Inchemistry, theAvogadro constant, commonly denotedNA,[1][2] is a conversion constant or ratio between anamount of substance and the number of particles that it contains. The particles in question are any designated elementary entity, such asmolecules,atoms,ions, orion pairs. It is anSI defining constant with the exact value6.02214076×1023 mol−1 (reciprocal mole).[3][4] The numerical value of this constant when expressed in terms of the mole is known as theAvogadro number, commonly denotedN0.[5][6] The Avogadronumber is an exact number equal to the number of constituent particles in one mole of any substance (by definition of themole), historically derived from the experimental determination of the number of atoms in 12 grams ofcarbon-12 (12C) before the2019 revision of the SI, i.e. the gram-to-dalton ratio, g/Da. Both the constant and the number are named after the Italian physicist and chemistAmedeo Avogadro.
The Avogadro constant is used as aproportionality factor to define theamount of substancen(X), in a sample of a substanceX, in terms of the number of elementary entitiesN(X) in that sample:
.
The Avogadro constantNA is also the factor that converts the averagemassm(X) of one particle of a substance to itsmolar massM(X).[7] That is,M(X) =m(X) ⋅NA. Applying this equation to12C with an atomic mass of exactly 12 Da and a molar mass of 12 g/mol yields (after rearrangement) the following relation for the Avogadro constant:NA = (g/Da) mol−1, making the Avogadro numberN0 = g/Da. Historically, this was precisely true, but since the 2019 revision of the SI, the relation is now merely approximate, although equality may still be assumed with high accuracy.
The constantNA also relates themolar volume (the volume per mole) 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 about18mL/mol, the volume occupied by one molecule of water is about18/(6.022×1023) mL, or about0.030 nm3 (cubicnanometres). For acrystalline substance, it provides as similarly relationship between the volume of a crystal to that of itsunit cell.
Approximate definition of a mole based on 12 grams of carbon-12
The Avogadro constant was historically derived from the old definition of themole as theamount of substance in 12 grams ofcarbon-12 (12C). By this old definition, the numerical value of the Avogadro constant in mol−1 (the Avogadro number) was a physical constant that had to be determined experimentally.
The historical relationship of the Avogadro constant to themolar mass of carbon-12,M(12C), and itsatomic mass,m(12C), can be expressed in the following equation:Thus,N0, the numerical value ofNA when expressed in mol−1, was equal to the number ofdaltons in a gram (g/Da), where the dalton is defined as1/12 of the mass of a12C atom.[8]
The redefinition of the mole in 2019, as being the amount of substance consisting of exactly6.02214076×1023elementary entities,[9] means that the mass of 1 mole of a substance is now exactly the product of the Avogadro number and the average mass of one of the entities involved. The dalton, however, is still defined as1/12 of the mass of a12C atom, which must be determined experimentally and is known only with finiteaccuracy. Thus, prior experiments that aimed to determine the numerical value of the Avogadro constant when expressed in reciprocal moles—i.e. the Avogadro number (now numerically fixed)—are re-interpreted as measurements of the numerical value in grams of the dalton.
By the old definition of mole, the numerical value of the mass of one mole of a substance expressed in grams (i.e., its molar mass in g/mol or kg/kmol), was precisely equal to the average mass of one particle expressed in daltons. With the new definition, this numerical equivalence is no longer exact, as it is affected by the uncertainty in the value of the gram-to-dalton (g/Da) mass-unit ratio. However, it may still be assumed for all practical purposes. For example, the average mass of one molecule ofwater is about 18.0153 daltons, and an amount of one mole of water has a corresponding macroscopic mass of about 18.0153 grams. Also, the Avogadro number is the approximate number ofnucleons (protons andneutrons) in one gram of ordinarymatter.
An amount of substance consisting of just a single elementary entity might be thought of as an "elementary amount", analogous to theelementary charge,e. Lettingna denote this elementary amount, then1 mol =N0na. With the mole defined such thatNA =N0/mol, this can be rearranged as1 mol =N0/NA. Thus,na = 1/NA, the reciprocal of the Avogadro constant. The fundamental definition of the Avogadro constant itself is therefore one per elementary amount (NA = 1/na), independent of any macroscopic base unit chosen for the physical quantity. (Since there is an aggregate of an Avogadro number of elementary entities in one mole, the Avogadro constant can also beexpressed (in terms of the mole) as an Avogadro number per mole—but this isnot its "definition".) The Avogadro constant, a well-defined quantity value with dimensionN−1, independent of the mole, is therefore abona fide defining constant for the 2019 redefinition of the mole.
