What Is Avogadro’s Number? Definition and Importance

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Avogadro's Number
Avogadro’s number is the number of particles in one mole of a substance.

Avogadro’s number is the number of units of any substance in one mole. It is also called Avogadro’s constant. Despite the name, Amedeo Avogadro did not discover or describe Avogadro’s number. Instead, it’s named in honor of Avogadro’s contributions to the field of chemistry.

Here is a look at the value and units of Avogadro’s number, why it’s important, and how its value is determined.

What Is Avogadro’s Number?

Avogadro’s number is a defined value that is exactly 6.02214076×1023. When used as a constant proportionality factor (NA), the number is dimensionless (no units). However, usually Avogadro’s number has units of a reciprocal mole or 6.02214076×1023 mol-1. Although all of the digits of the number are known, students usually use either 6.02 x 1023 or 6.022 x 1023, to keep consistent significant digits in chemistry calculations.

How Big Is Avogadro’s Number?

Avogadro’s number is one mole, so basically this is the same as asking how big a mole is. You can apply Avogadro’s number to anything:

  • Avogadro’s number of softballs would fill a sphere the size of the Earth.
  • One mole of red blood cells is more than all the red blood cells of every person alive right now.
  • Avogadro’s number of donuts would cover the Earth with a layer 5 miles deep.
  • A mole of moles (the animal) would weigh about half the mass of the Moon.
  • If you were given Avogadro’s number of pennies at birth, spent a million dollars every second of every day, and lived to age 100, you’d still have 99.99% of the pennies left.
  • It’s 18 milliliters of water molecules.

Determining Avogadro’s Number

The International Bureau of Weights and Measures (BIPM) defined the mole and Avogadro’s number in 2017. The International System of Units (SI) added this value to its list of one of the seven defining constants in 2019.

Prior to this date, Avogadro’s number was experimentally determined. So, most texts and articles describe slightly different values for Avogadro’s number. In 2017, the BIPM defined the number based on the number of atoms in 0.012 kilograms of the isotope carbon-12. Physicist Josef Perrin coined the name “Avogadro’s number” in 1909. He defined it as the number of molecules in 32 grams of oxygen.

Over the years, a few methods were used to calculate Avogadro’s number before it was defined:

  • In 1865, Josef Loschmidt estimated the number of particles (n0) in a volume of gas based on its pressure (p0) and absolute temperature (T0) and the gas constant R. His number is called the Loschmidt constant (n0 or L). It is related to Avogadro’s number:
    n0 = (p0*NA)/(RT0)
  • Josef Perrin used several experimental methods to calculate Avogadro’s number, earning him the 1926 Nobel Prize in Physics.
  • In 1910, Robert Millikan measured the charge of a single electron. Dividing the total charge on one mole of electrons by the charge on a single electron gives Avogadro’s number.
  • Other methods to calculate Avogadro’s number involved measurements of x-rays, black-body radiation, Brownian motion, and particle emission.

Importance of Avogadro’s Number

The reason Avogadro’s number is important is that is serves as a bridge between the very large numbers and familiar, manageable units. For example, because of Avogadro’s number we calculate the mass of one mole of water to be 18.015 grams. Without this proportionality constant giving us the mole, we’d have to write out “6.02214076×1023 water molecules has a mass of 18.015 grams”.

Basically, Avogadro’s number let us write the mass of one mole of a substance in small numbers (the molecular weight). It also lets us write the ratios between reactants and products in a chemical equation. This greatly simplifies calculations.

References

  • IUPAC (1997). “Avogadro Constant, NA, L”. Compendium of Chemical Terminology (the “Gold Book”) (2nd ed.). Blackwell Scientific Publications. doi:10.1351/goldbook
  • Kotz, John C.; Treichel, Paul M.; Townsend, John R. (2008). Chemistry and Chemical Reactivity (7th ed.). Brooks/Cole. ISBN 978-0-495-38703-9.
  • Murrell, John N. (2001). “Avogadro and His Constant”. Helvetica Chimica Acta. 84 (6): 1314–1327.  doi:10.1002/1522-2675(20010613)84:6<1314::AID-HLCA1314>3.0.CO;2-Q