To cut a long story short¹, the mole (abbreviated 'mol') is a fundamental unit, defined as 'the amount of substance which contains as many particles as there are atoms in 12 g (grammes) of ¹²C'. And 12 g of ¹²C contain approximately² 6.022 10²³ atoms. A few obvious questions are promptly raised: 'Why would one use such a complicated number?' and 'What is it good for?'

Some people have defined practical chemistry as being glorified cookery. That being the case, if one was baking a cake, one would need to measure out the requisite quantities of ingredients. This is usually done by weighing. The chemist on the other hand is often needing to synthesise new compounds. In order to make a compound, he will follow a recipe, much like baking a cake. However, a chemist needs to mix together precisely the correct amounts of starting materials, in an ideal case, according to the chemical equation. For example, a neutralization reaction (see also Acidity and Basicity)³:

NaOH + HCl -> NaCl + H₂O

Sodium hydroxide reacts with hydrochloric acid on a 1:1 ratio to form sodium chloride (~ table salt) and water in a ratio of 1:1. Any other ratio will leave an excess of hydroxide or acid, resulting in an alkaline or acidic product. So, to get the desired result, a neutral product, with no excess of base or acid, the reacts (sp?) have to be mixed together in the exact proportions, molecule-wise⁴.

The problem now is that the NaOH and the HCl molecules have different molecular masses (6.6 10^-26 kg and 6.0 10^-26 kg). So simply adding 100 grammes of NaOH and 100 grammes of HCl will not lead to the desired result, there will be an excess of HCl, as there are more HCl molecules in 100 grammes than NaOH. To make things right chemists have to known how many molecules are in a given mass, in grammes, of a certain substance. In that way it is possible to achieve the ideal ratio by weighing the substances and mixing them together.

So, it is not difficult, but complicated to calculate the mass of a molecule, finding out how many of them are in a given mass and then calculating how much mass is needed of the other compound so that the ratios fit, all using numbers with absurd exponents like 10^-20. This is the reason why chemists came up with the concept of the 'mole'. It makes calculations in terms of number of atoms astonishingly easy. One mole is a conversion factor between atomic mass units, which are tabulated in the periodic table and add up for every molecule⁵, and grammes.

Using the previous example, the calculation goes like this: The molecular mass of NaOH is 40 in atomic units⁶. So 100 grammes of NaOH correspond to 2.5 moles (100/40) of NaOH (or 15.1 10²³ molecules). To carry out a neutralization raction with this amount of NaOH, 2.5 moles of HCl (molecular mass is 36.5 atomic units) are needed, which correspond to 91.25 grammes (2.5 x 36.5)⁷.