The mole

The mole is a convenient unit that allows us to count extremely large numbers of atoms and molecules.

Avogadro's constant has a value of 6.02 x 10^23^. This very large number represents how many particles are contained in one mole.

The equation linking the number of moles, the number of particles, and Avogadro's constant is:

$\text{number of moles }=\frac{\text{number of particles}}{\text{Avogadro’s constant}}$

where particles refers to atoms, molecules, or ions, electrons.

Worked example 1 - Calculating number of moles

Calculate the number of moles in 2.71 x 10^24^ molecules of chlorine.

Avogadro's constant = 6.02 x 10²³ mol^-1

Step 1: Equation

$\text{number of moles }=\frac{\text{number of particles}}{\text{Avogadro’s constant}}$

Step 2: Substitution and correct evaluation

$\text{number of moles }=\frac{(2.71\times {10}^{24})}{(6.02\times {10}^{23})}=4.50\text{ mol}$

Worked example 2 - Calculating number of atoms

Calculate the number of oxygen atoms in a 2.5 moles of oxygen atoms.

Avogadro's constant = 6.02 x 10²³ mol^-1

Step 1: Rearrange equation

Number of atoms = number of moles × Avogadro's constant

Step 2: Substitution and correct evaluation

Number of atoms = 2.5 × (6.02 × 10²³)= 1.5 × 10²⁴ atoms

Relating moles, mass, and molar mass

The molar mass (M) represents the mass in grams of 1 mole of a given substance.

• Molar mass is measured in units of grams per mole (g mol^-1).
• Molar mass is numerically equal to relative molecular/formula mass.

The equation linking the number of moles, mass in grams, and molar mass is:

$\text{number of moles }=\frac{\text{mass in g}}{\text{molar mass}}$

Or:

$n=\frac{m}{\text{M}}$

Where:

• n = number of moles (mol)
• m = mass (g)
• M = molar mass (g mol^-1^)

If molar mass (M) is be replaced by relative formula/molecuar mass (M_r_), the equation becomes:

$n=\frac{m}{{\text{M}}_{\text{r}}}$

Worked example 3 - Calculating number of moles

Calculate the number of moles in 10.0 g of water (H₂O).

Step 1: Calculate M_r of H₂O

H: 1.0 × 2 = 2.0

O: 16.0 × 1 = 16.0

M_r = 2.0 + 16.0 = 18.0 g mol^-1^

Step 2: Equation

$n=\frac{m}{M_r}$

Step 3: Substitution and correct evaluation

$\text{n }=\frac{10.0}{18.0}=0.56\text{ mol}$

Worked example 4 - Calculating mass

Calculate the mass of 7.0 moles of magnesium oxide (MgO).

Step 1: Calculate M_r of MgO

Mg: 24.3 × 1 = 24.3

O: 16.0 × 1 = 16.0

M_r = 24.3 + 16.0 = 40.3 g mol^-1^

Step 2: Equation

$m=n\times M_r$

Step 3: Substitution and correct evaluation

m = 7.0 × 40.3 = 282.1 g