Science
What is a mole in chemistry, and how do you calculate moles?
Quick answer
A mole is the chemist's counting unit: 6.02 × 10²³ particles. To find the number of moles, divide the mass by the molar mass: n = m ÷ M.
In one sentence
A mole is a fixed number of particles, 6.02 × 10²³, that lets chemists count atoms and molecules by weighing them.
Explained
Atoms are far too small to count one by one. A single drop of water contains far more molecules than there are grains of sand on a big beach. So chemists use a counting unit, in the same way that a "dozen" means 12 eggs and a "ream" means 500 sheets of paper. The chemist's unit is the mole (symbol mol), and one mole means:
1 mol = 6.02 × 10²³ particles (the Avogadro constant, N_A)
That number is written in scientific notation: 602,000,000,000,000,000,000,000. Since 2019 it has been fixed exactly at 6.02214076 × 10²³, but 6.02 × 10²³ is enough for school. The "particles" can be atoms, molecules or ions; you just need to say which. The quantity measured in moles is called the amount of substance, with the symbol n.
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Why such a strange number? Because it makes the link to the periodic table simple. One mole of carbon-12 atoms has a mass of almost exactly 12 g, and in general the mass of one mole of any substance, in grams, is equal to its relative atomic mass (Ar) or relative formula mass (Mr). This mass is called the molar mass, M, measured in g/mol.
- Carbon, C: Ar = 12, so M = 12 g/mol.
- Water, H₂O: Mr = 2 × 1 + 16 = 18, so M = 18 g/mol.
- Carbon dioxide, CO₂: Mr = 12 + 2 × 16 = 44, so M = 44 g/mol.
This gives the most important formula on the topic, often drawn as a formula triangle:
number of moles = mass ÷ molar mass, n = m ÷ M
with m in grams and M in g/mol. Rearranged, m = n × M. Two more formulas use the same idea:
- Number of particles: N = n × N_A. Two moles of water contain 2 × 6.02 × 10²³ = 1.204 × 10²⁴ molecules.
- Gases: one mole of any gas takes up the same volume at the same temperature and pressure: about 24 L (24 dm³) at room temperature and about 22.4 L at 0 °C (both at 1 atm). So n = V ÷ 24 at room temperature.
- Solutions: concentration c = n ÷ V, in mol/L (mol/dm³), with V in litres.
Moles are what make chemical equations useful. The equation 2H₂ + O₂ → 2H₂O says that 2 mol of hydrogen react with 1 mol of oxygen to make 2 mol of water. Those numbers are a mole ratio, and they let you predict masses before you do a reaction.
Examples
| Substance | Formula | Molar mass | Mass | Moles |
|---|---|---|---|---|
| Water | H₂O | 18 g/mol | 36 g | 2 mol |
| Carbon dioxide | CO₂ | 44 g/mol | 11 g | 0.25 mol |
| Table salt | NaCl | 58.5 g/mol | 117 g | 2 mol |
| Calcium carbonate | CaCO₃ | 100 g/mol | 50 g | 0.5 mol |
| Glucose | C₆H₁₂O₆ | 180 g/mol | 360 g | 2 mol |
Worked example: how many moles are there in 980 g of sulfuric acid, H₂SO₄? (H = 1, S = 32, O = 16.) Molar mass = 2 × 1 + 32 + 4 × 16 = 98 g/mol. Moles = 980 ÷ 98 = 10 mol.
Common mistakes
- Dividing the wrong way. n = m ÷ M, mass on top. 36 g of water is 36 ÷ 18 = 2 mol, not 18 ÷ 36.
- Forgetting the small numbers in a formula. In H₂O there are two hydrogen atoms: M = 2 × 1 + 16 = 18, not 17.
- Using the atom for a molecule. Oxygen gas is O₂, so its molar mass is 32 g/mol, not 16.
- Mixing units. Use grams with g/mol, and litres with mol/L. 250 mL is 0.25 L.
Step by step
Step by step
- Write the formulaFor example H₂SO₄, and read off how many of each atom it contains.
- Find the molar massAdd up the relative atomic masses from the periodic table: 2 × 1 + 32 + 4 × 16 = 98 g/mol.
- Choose the formula you needMass: n = m ÷ M. Particles: n = N ÷ N_A. Gas: n = V ÷ molar volume. Solution: n = c × V.
- Substitute and calculateKeep the units in the working so you can see they cancel.
- Check the sizeA few grams of a small molecule is a small fraction of a mole; a kilogram is often many moles.
Practice questions
Mole calculations
Try each one, then check your answer.
- Find the molar mass of water, H₂O. (H = 1, O = 16)
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2 × 1 + 16 = 18 g/mol - Find the molar mass of carbon dioxide, CO₂. (C = 12, O = 16)
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12 + 2 × 16 = 44 g/mol - How many moles are there in 36 g of water?
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36 ÷ 18 = 2 mol - How many moles are there in 88 g of CO₂?
