Avogadro’s Number

Core Concept

Avogadro's number ($N_A$) is defined as exactly $6.02214076 \times 10^{23}$ particles per mole. For most chemistry courses, using $6.022 \times 10^{23}$ is the standard level of precision.

Just as "a dozen" always means 12 items, "a mole" always means $6.022 \times 10^{23}$ items. This number was originally chosen because it is the number of atoms in exactly 12 grams of Carbon-12.

Moles to Particles: Multiply the number of moles by $N_A$.

$$\text{Particles} = \text{moles} \times (6.022 \times 10^{23})$$

Particles to Moles: Divide the number of particles by $N_A$.

$$\text{moles} = \frac{\text{number of particles}}{6.022 \times 10^{23}}$$

Practice Tips

Identify Your "Target" Particle: Before calculating, ask: "Am I looking for atoms, molecules, or formula units?" If a problem asks for atoms in 1 mole of $H_2O$, you must multiply Avogadro's number by 3 (2 Hydrogen + 1 Oxygen).
Calculator "EE" Key: When entering $6.022 \times 10^{23}$ into a calculator, use the EE or EXP button. This tells the calculator the value is a single number, preventing order-of-operation errors during division.
The Conversion Map: Always set up your dimensional analysis so that units cancel out.
- To go from Moles $\rightarrow$ Particles: Multiply by $6.022 \times 10^{23}$.
- To go from Particles $\rightarrow$ Moles: Divide by $6.022 \times 10^{23}$.
Check the Exponent: If you are calculating the number of atoms in a visible sample, your answer should almost always have a large positive exponent (around $10^{22}$ to $10^{25}$). If you get a negative exponent, you likely divided when you should have multiplied.

Test Yourself

Assorted Multiple Choice

Which of the following best describes the physical significance of Avogadro's number in a laboratory setting?

Podcast Episode

Episode

Avogadro's Number

Companion Guides

Coming soon

Student Guide Teacher Guide

Practice Problems & Worked Out Examples 🔒

Browse by category

01

Mole to/from Particle Conversion (Single-Step)

→ 02

Mass to/from Particle Conversion (Two-Step)

→ 03

Counting Sub-Atomic/Internal Particles (Multi-Step)

→ 04

Conceptual Understanding and Comparison

→ 05

Determining Avogadro's Number or Molar Mass

→ 06

Other / Uncategorized

→ 07

Assorted Multiple Choice

→

Core Concept

Calculation: To calculate the number of particles in a sample, multiply the amount of the substance in moles by Avogadro's number. For example, if you have 2 moles of water, the number of water molecules present would be 2 × 6.022 × 10²³ = 1.2044 × 10²⁴ molecules.

Relationship to molar mass: Avogadro's number is also related to the molar mass of a substance. The molar mass is the mass of one mole of a substance in grams. The molar mass of a substance can be calculated by dividing the mass of a sample by the number of moles present, which can then be used to calculate the number of particles using Avogadro's number.
Importance: Avogadro's number is a crucial concept in many areas of chemistry, including stoichiometry, gas laws, and thermodynamics. It provides a way to relate the number of particles in a sample to its macroscopic properties, such as volume and pressure.
Units: Avogadro's number has units of particles per mole (or molecules per mole).
Experimental determination: The value of Avogadro's number can be determined experimentally by a variety of methods, including X-ray crystallography, electron microscopy, and measurements of the density and viscosity of gases.
Use in the mole concept: Avogadro's number is an integral part of the mole concept, which is used to relate the number of particles in a sample to its mass and volume.
Applications: Avogadro's number is used in many applications in chemistry, including in the calculation of reaction stoichiometry, the determination of molecular weight, and the analysis of gas properties.

Brain Hack Tip

🧠 Here is a tip of how to remember how to correctly convert using moles 🧠

Remember to “mole-tiply”

When converting to moles to anything (grams or particles) you will start with moles and multiply by the correct conversion factor.

moles —> grams (multiply by molar mass)

moles —> particles (multiply by avogradro’s number)

Topic Related Resources

Labs

Demos

Activities

Simulations

LAB — 01

Lab

Coming Soon...