The Mole and Avogadro Constant

Last updated: 17 August 2026

Diagnose → Learn → Master: Every study-note section includes 15 free MCQs — start with 5 Diagnostic MCQs to identify gaps in your understanding, then complete 10 Mastery MCQs near the end to check what you have learned.

Much of Chemistry happens on a scale that we cannot see. A small sample of water contains an enormous number of H₂O molecules, while even a tiny crystal of sodium chloride contains vast numbers of Na⁺ and Cl⁻ ions.

Counting these particles individually would clearly be impossible. Instead, chemists use the mole, a counting unit representing a fixed number of specified entities. It plays a role rather like the word “dozen”, except that the number represented by one mole is enormously larger.

The mole therefore provides the bridge between the microscopic world of atoms, molecules and ions and the measurable world of laboratory masses. Once this bridge is understood, calculations involving equations, solutions, gases, equilibria and energetics become much easier to organise.

Diagnostic Quiz

How Ready Are You for the Mole?

Try these five questions before reading the chapter. They check whether you already recognise the difference between moles, particles, formulae and mass.

5 quick prerequisite questions
Focus on common mole misconceptions
Every answer option is explained

What does 1 mol of oxygen molecules contain?

Exactly 1 oxygen molecule

A mole is not a single particle. It represents a very large fixed number of specified entities.

6.02 × 10²³ O₂ molecules

Correct. One mole contains approximately 6.02 × 10²³ specified entities. Here, the specified entities are O₂ molecules.

6.02 × 10²³ oxygen atoms

One mole of O₂ contains 6.02 × 10²³ molecules, but each molecule contains two oxygen atoms. The number of oxygen atoms is therefore twice this value.

2 oxygen atoms

Two oxygen atoms are present in one O₂ molecule, not in one mole of O₂.

A sample has a mass of 9.0 g and a molar mass of 18.0 g mol⁻¹. What amount of substance is present?

162 mol

This comes from multiplying mass by molar mass. To find moles from a mass, the mass must be divided by the mass of one mole.

2.0 mol

This reverses the required division. Since 9.0 g is half of 18.0 g, the amount must be half a mole rather than two moles.

18.0 mol

The molar mass is not itself the number of moles. It tells you the mass corresponding to one mole.

0.50 mol

Correct. n = m/M = 9.0/18.0 = 0.50 mol.

How many moles of oxygen atoms are present in 1 mol of O₂ molecules?

2 mol

Correct. Every O₂ molecule contains two oxygen atoms, so 1 mol of O₂ molecules contains 2 mol of oxygen atoms.

1 mol

There is 1 mol of O₂ molecules, but each molecule contains two atoms. The amount of oxygen atoms is therefore 2 mol.

0.5 mol

The subscript 2 means that the number of oxygen atoms is twice, not half, the number of O₂ molecules.

6.02 × 10²³ mol

6.02 × 10²³ is associated with the number of particles in one mole. It is not itself an amount expressed in moles.

Which description is most appropriate for the entities counted in 1 mol of solid sodium chloride?

NaCl molecules

Sodium chloride forms a giant ionic lattice and does not consist of individual NaCl molecules.

Sodium atoms only

Sodium chloride contains both Na⁺ and Cl⁻ ions. Counting sodium atoms alone does not represent the substance NaCl.

NaCl formula units

Correct. For an ionic solid, the formula represents the simplest whole-number ratio of ions, so formula units are the appropriate entities.

NaCl nuclei

NaCl does not represent a nucleus. It represents the ratio of sodium and chloride ions in the ionic lattice.

A sample contains 3.01 × 10²³ molecules. Which calculation gives the amount of substance in moles?

(3.01 × 10²³)(6.02 × 10²³)

Multiplying by the Avogadro constant would make an already enormous particle count even larger. To convert particles into moles, divide by the number of particles per mole.

(3.01 × 10²³)/(6.02 × 10²³)

Correct. n = N/L, giving 0.500 mol.

(6.02 × 10²³)/(3.01 × 10²³)

This division is reversed. It would give 2 rather than the 0.500 mol represented by half the Avogadro number of molecules.

