Moles, molar mass and particle counts
Connect a measured mass with an amount of substance and a specified particle count.
Cross-referenced from the related Cambridge IGCSE Chemistry 0620 or Physics 0625 teaching to the 0652 syllabus. Exact 0652 Core/Supplement objective coverage and this final-series course’s examiner fit still need specialist review. Written practice is self-checked and does not predict a Cambridge grade or demonstrate supervised laboratory competence.
Before you begin
- Calculate relative atomic, molecular or formula mass.
- Use powers of ten 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 water's molar mass when its relative molecular mass is 18?
What you will learn
- Use the mole and Avogadro constant to count specified particles.
- Rearrange n=m/M to calculate amount, mass or molar mass.
Specify the particles you are counting
A mole, symbol mol, is the unit for amount of substance. For this syllabus, use the Avogadro constant 6.02×10²³ per mole: one mole of specified particles contains 6.02×10²³ of those particles. Name the entities, such as atoms, molecules, ions or formula units. One mole of O₂ molecules contains two moles of oxygen atoms because each molecule contains two atoms.
Do not call a mole a fixed mass. Different substances have different masses per mole. Molar mass M has units g/mol; using supplied relative masses, its numerical value matches Aᵣ for an element's atoms or Mᵣ for the specified molecular or formula unit. Relative mass itself has no unit. For example, water has Mᵣ=18 and molar mass 18 g/mol using H=1 and O=16.
Use the mass route and the particle route
For mass m in grams and molar mass M in g/mol, the amount n in mol is m/M. Rearranging gives m=nM and M=m/n. Keep the units visible so that a kilogram sample is converted to grams before using a g/mol value. An unknown molar mass can help determine an unknown relative atomic or molecular mass when the particle identity is stated.
Particle count N equals n times the Avogadro constant. To go backwards, divide N by that constant. If the question asks for all atoms in a molecular sample, first find its molecule count, then multiply by the number of atoms per molecule. Round the final answer sensibly after the complete calculation, rather than rounding each intermediate amount.
Sources for this lesson
Pause and explain
How many moles of oxygen atoms are in 0.40 mol of O₂ molecules?
Worked example
Find the amount, molecule count and total atom count in 9.0 g H₂O using M=18 g/mol and Avogadro constant 6.02×10²³/mol.
Show the worked solution
- Amount is n=9.0/18=0.50 mol of water molecules.
- Molecule count is 0.50×6.02×10²³=3.01×10²³.
- Each molecule has three atoms, so total atom count is 3×3.01×10²³=9.03×10²³ before final rounding.
Answer 0.50 mol; 3.01×10²³ molecules; 9.03×10²³ atoms (unrounded counts).
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
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.
Calculate the amount and molecule count in 22 g CO₂ using C=12 and O=16.
Give me a hint
Find molar mass, then divide mass by it before counting molecules.
Compare my reasoning
- Molar mass is 12+2×16=44 g/mol.
- n=22/44=0.50 mol.
- N=0.50×6.02×10²³=3.01×10²³ CO₂ molecules.
0.50 mol and 3.01×10²³ CO₂ molecules.
Look for these in your work
- The formula gives the molar mass.
- The final count names molecules, not all atoms.
An element's atoms have amount 0.20 mol and mass 5.4 g. Find molar mass, relative atomic mass and atom count.
Give me a hint
Use M=m/n; then separate the units of M and Aᵣ.
Compare my reasoning
- M=5.4/0.20=27 g/mol.
- The corresponding relative atomic mass is 27 with no unit.
- Atom count is 0.20×6.02×10²³=1.204×10²³ before rounding.
27 g/mol; Aᵣ=27; 1.204×10²³ atoms before rounding.
Look for these in your work
- Relative mass and molar mass have distinct units.
- Atom count uses the stated amount.
A sample contains 3.01×10²³ O₂ molecules. Calculate its amount of molecules, mass using O=16, and number of oxygen atoms.
Give me a hint
Divide by Avogadro's constant; O₂ has molar mass 32 g/mol and two atoms per molecule.
Compare my reasoning
- n=3.01×10²³/(6.02×10²³)=0.50 mol O₂.
- Mass is 0.50×32=16 g.
- There are 2×3.01×10²³=6.02×10²³ oxygen atoms.
0.50 mol O₂; 16 g; 6.02×10²³ oxygen atoms.
Look for these in your work
- The reverse particle calculation is explicit.
- The particle identity determines both molar mass and the atom multiplier.
Common mistakes
- Using the same mass for one mole of every substance.
- Answering an atom-count question with a molecule count.
- Putting a gram unit on Aᵣ or Mᵣ instead of distinguishing molar mass.
What can you explain now?
A sample contains 0.25 mol of a substance and has mass 11.0 g. Find its molar mass.
Compare with the explanation
44 g/mol
Rearrange n=m/M to M=m/n: 11.0/0.25=44 g/mol.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Explain the difference between relative mass and molar mass. Convert a mass into a molecule count, then into an atom count, naming the particles at every step.
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.