Avogadro's number

Avogadro's number, N_A, is defined as the number of atoms in 12 gram of carbon-12 atoms in their ground state at rest. By definition it is related to the atomic mass constant m_u by the relation

$N_{\mathrm {A} }m_{\mathrm {u} }=1/1000\quad {\hbox{exact}}.$

The exact factor 1/1000 appears here by the historic facts that the kilogram is the unit of mass and that in chemistry the mole is preferred over the Kmole. Recall that the atomic mass constant has the mass 1 u exactly (u is the unified atomic mass unit). Avogadro's number is indeed defined as number, a dimensionless quantity. Its latest numeric value is N_A = 6.022 141 79 10²³.

The SI definition of Avogadro's constant (also designated by N_A) is: the number of entities (such as atoms, ions, or molecules) per mole. (This definition requires, of course, a definition of mole that does not rely on N_A, but one that is in terms of ¹²C atoms). In this definition N_A has dimension mol⁻¹. The numeric value of Avogadro's constant is N_A = 6.022 141 79 10²³ mol⁻¹.

Because the mole and Avogadro's number are defined in terms of the atomic mass constant (one twelfth of the mass of a ¹²C atom), Avogadro's constant and Avogadro's number have by definition the same numerical value. In practice the two terms are used interchangeably.

History of Avogadro's number

Since 1811, when Amedeo Avogadro put forward the notion that equal volumes of gas (we now know ideal gas) contain equal number of particles, increasingly sophisticated methods of determining Avogadro’s constant have been developed over the past 200 years. These include the kinetic theory of gases, Brownian motion, measurement of the electron charge, black-body radiation, alpha particle emission, and X-ray measurements of crystals.

Without the belief that a macroscopic substance consists of minute particles (initially called atoms, later also molecules), it does not make sense to speak of Avogadro's number. This belief—atomism— was born in antiquity and grew further in importance with the developments of chemistry early in the 19th century. An important milestone was John Dalton’s law of multiple proportions published in 1804.