B.3.2—Amount of substance

Amount of substance

The amount of substance $$n$$ counts how many groups of $$N_A$$ particles are present:

$$n=\frac{N}{N_A}$$

where N is the number of particles and $$N_A$$ is the Avogadro constant.

Connect mass to moles

If molar mass is M, then

$$n=\frac{m}{M}$$

Use matching units for m and M. Once n is known, the number of particles is $$N=nN_A$$.

Use ratios efficiently

For equal numbers of particles, the samples contain equal amounts in moles even if their masses differ. For isotope or element comparisons, calculate moles before comparing particle counts.

Worked comparison from local Question Bank row 28984

For $40\,\mathrm{g}$ of argon-40, $n_{Ar}=40/40=1.0\,\mathrm{mol}$. For $8\,\mathrm{g}$ of helium-4, $n_{He}=8/4=2.0\,\mathrm{mol}$. Since $N=nN_A$,

$$\frac{N_{Ar}}{N_{He}}=\frac{1.0N_A}{2.0N_A}=\frac12$$

The larger argon mass does not mean more atoms; its molar mass is also larger.

Common trap

Do not confuse N (number of particles) with $$N_A$$ (particles per mole) or n (amount in moles).