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The Mole Concept

What is a mole in chemistry?

BeginnerReactions & Stoichiometry

What is it?

A mole is a counting unit for particles. One mole of anything contains 6.022 × 10²³ of those things. The particles can be atoms, molecules, ions or formula units.

The number 6.022 × 10²³ is called Avogadro’s number. The symbol for “one mole” is mol.

Key idea

A mole is a number of particles: 1 mol = 6.022 × 10²³ particles. Chemists use it because atoms are far too small and numerous to count one by one.

Why does it matter?

Atoms and molecules are extremely small. A single drop of water (about 0.05 g) contains roughly 1.7 × 10²¹ water molecules. Nobody can count particles like that, but we can weigh substances on a balance.

The mole is the bridge between the two worlds:

  • The particle world, where reactions happen one atom or molecule at a time.
  • The laboratory world, where we measure grams.

Balanced chemical equations are written in particles, and therefore in moles. For example,

2 HX2+OX2→2 HX2O\ce{2H2 + O2 -> 2H2O}

means 2 molecules of hydrogen react with 1 molecule of oxygen. It equally means 2 mol of HX2\ce{H2} react with 1 mol of OX2\ce{O2} to form 2 mol of HX2O\ce{H2O}. The mole lets you turn that ratio into masses you can actually weigh out. This is the basis of all stoichiometry.

How does it work?

1. The mole is a counting number

Just as “a dozen” always means 12, “a mole” always means 6.022 × 10²³. A mole of carbon atoms, a mole of water molecules and a mole of sodium ions all contain the same number of particles.

Think of it like this

A dozen eggs and a dozen watermelons contain the same number of items, but they have very different masses. In the same way, one mole of carbon atoms (12.01 g) and one mole of gold atoms (196.97 g) contain exactly the same number of atoms. Gold atoms are simply heavier.

The molar mass (symbol MM) is the mass of one mole of a substance, in grams per mole (g/mol).

Conveniently, the molar mass in g/mol has the same number as the atomic mass or formula mass in atomic mass units (u):

SubstanceMass of one particleMolar mass
Carbon atom, C\ce{C}12.01 u12.01 g/mol
Water molecule, HX2O\ce{H2O}2(1.008) + 16.00 = 18.02 u18.02 g/mol
Sodium chloride, NaCl\ce{NaCl}22.99 + 35.45 = 58.44 u58.44 g/mol

To find a molar mass, add up the atomic masses of all the atoms in the formula, taking account of the subscripts.

3. Two conversions do almost everything

Between mass and moles:

n=mMn = \frac{m}{M}

where nn is the amount in moles, mm is the mass in grams, and MM is the molar mass in g/mol.

Between moles and number of particles:

N=n×NAN = n \times N_\text{A}

where NN is the number of particles and NA=6.022×1023 mol−1N_\text{A} = 6.022 \times 10^{23}\ \text{mol}^{-1} is the Avogadro constant.

More precisely

Since 20 May 2019, the mole has been defined by fixing the Avogadro constant at exactly 6.022 140 76 × 10²³ mol⁻¹. Before that, one mole was defined as the number of atoms in exactly 12 g of carbon-12. Under today’s definition, one mole of carbon-12 has a mass extremely close to 12 g, but not exactly 12 g. For school and introductory university calculations, 6.022 × 10²³ is precise enough.

Visualise it

Mole map: three boxes stacked vertically. Mass in grams at the top, amount in moles in the middle, and number of particles at the bottom. To go from mass to moles, divide by the molar mass; from moles to mass, multiply by the molar mass. To go from moles to particles, multiply by Avogadro's number, 6.022 times ten to the 23; from particles to moles, divide by it.
The mole map: moles sit in the middle. Every conversion goes through moles.

Worked example

Worked example: From grams to moles to molecules

Question: How many moles of water, and how many water molecules, are in 36.0 g of water? (H = 1.008, O = 16.00)

  1. Find the molar mass of HX2O\ce{H2O}: M=2(1.008)+16.00=18.02M = 2(1.008) + 16.00 = 18.02 g/mol.
  2. Convert mass to moles: n=36.0 g18.02 g/mol=2.00 moln = \dfrac{36.0\ \text{g}}{18.02\ \text{g/mol}} = 2.00\ \text{mol}
  3. Convert moles to molecules: N=2.00 mol×6.022×1023 mol−1=1.20×1024N = 2.00\ \text{mol} \times 6.022 \times 10^{23}\ \text{mol}^{-1} = 1.20 \times 10^{24} molecules.

