Amount of Substance (C3.2)

The mole

One mole of any substance contains 6.02 × 10²³ particles (Avogadro's constant, Nₐ). This is the relative formula mass in grams.

Mole equations:

moles = mass (g) / Mᵣ
mass (g) = moles × Mᵣ
Mᵣ = mass / moles

Example: How many moles in 9 g of water (Mᵣ = 18)?
moles = 9 / 18 = 0.5 mol

Mole ratios from balanced equations

The coefficients in a balanced equation give the mole ratio of reactants and products.

Example: 2H₂ + O₂ → 2H₂O
2 mol H₂ reacts with 1 mol O₂ to produce 2 mol H₂O.

Worked example: How many grams of iron can be made from 80 g of Fe₂O₃?
(Fe₂O₃ + 3CO → 2Fe + 3CO₂; Mᵣ: Fe₂O₃ = 160, Fe = 56)

• Moles Fe₂O₃ = 80/160 = 0.5 mol
• Ratio 1:2 → moles Fe = 1.0 mol
• Mass Fe = 1.0 × 56 = 56 g

Limiting reactants

In a reaction, the limiting reactant is the one that is completely used up first — it determines how much product is made. The other reactant is in excess.

Identifying the limiting reactant: calculate moles of each reactant; compare to the mole ratio in the equation; the one with the smaller mole/ratio value is limiting.

Example: 4 g H₂ + 32 g O₂ → H₂O
Moles H₂ = 4/2 = 2 mol; moles O₂ = 32/32 = 1 mol.
Ratio H₂:O₂ = 2:1 → exactly right — neither is limiting (stoichiometric).

Example with excess: 4 g H₂ + 16 g O₂
Moles H₂ = 2 mol; moles O₂ = 0.5 mol.
Needed: 2 mol H₂ requires 1 mol O₂; only 0.5 mol O₂ available → O₂ is limiting.

Concentration

Concentration of a solution = amount of solute dissolved per unit volume of solution.

concentration (mol/dm³) = moles ÷ volume (dm³)
moles = concentration × volume

Also: concentration (g/dm³) = mass (g) ÷ volume (dm³)

Convert: 1 dm³ = 1 litre = 1000 cm³. So 250 cm³ = 0.25 dm³.

Worked example: What mass of NaCl is in 250 cm³ of 2.0 mol/dm³ solution? (Mᵣ NaCl = 58.5)
moles = 2.0 × 0.25 = 0.5 mol
mass = 0.5 × 58.5 = 29.25 g

Common exam errors

1. Dividing mass by Aᵣ instead of Mᵣ for compounds.
2. Forgetting to convert cm³ to dm³ in concentration calculations (÷ 1000).
3. Not identifying the limiting reactant from moles — must compare to the equation ratio.