Avogadro's number

Avogadro's number
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Name	Avogadro's number
Value	6.02214076×10^23 mol^−1
Units	per mole
Named after	Amedeo Avogadro

Avogadro's number is the fixed numerical value that defines the quantity of elementary entities in one mole, providing a bridge between the macroscopic amounts handled in laboratories and the microscopic counts of atoms and molecules. It underpins quantitative work across Chemistry, Physics, Materials science, Thermodynamics and connects to standards set by international bodies such as the International Bureau of Weights and Measures, the International System of Units, and the General Conference on Weights and Measures.

Definition and value

Avogadro's number is defined as exactly 6.02214076×10^23 per mole under the International System of Units after the 2019 redefinition of SI base units agreed by the General Conference on Weights and Measures, with the definition linking the mole to the fixed value of the constant rather than to a specific mass of Carbon-12. This constant is central to conversion between amounts expressed in moles and numbers of entities, serving alongside related standards maintained by the International Bureau of Weights and Measures and used in protocols of laboratories such as National Institute of Standards and Technology, Physikalisch-Technische Bundesanstalt, National Physical Laboratory, and Bureau International des Poids et Mesures.

Historical development

The concept evolved from early 19th-century work by Amedeo Avogadro who proposed a relation between gas volumes and particle counts, following experimental foundations laid by John Dalton, Joseph Louis Gay-Lussac, Amedeo Avogadro’s contemporaries, and later theoretical clarifications by Ludwig Boltzmann and James Clerk Maxwell. Determinations of the number progressed through contributions from figures and institutions like Jean Perrin, whose studies of Brownian motion connected to Albert Einstein’s theoretical work, and later X-ray crystallography studies influenced by William Henry Bragg, William Lawrence Bragg, and Max von Laue. The term "mole" and practical quantification were formalized through chemical nomenclature and standards debates involving organizations such as the International Union of Pure and Applied Chemistry and national standards institutes during the 19th and 20th centuries.

Measurement and determination methods

Historically, methods to determine the constant included electrochemical measurements influenced by work from Michael Faraday, optical and gas-kinetic approaches tied to James Clerk Maxwell and Ludwig Boltzmann, and Brownian-motion-based determinations following Jean Perrin and Albert Einstein. Modern high-precision determinations have relied on techniques such as X-ray crystal density methods applied to nearly perfect silicon spheres produced via industrial processes developed with expertise from institutions including Crystec, and measurement campaigns coordinated by National Institute of Standards and Technology, Institut für Kristallzüchtung, Physikalisch-Technische Bundesanstalt, and National Metrology Institute of Japan. Other approaches include watt balances (now called Kibble balances) tied to work by Brian Kibble and electrical metrology communities represented by International Electrotechnical Commission and Institute of Electrical and Electronics Engineers standards. Measurements combine precise lattice-parameter determination via X-ray diffraction, mass comparisons using mass spectrometry and balance technology, and surface characterization drawing on techniques from Scanning electron microscopy, Secondary ion mass spectrometry, and X-ray photoelectron spectroscopy.

Role in the mole and SI redefinition

The exact fixed value adopted during the 2019 redefinition of SI base units detached the definition of the mole from the kilogram artifact and linked it directly to a defined constant, aligning with parallel fixes such as Planck constant adoption that followed recommendations of the International Committee for Weights and Measures and resolutions at the General Conference on Weights and Measures. This change impacts laboratories and curricula influenced by standards from International Organization for Standardization and educational institutions such as Royal Society of Chemistry and American Chemical Society, while harmonizing with metrology networks including BIPM and national institutes like NIST and PTB.

Applications in chemistry and physics

Avogadro's number is used ubiquitously: converting between grams and atomic-scale counts in stoichiometric calculations within contexts described by IUPAC nomenclature, determining Avogadro-scale quantities in thermodynamics and statistical mechanics treatments as developed by Ludwig Boltzmann and Josiah Willard Gibbs, quantifying carrier densities in semiconductor devices designed by companies like Intel and TSMC, computing cross-sections in nuclear physics experiments at facilities such as CERN and Brookhaven National Laboratory, and expressing concentrations in biochemical assays used in institutions like Centers for Disease Control and Prevention and World Health Organization protocols. It also appears in materials characterization for crystallography labs at Diamond Light Source and European Synchrotron Radiation Facility and in educational problems used by universities such as University of Oxford and Massachusetts Institute of Technology.

Related constants and conversions

Avogadro's number connects to constants and quantities including the Boltzmann constant, the Planck constant, the Faraday constant (via Faraday's law), the gas constant R (with R = N_A k_B), and the atomic mass unit (with 1 u defined relative to carbon-12). It provides conversions between mole-based units and particle counts used in standards promulgated by BIPM, calculations in laboratories affiliated with NIST and PTB, and theoretical relations employed in works by Maxwell, Boltzmann, and Einstein.

Category:Stoichiometry