Avogadro number

The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining constant with an exact value of . It is named after the Italian scientist Amedeo Avogadro by Stanislao Cannizzaro, who explained this number four years after Avogadro's death while at the Karlsruhe Congress in 1860.

The numeric value of the Avogadro constant expressed in reciprocal moles, a dimensionless number, is called the Avogadro number. In older literature, the Avogadro number is denoted or , which is the number of particles that are contained in one mole, exactly .

The Avogadro number is the approximate number of nucleons (protons or neutrons) in one gram of ordinary matter. The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, in grams, is approximately the number of nucleons in one constituent particle of the substance. It is numerically equal (for all practical purposes) to the average mass of one molecule (or atom) the compound in daltons (unified atomic mass units); one dalton being of the mass of one carbon-12 atom. For example, the average mass of one molecule of water is about 18.0153 daltons, and one mole of water ( molecules) is about 18.0153 grams. Thus, the Avogadro constant is the proportionality factor that relates the molar mass of a substance to the average mass of one molecule.

The Avogadro constant also relates the molar volume of a substance to the average volume nominally occupied by one of its particles, 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 , or about (cubic angstroms). For a crystalline substance, it similarly relates its molar volume (in mol/mL), the volume of the repeating unit cell of the crystals (in mL), to 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 value , and redefined the mole as the amount of a substance under consideration that contains constituent particles of the substance. Under the new definition, the mass of one mole of any substance (including hydrogen, carbon-12, and oxygen-16) is times the average mass of one of its constituent particles – a physical quantity whose precise value has to be determined experimentally for each substance.

History

Origin of the concept

The Avogadro constant is named after the Italian scientist Amedeo Avogadro (1776–1856), 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 16 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.

First measurements

The value of Avogadro's number (not yet 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 of particles in an ideal gas, is now called the Loschmidt constant in his honor, and is related to the Avogadro constant, , by
:$n_0 = \frac$,
where is the pressure, is the gas constant, and is the absolute temperature. Because of this work, the symbol 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, should not be confused with the entirely different Loschmidt constant in English-language literature.)

Perrin himself determined Avogadro's number by several different experimental methods. He was awarded the 1926 Nobel Prize in Physics, largely for this work.

The electric charge per mole of electrons is a constant called the Faraday constant and has 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 (BIPM) 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 .

By this definition, the common rule of thumb that "one gram of matter contains 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, in the SI system the Avogadro constant had the dimensionality of reciprocal of amount of substance rather than of a pure number, and had the approximate value with units of mol. By this definition, the value of inherently had to be determined experimentally.

The BIPM also named the "Avogadro ''constant''", but the term "Avogadro number" continued to be used especially in introductory works.

SI redefinition of 2019

In 2017, the BIPM decided to change the definitions of mole and amount of substance. The mole was redefined as being the amount of substance containing exactly 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 dalton ( universal atomic mass unit) remains unchanged as of the mass of ¹²C. Thus, the molar mass constant is no longer exactly 1 g/mol, although the difference ( in relative terms, as of March 2019) is insignificant for practical purposes.

Connection to other constants

The Avogadro constant is related to other physical constants and properties.

* It relates the molar gas constant and the Boltzmann constant , which in the SI is defined to be exactly :
*: 
* It relates the Faraday constant and the elementary charge , which in the SI is defined as exactly :
*: 
* It relates the molar mass constant and the atomic mass constant currently
*: 

See also

* Mole Day
* CODATA 2018

References

External links

1996 definition of the Avogadro constant
from the IUPAC ''Compendium of Chemical Terminology'' ("''Gold Book''")

Some Notes on Avogadro's Number,
''(historical notes)''

An Exact Value for Avogadro's Number
– ''American Scientist''

Avogadro and molar Planck constants for the redefinition of the kilogram
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* Scanned version of "Two hypothesis of Avogadro", 1811 Avogadro's article, on
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Amount of substance
Fundamental constants
Dimensionless numbers of chemistry
Physical constants