Moles to Number of Particles: Using the Avogadro Constant

By Aniket Bhardwaj · 17 October 2026 · Updated 17 October 2026 · Class 11 Chemistry

The mole is a counting unit, like a dozen, but much larger. Almost every Class 11 numerical on the mole concept ends with a question such as "how many molecules?" or "how many atoms?". The bridge between the mole and the actual number of particles is the Avogadro constant. This page shows how to cross that bridge in both directions and how to count atoms and ions inside a molecule or formula unit.

The water example shows 0.4996 mol becoming 3.009 × 10²³ molecules and then 9.03 × 10²³ atoms. — Convert moles to molecules, then multiply by 3 atoms per H₂O molecule.

The formula

N = n × N_A
n = m ÷ M
N = (m ÷ M) × N_A

N is the number of particles (atoms, molecules or ions). n is the amount in moles. N_A is the Avogadro constant, which is exactly 6.02214076 × 10²³ mol⁻¹ in the present SI system. Most textbooks round it to 6.022 × 10²³, and some use 6.02 × 10²³. m is the mass in grams and M is the molar mass in g mol⁻¹. Use the number of significant figures your question allows, and use the same value of N_A throughout the question.

Note the particle you are counting. One mole of water has 6.022 × 10²³ molecules, but 3 × 6.022 × 10²³ atoms, because each H₂O has three atoms. Always write the particle after the number.

Worked example 1: molecules and atoms in water

Question. How many molecules and how many atoms are present in 9.0 g of water?

Moles. M(H₂O) = 18.015 g mol⁻¹, so n = 9.0 ÷ 18.015 = 0.4996 mol.

Molecules. N = 0.4996 × 6.022 × 10²³ = 3.009 × 10²³ molecules (with the exact N_A the answer is 3.0086 × 10²³).

Atoms. Each molecule has 3 atoms: 3.009 × 10²³ × 3 = 9.03 × 10²³ atoms, of which 6.02 × 10²³ are hydrogen and 3.01 × 10²³ are oxygen.

Worked example 2: atoms in carbon dioxide

Question. How many atoms are there in 5.00 g of CO₂?

Molar mass. 12.011 + 2(15.999) = 44.009 g mol⁻¹.

Moles. 5.00 ÷ 44.009 = 0.11361 mol.

Molecules. 0.11361 × 6.02214 × 10²³ = 6.842 × 10²² molecules.

Atoms. 3 atoms per molecule: 6.842 × 10²² × 3 = 2.053 × 10²³ atoms.

Worked example 3: mass of one molecule

Question. Find the mass of a single molecule of water in grams.

Idea. One mole weighs 18.015 g and contains 6.02214 × 10²³ molecules, so one molecule weighs M ÷ N_A.

Calculation. 18.015 ÷ 6.02214 × 10²³ = 2.991 × 10⁻²³ g.

This is why we never count molecules directly. The number is far too small to weigh one at a time.

Worked example 4: ions in sodium chloride

Question. How many Na⁺ and Cl⁻ ions are present in 11.7 g of NaCl?

Molar mass. 22.990 + 35.45 = 58.44 g mol⁻¹.

Moles. 11.7 ÷ 58.44 = 0.2002 mol of NaCl.

Formula units. 0.2002 × 6.022 × 10²³ = 1.206 × 10²³.

Ions. Each formula unit gives one Na⁺ and one Cl⁻, so there are 1.206 × 10²³ Na⁺ ions, 1.206 × 10²³ Cl⁻ ions and 2.411 × 10²³ ions in total. NaCl has no separate molecules, so say "formula units", not "molecules".

Worked example 5: electrons in a sample

Question. How many electrons are present in 1.8 g of water?

Moles. 1.8 ÷ 18.015 = 0.09992 mol.

Molecules. 0.09992 × 6.022 × 10²³ = 6.017 × 10²².

Electrons. One H₂O has 2(1) + 8 = 10 electrons, so the total is 6.017 × 10²³ electrons.

Common mistakes

Multiplying mass directly by N_A. Mass must be changed to moles first (n = m ÷ M). Only moles multiply N_A.
Mixing molecules and atoms. 0.5 mol of O₂ has 0.5 × N_A molecules but 1.0 × N_A atoms. Read what the question counts.
Forgetting that some elements are molecular. Hydrogen is H₂, chlorine is Cl₂, and so on. The mass of 1 mol of H₂ is 2.016 g, not 1.008 g.
Errors in powers of ten. When you multiply 0.4996 by 6.022 × 10²³, the answer is 3.009 × 10²³, not 3.009 × 10²². Put the answer in standard form and check the exponent.
Using "molecules" for ionic solids. NaCl, MgO and K₂SO₄ are counted as formula units.

Quick reference

You are given	Step 1	Step 2
Mass of a substance	n = m ÷ M	N = n × N_A
Number of particles	n = N ÷ N_A	m = n × M
Volume of a gas at STP	n = V ÷ molar volume	N = n × N_A
Atoms per molecule known	Find molecules first	Multiply by atoms per molecule

For gases at STP the molar volume is 22.4 L mol⁻¹ in older books (0 °C and 1 atm) and 22.7 L mol⁻¹ in books that use 1 bar. Use the one your textbook uses.

There is no dedicated Avogadro-number tool in the suite. For the molar mass step, the calculator suite can still help you check M before you multiply by N_A.

Open the Chemistry Calculator Suite →

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