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88 ÷ 44 = 2 mol - Find the mass of 3 mol of sodium chloride, NaCl. (Na = 23, Cl = 35.5)
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M = 58.5 g/mol; 3 × 58.5 = 175.5 g - Find the mass of 0.25 mol of calcium carbonate, CaCO₃. (Ca = 40, C = 12, O = 16)
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M = 40 + 12 + 48 = 100 g/mol; 0.25 × 100 = 25 g - How many moles are there in 360 g of glucose, C₆H₁₂O₆?
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M = 72 + 12 + 96 = 180 g/mol; 360 ÷ 180 = 2 mol - How many moles are there in 980 g of sulfuric acid, H₂SO₄? (S = 32)
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M = 2 + 32 + 64 = 98 g/mol; 980 ÷ 98 = 10 mol - How many moles are there in 3.42 g of sucrose, C₁₂H₂₂O₁₁?
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M = 144 + 22 + 176 = 342 g/mol; 3.42 ÷ 342 = 0.01 mol - How many molecules are there in 2 mol of water?
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2 × 6.02 × 10²³ = 1.204 × 10²⁴ molecules - How many atoms are there in 0.5 mol of iron?
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0.5 × 6.02 × 10²³ = 3.01 × 10²³ atoms - How many moles are 1.204 × 10²⁴ molecules?
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1.204 × 10²⁴ ÷ 6.02 × 10²³ = 2 mol - How many hydrogen atoms are there in 1 mol of water?
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Each H₂O has 2 H atoms: 2 mol of H atoms = 1.204 × 10²⁴ atoms - What volume do 2 mol of a gas occupy at 0 °C and 1 atm? (22.4 L/mol)
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2 × 22.4 = 44.8 L - What volume do 0.5 mol of CO₂ occupy at room temperature? (24 L/mol)
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0.5 × 24 = 12 L - 0.2 mol of sodium hydroxide is dissolved to make 0.5 L of solution. Find the concentration.
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c = 0.2 ÷ 0.5 = 0.4 mol/L
Word problems
Moles in real life
Try each one, then check your answer.
- A glass holds 180 g of water. How many moles of water is that, and how many molecules?
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180 ÷ 18 = 10 mol; 10 × 6.02 × 10²³ = 6.02 × 10²⁴ molecules - Hydrogen burns: 2H₂ + O₂ → 2H₂O. How many moles of water form from 4 mol of hydrogen, and what is their mass?
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The ratio H₂ : H₂O is 2 : 2, so 4 mol of water; 4 × 18 = 72 g - Heating limestone: CaCO₃ → CaO + CO₂. What mass of CO₂ is released from 50 g of CaCO₃?
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50 ÷ 100 = 0.5 mol CaCO₃ → 0.5 mol CO₂; 0.5 × 44 = 22 g - Methane burns: CH₄ + 2O₂ → CO₂ + 2H₂O. What mass of oxygen is needed to burn 8 g of methane? (CH₄ = 16 g/mol)
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8 ÷ 16 = 0.5 mol CH₄ needs 1 mol O₂; 1 × 32 = 32 g - You need 250 mL of a 0.1 mol/L salt (NaCl) solution. What mass of salt do you weigh out?
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n = 0.1 × 0.25 = 0.025 mol; 0.025 × 58.5 = 1.4625 g (about 1.46 g) - A party balloon holds 12 L of helium at room temperature (24 L/mol). How many moles is that, and what mass? (He = 4)
Show answer
12 ÷ 24 = 0.5 mol; 0.5 × 4 = 2 g
Questions people ask
What is a mole in simple words?
It is a number, like a dozen, but much bigger: 6.02 × 10²³. A mole of anything, atoms, molecules or ions, contains exactly that many particles.
What is the formula for moles?
n = m ÷ M: moles = mass in grams ÷ molar mass in g/mol. For particles, n = N ÷ N_A; for a gas at room temperature, n = V ÷ 24 L; for a solution, n = c × V.
How do you find the molar mass?
Add up the relative atomic masses of all the atoms in the formula, using the periodic table. For CO₂: 12 + 16 + 16 = 44, so the molar mass is 44 g/mol.
What is the symbol and unit of the mole?
The unit is the mole, symbol mol. The quantity it measures is the amount of substance, symbol n. It is one of the seven base units of the SI system.
How many moles are in a litre of gas?
At room temperature and pressure, 1 mol of any gas fills about 24 L, so 1 L is about 1/24 mol. At 0 °C and 1 atm, 1 mol fills about 22.4 L.
What is a mole ratio?
It is the ratio of the numbers in front of the formulas in a balanced equation. In 2H₂ + O₂ → 2H₂O the mole ratio of hydrogen to oxygen is 2 : 1.
What is mole fraction?
The mole fraction of one substance in a mixture is its number of moles divided by the total number of moles. Air is about 21% oxygen by volume, so the mole fraction of oxygen is about 0.21.
Quick quiz
The mole (amount of substance)
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How many particles are there in one mole of a substance?
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