Moles, molar mass and particle counts
Use the mole to connect mass and particle counts. Choose the correct entity and molar mass, keep units consistent and round the final answer.
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Mole questions depend on clear quantities and units. Keep Mᵣ, molar mass, and number of specified entities distinct from the start.
A mole counts a specified kind of entity
The mole, symbol mol, is the unit of amount of substance. One mole contains exactly 6.02214076 × 10²³ specified entities. These may be atoms, molecules, ions or specified groups such as formula units.
The Avogadro constant is N_A = 6.02214076 × 10²³ mol⁻¹. For the calculations in this lesson, use the rounded value:
N_A ≈ 6.02 × 10²³ mol⁻¹
If a question supplies a different rounded value, use that value. Always name what is being counted: a mole of oxygen atoms is different from a mole of O₂ molecules.
Keep the quantities and units distinct
- Amount of substance is written as n and measured in moles (mol).
- Molar mass M has units g mol⁻¹.
- At the precision used in this course, use the relative atomic, molecular or formula mass as the numerical value of M in g mol⁻¹. First check which entity the formula represents.
- Converting between mass, moles, and particles uses these two core equations:
- n = m/M
- N = nN_A
Convert through amount of substance
- n = m/M converts mass to amount of substance.
- N = nN_A converts amount to a count of the specified entity.
- Relative mass has no unit; molar mass has unit g mol⁻¹ when mass is measured in grams.
- Keep extra digits during the working, then round the final answer to a suitable precision.
A counting unit for atoms, molecules or ions
Just like “a dozen” means 12 items, one mole contains approximately 6.02 × 10²³ specified entities.
The particle can be atoms, molecules, ions, or formula units (for ionic compounds).
Choose the correct molar mass
Molar mass M is the mass of 1 mole of a substance.
- For atoms of an element, use Aᵣ: a mole of O atoms has molar mass 16 g mol⁻¹ when Aᵣ(O) = 16.
- For an element that consists of molecules, use the whole molecular formula: M(O₂) = 2(16) = 32 g mol⁻¹.
- For a molecular compound, add the contributions to its molecular formula; for an ionic compound, use its formula ratio.
Mᵣ has no units. Molar mass M has units g mol⁻¹.
Mass, amount and entity count
Where:
- n = amount of substance (mol)
- m = mass (g)
- M = molar mass (g mol⁻¹)
- N = number of particles (count)
- N_A ≈ 6.02 × 10²³ mol⁻¹
Check the entity and unit
- Writing N_A ≈ 6.02 × 10²³ without units (write mol⁻¹).
- Using Mᵣ as if it has units of g mol⁻¹ without stating it is molar mass M.
- Forgetting that “particles” could mean atoms, molecules, ions, or formula units.
- Counting atoms wrongly: 1 molecule of CO₂ has 3 atoms; 1 molecule of H₂O has 3 atoms.
- Not using consistent units (mass in g, not mg; if mg is given, convert).
Choose and check the conversion
- Identify the entity and calculate its molar mass if mass is involved.
- Convert mass to amount using n = m/M, or reverse with m = nM.
- Convert amount to entity count using N = nN_A, or reverse with n = N/N_A.
- Check the requested entity, unit and final precision.
If the question asks for “number of atoms” in a molecular substance, multiply by atoms per molecule at the end.
Worked examples
Modelled example 1
From water mass to amount
Problem
Calculate the number of moles in 9.0 g of water, H₂O. Given Aᵣ(H) = 1, Aᵣ(O) = 16.
Study the worked solution
Calculate molar mass
Method
Add the relative masses for two H atoms and one O atom.Reason
The formula H₂O determines the mass of one mole of water molecules.Working
M(H₂O) = 2(1) + 16 = 18 g mol⁻¹.Convert mass to amount
Method
Divide the sample mass by molar mass.Reason
n = m/M converts grams into moles.Working
n = 9.0/18 = 0.50 mol.Check the scale
Method
Compare 9.0 g with the mass of one mole.Reason
9.0 g is half of 18 g, so the amount should be half a mole.Working
n(H₂O) = 0.50 mol.
Guided practice 2
From amount to molecule count
Problem
How many molecules are present in 0.25 mol of carbon dioxide, CO₂?
Use the Avogadro constant
Hints
Hint 1: choose the direction
Starting with moles and finding particles means multiply by N_A.
Hint 2: substitute
N = 0.25 × 6.02 × 10²³.
View solution step by step
Choose the particle equation
Method
Use N = nN_A.Reason
Using the rounded constant, one mole contains approximately 6.02 × 10²³ specified entities.
