Revise The mole and the Avogadro constant for Cambridge 9701 (2.2)

The mole (symbol: mol) is the SI unit for the amount of substance. It is formally defined based on a standard: one mole is the amount of substance containing as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in exactly 12 grams of the carbon-12 isotope. This specific number of entities is known as the Avogadro constant.

The molar mass ($M$) of a substance is the mass of one mole of that substance. It is expressed in units of grams per mole (g mol^{-1}). Conveniently, the numerical value of the molar mass is the same as the relative atomic mass ($A_r$) for an element, or the relative molecular/formula mass ($M_r$) for a compound, which you can calculate using values from the Periodic Table.

Amount of substance ($n$) = $\frac{\text{mass } (m)}{\text{molar mass } (M_r)}$

For reactions in solution, we use concentration to describe the amount of a solute dissolved in a certain volume of solvent. Concentration is defined as the amount of substance (in moles) per unit volume. The standard unit for volume in these calculations is the decimetre cubed ($\mathrm{dm}^{3}$), which is equivalent to 1 litre.

Concentration ($c$) = $\frac{\text{amount of substance } (n)}{\text{volume } (V)}$

Avogadro's Law states that equal volumes of different gases, at the same temperature and pressure, contain the same number of molecules (and therefore the same number of moles). This leads to the concept of molar volume. For A-Level Chemistry, you need to know that at room temperature and pressure (r.t.p. - approx. 25°C and 1 atm), one mole of any ideal gas has a volume of $24\ \mathrm{dm}^{3}$ (or $24{,}000\ \mathrm{cm}^{3}$).

Amount of gas ($n$) = $\frac{\text{Volume of gas}}{\text{Molar volume}}$

At r.t.p., this becomes: $n = \frac{\text{Volume in }\mathrm{dm}^{3}}{24}$ or $n = \frac{\text{Volume in }\mathrm{cm}^{3}}{24000}$