Introducingna in place of1/NA, means thatn(X) =N(X)na—amount of substance is an aggregate ofN(X) elementary entities—which is easier to comprehend thanN(X) "reciprocal Avogadro constants". Also the molar mass is thenM(X) =m(X)/na—the entity mass per entity, which is self-evident.
The Avogadro constant is named after the Italian scientistAmedeo 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 ofatoms ormolecules regardless of the nature of the gas.[12]
The nameAvogadro's number was coined in 1909 by the physicistJean Perrin, who defined it as the number of molecules in exactly 32 grams ofoxygen gas.[14] This definition numerically equates the mass of a mole of a substance, in grams, to the mass of one molecule relative to the mass of a hydrogen atom. Because of thelaw of definite proportions, a hydrogen atom was the natural unit of atomic mass and was assumed to be1/16 of the atomic mass of oxygen.
The value of Avogadro's number (not yet known by that name) was first obtained indirectly byJosef Loschmidt in 1865, by estimating the number of particles in a given volume of gas.[15] This value, thenumber densityn0 of particles in anideal gas, is now called theLoschmidt constant in his honor, and is related to the Avogadro constant,NA, by
wherep0 is thepressure,R is thegas constant, andT0 is theabsolute temperature. Because of this work, the symbolL is sometimes used for the Avogadro constant,[16][2] and, inGerman literature, that name may be used for both constants, distinguished only by theunits of measurement.[17] (However,NA should not be confused with the entirely differentLoschmidt constant in English-language literature.)
Perrin himself determined the Avogadro number, which he called "Avogadro's constant" (constante d'Avogadro), by several different experimental methods. He was awarded the 1926Nobel Prize in Physics, largely for this work.[18]
X-ray crystallography uses the diffraction of X-rays by a crystal to accurately measure the distances between layers in its lattice, from which the volume occupied by each atom can be determined.[20][21] TheAvogadro Project used this technique to measure the unit cell dimensions of extremely pure single-crystal spheres of silicon-28, with the goal of a more accurate silicon-based definition of the Avogadro constant.[22]
By this definition, one mole of any substance contained exactly as many elementary entities as one mole of any other substance. However, this numberN0 was a physical constant that had to be experimentally determined since it depended on the mass (in grams) of one atom of12C, and therefore, it was known only to a limited number of decimal digits.[16] The common rule of thumb that "one gram of matter containsN0 nucleons" was exact for carbon-12, but slightly inexact for other elements and isotopes.
In the same conference, the BIPM also namedNA (the factor that related the amount of a substance to the corresponding number of particles) the "Avogadroconstant". However, the term "Avogadro number" continued to be used, especially in introductory works.[23] As a consequence of this definition,NA was not a pure number, but had thequantity dimension of reciprocal of amount of substance (N−1).
Before 2019, the mole was defined by the amount of substance in exactly 12 grams of carbon-12. Effective 20 May 2019, the BIPM defined the Avogadro constantNA as the exact value6.02214076×1023 mol−1, thus redefining the mole as the amount of a substance having exactly6.02214076×1023 constituent particles of that substance.[24][9] One consequence of this change is that the mass of a mole of12C atoms is no longer exactly 0.012 kg. On the other hand, the dalton, Da (a.k.a. unified atomic mass unit, u), remains unchanged as1/12 of the mass of12C.[25][26] Thus, themolar mass constant remains very close to but no longer exactly equal to 1 g/mol, although the difference (1.0×10−9 in relative terms for theCODATA 2022 recommended value) is insignificant for all practical purposes.[9][1]
^abH. P. Lehmann, X. Fuentes-Arderiu, and L. F. Bertello (1996): "Glossary of terms in quantities and units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)"; p. 963, item "Avogadro constant".Pure and Applied Chemistry, vol. 68, iss. 4, pp. 957–1000.doi:10.1351/pac199668040957
^Marvin Yelles (1971):McGraw-Hill Encyclopedia of Science and Technology, Vol. 9, 3rd ed.; 707 pages.ISBN978-0070797987
^Avogadro, Amedeo (1811). "Essai d'une maniere de determiner les masses relatives des molecules elementaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons".Journal de Physique.73:58–76.English translation.