3.01 × 10²³ − 6.02 × 10²³

The mole conversion is based on grouping entities into sets of 6.02 × 10²³, so subtraction is not appropriate.

Why chemists use the mole

Individual atoms and molecules have extremely small masses. A laboratory balance cannot count individual atoms or molecules, but it can measure a macroscopic mass containing an enormous collection of them.

Chemists therefore describe the size of such a collection using the amount of substance.

Symbol for amount of substance = n

Unit of amount of substance = mol

The physical quantity is called amount of substance; the mole is its SI unit. This distinction is similar to saying that mass is a physical quantity while the kilogram is a unit used to measure mass.

A mole is a counting unit, not a type of particle.

Saying “one mole” tells us the size of a collection, but we must still identify what is being counted. The entities might be atoms, molecules, ions, formula units, electrons or another specified particle.

The mole as a counting word

We already use counting words for ordinary objects:

one pair represents 2 objects;
one dozen represents 12 objects; and
one mole represents 6.02214076 × 10²³ specified entities.

The mole is simply a much larger counting unit because atoms, ions and molecules are unimaginably small.

One dozen eggs means 12 eggs.

One mole of O₂ molecules means 6.02214076 × 10²³ O₂ molecules.

In both cases, the counting word tells us the number of entities. It does not by itself tell us their individual mass or chemical identity.

The Avogadro constant

The number of specified entities corresponding to one mole is represented by the Avogadro constant, L.

L = 6.02214076 × 10²³ mol⁻¹

This numerical value is exact. In many A-Level calculations, the data provided are given to fewer significant figures, so the value is commonly used as:

L = 6.02 × 10²³ mol⁻¹

Some books use the symbol N_A instead of L. Both represent the Avogadro constant.

What does mol⁻¹ mean?

The unit mol⁻¹ means per mole. The Avogadro constant tells us the number of specified entities present for every mole.

6.02 × 10²³ specified entities per mole

This is why multiplying an amount in moles by the Avogadro constant produces a number of entities:

mol × mol⁻¹ = 1

The resulting particle number is a count rather than a measured quantity with a physical unit. We should nevertheless state what has been counted.

The definition of one mole

One mole is the amount of substance containing exactly 6.02214076 × 10²³ specified elementary entities.

The entity must be specified. It could be:

an atom;
a molecule;
an ion;
a formula unit;
an electron; or
another explicitly defined entity.

The chemical formula tells you what each entity contains.

One mole of H₂O molecules contains one mole of H₂O molecules, but each molecule contains two H atoms and one O atom. It therefore contains 2 mol of H atoms and 1 mol of O atoms.

One mole of different substances

Every one-mole sample contains the same number of the specified entity, whatever the substance. What changes is the identity, composition and mass of each entity.

Sample	Number of specified entities	Entity being counted
1 mol He	6.02 × 10²³	He atoms
1 mol O₂	6.02 × 10²³	O₂ molecules
1 mol H₂O	6.02 × 10²³	H₂O molecules
1 mol NaCl	6.02 × 10²³	NaCl formula units
1 mol Na⁺	6.02 × 10²³	Na⁺ ions
1 mol e⁻	6.02 × 10²³	Electrons

All six examples contain the same number of specified entities because each represents one mole. They do not, however, have the same mass.

One mole of molecules is not necessarily one mole of atoms

Consider 1 mol of oxygen gas, O₂. The entity specified by O₂ is the O₂ molecule. Each molecule contains two oxygen atoms.

1 mol O₂ contains 1 mol O₂ molecules.
1 mol O₂ contains 2 mol O atoms.
1 mol O₂ contains 6.02 × 10²³ O₂ molecules.
1 mol O₂ contains 1.204 × 10²⁴ O atoms.

1 mol O atoms contains 6.02 × 10²³ oxygen atoms.

1 mol O₂ molecules contains 6.02 × 10²³ O₂ molecules but 1.204 × 10²⁴ oxygen atoms.

Always ask whether the question is counting molecules or the atoms inside those molecules.

Converting between particles and moles

Let N represent the number of specified entities and n the amount of substance in moles.

