What you'll learn
The mole is the chemist's way of counting atoms and molecules, and it lets us calculate the masses of substances in reactions. In this guide you will learn the meaning of relative formula mass, what a mole is, how to use the relationship between mass, moles and Mr, how to find reacting masses from balanced equations, the idea of limiting reactants, and how to work with concentrations of solutions. These quantitative skills appear throughout the higher-mark calculation questions.
Key terms and definitions
Relative atomic mass (Aᵣ) — the average mass of an atom of an element relative to ¹²C.
Relative formula mass (Mᵣ) — the sum of the relative atomic masses of all the atoms in a formula.
Mole — the unit for amount of substance; one mole contains 6.02 × 10²³ particles (the Avogadro constant).
Limiting reactant — the reactant that is completely used up, stopping the reaction.
Concentration — the amount of solute in a given volume of solution (g/dm³ or mol/dm³).
Conservation of mass — the total mass of reactants equals the total mass of products.
Core concepts
Relative formula mass
The relative formula mass (Mᵣ) of a compound is found by adding up the relative atomic masses of all the atoms in its formula. For example, for water (H₂O): (2 × 1) + 16 = 18. For calcium carbonate (CaCO₃): 40 + 12 + (3 × 16) = 100. In a balanced equation, the total Mᵣ of the reactants equals the total Mᵣ of the products (conservation of mass).
The mole
A mole is an amount of substance containing 6.02 × 10²³ particles (the Avogadro constant). One mole of any substance has a mass in grams equal to its relative formula mass. So one mole of water weighs 18 g, and one mole of carbon weighs 12 g.
Mass, moles and Mr
The central relationship is:
moles = mass (g) ÷ Mᵣ
Rearranged: mass = moles × Mᵣ and Mᵣ = mass ÷ moles. Use this to convert between the mass of a substance and the number of moles.
Reacting masses from equations
A balanced equation gives the ratio of moles of reactants and products. To find a reacting mass:
- Work out the moles of the substance you know (mass ÷ Mᵣ).
- Use the equation's ratio to find the moles of the substance you want.
- Convert back to mass (moles × Mᵣ).
This lets you predict how much product forms, or how much reactant is needed.
Limiting reactants
When reactants are not in the exact ratio, one runs out first — the limiting reactant. It is completely used up and determines how much product is formed. The other reactant is in excess (some is left over). To find the limiting reactant, compare the moles of each (allowing for the equation's ratio); the one giving fewer moles of product is limiting.
Concentration of solutions
The concentration of a solution is the amount of solute per volume:
concentration (g/dm³) = mass (g) ÷ volume (dm³)
or in moles: concentration (mol/dm³) = moles ÷ volume (dm³). Remember 1 dm³ = 1000 cm³, so divide a volume in cm³ by 1000 to get dm³. A higher concentration means more solute in the same volume.
Worked examples
Example 1: Relative formula mass
Calculate the Mᵣ of carbon dioxide, CO₂ (Aᵣ: C = 12, O = 16).
Mᵣ = 12 + (2 × 16) = 12 + 32 = 44.
Example 2: Mass to moles
How many moles are in 36 g of water (Mᵣ = 18)?
moles = mass ÷ Mᵣ = 36 ÷ 18 = 2 moles.
Example 3: Concentration
250 cm³ of solution contains 20 g of solute. What is the concentration in g/dm³?
Volume = 250 ÷ 1000 = 0.25 dm³. Concentration = 20 ÷ 0.25 = 80 g/dm³.
Common mistakes and how to avoid them
Adding atomic masses wrongly. Multiply by the number of each atom (e.g. O₂ = 2 × 16 = 32).
Forgetting to convert cm³ to dm³. Divide cm³ by 1000 before using concentration formulae.
Using mass directly in equation ratios. Convert to moles first; ratios are in moles, not grams.
Misidentifying the limiting reactant. Compare moles (with the equation ratio), not just masses.
Rearranging the mole formula incorrectly. moles = mass ÷ Mᵣ; mass = moles × Mᵣ.
Exam technique for Moles and Reacting Masses
Calculate Mᵣ carefully, multiplying by the number of each atom.
Use moles = mass ÷ Mᵣ confidently and rearrange it as needed.
Follow the three-step method for reacting masses: moles → ratio → mass.
Identify the limiting reactant by comparing moles.
Convert volumes to dm³ before concentration calculations, and show all working.
Quick revision summary
The relative formula mass (Mᵣ) is the sum of the relative atomic masses in a formula (H₂O = 18, CaCO₃ = 100). A mole contains 6.02 × 10²³ particles, and one mole of a substance has a mass in grams equal to its Mᵣ. The key relationship is moles = mass ÷ Mᵣ (rearrange for mass or Mᵣ). To find reacting masses, convert the known mass to moles, use the mole ratio in the balanced equation, then convert back to mass. When reactants aren't in the exact ratio, the limiting reactant is fully used up and decides how much product forms (found by comparing moles). Concentration is amount per volume: g/dm³ = mass ÷ volume or mol/dm³ = moles ÷ volume, remembering to convert cm³ to dm³ by dividing by 1000. Calculate Mᵣ accurately, always work in moles for ratios, identify the limiting reactant by moles, convert volumes properly, and show your working step by step.