3.2.1 Moles
The mole: a fixed, enormous number of particles
Definition
Mole
The amount of a substance, measured in mol, where one mole has a mass in grams numerically equal to its relative formula mass.
Definition
Avogadro constant
The number of particles in one mole of any substance, equal to 6.02×10236.02 \times 10^{23}6.02×1023 per mole.
- Atoms are far too small to count one by one, so chemists count them in a large fixed group called the mole (mol).
- One mole of any substance contains 6.02×10236.02 \times 10^{23}6.02×1023 particles, a value called the Avogadro constant.
- Those particles may be atoms, molecules or ions, depending on what the substance is made of.
Key Idea
A mole is just a counting word for 6.02×10236.02 \times 10^{23}6.02×1023 particles, in the same way that a dozen always means twelve.
One mole weighs its relative formula mass in grams
Definition
Relative atomic mass
The weighted mean mass of the atoms of an element compared with one twelfth of the mass of a carbon-12 atom.
- The mass of one mole of a substance in grams is numerically equal to its relative atomic mass or relative formula mass.
- This mass in grams per mole is the molar mass.
Example
- Carbon has Ar=12A_r = 12Ar=12, so one mole of carbon atoms has a mass of 12 g12\ \text{g}12 g.
- Water has Mr=18M_r = 18Mr=18, so one mole of water has a mass of 18 g18\ \text{g}18 g.
Converting between mass and moles
- The number of moles is found from n=mMrn = \dfrac{m}{M_r}n=Mrm, where mmm is the mass in grams.
- Rearranged, the mass is m=n×Mrm = n \times M_rm=n×Mr.
Example
- 88 g88\ \text{g}88 g of carbon dioxide (Mr=44M_r = 44Mr=44) is 8844=2 mol\dfrac{88}{44} = 2\ \text{mol}4488=2 mol.
- 0.5 mol0.5\ \text{mol}0.5 mol of sodium chloride (Mr=58.5M_r = 58.5Mr=58.5) has a mass of 0.5×58.5=29.25 g0.5 \times 58.5 = 29.25\ \text{g}0.5×58.5=29.25 g.
Equal moles mean equal numbers of particles
- The same number of moles of two different substances contains the same number of particles, even though their masses differ.
- One mole of water and one mole of carbon dioxide both contain 6.02×10236.02 \times 10^{23}6.02×1023 molecules.
Exam technique
- Write moles to the unit mol\text{mol}mol and keep mass in grams, or the numbers will not match the formula mass.
- The Avogadro constant is given in the exam when you need it, so you do not have to memorise the digits.
Use the right formula mass for the particle
- For a single element, use its relative atomic mass.
- For a compound, use the relative formula mass of the whole formula.
- For an element that exists as molecules, such as oxygen, use the mass of the molecule, so O2\text{O}_2O2 has a molar mass of 32 g32\ \text{g}32 g per mole.
Self review
- How many particles are there in one mole of a substance?
- What is the mass of one mole of water, given Mr=18M_r = 18Mr=18?
- How many moles are in 80 g80\ \text{g}80 g of sodium hydroxide, given Mr=40M_r = 40Mr=40?
- What mass is 3 mol3\ \text{mol}3 mol of carbon dioxide, given Mr=44M_r = 44Mr=44?