Since every mole contains L entities:

N = nL

Rearranging gives:

n = N/L

Quantity required	Relationship	Meaning
Number of entities	N = nL	Multiply moles by the number of entities per mole
Amount of substance	n = N/L	Group the entities into sets of one mole
Avogadro constant	L = N/n	Number of entities per mole

Worked example: finding the number of atoms

Calculate the number of magnesium atoms in 0.250 mol of Mg.

N = nL

N = 0.250 × 6.02 × 10²³

N = 1.51 × 10²³

Answer: 1.51 × 10²³ magnesium atoms.

Worked example: finding the amount from a particle count

A sample contains 3.01 × 10²² CO₂ molecules. Calculate the amount of CO₂.

n = N/L

n = (3.01 × 10²²)/(6.02 × 10²³)

n = 0.0500 mol

Answer: 0.0500 mol of CO₂ molecules.

A useful sense check

Before accepting your answer, compare the given particle number with 6.02 × 10²³.

More than 6.02 × 10²³ entities means more than 1 mol.
Exactly 6.02 × 10²³ entities means 1 mol.
Fewer than 6.02 × 10²³ entities means less than 1 mol.

Use the direction of the conversion to decide whether to multiply or divide.

To turn moles into an enormous microscopic particle count, multiply by L. To turn a particle count into the smaller number of moles, divide by L.

Molar mass connects moles to laboratory mass

Particle numbers are useful conceptually, but in the laboratory we normally measure a substance using a balance. We therefore need another bridge connecting an amount in moles to a measurable mass.

The molar mass, M, is the mass of one mole of a substance.

M = m/n

Molar mass is commonly expressed in:

g mol⁻¹

The numerical value of the molar mass in g mol⁻¹ is equal to the corresponding relative atomic mass, relative molecular mass or relative formula mass.

Substance	Relative mass	Molar mass
Mg	Aᵣ = 24.3	24.3 g mol⁻¹
O₂	Mᵣ = 32.0	32.0 g mol⁻¹
H₂O	Mᵣ = 18.0	18.0 g mol⁻¹
NaCl	Relative formula mass = 58.5	58.5 g mol⁻¹

The numerical values may be the same, but the quantities are not.

Relative molecular mass of H₂O: Mᵣ = 18.0, with no unit.

Molar mass of H₂O: M = 18.0 g mol⁻¹.

Relative mass is a ratio. Molar mass is an actual mass per mole.

Converting between mass and moles

If one mole has mass M, a sample of mass m contains:

n = m/M

Rearranging gives:

m = nM

where:

n = amount of substance in mol;
m = mass in g; and
M = molar mass in g mol⁻¹.

Worked example: finding moles from mass

Calculate the amount of H₂O in 9.00 g of water.

First calculate the molar mass:

M(H₂O) = 2(1.0) + 16.0 = 18.0 g mol⁻¹

Then:

n = 9.00/18.0 = 0.500 mol

Answer: 9.00 g of H₂O corresponds to 0.500 mol of H₂O.

Worked example: finding mass from moles

Calculate the mass of 0.250 mol of NaCl.

M(NaCl) = 23.0 + 35.5 = 58.5 g mol⁻¹

m = nM

m = 0.250 × 58.5 = 14.6 g

Answer: The mass is 14.6 g.

Keep the mass units consistent.

If the molar mass is expressed in g mol⁻¹, the mass used in n = m/M must be in grams. Convert kg or mg to g before substituting.

Moving between mass, moles and particles

The most useful way to organise this topic is to place the mole at the centre. Mass and microscopic particle number are connected through the amount of substance.

Mass ⇌ amount in moles ⇌ number of entities

m ⇌ n ⇌ N

The two key relationships are:

n = m/M

N = nL

A reliable conversion route

Identify what entity is being counted.
Calculate the molar mass if a mass is involved.
Convert mass to moles using n = m/M.
Convert moles to particles using N = nL.
Apply the chemical formula if atoms or ions within each entity must be counted.

