The mole and Avogadro's constant
The mole
- Chemists count particles in groups called moles — like counting eggs in dozens.
- One mole always holds the same huge number of particles.
- The mole connects mass to number of particles.
The mole and Avogadro's constant
- One mole (mol) is the amount with as many particles as there are atoms in exactly 12 g of carbon-12.
- That number is the Avogadro constant: $N_A = 6.02 \times 10^{23}$ particles per mole.
- Always say what the particles are — atoms, molecules or ions.
Practice
One mole of any substance contains:
A mole always contains the Avogadro number of particles, 6.02 × 10²³.
Molar mass and $n = m/M$
- The molar mass $M$ is the mass of one mole, in grams — numerically equal to $A_r$ or $M_r$ (units $\text{g}/\text{mol}$).
- The key equation:
$$n = \frac{m}{M}$$
where $n$ = moles, $m$ = mass (g), $M$ = molar mass.
Practice
How many moles are in 36 g of water (M = 18 g/mol)?
n = m / M = 36 / 18 = 2 mol.
Practice
The molar mass of a substance (in g/mol) is:
The molar mass in grams equals the relative atomic or molecular mass.
Worked example
- How many moles in 36 g of water ($M = 18\ \text{g}/\text{mol}$)?
$$n = \frac{m}{M} = \frac{36}{18} = 2\ \text{mol}$$
Practice
What is the mass of 0.5 mol of NaCl (M = 58.5 g/mol)?
m = n × M = 0.5 × 58.5 = 29.25 g.
You've got it
Key idea
- one mole = $6.02 \times 10^{23}$ particles ($N_A$)
- molar mass $M$ = relative mass in grams ($\text{g}/\text{mol}$)
- $n = \dfrac{m}{M}$ (moles = mass ÷ molar mass)
- always state the particle type (atoms / molecules / ions)