simply contains the number, without reference to its origin.

Over time, the mole has become more precisely defined, and Avogadro’s number has been more accurately measured. Now, Avogadro’s number is exact, and the mole has the simplest definition it has ever had…

So why is it still so misunderstood?

Amount of Substance

‘Amount of substance’ is the name, like ‘mass’, given to a property of matter. It is a measure of the amount of entities (e.g., particles) in a substance. It is, however, a terrible name. Rather than being brief, memorable, and identifiable (like ‘mass’ is), it is a combination of common words with many meanings. ‘Amount of substance’ does not have a strong enough connection to countable, discrete entities, or to the requisite nature of the substance. The alternative suggested by IUPAC, ‘chemical amount’, is marginally better, mainly because including the word ‘chemical’ helps to confine the scope of its application. Neither term, however, experiences the respect in education that the property deserves.

The truth is that if students were taught ‘amount of substance’ in advance of the mole, it would be a lot easier for them to gain a tangible understanding of the value and meaning of the mole.

Common Misconceptions

It is quite common to find the mole sloppily defined, even in reputable textbooks; ‘amount of substance’, ‘mole’, and ‘1 mol’ are often conflated.

The mole is often treated like a named amount like ‘dozen’. However, the mole is not simply a number, it is a unit. The unit ‘kilogram’ is not the same as ‘1 kilogram’. Likewise ‘mole’ is not the same as ‘1 mole’, and ‘mole’ is definitely not the same as 6.02214076 \times 10^{23}.

Mass is a lot easier to get a feel for, so it’s substantially easier to distinguish between ‘mass’, ‘kilogram’, and ‘1 kilogram’ than it is between ‘amount of substance’, ‘mole’, and ‘1 mol’.

\begin{array}{c c c} \textbf{property} & \textbf{unit} & \textbf{quantity} \\ \hline \text{mass} & \text{kilogram} & \text{1 kg} \\ \text{amount of substance} & \text{mole} & \text{1 mol} \end{array}

In fact, ‘amount of substance’ is rarely even introduced, to the detriment of learning. Imagine trying to teach F = ma without mass… “Force is equal to the number of kilograms times the acceleration” sounds ridiculous.

However, this is exactly what happens in chemistry with ‘amount of substance’ and the mole. The formula m = nM is often read as “mass equals number of moles times molar mass”.

The full definition of the mole highlights the proper distinctions that should be made in and out of the classroom:

The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214076 \times 10^{23} 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.

The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

IUPAC, 08/01/18

The mole is the unit for amount of substance; it is a way of describing the number of entities in a substance in a way that is convenient. It is a powerful tool that humanity chose in the same way we chose the kilogram, the second, or the meter–they frame features of the universe in terms of what humans experience in their day-to-day lives.

Do you think ‘amount of substance’ is worth teaching? Would you rather the mole was redefined as just a number? Let me know in the comments.

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