Worked example: molecules in a measured mass

Calculate the number of H₂O molecules in 9.00 g of water.

n(H₂O) = 9.00/18.0 = 0.500 mol

N(H₂O) = 0.500 × 6.02 × 10²³

N(H₂O) = 3.01 × 10²³

Answer: 9.00 g of water contains 3.01 × 10²³ H₂O molecules.

Worked example: mass from a number of molecules

Calculate the mass of 3.01 × 10²² CO₂ molecules.

Convert the number of molecules into moles:

n(CO₂) = (3.01 × 10²²)/(6.02 × 10²³) = 0.0500 mol

The molar mass of CO₂ is:

M(CO₂) = 12.0 + 2(16.0) = 44.0 g mol⁻¹

m = 0.0500 × 44.0 = 2.20 g

Answer: The mass of 3.01 × 10²² CO₂ molecules is 2.20 g.

Choosing the correct entity

Mole questions become much easier when you identify exactly what the chemical formula represents before starting the calculation.

Species or substance	Suitable entity	Example
Monatomic element	Atoms	1 mol Ne contains 6.02 × 10²³ Ne atoms
Molecular substance	Molecules	1 mol NH₃ contains 6.02 × 10²³ NH₃ molecules
Ionic solid	Formula units	1 mol MgCl₂ contains 6.02 × 10²³ MgCl₂ formula units
Individual ion	Ions	1 mol SO₄²⁻ contains 6.02 × 10²³ SO₄²⁻ ions
Subatomic particle	Specified particle	1 mol e⁻ contains 6.02 × 10²³ electrons

Why ionic substances are described using formula units

Solid sodium chloride does not consist of separate NaCl molecules. Na⁺ and Cl⁻ ions form an extended giant ionic lattice.

The formula NaCl therefore represents the simplest whole-number ratio of Na⁺ ions to Cl⁻ ions.

1 mol NaCl = 1 mol NaCl formula units

Since each formula unit represents one Na⁺ ion for every one Cl⁻ ion:

1 mol NaCl contains 1 mol Na⁺ ions;
1 mol NaCl contains 1 mol Cl⁻ ions; and
1 mol NaCl contains 2 mol ions in total.

Incorrect: 1 mol of sodium chloride contains 6.02 × 10²³ NaCl molecules.

Correct: 1 mol of sodium chloride contains 6.02 × 10²³ NaCl formula units.

The distinction reflects the structure of ionic solids.

Using chemical formulae to count particles

A chemical formula tells us the composition of one molecule or formula unit. The same numerical ratios apply when we work in moles.

Example: H₂O

Each H₂O molecule contains two H atoms and one O atom.

Sample	Hydrogen atoms	Oxygen atoms	Total atoms
1 H₂O molecule	2	1	3
1 mol H₂O molecules	2 mol	1 mol	3 mol
6.02 × 10²³ H₂O molecules	1.204 × 10²⁴ atoms	6.02 × 10²³ atoms	1.806 × 10²⁴ atoms

Example: MgCl₂

Each MgCl₂ formula unit represents one Mg²⁺ ion and two Cl⁻ ions.

1 mol MgCl₂ contains 1 mol Mg²⁺ ions.
1 mol MgCl₂ contains 2 mol Cl⁻ ions.
1 mol MgCl₂ contains 3 mol ions in total.

Example: Al₂(SO₄)₃

Each Al₂(SO₄)₃ formula unit contains:

2 Al atoms;
3 S atoms; and
3 × 4 = 12 O atoms.

Therefore, 1 mol of Al₂(SO₄)₃ formula units contains:

2 mol Al atoms;
3 mol S atoms; and
12 mol O atoms.

Formula subscripts become mole ratios.

If one molecule or formula unit contains four atoms of a particular element, one mole of those molecules or formula units contains four moles of those atoms.

Worked examples involving particles within formulae

Example 1: hydrogen atoms in water

Calculate the number of hydrogen atoms in 0.250 mol of H₂O.

Each H₂O molecule contains two H atoms:

Amount of H atoms = 2 × 0.250 = 0.500 mol

Number of H atoms = 0.500 × 6.02 × 10²³

Number of H atoms = 3.01 × 10²³

Answer: 3.01 × 10²³ hydrogen atoms.

