## Stoichiometry and the mole concept

### The mole

A mole of a substance is the amount of substance that contains the same number of particles as the number of carbon atoms in 12 grams of carbon-12.

12 g of carbon-12 contains 602 000 000 000 000 000 000 000 carbon atoms!
This number is known as the Avogadro constant or Avogadro number and is conveniently written in standard form as 6.02 × 1023.

Since the number of atoms in 12 g of carbon-12 is equal to the Avogadro number we can also define a mole of a substance as follows:

A mole of a substance is the amount of substance that the Avogadro number of particles.

In both definitions we defined the mole in terms of the number of particles. These particles represent the smallest unit of the substance being referred to and they can either be atoms, molecules or ions. For example, one mole of:

• a monoatomic substance like carbon contains 6.02 × 1023 atoms of C.
• a diatomic element like hydrogen gas contains 6.02 × 1023 molecules of H2.
• a covalent compound like water contains 6.02 × 1023 molecules H2O.
• an ionic compound like sodium chloride contains 6.02 × 1023 ions of sodium (Na+) and 6.02 × 1023 ions of chlorine (Cl).

### Mass of 1 mole of a substance (molar mass)

Molar mass is the mass of one mole of a substance.

Molar mass of a substance is numerical equal to the relative atomic mass (Ar) or relative molecular (Mr) of that substance expressed in grams. For example:

• sodium is an element made of single sodium atoms and its Ar is 23. This means that the molar mass of sodium is 23 grams.
• nitrogen is an element made up of pairs of atoms (diatomic). The Ar of each nitrogen atom is 14 and since nitrogen is diatomic, the Mr of nitrogen gas (N2) is 28. This means that the molar mass of nitrogen gas is 28 grams.

### Converting moles to mass

To calculate the mass of a substance given the number of moles, you use the following formulae:

Mass of a substance = number of moles × molar mass

For example, calculate the mass of:

1. 0.1 moles of carbon atoms.
2. 0.2 moles of nitrogen molecules.
3. 0.5 moles of water molecules.
4. 10 moles of carbon dioxide.

1. Ar of carbon = 12

Molar mass of carbon atoms = 12 g

Mass of a substance = number of moles × molar mass

Mass = 0.1 × 12 g

= 1.2 g

2. Mr of nitrogen gas = 28

Molar mass of nitrogen gas = 28 g

Mass of a substance = number of moles × molar mass

Mass = 0.2 × 28 g

= 5.6 g

3. Mr of water = 18

Molar mass of water = 18 g

Mass of a substance = number of moles × molar mass

Mass = 0.5 × 18 g

= 9 g

4. Mr of carbon dioxide = 44

Molar mass of carbon dioxide = 44 g

Mass of a substance = number of moles × molar mass

Mass = 10 × 44 g

= 440 g

### Converting mass to moles

To calculate number of moles, given mass of a substance, just rearrange the above formula to get:

Number of moles = $latex \frac{mass}{molar\ mass}$

For example, calculate the number of moles of oxygen molecules in 64 g of oxygen?

Number of moles = $latex \frac{mass}{molar\ mass}$

Number of moles = $latex \frac{64}{32}$

= 2 moles of oxygen molecules.