Avogadro’s number

Avogadro’s number is the number of particles in one mole of any substance. Its numerical value is 6.02225 × 10²³. One mole of oxygen gas contains 6.02 × 10²³ molecules of oxygen, while one mole of sodium chloride contains 6.02 × 10²³ sodium ions and 6.02 × 10²³ ions. Avogadro’s number is used extensively in calculating the volumes, masses, and numbers of particles involved in chemical changes.

The concept that a mole of any substance contains the same number of particles arose out of research conducted in the early 1800s by the Italian physicist Amedeo Avogadro (1776-1856). Avogadro based his work on the earlier discovery by Joseph Gay-Lussac that gases combine with each other in simple, whole-number ratios of volumes. For example, one liter of oxygen combines with two liters of hydrogen to make two liters of water vapor.

Avogadro argued that the only way Gay-Lussac’s discovery could be explained was to assume that one liter of any gas contains the same number of particles as one liter of any other gas. To explain the water example above, he further hypothesized that the particles of at least some gases consist of two particles bound together, a structure to which he gave the name molecule.

For all elements and compounds, not just gases, a given weight must contain a certain number of atoms or molecules. A weight (in grams) equal to the atomic or molecular weight of the substance—that is, one mole of any element or compound—must contain the same number of atoms or molecules, because there is always a constant relationship between atomic weights and grams. (One atomic mass unit = 1.66 × 10^-22 g.) The number of atoms or molecules in one mole of an element or compound has been named Avogadro’s number, in honor of this realization.

The question then became, “What is this number of particles in a liter of any gas?” Avogadro himself never attempted to calculate this. Other scientists did make that effort, however. In 1865 the German physicist J. Loschmidt estimated the number of molecules in a liter of gas to be 2.7 × 10²². The accepted value today is 2.69 × 10²².

See also Atomic weight.