Example 2: chloride ions in magnesium chloride

Calculate the number of Cl⁻ ions in 0.400 mol of MgCl₂.

Each formula unit contains two Cl⁻ ions:

Amount of Cl⁻ ions = 2 × 0.400 = 0.800 mol

Number of Cl⁻ ions = 0.800 × 6.02 × 10²³

Number of Cl⁻ ions = 4.82 × 10²³

Answer: 4.82 × 10²³ Cl⁻ ions.

Example 3: oxygen atoms in aluminium sulfate

Calculate the number of oxygen atoms in 0.250 mol of Al₂(SO₄)₃.

Each formula unit contains 12 oxygen atoms:

Amount of O atoms = 12 × 0.250 = 3.00 mol

Number of O atoms = 3.00 × 6.02 × 10²³

Number of O atoms = 1.81 × 10²⁴

Answer: 1.81 × 10²⁴ oxygen atoms.

Example 4: electrons in a sample of ions

Calculate the number of electrons present in 0.200 mol of Mg²⁺ ions.

Magnesium has proton number 12. A neutral Mg atom contains 12 electrons, so Mg²⁺ contains:

12 − 2 = 10 electrons per Mg²⁺ ion

Therefore:

Amount of electrons = 10 × 0.200 = 2.00 mol

Number of electrons = 2.00 × 6.02 × 10²³

Number of electrons = 1.20 × 10²⁴

Answer: 1.20 × 10²⁴ electrons.

What one mole does and does not mean

Equal amounts in moles contain equal numbers of specified entities. They do not necessarily have equal masses or equal total numbers of atoms.

Statement	Correct?	Reason
1 mol of every substance contains the same number of specified entities	Yes	Every mole contains 6.02214076 × 10²³ specified entities
1 mol of every substance has the same mass	No	Different substances have different molar masses
1 mol of every substance contains the same total number of atoms	No	Different molecules and formula units contain different numbers of atoms
1 mol always refers to molecules	No	The specified entity can also be an atom, ion, formula unit or other particle
1 mol O₂ contains 2 mol O atoms	Yes	Each O₂ molecule contains two oxygen atoms

1 mol He atoms has a mass of approximately 4.0 g.

1 mol O₂ molecules has a mass of approximately 32.0 g.

Both samples contain the same number of specified entities, but their entities have different masses.

Units, standard form and significant figures

Mole calculations combine several different quantities, so correct notation and units are important.

Quantity	Symbol	Usual unit
Amount of substance	n	mol
Mass	m	g
Molar mass	M	g mol⁻¹
Number of entities	N	No physical unit
Avogadro constant	L	mol⁻¹

Writing particle numbers in standard form

Particle numbers are usually enormous and are conveniently expressed in standard form.

602 000 000 000 000 000 000 000 = 6.02 × 10²³

When using a value of the Avogadro constant supplied in an examination, use that supplied value and report the final answer to an appropriate number of significant figures.

A particle count is not expressed in mol.

“3.01 × 10²³ molecules” is a number of molecules, whereas “0.500 mol of molecules” is an amount of substance. They describe the same sample in different ways, but the quantities are not interchangeable.

Common mistakes with the mole and the Avogadro constant

Common mistake	Why it is wrong	Correct approach
Writing that 1 mol is simply 6.02 × 10²³ particles	The type of entity has not been specified	State atoms, molecules, ions, formula units or another specified entity
Using N = n/L	Moles must be multiplied by the number of entities per mole	Use N = nL
Multiplying a particle count by L to obtain moles	The entities must be grouped into sets of L	Use n = N/L
Writing the Avogadro constant without mol⁻¹	The constant represents the number of entities per mole	Write L = 6.02 × 10²³ mol⁻¹
Giving Mᵣ the unit g mol⁻¹	Relative molecular mass is a ratio and has no unit	Use g mol⁻¹ for molar mass, M
Using kg with a molar mass in g mol⁻¹	The mass units are inconsistent	Convert the mass to g first
Saying that 1 mol O₂ contains 1 mol O atoms	Each O₂ molecule contains two oxygen atoms	1 mol O₂ contains 2 mol O atoms
Referring to NaCl molecules	NaCl forms a giant ionic lattice	Refer to NaCl formula units
Ignoring brackets in Al₂(SO₄)₃	The outside subscript applies to every atom inside the bracket	Count 3 S atoms and 12 O atoms per formula unit
Assuming equal numbers of particles have equal masses	Different entities have different molar masses	Use the correct molar mass for each substance

Mole-calculation checklist

Identify the entity

Decide whether atoms, molecules, ions or formula units are involved.
Read the chemical formula carefully.
Check whether particles within each entity must be counted.
State the entity in the final answer.

