Relate relative masses to moles and particle counts
Use the carbon-12 mass reference to interpret relative masses, then convert between sample mass, amount and number of specified particles.
AS Level; Cambridge International Chemistry 9701, 2025–2027 syllabus. Use the data and constants supplied for the question, show mole-ratio working, and report a justified number of significant figures. Written practice is self-checked
Before you begin
- Use common chemical symbols and formulae, and rearrange a simple equation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the unified atomic mass unit defined as?
What you will learn
- Define the unified atomic mass unit and relative masses
- Distinguish relative mass from molar mass
- Use the mole and Avogadro constant to count specified entities
Relative masses compare with one twelfth of carbon-12
The unified atomic mass unit, u, is one twelfth of the mass of one carbon-12 atom. Relative atomic mass Ar, relative isotopic mass, relative molecular mass Mr and relative formula mass compare a particle's mass with this reference. Because they are ratios, relative masses have no unit.
For a molecule, Mr is the sum of the relative atomic masses of its atoms. For an ionic solid, use relative formula mass for the formula unit; the solid is not made of separate molecules. Molar mass has units, commonly g mol⁻¹, and has the same numerical value as Ar, Mr or formula mass at the precision used.
A mole counts specified entities
One mole contains the Avogadro constant, NA, of specified entities. State what is being counted: atoms, molecules, ions or formula units. One mole of O₂ molecules contains two moles of oxygen atoms, so the entity matters.
Use n=m/M for mass and n=N/NA for particle count. M is molar mass, n is amount in mol, and N is the number of specified entities. Check units: grams divided by g mol⁻¹ gives mol; amount multiplied by mol⁻¹ gives a count. Use the value of NA supplied by the paper when one is given.
Pause and explain
Which quantity has units of g mol⁻¹?
Worked example
How many molecules are in 9.0 g of water? Use Mr(H₂O) = 18.0 and NA = 6.02 × 10²³ mol⁻¹.
Show the worked solution
- Amount n = m/M = 9.0/18.0 = 0.50 mol.
- Each mole contains 6.02 × 10²³ molecules.
- Multiply 0.50 by NA and report molecules.
Answer 3.01 × 10²³ H₂O molecules.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find the amount and number of molecules in 8.8 g of CO₂. Use Mr = 44.0 and NA = 6.02 × 10²³ mol⁻¹.
Give me a hint
First find moles; then multiply by Avogadro's constant.
Compare my reasoning
- n = 8.8/44.0.
- Convert 0.20 mol to molecules using NA.
- Keep the entity label as CO₂ molecules.
0.20 mol; 1.20 × 10²³ CO₂ molecules.
Look for these in your work
- Amount calculated as m/M
- Particle count uses NA
- Molecules distinguished from atoms
A particle has mass 24 times the unified atomic mass unit. State its relative mass and explain whether it has a unit.
Give me a hint
Relative mass is a ratio against the reference particle mass.
Compare my reasoning
- Compare the particle's mass with u.
- A ratio of equal kinds of mass is dimensionless.
- Do not confuse it with mass per mole.
Its relative mass is 24 and has no unit. A molar mass of about 24 g mol⁻¹ would be a separate quantity with units.
Look for these in your work
- Ratio value correct
- Dimensionless status explained
- Relative mass distinguished from molar mass
A container holds 0.25 mol of CaCl₂ formula units. How many moles of chloride ions does it contain, and why is the entity important?
Give me a hint
Read the subscripts in one formula unit before multiplying by amount.
Compare my reasoning
- Each CaCl₂ formula unit contains two Cl⁻ ions.
- Multiply 0.25 mol formula units by 2.
- Label the result as moles of chloride ions.
0.50 mol of Cl⁻ ions. Each formula unit contains two chloride ions, so the ion count is twice the formula-unit amount.
Look for these in your work
- Subscript interpreted
- Amount scaled by the particle count
- Formula units and ions distinguished
Common mistakes
- Attaching a unit to Ar or Mr
- Calling the relative formula mass of an ionic solid a molecular mass
- Counting atoms when the question asks for molecules
- Using n=mM instead of n=m/M
What can you explain now?
What is the unified atomic mass unit defined as?
Compare with the explanation
One twelfth of the mass of a carbon-12 atom
That is the specified reference mass.
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Make it stick
How do relative mass, molar mass, amount and particle count differ, and what entity are you counting?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.