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Avogadro Constant Calculator: Number of Particles

The Avogadro constant is 6.02 × 10²³ per mole: the number of particles in one mole. Number of particles = moles × Avogadro constant, or N = n × NA; from a mass, first find the moles with n = m / M.

Number of particles formula: N = n × NA

From moles
N = n·NA
N = n·NAn = NNA
From mass
N = mM·NA
N = mM·NAm = N·MNA
Number of atoms
Natoms = n·k·NA
Natoms = n·k·NAn = Natomsk·NA
N
number of particles
n
number of moles, mol
NA
Avogadro constant, mol⁻¹
m
mass, g
M
molar mass, g/mol
Natoms
number of atoms
k
atoms in one molecule

The legend lists the base units: g, mol, dm³ and g/mol. You can enter mg, kg, cm³ and other units; the calculator converts them and shows the conversion as a step. Relative atomic masses are rounded as in the GCSE periodic table, for example Cl = 35.5 and Cu = 63.5.

3.01 · 10²³—
mol⁻¹
Nnumber of particles
3.01 · 10²³
number of particles: 3.01 · 10²³
0.5 mol of substance contains 3.01 · 10²³ particles (N_A = 6.02 · 10²³ mol⁻¹). Zoom in from the spoonful to its molecules.

Step-by-step solution

  1. FormulaN = n·NA
  2. SubstituteN = 0.5 mol · 6.02 · 10²³ mol⁻¹
  3. AnswerN ≈ 3.01 · 10²³
What mass is that? n = 0.5 mol → m

Avogadro constant examples

  1. Example 1

    How many atoms are there in 3 mol of iron? The Avogadro constant is 6.02 · 10²³ mol⁻¹.

    Given:n = 3 molNA = 6.02 · 10²³ mol⁻¹
    1. FormulaN = n·NA
    2. SubstituteN = 3 mol · 6.02 · 10²³ mol⁻¹
    3. AnswerN ≈ 1.81 · 10²⁴

  2. Example 2

    Calculate the number of molecules in 22 g of carbon dioxide, CO₂. The Avogadro constant is 6.02 · 10²³ mol⁻¹.

    Given:CO₂m = 22 gNA = 6.02 · 10²³ mol⁻¹
    1. Molar massM(CO₂) = 12 + 2·16 = 44 g/mol
    2. FormulaN = mM·NA
    3. SubstituteN = 22 g44 g/mol · 6.02 · 10²³ mol⁻¹
    4. AnswerN ≈ 3.01 · 10²³

  3. Example 3

    A sample of water, H₂O, contains 0.1 mol of molecules. Using 6.02 · 10²³ mol⁻¹ for the Avogadro constant, calculate the total number of atoms in the sample.

    Given:H₂On = 0.1 molNA = 6.02 · 10²³ mol⁻¹
    1. Atoms in one formula unitk(H₂O) = 2 + 1 = 3
    2. FormulaNatoms = n·k·NA
    3. SubstituteNatoms = 0.1 mol · 3 · 6.02 · 10²³ mol⁻¹
    4. AnswerNatoms ≈ 1.81 · 10²³

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What is the Avogadro constant?

Atoms and molecules are far too small to count one by one, so chemists count them in moles. The Avogadro constant, 6.02 × 10²³ per mole, is the number of particles in one mole of any substance: 12 g of carbon, 18 g of water and 44 g of carbon dioxide each contain 6.02 × 10²³ particles. It links the amount in moles to the actual number of particles: N = n × NA.

When you start from a mass, first convert it to moles with n = m ÷ Mr, then multiply by the Avogadro constant. Be clear about what you are counting. One molecule of water, H₂O, has three atoms, so one mole of water contains 6.02 × 10²³ molecules but 3 × 6.02 × 10²³ = 1.806 × 10²⁴ atoms. The Avogadro constant is in the GCSE Higher tier, and its value is usually given in the question.

To get a feel for the size: a teaspoon of water, about 5 g, holds roughly 1.7 × 10²³ molecules. Counting one molecule a second, you would need about 5 × 10¹⁵ years, far longer than the age of the universe. That is why these answers come out in standard form.

Common mistakes

  • Counting molecules when the question asks for atoms. Multiply by the number of atoms in one molecule, for example 3 for H₂O.
  • Skipping the moles step when you start from a mass. Divide by Mr first, then multiply by the Avogadro constant.
  • Using the Ar of one atom for a gas made of molecules: one mole of O₂ has a mass of 32 g, not 16 g.
  • Leaving the answer out of standard form, such as 18.06 × 10²³. Write it as 1.806 × 10²⁴.

More chemistry formulas

MolesRelative formula massPercentage by massPeriodic tableAll chemistry equations

Frequently asked questions

6.02 × 10²³ per mole. It is the number of atoms, molecules or ions in one mole of a substance.

Multiply the number of moles by the Avogadro constant: N = n × 6.02 × 10²³. For 2 mol, that is 1.204 × 10²⁴ particles.

Convert the mass to moles (mass ÷ Mr), multiply by 6.02 × 10²³ to get molecules, then by the number of atoms in one molecule. For 32 g of O₂: 1 mol × 6.02 × 10²³ × 2 = 1.204 × 10²⁴ atoms.

It is in the Higher tier. Exam questions usually give the value, but you need to know what it means and how to use it.

They have the same value. The Avogadro constant has a unit, per mole (mol⁻¹), while Avogadro's number is the plain number 6.02 × 10²³.