Convert mass and moles

Calculate the correct molar mass.
Keep the mass in g when using g mol⁻¹.
Use n = m/M to find moles.
Use m = nM to find mass.

Convert moles and particles

Use N = nL to find the number of entities.
Use n = N/L to find moles.
Use the value of L supplied in the question or data booklet.
Express very large particle numbers in standard form.

Use the chemical formula

Treat subscripts as particle and mole ratios.
Apply brackets correctly.
Find the amount of the required particle before using L.
Check whether the question asks for one type of particle or the total number.

Mastery Quiz

The Mole and the Avogadro Constant Mastery Quiz

Now apply the chapter to multi-step particle, mass and formula calculations. These questions focus on reasoning about what is actually being counted rather than simply recalling equations.

10 application-focused questions
Includes multi-step mole and particle calculations
Every answer option is explained

A sample contains 3.60 g of H₂O. How many H₂O molecules are present? Use L = 6.02 × 10²³ mol⁻¹.

3.01 × 10²² molecules

This would correspond to 0.0500 mol. However, 3.60 g of water is 3.60/18.0 = 0.200 mol.

3.34 × 10²² molecules

This does not result from correctly combining the molar mass of water with the Avogadro constant.

1.20 × 10²³ molecules

Correct. n = 3.60/18.0 = 0.200 mol, so N = 0.200 × 6.02 × 10²³ = 1.20 × 10²³ molecules.

6.02 × 10²³ molecules

This is the number of molecules in 1 mol. The sample contains only 0.200 mol of H₂O.

How many oxygen atoms are present in 0.300 mol of CO₂?

3.61 × 10²³ oxygen atoms

Correct. Each CO₂ molecule contains two O atoms, so there are 0.600 mol of O atoms. Hence N = 0.600 × 6.02 × 10²³ = 3.61 × 10²³.

1.81 × 10²³ oxygen atoms

This is the number of CO₂ molecules in 0.300 mol. It does not account for the two O atoms in each molecule.

6.02 × 10²³ oxygen atoms

This corresponds to 1 mol of oxygen atoms. The sample contains 0.600 mol of oxygen atoms.

1.20 × 10²⁴ oxygen atoms

This corresponds to approximately 2 mol of oxygen atoms, which is much larger than the 0.600 mol present.

A sample contains 0.250 mol of Al₂(SO₄)₃. What amount of sulfate ions, SO₄²⁻, is represented by the formula?

0.250 mol

This ignores the subscript 3 outside the sulfate bracket.

0.500 mol

The subscript 2 belongs to aluminium. There are three sulfate ions for each Al₂(SO₄)₃ formula unit.

1.00 mol

This would imply four sulfate ions per formula unit. The chemical formula shows three.

0.750 mol

Correct. There are three SO₄²⁻ ions per formula unit, so 3 × 0.250 = 0.750 mol of sulfate ions.

A sample contains 1.505 × 10²³ molecules of a substance. Its mass is 11.0 g. What is its molar mass? Use L = 6.02 × 10²³ mol⁻¹.

2.75 g mol⁻¹

This results from dividing the mass by four rather than recognising that the particle count represents one quarter of a mole.

44.0 g mol⁻¹

Correct. The amount is (1.505 × 10²³)/(6.02 × 10²³) = 0.250 mol. Therefore M = 11.0/0.250 = 44.0 g mol⁻¹.

11.0 g mol⁻¹

11.0 g is the mass of the sample, not the mass of one mole. The sample contains only 0.250 mol.

