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### Thermodynamics: Mole

A mole is a counting unit and means 6.02214076 × 1023 items. Let us denote this number by N. We know other counting units like a "dozen" which is 12 items. So, 1.5 dozen eggs are 18 eggs, and 1.5 moles atoms are 30 × 1023 atoms.

So far, so good. But why was such a strange number chosen to count items like atoms, molecules, ions or electrons? This has something to do with mass of atoms. The mass of an atom is about 1.660538921 × 10-24 g. So, 1 mole of atoms has the mass N * 1.998467052 × 1023 = 1 g. 1 mole of a compound with K atoms per molecule has the mass K grams. For example, 1 mole of carbon 12C has the mass 12 g and 1 mole of water H2O has the mass 2 * 1 + 16 = 18 g.

Moles useful for computing the mass balance in chemical reactions. For example, the electrolysis of water proceeds according to:

2 H2O → 2 H2 + O2

This means that 2 molecules of water are decomposed into 2 molecules of hydrogen and 1 molecule of oxygen. This proportionality is valid for any number of molecules, so also for moles: 2 moles of water are decomposed into 2 moles of hydrogen and 1 mole of oxygen. The mole weights of the substances are by the number of atoms in the respective molecules:

Substance Mol weight
H2 2 * 1 = 2
O2 2 * 16 = 32
H2O 2 * 1 + 16 = 18

2 H2 O [2 * 18 g] → 2 H2 [2 * 2 g] + O2 [32 g]

The electrolysis of 36 g water produces 4 g of hydrogen and 32 g of oxygen.

Remark:
The number N = 6.02214076 × 1023 is called the Avogadro number after the scientist Amedeo Avogadro (1776–1856).