Mole Concept and Molar Masses

The Need for a Counting Unit

Atoms and molecules are extremely small in size, and their numbers in even a small amount of any substance are really very large. To handle such large numbers, a unit of convenient magnitude is required — just as we denote one dozen for 12 items, score for 20 items, or gross for 144 items, chemists use the idea of the mole to count entities at the microscopic level (atoms, molecules, particles, electrons, ions, etc.).

In the SI system, the mole (symbol mol) was introduced as the seventh base quantity for the amount of a substance.

The Definition of a Mole

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 a specified group of particles.

To appreciate the largeness of this number, the book writes it out with all its zeroes, without powers of ten:

Hence, so many entities (atoms, molecules or any other particle) constitute one mole of a particular substance. We can therefore say:

• 1 mol of hydrogen atoms = $6.022 \times 10^{23}$ atoms
• 1 mol of water molecules = $6.022 \times 10^{23}$ water molecules
• 1 mol of sodium chloride = $6.022 \times 10^{23}$ formula units of sodium chloride

Determining the Avogadro Number

How was this enormous number determined? The key lies in the carbon-12 atom. The mass of a single carbon-12 atom was determined by a mass spectrometer and found to be $1.992648 \times 10^{-23}$ g. Knowing that one mole of carbon weighs 12 g, the number of atoms in it is equal to:

This experimentally determined value underlies the exact number fixed in the modern definition above. For most practical calculations we use the rounded value $6.022 \times 10^{23}$.

Molar Mass

Having defined the mole, it is easier to know the mass of one mole of a substance or its constituent entities: