UNIT OF THE MONTH April 2019: Mole

602 214 076 000 000 000 000 000, or approximately 602 trillion, has 24 digits. As unimaginably large as this number may seem to us, we encounter trillions of things constantly in everyday life! In a standard balloon, for example, there are about 50 trillion air molecules (that means about 39 trillion nitrogen molecules, 10 trillion oxygen molecules and half a trillion argon atoms). A standard painkiller contains around 1.7 trillion molecules of the active ingredient – for example acetylsalicylic acid. One litre of mineral water contains about 1 trillion sodium atoms. As you can see: large quantities appear when we look at extremely small things, such as atoms and molecules. In physics and chemistry, atoms and molecules are very often dealt with, but scientists don’t always want to juggle with such large numbers. This is why large particle numbers are combined into a kind of "imaginary count bundle" and this bundle is the unit of the month for April: the mole, the unit of an amount of substance.

By using the mole, particle numbers can be expressed in a much more manageable way. Instead of "in a balloon there are about 10 trillion oxygen molecules" we can say, "in a balloon there are about 0.02 mole of oxygen". The conversion factor between the number of particles and the amount of substance (and in a way and our special count bundle) is the so-called Avogadro constant NA. This states that one mole contains 602 214 076 000 000 000 000 000 particles. Needless to say, we usually don't care about the number of oxygen atoms in a balloon. However, in medicines or food, and many other areas of life, it is important to know how much there is of something. In pharmacy and analytical chemistry, for example, the amount of substance and the so-called molar quantities are used all the time, because it is easier to calculate with sizes such as "0.01 mol per litre" instead of "6 022 140 760 000 000 000 particles per litre".

At the beginning of the 20th century, before the amount of substance was introduced as a physical quantity with the associated unit mole, terms such as "gram atom" and "gram molecule" were used to describe quantities of chemical elements or compounds. These quantities referred to the relative atomic or molecular weights. The reference value for these relative weights was the atomic weight of oxygen, which was generally agreed to be 16. After some disagreement between physics and chemistry as to which oxygen is meant exactly [1], the International Union of Pure and Applied Physics (IUPAP) and the International Union of Pure and Applied Chemistry (IUPAC) agreed in 1960 to assign the value of 12 to the so-called atomic weight of the isotope [2] made of carbon with the mass number 12 (12C), correctly referred to as the relative atomic mass Ar(12C). From then on, this was used as the reference value.

At the suggestion of IUPAP, IUPAC and ISO, a definition of the mole as a unit for the quantity of the substance was developed at the end of the 1960s. Decided at the 14th General Conference on Weights and Measures (CGPM) in 1971, it has applied within the International System of Units (SI) until today, and will do so until 19 May 2019. It reads: 

  1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram 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.

From 20 May 2019, the definition of the mole will be as follows:

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 the unit mol1 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.

What does this change mean for the mole? Even if the two definitions look very different at first glance, in reality the answer is: not much. As for all the other basic units, a constant is the basis of the definition from May 20 onwards. In the case of the amount of substance and its unit, the mole, it is the Avogadro constant. Yet, even if this constant is not explicitly mentioned in the formulation valid until May 19, 2019, it is already closely linked to the current definition, as the Avogadro constant corresponds to the number of particles contained in 12 g of the carbon isotope 12C.

How much or few many things can represent is clearly illustrated by the mole, the unit of the month in April. Let’s take 602 trillion (or one mole) molecules of water. All this fits into a single egg cup. But, if you placed just 0.01 mole of eggs upright next to each other, you could cover an area as large as the surface of our sun [3]. How many eggs is that? Put it this way, even if every person alive today found an Easter egg every minute – it would take over a hundred million years to find one mole of Easter eggs. Can you think of any more number games and thought experiments? Feel free to write to us and tell us your ideas! Whoever writes the 602-trillionth message gets a hand-painted Easter egg.

[1] Oxygen occurs in nature in three different isotopes [2]. By means of physical measuring methods these isotopes can be separated due to their different masses. In physics, the value 16 was attributed to the lightest oxygen isotope. In chemistry, the value 16 was attributed to the natural mixture of isotopes, which for them was the naturally occurring element oxygen.

[2] Isotopes of an element have the same number of protons in the atomic nucleus, but different numbers of neutrons. The atoms of different isotopes of an element therefore have different weights. Oxygen has three different natural isotopes; all have 8 protons in the atomic nucleus, the isotope 16O has 8 neutrons, 17O has 9 neutrons and 18O has 10 neutrons in the atomic nucleus in addition to the 8 protons.

[3] With 1 mol of eggs you could stack 100 layers of densely packed eggs on the sun. This is of course only a thought experiment! There would be many difficult boundary conditions for the actual implementation. And a huge amount of scrambled eggs.