Moles and masses - Higher
There is a relationship between a relative atomic massThe mean relative mass of the atoms of the different isotopes in an element. It is the number of times heavier an atom is than one-twelfth of a carbon-12 atom. (Ar) or relative formula massThe sum of the relative atomic masses of the atoms in a chemical formula. (Mr), and the massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). of one moleThe amount of substance that contains the same number of particles as there are atoms in 12 g of carbon-12 (contains the Avogadro's constant 6.0 ×10²³ number of particles). of a substance:
Some examples are given in the table below.
| Substance | Formula | Ar or Mr | Mass of 1 mol (g) |
| Calcium | Ca | 40.1 | 40.1 |
| Oxygen | O2 | 2 × 16.0 = 32.0 | 32.0 |
| Calcium carbonate | CaCO3 | 40.1 + 12.0 + (3 × 16.0) = 100.1 | 100.1 |
| Substance | Calcium |
|---|---|
| Formula | Ca |
| Ar or Mr | 40.1 |
| Mass of 1 mol (g) | 40.1 |
| Substance | Oxygen |
|---|---|
| Formula | O2 |
| Ar or Mr | 2 × 16.0 = 32.0 |
| Mass of 1 mol (g) | 32.0 |
| Substance | Calcium carbonate |
|---|---|
| Formula | CaCO3 |
| Ar or Mr | 40.1 + 12.0 + (3 × 16.0) = 100.1 |
| Mass of 1 mol (g) | 100.1 |
This relationship is useful because it makes it possible to work out the mass of reactants needed to make a particular mass of product. It is also possible to work out which reactant will be used up.
Calculating number of moles
The number of moles of a given mass substance is calculated using:
Use Ar instead of Mr for metals or separate atomThe smallest part of an element that can exist..
Question
Calculate the number of moles of carbon atoms in 6.0 g of carbon. (Relative atomic mass: C = 12.0)
number of moles = \(\frac{mass}{A_r}\)
number of moles = \(\frac{6.0}{12.0}\)
= 0.50 mol
Calculating masses
To calculate the mass if given the number of moles and the relative formula mass, the equation must be rearranged to make mass the subject.
One way to remember this is ‘mass equals mister mole’.
Question
Calculate the mass of 0.25 mol of carbon dioxide molecules. (Relative formula mass: CO2 = 44.0)
mass = 44.0 × 0.25
= 11 g
The calculation is the same if a substance is a metal or exists as separate atoms, but its Ar is used instead of an Mr.
Example
Question
Calculate the mass of 0.125 moles of iron. (Relative atomic mass: Fe = 55.8)
mass = 55.8 × 0.125
= 6.98 g (to 3 significant figures)