22.0 g mol⁻¹

This would be correct if the sample contained 0.500 mol, but the particle count corresponds to 0.250 mol.

Which pair contains the same number of He atoms and O₂ molecules respectively? Take Aᵣ(He) = 4.0 and Mᵣ(O₂) = 32.0.

4.0 g He and 4.0 g O₂

4.0 g He contains 1 mol of He atoms, whereas 4.0 g O₂ contains only 4.0/32.0 = 0.125 mol of O₂ molecules. The numbers being compared are therefore not equal.

8.0 g He and 32.0 g O₂

8.0 g He contains 2 mol of He atoms, while 32.0 g O₂ contains 1 mol of O₂ molecules. Therefore, the number of He atoms is twice the number of O₂ molecules.

4.0 g He and 32.0 g O₂

Correct. 4.0 g He contains 1 mol of He atoms, while 32.0 g O₂ contains 1 mol of O₂ molecules. Each sample therefore contains 6.02 × 10²³ of the entity being compared.

2.0 g He and 32.0 g O₂

2.0 g He contains 0.500 mol of He atoms, whereas 32.0 g O₂ contains 1 mol of O₂ molecules. The O₂ sample therefore contains twice as many O₂ molecules as there are He atoms in the helium sample.

A student writes: “The relative molecular mass of CO₂ is 44.0 g mol⁻¹.” What is wrong with this statement?

The numerical value 44.0 is incorrect

The numerical value is correct because 12.0 + 2(16.0) = 44.0. The problem is the unit.

CO₂ has no relative molecular mass because it is a gas

Molecular substances have relative molecular masses regardless of whether they are gases, liquids or solids.

The value should be written as 22.0

CO₂ contains one carbon atom and two oxygen atoms, giving a relative molecular mass of 44.0.

Relative molecular mass has no units

Correct. Mᵣ is a relative ratio and has no units. The molar mass of CO₂, however, is 44.0 g mol⁻¹.

How many electrons are contained in 0.300 mol of Al³⁺ ions? Aluminium has proton number 13.

1.81 × 10²⁴ electrons

Correct. Al³⁺ has 13 − 3 = 10 electrons per ion. Therefore 0.300 mol of Al³⁺ contains 3.00 mol of electrons, giving 3.00 × 6.02 × 10²³ = 1.81 × 10²⁴ electrons.

1.81 × 10²³ electrons

This is the number of Al³⁺ ions in 0.300 mol. Each ion contains ten electrons, so the electron count must be ten times larger.

2.35 × 10²⁴ electrons

This effectively counts 13 electrons per particle, which would apply to neutral aluminium atoms rather than Al³⁺ ions.

5.42 × 10²³ electrons

This does not correctly account for the ten electrons present in each Al³⁺ ion.

What is the total amount of atoms represented in 0.100 mol of Al₂(SO₄)₃ formula units?

0.700 mol of atoms

This undercounts the oxygen atoms. Each formula unit contains 2 + 3 + 12 = 17 atoms.

1.70 mol of atoms

Correct. Al₂(SO₄)₃ contains 2 Al + 3 S + 12 O = 17 atoms per formula unit. Therefore 0.100 mol of formula units represents 1.70 mol of atoms.

0.170 mol of atoms

The factor of 17 must multiply 0.100 mol, giving 1.70 mol rather than 0.170 mol.

17.0 mol of atoms

Seventeen moles of atoms would be present in 1.00 mol of formula units. The sample contains only 0.100 mol.

A student has 0.200 mol of MgCl₂. Which statement about the ions represented by this amount is correct?

It represents 0.200 mol of ions in total

Each formula unit represents three ions in total: one Mg²⁺ and two Cl⁻. The total amount of ions is therefore 0.600 mol.

It represents 0.400 mol Mg²⁺ and 0.200 mol Cl⁻

The coefficients are reversed. Each formula unit has one Mg²⁺ ion and two Cl⁻ ions.

It represents 0.200 mol Mg atoms and 0.200 mol chlorine molecules

MgCl₂ is an ionic compound. Its formula represents Mg²⁺ and Cl⁻ ions, not neutral Mg atoms and Cl₂ molecules.

