What Is the Avogadro Constant?

The Avogadro constant, $N_{\mathrm A}$, is the number of specified elementary entities in one mole: exactly $6.02214076 \times 10^{23}\ \mathrm{mol}^{-1}$. In IB Chemistry SL and HL calculations, it is usually given or used as $6.02 \times 10^{23}\ \mathrm{mol}^{-1}$.

A mole is the SI unit for amount of substance. One mole always contains the same number of entities, but those entities may be atoms, molecules, ions, electrons or formula units. Therefore, the type of particle must always be identified.

The constant acts as a counting conversion, rather like 12 objects per dozen, except that one mole represents an enormously larger fixed collection. Since $N_{\mathrm A}$ has units of $\mathrm{mol}^{-1}$, multiplying it by an amount in moles cancels the mole unit and gives a dimensionless number of entities.

The relationship between the number of particles, $N$, and the amount in moles, $n$, is:

$$N=nN_{\mathrm A}$$

It can also be rearranged:

$$n=\frac{N}{N_{\mathrm A}}$$

To choose the correct form, follow the units. Convert moles to entities by multiplying by $N_{\mathrm A}$; convert entities to moles by dividing by $N_{\mathrm A}$. The numerical answer for entities should normally be written in scientific notation because particle numbers are extremely large.

For example, calculate the number of carbon dioxide molecules in $0.250\ \mathrm{mol}$ of $\mathrm{CO}_2$:

$$N=(0.250\ \mathrm{mol})(6.02 \times 10^{23}\ \mathrm{mol}^{-1})=1.51 \times 10^{23}\ \text{molecules}$$

Each $\mathrm{CO}_2$ molecule contains two oxygen atoms, so this sample contains $3.02 \times 10^{23}$ oxygen atoms. If total atoms are requested, count three atoms per molecule, giving $4.53 \times 10^{23}$ atoms. An ionic compound such as is counted in formula units, not molecules, because it forms an extended ionic lattice.

A common misconception is that the Avogadro constant and the mole are the same thing. They are not: the mole is a unit of amount, while the Avogadro constant is the conversion factor linking moles to entities.

The relationship can be combined with molar mass: first use $n=\frac{m}{M}$, then apply $N=nN_{\mathrm A}$.

For IB questions on Structure 1.4, identify the requested entity, show substitutions and units, and give an appropriately rounded final answer.