The Mole and Avogadro’s Number
The mole (symbol mol) is the SI unit of amount of substance, defined as exactly 6.02214076 × 1023 elementary entities, and this number is called Avogadro’s number or the Avogadro constant (NA). In brief: one mole of any substance contains 6.022 × 1023 particles (atoms, molecules, ions or formula units), and its mass in grams equals its atomic, molecular or formula mass: 1 mol of carbon atoms is about 12.01 g, and 1 mol of water is 18.02 g.
Atoms and molecules are so small that even a tiny sample contains an enormous number of them. The mole gives chemists a convenient unit for counting these particles in the same way that a dozen is a convenient unit for eggs. This article explains the idea of the mole, the size of Avogadro’s number, the link between moles, mass and number of particles, includes a table comparing amounts of familiar substances, works through examples that show the scale, explains the 2019 redefinition and tells the history of the concept.
What is the mole?
A mole is a counting unit like a dozen (12), a gross (144) or a pair (2), but it is much larger. The unit applies to any kind of “elementary entity”: atoms, molecules, ions, electrons or formula units. You must always say what the entities are: “1 mol of oxygen atoms” is not the same as “1 mol of oxygen molecules”. The quantity measured in moles is called the amount of substance and has the symbol n.
How large is Avogadro’s number?
NA = 6.02214076 × 1023 mol−1, which is usually rounded to 6.022 × 1023. This is 602,214,076,000,000,000,000,000. Some comparisons give an idea of the size:
- If you counted one particle each second, it would take 6.022 × 1023 ÷ 3.156 × 107 s per year = 1.9 × 1016 years, which is about 1.4 million times the age of the universe (13.8 billion years).
- A mole of grains of rice would cover the land area of the Earth to a depth of many meters (more than 100 meters).
- There are about 6 × 1023 water molecules in 18 mL of water, which is less than two tablespoons.
What relationships connect moles, mass and particles?
| Quantity | Formula | Unit |
|---|---|---|
| Number of particles (N) | N = n × NA | particles |
| Mass (m) | m = n × M | g |
| Amount (n) from mass | n = m ÷ M | mol |
| Amount (n) from particles | n = N ÷ NA | mol |
| Volume of gas at STP (V) | V = n × 22.4 L/mol | L |
| Solution concentration (c) | c = n ÷ V (V in L) | mol/L |
One mole of familiar substances
| Substance | Entities | Mass of 1 mol (g) | Approximate volume or appearance |
|---|---|---|---|
| Carbon (graphite) | C atoms | 12.01 | About 5.3 cm3 of solid |
| Iron | Fe atoms | 55.85 | About 7.1 cm3, a small cube of 1.9 cm |
| Water | H2O molecules | 18.02 | 18 mL of liquid |
| Sodium chloride | NaCl formula units | 58.44 | About 27 cm3, roughly two tablespoons |
| Sucrose | C12H22O11 molecules | 342.3 | About two cups of sugar |
| Oxygen gas | O2 molecules | 32.00 | 22.4 L at STP |
Worked examples
- Number of atoms in a mole. 1.00 mol of copper contains 6.022 × 1023 atoms and has a mass of 63.55 g.
- Number of molecules from moles. 0.250 mol of water: N = 0.250 × 6.022 × 1023 = 1.51 × 1023 molecules.
- Moles from the number of particles. 3.01 × 1022 molecules of CO2: n = 3.01 × 1022 ÷ 6.022 × 1023 = 0.0500 mol.
- Atoms in a molecule. 1.00 mol of CO2 contains 1.00 mol of C atoms and 2.00 mol of O atoms: a total of 3.00 mol of atoms, or 3 × 6.022 × 1023 = 1.81 × 1024 atoms.
- Mass of one atom. One carbon atom has a mass of 12.011 g ÷ 6.022 × 1023 = 1.994 × 10−23 g, which is 1.994 × 10−26 kg.
- Size of the number. A drop of water of 0.050 g contains 0.050 ÷ 18.015 = 2.8 × 10−3 mol, or 2.8 × 10−3 × 6.022 × 1023 = 1.7 × 1021 molecules. Even a single drop therefore holds more than a billion billion molecules.
How is the mole defined?
Until 2019, the mole was defined as the amount of substance that contains as many entities as there are atoms in exactly 12 g of carbon-12, and Avogadro’s number was a measured quantity. Since 20 May 2019, the SI defines the mole by fixing the numerical value of the Avogadro constant at exactly 6.02214076 × 1023 mol−1. The kilogram was redefined at the same time through the Planck constant. As a result, the molar mass of carbon-12 is no longer exactly 12 g/mol, but is equal to it within a relative uncertainty of about 10−9.
Who was Avogadro?
Amedeo Avogadro, an Italian scientist, proposed in 1811 that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, and that elementary gases such as hydrogen and oxygen exist as diatomic molecules. His idea was ignored for decades, until Stanislao Cannizzaro revived it at the Karlsruhe Congress in 1860. The number of particles in a mole was first estimated in 1865 by Josef Loschmidt from the kinetic theory of gases. Jean Perrin measured it in the early 1900s by several independent methods, including Brownian motion, and in 1909 he proposed the name “Avogadro’s number”. He received the Nobel Prize in Physics in 1926. The word “mole” was introduced by Wilhelm Ostwald around 1893, from the German for molecule.
Which mistakes are common?
Mistake 1: Not specifying the entity
Say “1 mol of O2 molecules” or “1 mol of O atoms”. The mass and the number of atoms differ by a factor of 2.
Mistake 2: Confusing mole and mass
A mole is a number of particles. One mole of lead has a much greater mass than one mole of carbon.
Mistake 3: Treating Avogadro’s number as the number of particles in a gram
It is the number of particles in one mole, and the mass of the mole depends on the substance.
Mistake 4: Forgetting to count the atoms in the formula
One mole of Al2(SO4)3 contains 2 mol of Al, 3 mol of S and 12 mol of O atoms.