Relative Masses and Reacting Masses (No Mole)

CIE IGCSE Chemistry· 3.2· 12 min read

1. 1. Relative Atomic Mass ($A_r$) and Relative Formula Mass ($M_r$)★★☆☆☆⏱ 4 min

📘 Definition

Relative Atomic Mass ($A_r$)

The average mass of one atom of an element, compared to 1/12 the mass of one carbon-12 atom.

Example:

$A_{r}$ of hydrogen = 1, $A_{r}$ of oxygen = 16

Relative formula mass ( $M_{r}$ ) is the sum of the relative atomic masses of all atoms in a compound's chemical formula. $A_{r}$ and $M_{r}$ are relative values, so you do not need to write units for them in your answers.

📐 Worked Example

Calculate the relative formula mass of glucose, $C_{6} H_{12} O_{6}$ , using $A_{r}$ values: C=12, H=1, O=16.

1
Step 1: Count the number of each atom in the formula: 6 carbon, 12 hydrogen, 6 oxygen atoms
2
Step 2: Multiply each atom count by its $A_{r}$ value: 6×12 = 72, 12×1 = 12, 6×16 = 96
3
Step 3: Sum the values to get $M_{r}$ : 72 + 12 + 96 = 180
4
$M_r(C_6H_{12}O_6) = (6 \times 12) + (12 \times 1) + (6 \times 16) = 180$

2. 2. Law of Conservation of Mass★★☆☆☆⏱ 3 min

📘 Definition

Conservation of Mass

No atoms are created or destroyed during a chemical reaction, so the total mass of reactants equals the total mass of products in a closed system.

Example:

If 4g of hydrogen reacts fully with 32g of oxygen, 36g of water is produced.

📐 Worked Example

For the reaction: $2 M g + O_{2} \to 2 M g O$ . If 48g of magnesium reacts fully with 32g of oxygen, what mass of magnesium oxide is formed?

1
Step 1: Apply conservation of mass rule: total reactant mass = total product mass
2
Step 2: Add the masses of the two reactants: 48g + 32g = 80g
3
Step 3: The mass of magnesium oxide formed is 80g

3. 3. Calculating Reacting Masses Using Mass Ratios★★★☆☆⏱ 5 min

For balanced chemical equations, the ratio of the total relative masses of reactants and products equals the ratio of their actual reacting masses. You can use this ratio to find unknown masses without using the mole concept.

📐 Worked Example

Use the balanced equation $2 H_{2} + O_{2} \to 2 H_{2} O$ to find the mass of water formed when 8g of hydrogen reacts fully with excess oxygen. Use $A_{r}$ values: H=1, O=16.

1
Step 1: Calculate total relative mass for each substance (multiply $M_{r}$ by balancing number): 2 $H_{2}$ = 2×(2×1) = 4, 2 $H_{2} O$ = 2×18 = 36
2
Step 2: Write the mass ratio of the substances you need: $H_{2} : H_{2} O = 4 : 36 = 1 : 9$
3
Step 3: Scale the ratio to match the known mass: 1 part $H_{2}$ = 8g, so 9 parts $H_{2} O$ = 8 × 9 = 72g
4
Step 4: Verify with conservation of mass: 8g $H_{2}$ + 64g $O_{2}$ = 72g $H_{2} O$ , which is correct.

4. Common Pitfalls

Wrong move:

Forgetting to multiply $A_{r}$ by the number of atoms in a formula when calculating $M_{r}$

Why:

Leads to incorrect $M_{r}$ values that break all subsequent calculations

Correct move:

List each atom count first, multiply by its $A_{r}$ , then sum all values to get $M_{r}$

Wrong move:

Ignoring balancing numbers when calculating reacting mass ratios

Why:

The mass ratio only matches real reacting masses if you account for the number of molecules of each substance in the balanced equation

Correct move:

Multiply each substance's $M_{r}$ by its balancing coefficient before calculating the ratio

Wrong move:

Adding units to $A_{r}$ or $M_{r}$ values

Why:

$A_{r}$ and $M_{r}$ are relative values with no units, so adding units will lose marks

Correct move:

Only add units (usually grams) to actual reacting mass values in your final answer

Wrong move:

Using an inverted ratio (e.g. product:reactant instead of reactant:product)

Why:

Leads to an incorrect scaled mass value for the unknown substance

Correct move:

Write the ratio clearly with labels for each substance before substituting the known mass

5. Quick Reference Cheatsheet

Concept	Method	Example
Relative Atomic Mass ( $A_{r}$ )	Provided on exam front page, no calculation needed	$A_{r} (C) = 12$
Relative Formula Mass ( $M_{r}$ )	Sum of (number of each atom × $A_{r}$ of atom) in formula	$M_{r} (C O_{2}) = 12 + (2 \times 16) = 44$
Conservation of Mass	Total mass of reactants = Total mass of products	12g C + 32g $O_{2}$ = 44g $C O_{2}$
Reacting Mass Calculation	Calculate total $M_{r}$ × balancing coefficient for relevant substances Simplify to mass ratio Scale ratio to match known mass	Ratio $H_{2} : H_{2} O = 4 : 36 = 1 : 9$ , so 8g $H_{2}$ makes 72g $H_{2} O$

6. Frequently Asked

Do I need to memorise $A_{r}$ values for the exam?

No, all required relative atomic mass values are printed on the first page of your exam paper. You only need to use the provided values for calculations.

Can I use mole calculations for these questions if I know them?

Core exam questions for this subtopic do not require mole calculations, but you will still get full marks if you use them correctly. We recommend practicing the ratio method outlined here to avoid unnecessary mistakes.

Going deeper

syllabusCIE IGCSE Chemistry 0620 2026-2028 SpecificationRefer to section 3.2 for official content

What's Next

Now that you have mastered relative masses and reacting mass calculations without the mole concept, you are ready to move on to more Core stoichiometry content for CIE IGCSE Chemistry 0620. This foundational knowledge is critical for understanding how chemical reactions follow quantitative rules, which will appear in both Paper 1 (multiple choice) and Paper 2 (structured) Core exams. You will build on these skills when you learn about concentration calculations in g/dm³, another Core stoichiometry outcome, before moving to Extended content if you are taking the Extended tier. Practice as many structured reacting mass questions as possible to build confidence, and always cross-check your answers using the conservation of mass rule to catch calculation errors early.