Answer: 36.0 g of water is 2.00 mol, which is 1.20 × 10²⁴ molecules.

Check the units: g ÷ (g/mol) leaves mol, and mol × mol⁻¹ leaves a pure number of molecules.

Worked example: From moles to grams

Question: What is the mass of 0.250 mol of sodium chloride, NaCl\ce{NaCl}? (Na = 22.99, Cl = 35.45)

  1. Find the molar mass: M=22.99+35.45=58.44M = 22.99 + 35.45 = 58.44 g/mol.
  2. Rearrange n=mMn = \dfrac{m}{M} to give m=n×Mm = n \times M.
  3. Substitute: m=0.250 mol×58.44 g/mol=14.6 gm = 0.250\ \text{mol} \times 58.44\ \text{g/mol} = 14.6\ \text{g}

Answer: 0.250 mol of sodium chloride has a mass of 14.6 g.

Common mistake

Common mistake: Mixing up atoms and molecules

One mole of oxygen gas, OX2\ce{O2}, contains 6.022 × 10²³ molecules but twice as many atoms (1.204 × 10²⁴), because each molecule has two oxygen atoms. Its molar mass is 2 × 16.00 = 32.00 g/mol, not 16.00 g/mol.

Always ask: a mole of what? Atoms, molecules or ions? Write the formula and count the atoms in it.

Common mistake: Multiplying when you should divide

Students often multiply mass by molar mass to get moles. Let the units guide you: to cancel grams, you must divide by g/mol. If your answer’s units don’t come out as mol, the setup is upside down.

Notation note

Textbooks use slightly different names and symbols for the same ideas:

  • Amount of substance (nn) is the quantity measured in moles. “Number of moles” means the same thing.
  • Atomic mass unit: many textbooks write amu. The symbol accepted in the SI is u (also called the dalton, Da).
  • Formula weight and molecular weight are older textbook names for the mass of one formula unit or molecule in u. Many textbooks now say formula mass and molecular mass instead.
  • The Avogadro constant, NAN_\text{A} = 6.022 × 10²³ mol⁻¹, has units. Avogadro’s number is the same value written as a plain number.

Remember this

Remember this

  • 1 mol = 6.022 × 10²³ particles.
  • Molar mass (g/mol) has the same number as the atomic or formula mass (u).
  • moles = mass ÷ molar mass, and particles = moles × 6.022 × 10²³.
  • Always ask: a mole of what?

Watch the video

Key points

  • [Key point 1]
  • [Key point 2]
  • [Key point 3]

Video page with transcript →

Test yourself

Check your understanding before moving on.

Flashcards

11 cards

  1. Question
    What is a mole?
    Answer

    A counting unit for particles. One mole contains 6.022×10236.022 \times 10^{23} particles (atoms, molecules, ions or formula units).

  2. Question
    What is the value of the Avogadro constant, to four significant figures?
    Answer

    NA=6.022×1023N_\text{A} = 6.022 \times 10^{23} mol⁻¹

  3. Question
    What is molar mass?
    Answer

    The mass of one mole of a substance, in g/mol. It has the same number as the atomic or formula mass in u.

  4. Question
    Which formula converts a mass in grams into moles?
    Answer

    n=mMn = \dfrac{m}{M} (moles = mass ÷ molar mass)

  5. Question
    Which formula converts moles into a number of particles?
    Answer

    N=n×NAN = n \times N_\text{A} (particles = moles × 6.022×10236.022 \times 10^{23})

  6. Question
    What is the molar mass of water, HX2O\ce{H2O}? (H = 1.008, O = 16.00)
    Answer

    2(1.008)+16.00=18.022(1.008) + 16.00 = 18.02 g/mol

  7. Question
    What is the mass of one mole of oxygen gas, OX2\ce{O2}? (O = 16.00)
    Answer

    32.00 g. Each OX2\ce{O2} molecule contains two oxygen atoms, so M=2×16.00M = 2 \times 16.00 g/mol.

