A mole is a fixed number of particles, $6.02 \times 10^{23}$, used to count atoms and molecules in chemistry. To calculate moles at GCSE you divide mass by relative formula mass ($n = m \div M_r$), or use gas volume, or use concentration and volume for a solution, depending on what the question gives you.
What is a mole and why do chemists use it?
Atoms and molecules are far too small and numerous to count individually, so chemists use the mole as a counting unit, in the same way a "dozen" always means 12 items. One mole of any substance always contains the same number of particles: $6.02 \times 10^{23}$, known as Avogadro's constant. This lets chemists convert between the mass of a substance and the actual number of particles it contains.
What is the formula for calculating moles from mass?
The most common GCSE moles calculation uses this formula, linking moles (n), mass (m) in grams, and relative formula mass ($M_r$):
$$n = \frac{m}{M_r}$$
Rearranged, this also gives mass ($m = n \times M_r$) and relative formula mass ($M_r = m \div n$), so the same triangle of values answers all three types of question.
How do you calculate moles from mass, step by step?
- Write down the mass of the substance given in the question, in grams.
- Work out the relative formula mass ($M_r$) by adding up the relative atomic masses of every atom in the formula.
- Divide the mass by the relative formula mass: $n = m \div M_r$.
- Give your answer in moles (mol), including units, and round appropriately if the question asks for a specific number of decimal places or significant figures.
Worked example: Calculate the number of moles in 22g of carbon dioxide, CO₂ ($M_r$ = 44, since C = 12 and O = 16, giving $12 + (16 \times 2) = 44$).
$$n = \frac{22}{44} = 0.5 \text{ mol}$$
How do you calculate moles from the volume of a gas?
At GCSE, one mole of any gas occupies 24 dm³ (24,000 cm³) at room temperature and pressure (RTP). This gives a second formula:
$$n = \frac{\text{volume in dm}^3}{24}$$
Worked example: Calculate the number of moles in 6 dm³ of oxygen gas at RTP.
$$n = \frac{6}{24} = 0.25 \text{ mol}$$
How do you calculate moles from a solution's concentration?
For a solution, moles are linked to concentration (c, in mol/dm³) and volume (v, in dm³) by:
$$n = c \times v$$
Remember to convert a volume given in cm³ into dm³ first, by dividing by 1000.
Worked example: Calculate the number of moles of sodium hydroxide in 250 cm³ of a 2 mol/dm³ solution.
First convert volume: $250 \div 1000 = 0.25$ dm³.
$$n = 2 \times 0.25 = 0.5 \text{ mol}$$
How do you find the number of particles once you have the moles?
Once you know the number of moles, multiply by Avogadro's constant to find the actual number of particles:
$$\text{Number of particles} = n \times 6.02 \times 10^{23}$$
Worked example: How many molecules are in 0.5 mol of carbon dioxide?
$$0.5 \times 6.02 \times 10^{23} = 3.01 \times 10^{23} \text{ molecules}$$
What mistakes do students commonly make with moles calculations?
Forgetting to convert units. Volumes must be in dm³ for both the gas formula and the concentration formula, so a volume given in cm³ must be divided by 1000 before it is used — a very common lost mark.
Mixing up mass and $M_r$. Mass is the specific amount used in that question, in grams, while $M_r$ is a fixed property of the substance calculated from the periodic table. Swapping them in the formula gives an answer that is wildly out of scale.
Not showing the rearranged formula. GCSE mark schemes usually award a mark for correctly rearranging $n = m \div M_r$ before substituting numbers, so always write the formula, then the rearrangement if needed, then the substitution, as separate working lines.
Frequently asked questions
What is Avogadro's constant and why is it that number?
Avogadro's constant is $6.02 \times 10^{23}$, the number of particles in exactly one mole of any substance. It was defined so that the mass of one mole of a substance, in grams, matches its relative formula mass, which makes converting between mass and number of particles far more convenient for chemists. You are given this constant in the GCSE exam data sheet, so you do not need to memorise the digits, only how to use it.
What is relative formula mass and how do you work it out?
Relative formula mass ($M_r$) is the sum of the relative atomic masses of every atom shown in a chemical formula. For water, H₂O, you add two hydrogen atoms (1 each) and one oxygen atom (16), giving $M_r = (1 \times 2) + 16 = 18$. Relative atomic masses are provided on the periodic table in your exam, so this is a lookup-and-add calculation rather than something to memorise.
What is the difference between relative formula mass and molar mass?
Relative formula mass ($M_r$) is a number with no units, calculated by adding atomic masses. Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol), and it has the same numerical value as $M_r$. So for CO₂, the relative formula mass is 44, and the molar mass is 44 g/mol — the number is identical, only the units and the way it is described differ.
Why do chemists use moles instead of just measuring mass?
Different substances have different masses per particle, so equal masses of two substances rarely contain equal numbers of particles or reacting units. Moles let chemists compare and react substances based on the actual number of particles involved, which is what balanced chemical equations describe. This makes moles essential for working out exact reacting quantities in practical chemistry and in exam calculations.
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