Working
N = 0.25 × 6.02 × 10²³.Calculate and name the entity
Method
Multiply and attach the requested particle label.Reason
The question asks for molecules, not atoms.Working
N = 1.505 × 10²³ molecules before rounding, or 1.5 × 10²³ molecules to two significant figures.
Common misconception 3
Count atoms after counting molecules
Learner response
How many atoms are there in 0.10 mol of CO₂ molecules? A student gives 6.02 × 10²² atoms because they multiply only by N_A. Explain the mistake and correct the answer.
Separate molecule count from atom count
View solution step by step
Find molecules first
Method
Convert 0.10 mol into the number of CO₂ molecules.Reason
N_A counts the specified entities, which here are molecules.Working
N(molecules) = 0.10 × 6.02 × 10²³ = 6.02 × 10²².Count atoms in each molecule
Method
Read one C and two O atoms from CO₂.Reason
Each molecule therefore contains three atoms altogether.Working
1 + 2 = 3 atoms per molecule.Correct the result
Method
Multiply the molecule count by three.Reason
The required entity is atoms, not molecules.Working
N(atoms) = 1.806 × 10²³ before rounding, or 1.8 × 10²³ atoms to two significant figures.
Examiner practice 4
From magnesium mass to atom count
Examination question
Calculate the number of atoms in 4.0 g of magnesium. Given Aᵣ(Mg) = 24. [4 marks]
Show the molar-mass and mole steps
View solution step by step
State molar mass
1 markMethod
Convert the supplied Aᵣ into molar mass.Reason
Mass-to-mole calculations require M in g mol⁻¹.Working
M(Mg) = 24 g mol⁻¹.Find moles
1 markMethod
Divide mass by molar mass.Reason
n = m/M.Working
n = 4.0/24 ≈ 0.1667 mol; keep the unrounded value for the next step.Convert to atoms
1 markMethod
Multiply moles by N_A.Reason
The formula Mg represents magnesium atoms, so the amount here counts atoms rather than molecules.Working
N = (4.0/24) × 6.02 × 10²³.Report the answer
1 markWorking
N ≈ 1.0 × 10²³ atoms to two significant figures.
Self-mark with the mark scheme
Compare your response with each mark point. Select a point only when your response contains that evidence.
Self-mark molar mass, moles, particle conversion and final labelled value.
Challenge 5
From molecule count to amount
Reverse-direction transfer
How many moles are in 3.01 × 10²³ molecules of CO₂?
Reverse the Avogadro conversion
Hints
Hint 1: reverse direction
Particles to moles uses division by N_A, the reverse of N = nN_A.
View solution step by step
Rearrange the relationship
Method
Use n = N/N_A.Reason
The number of particles is known and the amount is unknown.
Working
n = (3.01 × 10²³)/(6.02 × 10²³).
Cancel the common power and calculate
Method
Divide the coefficients.Reason
The common factor 10²³ cancels.Working
n = 3.01/6.02 = 0.500 mol to three significant figures.
Try it yourself
Mind stretcher 1: Count the ions released on dissolvingExtension
Question: 0.20 mol of sodium chloride dissolves completely. How many chloride ions, Cl⁻, are released into the solution?
Show answer
Chloride ions already exist in solid sodium chloride. Dissolving separates them: each formula unit supplies one chloride ion to the solution.
The amount of Cl⁻ in solution is 0.20 mol.
Mind stretcher 2: Distinguish relative mass from molar massExtension
Question: A student writes: “Mᵣ(H₂O) = 18 g mol⁻¹”. What is wrong, and what should it be?
Show answer
Mᵣ has no units. Mᵣ(H₂O) = 18.
The molar mass is M(H₂O) = 18 g mol⁻¹.
Mind stretcher 3: A mole of oxygen: which entity?Extension
A sample contains 0.10 mol of O₂ molecules. Given Aᵣ(O) = 16, find its mass and the amount, in mol, of oxygen atoms in it.
Show answer
The molar mass of O₂ is 2(16) = 32 g mol⁻¹, so the mass is 0.10(32) = 3.2 g.
Each molecule contains two oxygen atoms, so the amount of oxygen atoms is 2(0.10) = 0.20 mol. The sample has 0.10 mol of molecules and 0.20 mol of atoms; both statements describe the same sample.
Practise and check
See what you know across this topic, then go back to anything you got wrong.
Syllabus and review details
- SEC G3 Pure Chemistry 2027 · 2027
Content structure and subject content, PDF pages 9–24
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