It represents 0.200 mol Mg²⁺ and 0.400 mol Cl⁻

Correct. The 1:2 ratio in MgCl₂ means that 0.200 mol of formula units corresponds to 0.200 mol Mg²⁺ ions and 0.400 mol Cl⁻ ions.

Two samples each contain exactly 6.02 × 10²³ specified entities. Sample X contains Ne atoms while sample Y contains NH₃ molecules. Which conclusion must be correct?

X and Y must have the same mass

Equal numbers of entities do not imply equal mass. Ne atoms and NH₃ molecules have different molar masses.

X and Y contain the same total number of atoms

Each Ne entity is one atom, whereas each NH₃ molecule contains four atoms. Sample Y therefore contains more atoms in total.

X and Y each contain 1 mol of their specified entity

Correct. A collection of approximately 6.02 × 10²³ specified entities corresponds to 1 mol, regardless of the chemical identity of those entities.

X and Y must occupy the same volume

The mole fixes the number of specified entities, not the volume occupied by the sample. Volume depends on the substance and conditions.

Frequently asked questions

Questions students often ask about the mole

These questions clarify the language and reasoning that often cause difficulty when mole calculations become part of longer A-Level Chemistry problems.

Is the Avogadro constant just a very large number?

It has a very large numerical value, but it is a physical constant with the unit mol⁻¹. It tells us the number of specified entities corresponding to each mole of substance.

Why is the Avogadro constant sometimes written as N_A instead of L?

Both symbols are used for the same constant. In this article, L is used, but you should recognise N_A when it appears in other textbooks or references.

Does one mole of every substance have the same mass?

No. One mole of every substance contains the same number of specified entities, but the masses of those entities differ. The molar mass therefore depends on the substance.

Does one mole of every substance contain the same number of atoms?

Not necessarily. One mole of He contains 1 mol of atoms because helium is monatomic. One mole of O₂ contains 2 mol of atoms, while one mole of H₂O contains 3 mol of atoms in total.

Can an amount of substance be smaller than one mole?

Yes. The mole is simply a unit. A sample may contain 0.5 mol, 0.020 mol or any other amount, just as a mass may be smaller than one kilogram.

Why does molar mass have the same numerical value as relative mass?

The relative-mass scale and the definition of the mole connect microscopic particle masses with macroscopic amounts. Consequently, an element with Aᵣ = 24.3 has a molar mass numerically equal to 24.3 g mol⁻¹.

The quantities are still different: relative mass has no unit, whereas molar mass is a mass per mole.

Should I multiply by the formula subscript before or after using the Avogadro constant?

Either order gives the same result if done consistently, because multiplication can be performed in either order.

A clearer method is usually to use the formula first to determine the amount of the required atoms or ions in moles, then multiply by the Avogadro constant.

Can the mole be used for electrons and other subatomic particles?

Yes. A mole can refer to any specified elementary entity. For example, 1 mol of electrons contains 6.02214076 × 10²³ electrons.

Why does the number of particles have no physical unit?

It is a count rather than a quantity such as mass or volume. For example, 3.01 × 10²³ molecules simply means that this many molecules have been counted. The entity should still be stated clearly.

Why should I convert through moles instead of trying to go directly from mass to particles?

Molar mass connects mass to moles, while the Avogadro constant connects moles to particles. Writing the conversion as mass → moles → particles makes the physical reasoning clear and greatly reduces the chance of multiplying or dividing by the wrong quantity.

Is the mole still defined using 12 g of carbon-12?

The modern definition fixes the Avogadro constant at exactly 6.02214076 × 10²³ mol⁻¹. One mole therefore contains exactly this number of specified elementary entities.

Carbon-12 remains important in the relative atomic mass scale, but the present definition of the mole is based directly on the fixed Avogadro constant.

The mole turns an otherwise unmanageable microscopic particle count into a useful measurable quantity. Molar mass connects laboratory mass to moles, while the Avogadro constant connects moles to atoms, molecules, ions and formula units. Once you can move confidently between mass, amount and particle number—and read the ratios hidden inside a chemical formula—the mole becomes the central calculation language used throughout quantitative Chemistry.