The mole (symbol: mol) is a unit used in chemistry to express the amount of a substance. It is defined as the amount of a substance that contains the same number of elementary entities (such as atoms, molecules, or ions) as there are atoms in exactly 12 grams of carbon-12.
The mole is considered a dimensionless quantity because it represents a pure number, much like the dozen. Therefore, the mole does not have a dimensional formula. However, it is often used in combination with other units to express quantities like molar mass, molar volume, and molar concentration, which do have dimensional formulas.
For example, the dimensional formula for molar mass (mass per mole) would be:
[Molar mass] = [Mass] / [Amount of substance] = kg / mol
Similarly, the dimensional formula for molar volume (volume per mole) would be:
[Molar volume] = [Volume] / [Amount of substance] = m³ / mol
In summary, while the mole itself is dimensionless, it is used in conjunction with other units to express various chemical quantities, each of which has its own dimensional formula.