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What is Avogadro's Number? Definition and Uses

Avogadro's number is a numerical value that indicates the number of elementary particles contained in one mole of a substance. Its exact value is:

N0=6.02214076×1023N_0 = 6.02214076 \times 10^{23}

This number means that one mole of atoms, molecules, or ions always contains exactly that many particles. It's usually denoted as N0N_0.

Avogadro's number itself is dimensionless, since it represents only a count of particles. The related quantity with units is the Avogadro constant, denoted NAN_A, which has units of  mol−1\rm{\ mol^{-1}} (per mole), and expresses the number of particles per unit amount of substance.

The Avogadro constant is the official SI constant that defines the mole and has the exact value:

NA=6.02214076×1023 mol−1N_A = 6.02214076 \times 10^{23}\rm{\ mol^{-1}}

Avogadro's number refers specifically to the numerical value of this constant without units. While the two terms are often used interchangeably in practice, they describe different concepts: the Avogadro constant is a physical constant with units, while the Avogadro's number is simply a numerical value.

Understanding what Avogadro's number is helps explain how scientists relate microscopic particles to measurable amounts of a substance.

Avogadro's number is primarily used as a proportionality factor that links the number of particles in a substance to the amount of matter in moles. It enables chemists to convert between microscopic quantities, such as atoms or molecules, and macroscopic amounts that can be weighed or measured. The relationship can be expressed as:

N=n×NA​N = n \times N_A​

where NN is the number of particles, nn is the number of moles, and NAN_A is Avogadro constant, 6.022×1023 mol−16.022 \times 10^{23}\rm{\ mol^{-1}}.

In practice, Avogadro's number is used to:

  • Convert between moles and particles;
  • Relate particle counts to mass or volume;
  • Interpret mole ratios in chemical equations; and
  • Connect gas measurements to molecular quantities.

For example, if you know there are 1.204 × 1024 water molecules, you can calculate the number of moles using:

n=NNA=1.204×1024 molecules6.022×1023 mol−1=2 mol\begin{aligned} n &= \frac{N}{N_A} \\[1.2em] &= \frac{1.204\times 10^{24} \ \rm{molecules}}{6.022 \times 10^{23}\rm{\ mol^{-1}}} \\[1em] &= \rm{2 \ mol} \end{aligned}

💡 For faster conversions between moles and individual atoms or molecules, a molecule moles to atoms calculator can perform this calculation instantly using Avogadro’s constant.

From here, you can find the total mass by multiplying by the molar mass of the substance. For water, its molar mass is 18 g/mol:

mass=n × molar mass=2 mol×18 g/mol=36 g\begin{aligned} \rm{mass} &= n \rm{\ \times \ molar \ mass} \\ &= \rm{2 \ mol \times 18 \ g/mol = 36 \ g} \end{aligned}

Similarly, Avogadro's number can be used to calculate the volume of a gas or, in stoichiometry, to determine the number of particles from mole ratios.

Understanding why Avogadro's number is important enables the calculation of particle counts in reactions, the prediction of product yields, and consistency in chemical measurements.

Avogadro's law is related to gases, and it states that equal volumes of gases at the same temperature and pressure contain the same number of particles. By measuring the volume, pressure, and temperature of a gas, it's possible to estimate the number of particles in a known amount of substance.

The law is named after the Italian scientist Amedeo Avogadro, who in 1811 suggested that two samples of an ideal gas with the same volume, temperature, and pressure contain the same number of molecules.

Years later, in 1909, Jean Perrin coined the term for Avogadro's number, defining it as the number of molecules in one gram-molecular volume of an ideal gas at standard conditions (22.414 liters, which, for example, is 32 grams of oxygen gas). Using the proportionality implied by Avogadro's law, Perrin calculated the exact number of particles in one mole of a substance.

Avogadro's number is important because it links measurable amounts of substances to the exact number of atoms or molecules they contain.

It enables the calculation of the number of particles in reactions, the prediction of how much product can form, and the consistent measurement of chemical quantities. One mole of any substance always contains the same number of particles, regardless of its type.

No, they are related, but not identical. Avogadro's number is the dimensionless numerical value 6.02214076 × 10²³, while the Avogadro constant is a physical quantity that has the same value expressed with units of mol⁻¹ (per mol) and used as an SI defining constant.

No. This number is dimensionless, but in practice it is used to express the number of particles per mole.

The term was coined by Jean Perrin, who named it in honor of Amedeo Avogadro, the scientist who proposed a method to calculate the amount of gas in a container, now known as Avogadro's law.

This article was written by Gabriela Diaz and reviewed by Steven Wooding.