### Thermodynamics: Mole

- Mole 🢀
- Gas Volume
- States of Matter
- Heat
- Enthalpy
- Thermodynamics
- Adiabatic Process
- Mass Energy Conservation
- Carnot Engine

A mole is a counting unit and means 6.02214076 × 10^{23} 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 × 10^{23} 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 × 10^{23} = 1 g.
1 mole of a compound with K atoms per molecule has the mass K grams.
For example, 1 mole of carbon ^{12}C has the mass 12 g
and 1 mole of water H_{2}O 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 H_{2}O → 2 H_{2} + O_{2}

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 |
---|---|

H_{2} | 2 * 1 = 2 |

O_{2} | 2 * 16 = 32 |

H_{2}O | 2 * 1 + 16 = 18 |

2 H_{2} O [2 * 18 g] → 2 H_{2} [2 * 2 g] + O_{2} [32 g]

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

Remark:

The number N = 6.02214076 × 10^{23} is called the **Avogadro number**
after the scientist Amedeo Avogadro (1776–1856).