Amount of Substance and the Mole

Paper 4

Physics9702

A gas holds a very large number of molecules. There are two ways to say how many.

One way is a plain count of molecules. The other way is the amount of substance, measured in moles. This lesson moves between them.

Amount of substance is one of the SI base quantities. Its unit is the (mol).
One mole of any substance contains $6.02 \times 10^{23}$ particles. The particles may be atoms, molecules or ions, so a question always says which.
The $N_A$ is the number of particles per unit amount of substance. That sentence is the one-mark answer (9702/41/O/N/24 Q3(a)(i)).

Definition

1 mark

What is meant by one mole?

Model answer: One mole is the amount of substance that contains a number of particles equal to the Avogadro constant.

Definition

1 mark

What is meant by Avogadro constant?

Model answer: The number of particles per unit amount of substance.

n = \dfrac{N}{N_A}

Symbols

$n$ = amount of substance (mol)
$N$ = number of particles (a plain count) (no unit)
$N_A$ = Avogadro constant, 6.02 × 10²³ (mol⁻¹)

Where it comes from. One mole holds $N_A$ particles. So the number of moles is the total count divided by the count in one mole.
When you use it. A question gives one of the two counts and asks for the other. This is the only step needed.
Mass and moles. The molar mass $M$ is the mass of one mole. Keep the units matched: if $M$ is in g mol⁻¹, then $m$ comes out in g.
$m=nM$

Worked example

Smallest case: molecules to moles

A container holds $3.2 \times 10^{24}$ oxygen molecules. Find the amount of gas in moles.

Divide the number of molecules by the Avogadro constant.
$n=\dfrac{N}{N_A}$
$n=\dfrac{3.2\times10^{24}}{6.02\times10^{23}}$
$n=5.3\ \mathrm{mol}$

Answer

n = 5.3\ \text{mol}

Common mistake

Capital

N

is a count of molecules. Small

n

is an amount in moles. They differ by a factor of

6.02 \times 10^{23}

. Read the symbol in the question before you choose an equation.

Amount of Substance and the Mole

A gas holds a very large number of molecules. There are two ways to say how many.

One way is a plain count of molecules. The other way is the amount of substance, measured in moles. This lesson moves between them.