The Avogadro constant (symbols: L, NA), also called the Avogadro number, is the number of atoms in exactly 12 grams of 12C. A mole is defined as this number of "entities" (usually, atoms or molecules) of any material.[1][2] The currently accepted value for this number is:[3]

$N_A = (6.022 \, 141 \, 79\pm 0.000 \, 000 \, 30)\,\times\,10^{23} \mbox{ mol}^{-1} \,$

The value of Avogadro's constant was first indicated by Johann Josef Loschmidt who, in 1865, computed the number of particles in one cubic centimetre of gas held at standard conditions. The term Loschmidt constant is thus more correctly applied for this value, which can be said to be proportional to the Avogadro number. However, in the German language literature, "Loschmidt constant" refers to both this quantity as well as the number of entities in a mole.

## History and etymology

The Avogadro constant is named after the early nineteenth century Italian scientist Amedeo Avogadro, who is credited (1811) with being the first to realize that the volume of a gas (strictly, of an ideal gas) is proportional to the number of atoms or molecules. The French chemist Jean Baptiste Perrin in 1909 proposed naming the constant in honor of Avogadro. American chemistry textbooks picked it up in the 1930s followed by high school textbooks starting in the 1950s.[4]

### Loschmidt: Measuring the Avogadro Number

Avogadro never attempted to measure the constant: the numerical value was first estimated by the Austrian physicist Johann Josef Loschmidt in 1865 using the kinetic theory of gases.[5] In German-speaking countries, the constant is sometimes referred to as the Loschmidt constant or Loschmidt's number, but what Loschmidt actually measured is the number of particles per unit volume of an ideal gas, i.e. the number density of particles in an ideal gas. Thus, the term Loschmidt constant is more appropriate to the number of particles per unit of gas, Symbol: no:[6]

$n_\circ = \frac{p}{k_B T} \,$

equal to (2.686 7774 ± 0.000 0047) × 1025 m−3 at 273.15 K and 101.325 kPa with kB the Boltzmann constant, T the temperature and p the pressure.

This constant is related to the Avogadro constant by the relation:

$R = N_Ak_B \,$

with kB the Boltzmann constant, and R the gas constant, hence

$N_A = \frac{n_\circ R T}{p} \,$

However, in German scientific literature, the term Loschmidt constant is used ambiguously - it often refers to what has come to be known as Avogadro number.[7] However, Boltzmann had first used the term for the sense in which Loschmidt had measured it - the number of particles in a unit volume of gas. Thus, its use in referring to the related Avogadro number leads to confusion and is usually deprecated. For the same reason, sometimes the Avogadro Number is denoted as L as opposed to NA in German texts.[5]

### Standardization of the mole

Before 1960, there were conflicting definitions of the mole, and hence of the Avogadro number (as it was known at the time), based on 16 grams of oxygen: physicists generally used oxygen-16 while chemists generally used the "naturally occurring" isotope ratio.

Switching, in 1960, to 12 grams of carbon-12 as the basis ended this dispute and had other advantages.[8] At this time, the Avogadro number was defined as the number of atoms in 12 grams of carbon-12, that is as a dimensionless quantity, while a mole was defined as one Avogadro number of atoms, molecules or other entities.

When the mole entered the International System of Units (SI), in 1971, the definitions were interchanged.

In 1971, a mole was defined as the number of atoms in 12 grams of carbon-12, with its own dimension, namely "amount of substance".[9] Avogadro's number became a physical constant with the unit of reciprocal moles (mol−1).

While Avogadro’s constant is a dimensionless quantity, it is currently based on a single physical property (the defined gram, hence the golden karat). Since instruments are unable to measure that property accurately beyond 10 places it is not known to an integer value. The Binary Mole, on the other hand, defines a precise integer value for the units that occur in a mole without any such analytical attachment.[10] Thus, the binary mole is an integer of 24 digits:

No = 279 = 604 462 909 807 314 587 353 088
or 6.0446 x 1023 to 5-significant digits for mathematical calculations.

