AS-Level Amounts of Substance
The number of moles in a sample can be calculated using the formula:
number of moles = mass (g) / molar mass
The molar mass (relative molecular mass or relative formula mass) of a compound is calculated by adding up all the relative atomic masses of the atoms within the compound’s formula.
Calculating Number of Moles Using Mass
There are two main ways of measuring how much of a substance you have - mass and volume.
We know that atoms of different elements have different relative atomic masses (see relative atomic mass); we also know that these atomic masses refer to the mass (in grams) of one mole’s worth of that atom.
Let’s take oxygen. Oxygen has a relative atomic mass of 16. This means, 1 mole of oxygen atoms has a combined mass of 16g.
This means we can say:
number of moles = mass (grams) / relative atomic mass (grams per mole)
Let’s check: if we have 16g of oxygen, how many moles do we have?
We need to know the mass (16g) and we can look-up the relative atomic mass of oxygen on the periodic table (16 g per mole).
number of moles = 16g / 16g per mole = 1 mole
There is a problem, and you may have spotted it. Oxygen does not actually exist as lone atoms – oxygen is found in elemental form (bonded to itself) as the molecule O .
O is a molecule, not an atom. So, we cannot use relative atomic mass to calculate the number of moles we have in a given mass. Instead, we need to use relative molecular mass.
Relative molecular mass is the relative atomic masses of all the atoms within a molecule added together. In one molecule of oxygen (O ) we have two atoms of oxygen. The relative atomic mass of oxygen is 16 g per mole. If we have two atoms, then the relative molecular mass will be 16 + 16 = 32 g per mole.
So, if we have 16 grams of oxygen gas. How many moles of oxygen molecules (O ) would we have?
Remember the equation:
number of moles = mass (grams) / relative molecular mass (grams per mole)
mass of O = 16 grams
relative molecular mass = 16 + 16 = 32 grams per mole
number of moles = 16 / 32 = 0.5 moles
This means we have 0.5 moles of O molecules in 16 grams of oxygen gas. The number of oxygen atoms in 16 grams of oxygen gas would simply be 1 mole.
If we have 0.5 moles of O molecules and 1 molecule is made of 2 oxygen atoms then the number of oxygen atoms we have would be 0.5 x 2 = 1 mole.