The Avogadro number, sometimes denoted N or N0, is the number of constituent particles (usually molecules, atoms or ions) that are contained in one mole, the international (SI) unit of amount of substance: by definition, exactly 6.02214076×1023, and it is dimensionless. It is named after the scientist Amedeo Avogadro (1776–1856).
The Avogadro constant, usually denoted by NA or L is the factor that, multiplied by the amount of substance in a sample, measured in moles, gives the number of constituent particles in that sample. Its numerical value is defined as being the Avogadro number, and its unit is the reciprocal of mole; that is, NA = 6.02214076×1023 mol−1.
The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the average mass of one molecule of the compound, in atomic mass units (daltons); one dalton being 1/12 of the mass of one carbon-12 atom, which is approximately the mass of one nucleon (proton or neutron). For example, the average mass of one molecule of water is about 18.0153 daltons, and one mole of water (N molecules) is about 18.0153 grams. Thus, the Avogadro constant NA is the proportionality factor that relates the molar mass of a substance to the average mass of one molecule; and the Avogadro number is also the approximate number of nucleons in one gram of ordinary matter.
The Avogadro constant also relates the molar volume of a substance to the average volume nominally occupied by one of its particle, when both are expressed in the same units of volume. For example, since the molar volume of water in ordinary conditions is about 18 mL/mol, the volume occupied by one molecule of water is about (18/6.022)×10−23 mL, or about 30 Å3 (cubic angstroms). For a crystaline substance, it similarly relates its molar volume (in mL/mol), the volume of the repeating unit cell of the crystals (in mL), and the number of molecules in that cell.
The Avogadro number (or constant) has been defined in many different ways through its long history. Its approximate value was first determined, indirectly, by Josef Loschmidt in 1865. (Avogadro's number is closely related to the Loschmidt constant, and the two concepts are sometimes confused.) It was initially defined by Jean Perrin as the number of atoms in 16 grams of oxygen. It was later redefined in the 14th conference of the International Bureau of Weights and Measures (BIPM) as the number of atoms in 12 grams of the isotope carbon-12 (12C). In each case, the mole was defined as the quantity of a substance that contained the same number of atoms as those reference samples. In particular, when carbon-12 was the reference, one mole of carbon-12 was exactly 12 grams of the element.
These definitions meant that the value of the Avogadro number depended on the experimentally determined value of the mass (in grams) of one atom of those elements, and therefore it was known only to a limited number of decimal digits. However, in its 26th Conference, the BIPM adopted a different approach: effective 20 May 2019, it defined the Avogadro number as the exact integer N = 6.02214076×1023, and redefined the mole as N constituent particles of the substance in consideration. Under the new definition, the mass of one mole of any substance (including hydrogen, carbon-12, and oxygen-16) is N times the average mass of one of its constituent particles—a physical quantity whose precise value has to be determined experimentally for each substance.
Origin of the concept
The Avogadro constant is named after the Italian scientist Amedeo Avogadro, who, in 1811, first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules regardless of the nature of the gas.
The name Avogadro's number was coined in 1909 by the physicist Jean Perrin, who defined it as the number of molecules in exactly 32 grams of oxygen. The goal of this definition was to make the mass of a mole of a substance, in grams, be numerically equal to the mass of one molecule relative to the mass of the hydrogen atom; which, because of the law of definite proportions, was the natural unit of atomic mass, and was assumed to be 1/16 of the atomic mass of oxygen.
The value of Avogadro's number (still not known by that name) was first obtained indirectly by Josef Loschmidt in 1865, by estimating the number of particles in a given volume of gas. This value, the number density n0 of particles in an ideal gas, is now called the Loschmidt constant in his honor, and is related to the Avogadro constant, NA, by
where p0 is the pressure, R is the gas constant, and T0 is the absolute temperature. Because of this work, the symbol L is sometimes used for the Avogadro constant, and, in German literature, that name may be used for both constants, distinguished only by the units of measurement. (However, NA should not to be confused with the entirely different Loschmidt constant in the English language literature.)
The electric charge per mole of electrons is a constant called the Faraday constant and had been known since 1834 when Michael Faraday published his works on electrolysis. In 1910, Robert Millikan obtained the first measurement of the charge on an electron. Dividing the charge on a mole of electrons by the charge on a single electron provided a more accurate estimate of the Avogadro number.
SI definition of 1971
In 1971 the International Bureau of Weights and Measures (IBPM) decided to regard the amount of substance as an independent dimension of measurement, with the mole as its base unit in the International System of Units (SI). Specifically, the mole was defined as an amount of a substance that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12.
By this definition, the common rule of thumb "one gram of matter contains N nucleons" was exact for carbon-12, but slightly inexact for other elements and isotopes. On the other hand, one mole of any substance contained exactly as many molecules as one mole of any other substance.
As a consequence of this definition, the Avogadro constant NA was no longer a pure number in the SI system, but had the dimensionality of reciprocal of amount of substance, and the approximate value 6.02×1023 in units of mol−1. According to this definition, the value of NA inherently had to be determined experimentally.
The IBPM also named NA the "Avogadro constant", but the term "Avogadro number" continued to be used especially in introductory works.
SI redefinition of 2019
In 2017, the IBPM decided to change the definitions of mole and amount of substance. The mole was redefined as being the amount of substance containing exactly 6.02214076×1023 elementary entities. One consequence of this change is that the mass of a mole of 12C atoms is no longer exactly 0.012 kg. On the other hand, the atomic mass unit (dalton) remains unchanged as 1/12 of the mass of 12C. Thus, the molar mass constant is no longer exactly 1 g/mol, although the difference (4.5×10−10 in relative terms, as of November 2018) is insignificant for practical purposes.
The Avogadro constant in other unit systems
In other measurement systems where the unit of amount of substance is not the SI mole, the Avogadro constant NA is taken to mean the number of particles in said unit, and will have a different value.
For example, if quantities of a substance are measured in pound-mole (lb-mol), then the Avogadro constant NA is 2.73159734(12)×1026 lb-mol−1. If the ounce-mole (oz-mol) is used instead, NA is 1.707248434(77)×1025 oz-mol−1. However, these units are hardly used nowadays.
Connection to other constants
The Avogadro constant, NA is related to other physical constants and properties.
- It relates the molar gas constant R and the Boltzmann constant kB, which in the SI (since 20 May 2019) is defined to be exactly 1.380649×10−23 J/K:
- = 8.31446261815324 J⋅K−1⋅mol−1
- It relates the Faraday constant F and the elementary charge e, which in the SI (since 20 May 2019) is defined as exactly 1.602176634×10−19 coulombs:
- = 96485.3321233100184 C/mol
- It relates the molar mass constant, Mu and the atomic mass constant mu, currently 1.66053906660(50)×10−27 kg:
- = 0.99999999965(30)×10−3 kg⋅mol−1.
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