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The actual masses of atoms and molecules are too small to be of practical use in calculations. Therefore a special quantity, called a mole, is used.

In terms of mass, a mole (mol) is the relative atomic mass (A_r) of an element in grams, or the relative formula mass (M_r) in grams if it's a compound. Examples for elements and compounds are given in the table below, along with its formula, relative formula mass (RFM) and the mass of 1 mole.

Avogadro constant

As the mole quantity is based on the relative masses of atoms, there is a relationship between a mole of a substance and the number of particles it contains. As atoms and molecules are so small the number in a mole is very large. This number is called the Avogadro constant, and it is equal to: 602,000,000,000,000,000,000,000 (= 6.02 × 10²³) formulae units.

The Avogadro constant is defined as: the number of carbon atoms in exactly 12 g of carbon-12, ¹²C.

One mole, 1 mol, of a substance is defined as: the Avogadro constant number of particles (which is 6.02 × 10²³ atoms, molecules, formulae or ions of that substance).

For example:

• the formula of methane is CH₄
• the relative atomic mass (A_r) of C = 12
• the A_r of H = 1
• so the relative formula mass (M_r) of CH₄ = 12 + (4 × 1) = 16
• so 1 mole of methane = 16 g of methane and contains 6.02 × 10²³ molecules
• 16 g of methane = 6.02 × 10²³ as there are 5 atoms in each formulae (molecule)
• 16 g of methane = 5 × 6.02 × 10²³ = 3.01 × 10²⁴ atoms

Calculating the number of particles

The number of particles of a substance can be calculated using:

• the Avogadro constant number (6.02 × 10²³)
• the amount of substance in mole

Number of particles = 6.02 × 10²³ × mol

Example

Calculate the number of water molecules in 0.5 mol of water.

Number of water molecules = 6.02 10²³ × 0.5

= 3.01 × 10²³

It is important to be clear about the particles involved. For example, 3.01 × 10²³ water molecules contain 9.03 × 10²³ atoms. This is because a water molecule, H₂O, contains three atoms.