The mole and the Avogadro constant — common mistakes

A very common mistake is forgetting to convert volumes given in $\mathrm{cm}^{3}$ to $\mathrm{dm}^{3}$. Remember that $1\ \mathrm{dm}^{3} = 1000\ \mathrm{cm}^{3}$. To convert from $\mathrm{cm}^{3} to \mathrm{dm}^{3}$, you must divide by 1000. Always check your units before calculating!

The molar volume of 24 $\mathrm{dm}^{3} mol^{-1} is an approximation used in exams and is only valid for gases at r$.t.p. Do not use it for solids, liquids, or gases at other temperatures and pressures unless you are given a different value for the molar volume.

Carbon-12 was chosen as the standard because it is a common, stable, and easily purified solid. Using a specific isotope (carbon-12) provides a precise and reproducible standard for defining the atomic mass unit and, by extension, the mole.

Relative molecular mass ($M_r$) is a ratio and has no units. It's the mass of a molecule compared to 1/12th the mass of a carbon-12 atom. Molar mass ($M$) is the mass of one mole of a substance and has units of g mol^{-1}. Numerically, they are the same value.

Yes, if you want the final concentration to be in the standard units of mol dm^{-3}. The formula $c = n/V$ requires volume ($V$) to be in $\mathrm{dm}^{3} to give concentration ($c$) in mol dm^{-3}$. It's a critical step that is often tested.

No, absolutely not. The molar volume of 24 $\mathrm{dm}^{3} mol^{-1} applies only to gases at room temperature and pressure$. The volume of one mole of a liquid or solid is much smaller and depends on its density. For example, one mole of water (18 g) has a volume of only about 18 $\mathrm{cm}^{3}$.