IGCSE Chemistry 0620

Topic: Stoichiometry - Relative Masses of Atoms and Molecules

Objective: Calculate reacting masses in simple proportions. Calculations will not involve the mole concept.

Understanding Relative Mass

The relative mass of an atom or molecule is a comparison of its mass to the mass of a carbon-12 atom, which is defined as 12 atomic mass units (amu). We often use the term 'relative atomic mass' (Ar) for atoms and 'relative molecular mass' (Mr) for molecules.

Example: The relative atomic mass of Hydrogen (H) is approximately 1. The relative atomic mass of Oxygen (O) is approximately 16.

Calculating Reacting Masses

When substances react, the mass of the reactants and products are related by simple proportions. We can use the relative masses to calculate the mass of one substance if the masses of the other substances are known.

The basic principle is: mass = (mass of reactant) x (mass fraction of reactant)

Where the mass fraction of a reactant is its relative mass divided by the sum of the relative masses of all reactants.

Worked Examples

Example 1: Mass of Oxygen Produced

When magnesium burns in oxygen, magnesium oxide is formed. 1 gram of magnesium reacts completely with 40 grams of oxygen.

Calculate the mass of oxygen produced when 20 grams of magnesium react.

1. Identify the reactants: Magnesium (Mg) and Oxygen (O₂)
2. Find the relative masses: Ar(Mg) = 24, Mr(O₂) = 32
3. Calculate the mass fraction of oxygen: $$ \text{Mass fraction of O}_2 = \frac{\text{Mr(O}_2)}{\text{Ar(Mg) + Mr(O}_2)} = \frac{32}{24 + 32} = \frac{32}{56} = \frac{4}{7} $$
4. Calculate the mass of oxygen produced: $$ \text{Mass of O}_2 = \text{mass of Mg} \times \text{Mass fraction of O}_2 = 20 \text{ g} \times \frac{4}{7} = \frac{80}{7} \approx 11.4 \text{ g} $$

Example 2: Mass of Product Formed

When carbon dioxide is decomposed, 44 grams of carbon dioxide produce 12 grams of carbon and 32 grams of oxygen.

Calculate the mass of carbon dioxide that produces 24 grams of carbon.

1. Identify the reactants and products: Carbon Dioxide (CO₂), Carbon (C), Oxygen (O₂)
2. Find the relative masses: Mr(CO₂) = 44, Ar(C) = 12, Mr(O₂) = 32
3. Calculate the mass fraction of carbon dioxide: $$ \text{Mass fraction of CO}_2 = \frac{\text{Mr(CO}_2)}{\text{Ar(C) + Mr(O}_2 + \text{Ar(C)})} = \frac{44}{12 + 32 + 12} = \frac{44}{56} = \frac{11}{14} $$
4. Calculate the mass of carbon dioxide: $$ \text{Mass of CO}_2 = \frac{\text{mass of C}}{\text{Mass fraction of CO}_2} = \frac{24 \text{ g}}{\frac{11}{14}} = \frac{24 \times 14}{11} = \frac{336}{11} \approx 30.5 \text{ g} $$

Table of Relative Masses

Substance	Relative Atomic Mass (Ar)	Relative Molecular Mass (Mr)
Hydrogen (H)	1	2
Carbon (C)	12	12
Oxygen (O)	16	32
Nitrogen (N)	14	28
Sodium (Na)	23	23
Chlorine (Cl)	35.5	35.5
Water (H2O)	2	18
Carbon Dioxide (CO2)	12	44

Note: These are approximate values. The exact values can vary slightly depending on the source.