## Application

The Avogadro constant can be applied to any substance. It corresponds to the number of atoms or molecules needed to make up a mass equal to the substance's atomic or molecular mass, in grams. For example, the atomic mass of iron is 55.847 g/mol, so NA iron atoms (i.e. one mole of iron atoms) have a mass of 55.847 g. Conversely, 55.847 g of iron contains NA iron atoms. The Avogadro constant also enters into the definition of the unified atomic mass unit, u:

$1 \ u = \frac{1}{N_A} \ g = (1.660 \, 538\, 86 \pm 0.000\, 000\, 28) 10^{-24} \ g$

Because of its role as a scaling factor, the Avogadro number provides the link between a number of useful physical constants when moving between the atomic scale and the macroscopic scale. For example, it provides the relationship between:

$R = k_BN_A = 8.314 \, 472 \, \pm \, 0.000 \, 015 \, \mbox{J}\cdot\mbox{mol}^{-1}\mbox{K}^{-1}\,$
in J mol−1 K−1
$F = N_Ae = 96 \, 485.3383 \, \pm \,0.0083 \,\, \mbox{C}\cdot\mbox{mol}^{-1} \,$
in C mol−1

## Measurement of the Avogadro constant

File:Silicon-unit-cell-labelled-3D-balls.png
Ball-and-stick model of the unit cell of silicon. X-ray diffraction experiments can determine the length of the cell, a, which can in turn be used to calculate a value for Avogadro's constant

A number of methods can be used to measure the Avogadro constant. One modern method is to calculate the Avogadro constant from the density (ρ) of a crystal, the relative atomic mass (M), and the unit cell length (a) determined from x-ray crystallography.[11] Very accurate values of these quantities for silicon have been measured at the National Institute of Standards and Technology (NIST) and used to obtain the value of the Avogadro constant:

$N_A = \frac{8M}{a^3\rho} \,$.
based on silicon.[12]

## References and notes

1. International Union of Pure and Applied Chemistry Commission on Physiochemical Symbols Terminology and Units (1993). Quantities, Units and Symbols in Physical Chemistry (2nd Edition). Oxford: Blackwell Scientific Publications. ISBN 0-632-03583-8. Retrieved on 2006-12-28.  International Union of Pure and Applied Chemistry Commission on Quantities and Units in Clinical Chemistry; International Federation of Clinical Chemistry Committee on Quantities and Units (1996). "Glossary of Terms in Quantities and Units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)". Pure Appl. Chem. 68: 957–1000. Retrieved on 2006-12-28.
2. International Union of Pure and Applied Chemistry Commission on Atomic Weights and Isotopic Abundances (1992). "Atomic Weight: The Name, Its History, Definition and Units". Pure Appl. Chem. 64: 1535–43. Retrieved on 2006-12-28.
3. How and When Did Avogadro's Name become Associated with Avogadro's Number? Jensen, William B. J. Chem. Educ. 2007 84 223. Link
4. 5.0 5.1 Bader, Alfred; Parker, Leonard. "Joseph Loschmidt, Physicist and Chemist". Physics Today Online (March 2001). Retrieved on 2006-12-28.
5. National Institute of Standards and Technology (February 2006). Fundamental physical constants: Physico-chemical constants. Retrieved on 2006-12-28.
6. S. E. Virgo (933). "Loschmidt's Number". Science Progress 27: 634-649.
7. Bureau international des poids et mesures (March 2006). Unit of amount of substance (mole). Retrieved on 2006-12-28.
8. BIPM Unit of amount of substance (mole)retrieved 24 January 2008
9. Williams, Joel M (2005), Challenging Science, Author House. Williams, Joel M (1996), Moles, Bits and Cubes e-versions [1] [2].
10. Mineralogy Database (2000-2005). Unit Cell Formula. Retrieved on 2007-12-09.
11. Mineralogy Database (2000-2005). Unit Cell Dimensions for Silicon. Retrieved on 2007-12-09.