  8. Question
    How many oxygen atoms are in 1 mol of OX2\ce{O2}?
    Answer

    2 mol of O atoms, which is 1.204×10241.204 \times 10^{24} atoms.

  9. Question
    Do 1 mol of carbon and 1 mol of gold contain the same number of atoms?
    Answer

    Yes, both contain 6.022×10236.022 \times 10^{23} atoms. Their masses differ (12.01 g and 196.97 g) because gold atoms are heavier.

  10. Question
    What is the name of the quantity measured in moles, and its symbol?
    Answer

    Amount of substance, symbol nn. Its unit is the mole (mol).

  11. Question
    How has the mole been defined since 2019?
    Answer

    By fixing the Avogadro constant at exactly 6.022 140 76×10236.022\,140\,76 \times 10^{23} mol⁻¹.

Quiz

7 questions

  1. Question 1EasyHow many particles are in one mole of a substance?
    Show answer

    Answer: 6.022×10236.022 \times 10^{23}

    A mole is a fixed counting number, like a dozen. One mole of any substance contains 6.022×10236.022 \times 10^{23} particles. The mass of a mole depends on the substance, but the number of particles does not.

  2. Question 2EasyWhat is the molar mass of carbon dioxide, COX2\ce{CO2}? (C = 12.01, O = 16.00)
    Show answer

    Answer: 44.01 g/mol

    One carbon atom plus two oxygen atoms: 12.01+2(16.00)=44.0112.01 + 2(16.00) = 44.01 g/mol. The answer 28.01 g/mol forgets the subscript 2 (it is the molar mass of CO).

  3. Question 3MediumHow many moles are in 9.00 g of water, HX2O\ce{H2O}? (M = 18.02 g/mol)
    Show answer

    Answer: 0.499 mol

    n=mM=9.00 g18.02 g/mol=0.499n = \dfrac{m}{M} = \dfrac{9.00\ \text{g}}{18.02\ \text{g/mol}} = 0.499 mol. The answer 162 mol comes from multiplying instead of dividing. Check the units: g ÷ (g/mol) gives mol.

  4. Question 4MediumWhat is the mass of 0.500 mol of sodium chloride, NaCl\ce{NaCl}? (M = 58.44 g/mol)
    Show answer

    Answer: 29.2 g

    m=n×M=0.500 mol×58.44 g/mol=29.2m = n \times M = 0.500\ \text{mol} \times 58.44\ \text{g/mol} = 29.2 g. The answer 117 g comes from dividing 58.44 by 0.500 instead of multiplying.

  5. Question 5MediumHow many oxygen atoms are in 1.00 mol of oxygen gas, OX2\ce{O2}?
    Show answer

    Answer: 1.204×10241.204 \times 10^{24}

    1.00 mol of OX2\ce{O2} contains 6.022×10236.022 \times 10^{23} molecules. Each molecule has 2 oxygen atoms, so there are 2×6.022×1023=1.204×10242 \times 6.022 \times 10^{23} = 1.204 \times 10^{24} atoms.

  6. Question 6HardWhich sample contains more atoms: 1 mol of helium, He\ce{He}, or 1 mol of hydrogen gas, HX2\ce{H2}?
    Show answer

    Answer: 1 mol of HX2\ce{H2}

    Both samples contain the same number of particles, 6.022×10236.022 \times 10^{23}. Helium particles are single atoms, but each HX2\ce{H2} molecule contains two atoms. So 1 mol of HX2\ce{H2} contains twice as many atoms.

  7. Question 7HardSince 2019, how is the mole defined?
    Show answer

    Answer: By fixing the numerical value of the Avogadro constant exactly

    In the 2019 revision of the SI, the Avogadro constant was fixed at exactly 6.022 140 76×10236.022\,140\,76 \times 10^{23} mol⁻¹. The carbon-12 definition was used before 2019, and many textbooks still mention it.

Notes and downloads

References

  1. Brown, T. L.; LeMay, H. E., Jr.; Bursten, B. E.; Murphy, C. J.; Woodward, P. M.; Stoltzfus, M. W. Chemistry: The Central Science, 15th ed.; Pearson, 2022.
  2. Bureau International des Poids et Mesures (BIPM). The International System of Units (SI), 9th ed.; BIPM, 2019. Link

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