Avogadro's number

Avogadro's number
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Name	Avogadro's number
Value	6.02214076
Uncertainty	(exact)
Units	per mole
Namedafter	Amedeo Avogadro

Avogadro's number. It is the fixed numerical factor defining the mole, one of the seven SI base units, as the amount of substance containing exactly this number of elementary entities. This fundamental constant provides a crucial bridge between the macroscopic scale of laboratory measurements and the atomic-scale world of individual particles, enabling precise calculations in chemistry and physics. Its exact value, established by international agreement, underpins the modern International System of Quantities.

Definition and value

Avogadro's number is defined as exactly 6.02214076 × 10²³ elementary entities per mole, a decision ratified in 2019 by the General Conference on Weights and Measures. This definition effectively ties the mole to this specific number, making the constant a cornerstone of the revised SI base unit system. The elementary entity can be any identifiable particle, such as an atom, molecule, ion, electron, or even a specified group of particles. Consequently, one mole of any substance contains precisely this number of the chosen constituent particles, allowing for direct proportionality between atomic mass and measurable mass.

Historical development

The conceptual foundation stems from the early 19th-century hypothesis proposed by Amedeo Avogadro, which posited that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. This idea was later championed by Stanislao Cannizzaro at the 1860 Karlsruhe Congress, helping to resolve confusion over atomic masses. The first credible estimates of the constant's magnitude emerged from the work of Johann Josef Loschmidt, who calculated the number of molecules in a given volume of gas, a value later termed the Loschmidt constant. Throughout the early 20th century, scientists like Jean Baptiste Perrin, who studied Brownian motion, and Robert Millikan, with his oil-drop experiment, provided increasingly accurate measurements, with Perrin coining the term "Avogadro's constant."

Role in chemistry and physics

This constant is indispensable for converting between atomic-scale and laboratory-scale quantities. It allows the unified atomic mass unit (u) to be related to the gram, meaning the molar mass of any element, expressed in grams per mole, is numerically equal to its average atomic mass in u. This relationship is central to stoichiometric calculations in chemical reactions, determining yields and reactant masses. In physics, it links macroscopic properties like the Faraday constant for electrolysis to the charge of a single electron, and appears in the ideal gas law through the Boltzmann constant. The constant also connects the Planck constant to macroscopic electrical measurements via the Josephson effect and Quantum Hall effect.

Measurement and determination

Historically, methods involved using the Avogadro Project, an international effort to determine the constant by counting atoms in an ultra-pure, nearly perfect single crystal of silicon-28. This technique involved precise measurements of the crystal's lattice parameter via X-ray crystallography, its volume, and its mass to calculate the number of atoms present. Other pioneering methods included electrolysis experiments to measure the Faraday constant and, by extension, the charge per mole of electrons. Earlier work by Jean Baptiste Perrin used observations of Brownian motion and sedimentation equilibrium to estimate the constant, for which he was awarded the 1926 Nobel Prize in Physics.

Related concepts and constants

Avogadro's number is intimately connected to several other fundamental constants. It is the proportionality factor between the molar gas constant (R) and the Boltzmann constant (k_B), expressed as R = N_Ak_B. Similarly, it relates the Faraday constant (F) to the elementary charge (e), with F = N_Ae. The Loschmidt constant, which gives the number density of molecules in an ideal gas at standard conditions, is also derived using it. Furthermore, its fixed definition is part of a network that now defines the kilogram, ampere, and kelvin in terms of fundamental constants like the Planck constant, elementary charge, and Boltzmann constant.

Category:Physical constants Category:Units of amount of substance Category:Physical quantities