Chemistry · Lesson

Amount of substance, the mole and Avogadro's constant

Use the mole to connect a specified kind of entity with a very large count. Track molecules, atoms and formula units without switching between them silently.

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By the end, you can

Define the mole using a specified entity.
Convert between amount n and count N.
Count constituent atom amounts in an amount of molecules.

A laboratory-scale counting bridge

One water molecule is too small to weigh individually with an ordinary laboratory balance. A chemical sample can contain an enormous number of molecules. Amount of substance provides a bridge between that entity count and laboratory-scale quantities. Its SI unit is the mole, symbol mol. Always say what is being counted: water molecules, sodium ions, carbon atoms or a specified formula-unit composition.

One mole contains exactly 6.02214076 × 10²³ specified elementary entities. This number is the fixed value of the Avogadro constant Nₐ when expressed in mol⁻¹. An entity may be an atom, molecule, ion, electron or specified group of particles. The definition does not say that one mole of every substance has the same mass or volume.

Distinguish N from n

Write N for the number of entities and n for amount of substance. Their relation is N = nNₐ. If n = 0.500 mol of water molecules, multiplying by the Avogadro constant gives about 3.01 × 10²³ molecules. Using 0.5 as an exact arithmetic input gives 3.01107038 × 10²³; a measured amount should retain its own precision and uncertainty.

The inverse relation is n = N/Nₐ. The unit check matters: a count divided by a constant with unit mol⁻¹ gives mol. A count is not itself a mass. To reach grams, you also need the mass per amount for the specified substance, introduced in the molar-mass lesson.

The entity decides what one mole means

One mole of H₂O molecules contains two moles of hydrogen atoms and one mole of oxygen atoms within those molecules. The formula supplies the constituent ratio. The total atom amount is three moles, while the molecular amount is still one mole. These statements count different specified entities in the same material.

For an ionic solid such as NaCl, speak of formula units or its constituent ion amounts rather than separate NaCl molecules. One mole of NaCl formula-unit composition corresponds to one mole of sodium ions and one mole of chloride ions in the ideal solid. This is composition bookkeeping, not an assertion of isolated paired objects.

One sample, several specified entity counts

Specified entity	Amount / mol	Relation to water-molecule amount
H₂O molecules	0.500	n
H atoms within H₂O	1.00	2n
O atoms within H₂O	0.500	n
All constituent atoms	1.50	3n

Amounts implied by 0.500 mol of H₂O molecules. Hydrogen and oxygen atoms are constituents of the molecules; their atom amounts do not add extra water molecules.

An exact definition does not make a sample exact

The present SI mole definition fixes the Avogadro constant exactly. Older texts may introduce the mole through a mass of carbon-12; that is historical context rather than the current defining relation. The molar mass of carbon-12 is no longer an exact defining 12 g/mol constant in the present SI, although 12 g/mol remains an excellent introductory approximation.

An actual sample amount still depends on measurement, composition and purity. An exact counting constant cannot remove uncertainty from a balance reading or identify contaminants. Keep the exact unit definition separate from a claim about how well a particular sample amount is known.

Worked examples

Half a mole of water molecules

For an arithmetic example with n = 0.5 mol of H₂O molecules, find the molecular count and constituent atom amounts.

N = nNₐ = 0.5 mol × 6.02214076 × 10²³ mol⁻¹.
The molecular count is 3.01107038 × 10²³.
Each water molecule has two H and one O, so the hydrogen-atom amount is 1.0 mol and oxygen-atom amount is 0.5 mol.

The molecular count and atom amounts refer to the same sample but specify different entities. Final reporting for a measured sample depends on its precision.

Try it yourself

Does one mole of atoms contain the same entity count as one mole of molecules?
Show the answer and reasoning
Yes, when each specified entity is counted once.
The entity types differ, but the mole fixes the same number of specified entities.
How many moles of oxygen atoms are contained in 2 mol of CO₂ molecules?
Show the answer and reasoning
4 mol of O atoms.
Each molecule contains two oxygen atoms.
A sample contains one quarter of 6.02214076 × 10²³ specified entities. What is its amount?
Show the answer and reasoning
0.25 mol.
Divide N by Nₐ.
Does the exact Avogadro constant make a measured sample’s mass and purity exact?
Show the answer and reasoning
No.
The definition fixes the counting relation, not the quality of the sample or its measurement.

What to carry forward

Specify the entity whenever you state a chemical amount.
The mole fixes an exact entity count through Nₐ.
Use N = nNₐ and n = N/Nₐ.
Formula ratios connect molecular or formula-unit amounts to constituent amounts.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.