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Avogadro's number, also called Avogadro's constant (NA), named after Amedeo Avogadro, is formally defined to be the number of carbon-12 atoms in 12 grams (0.012 kg) of unbound carbon-12 in its rest-energy electronic state. The current best estimate of this number is (6.0221415 ± 0.0000010)×1023. Portrait of Amedeo Avogadro Count Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e Cerreto (August 9, 1776â€“July 9, 1856) was an Italian chemist, most noted for his contributions to the theory of molarity and molecular weight. ... Carbon 12 is a stable isotope of the element carbon. ...

A mole is defined in the SI as Avogadro's number of particles of any kind of substance (atoms, ions, molecules, or formula units). In the SI, this unit is abbreviated mol. The mole is widely used as a macroscopic unit of amount of substance. The mole and its simple conversions into different units of measurements. ... Properties For other uses, see Atom (disambiguation). ... An ion is an atom or group of atoms that normally are electrically neutral and achieve their status as an ion by loss (or addition) of an electron(s). ... In chemistry, a molecule is an aggregate of at least two atoms in a definite arrangement held together by special forces. ... A formula unit in chemistry is the empirical formula of an ionic or covalent network solid compound used as an independent entity for stoichiometric calculations. ... Amount of substance of an object is a physical quantity that measures the number of elementary entities in the object compared with the number of elementary entities in 0. ...

Avogadro's number is named after the early nineteenth century Italian scientist Amedeo Avogadro. It appears that Jean Baptiste Perrin was the first to name it. Perrin called it "Avogadro's constant" and it is still sometimes known by that name. The numerical value was first estimated by Johann Josef Loschmidt in 1865 using the kinetic gas theory. In German-speaking countries, the number may still be referred to as Loschmidt's number. Unfortunately, in a few cases (mainly in the older literature) Loschmidt's number refers to the number of atoms (or molecules) in a cubic centimeter, a usage now disparaged, viz: [1]. Portrait of Amedeo Avogadro Count Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e Cerreto (August 9, 1776â€“July 9, 1856) was an Italian chemist, most noted for his contributions to the theory of molarity and molecular weight. ... Jean Baptiste Perrin (b. ... Johann Josef Loschmidt (March 15, 1821 - July 8, 1895) was an Austrian physicist and chemist. ... 1865 (MDCCCLXV) is a common year starting on Sunday. ... The kinetic theory of gases is a theory that explains the macroscopic properties of gases by consideration of their composition at a molecular level. ... In chemistry and physics, the Loschmidt number is the number density of an ideal gas at standard temperature and pressure, . It is named after the Austrian chemist Johann Josef Loschmidt, who calculated, in 1865, the number of molecules of such a gas in one cubic centimeter. ...

In the nineteenth century physicists measured the mass of one atom of hydrogen to be about 1/(6.023x1023) grams; they were trying to evaluate how many molecules of an ideal gas would fit in 1 cubic centimeter [2] at STP ... which is related to Avogadro's number via the ideal gas law. Before 1960, there were conflicting definitions based 16 grams of oxygen : physicists generally used oxygen-16 while chemists generally used the "naturally occurring" isotope ratio. Switching to 12 grams of carbon-12 ended this dispute and had other advantages [3]. An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. ... In chemistry and other sciences, STP or standard temperature and pressure is a standard set of conditions for experimental measurements, to enable comparisons to be made between sets of data. ...

## Application

Avogadro's number can be applied to any substance. It corresponds to the number of atoms or molecules needed to make up a mass equal to the substance's atomic or molecular mass, in grams. For example, the atomic mass of iron is 55.847 u, so Avogadro's number of iron atoms (i.e. one mole of iron atoms) have a mass of 55.847 g. Conversely, 55.847 g of iron contains Avogadro's number of iron atoms. Thus Avogadro's number NA corresponds to the conversion factor between grams (g) and atomic mass units: The atomic mass of a chemical element is the mass of an atom at rest, most often expressed in unified atomic mass units. ... The molecular mass (abbreviated MM) of a substance, called molecular weight and abbreviated as MW, is the mass of one molecule of that substance, relative to the unified atomic mass unit u (equal to 1/12 the mass of one atom of carbon-12). ... The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. ...

$1 mbox{g}=N_{rm A} mbox{u}.$

## Chemical significance of Avogadro's number

The definition of Avogadro's number depends on the definition of the kilogram. The latter is based on arbitrary convention, namely the mass of a particular "standard" cylinder of metal in France. This means that the particular value of Avogadro's number is the result of convention; there is no physical reason for it. For this reason, Avogadro's number is not considered a fundamental constant in the strictest sense. However, for practical purposes, Avogadro's number is regarded as a chemical constant. In physics, fundamental physical constants are, in the strictest sense, physical constants that are independent of systems of units and hence are dimensionless numbers. ...

Avogadro's number can be regarded as a conversion factor between the microscopic mass system (atomic mass units or Daltons) and the kilogram system. The microscopic mass system is based on the mass of carbon-12, while the kilogram system is currently based on the mass of a particular "standard" cylinder of metal in France. So naturally there's no simple conversion factor between the two. However, if a method were developed to count atoms, it would be possible to redefine the kilogram in a way that did not depend on an arbitrary cylinder of metal. The number of atoms picked would presumably be equal or close to the latest accepted value of Avogadro's number. In that case, the kilogram would be redefined as the mass of Avogadro's number of carbon-12 atoms. The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. ... The international prototype, made of platinum-iridium, which is kept at the BIPM under conditions specified by the 1st CGPM in 1889. ...

Because of its role as a scaling factor, Avogadro's number provides the link between a number of useful physical constants when moving between an atomic mass scale and a kilogram (SI) scale. For example, it provides the relationship between: Cover of brochure The International System of Units. ...

In the 19th century physicists measured the mass of one atom of hydrogen to be about 6.02214199×10-23 grams. The gram was originally defined to be the mass of a cubic centimeter of pure water at standard temperature and pressure [4]. As experiments became more accurate, it was found that water was contaminated with variable amounts of heavy water, which made it undesirable to maintain a standard with hydrogen having one atomic mass unit. Carbon was found to have a more constant isotopic composition, and it was also possible to separate pure carbon-12. Therefore, the atomic mass unit was changed to 112 the mass of an atom of carbon-12. Hence 12 grams of carbon-12 has about 6.0221415×1023 atoms. The recent history and more details can be found in the document, Atomic Weight: The Name, Its History, Definition and Units. Molar gas constant (also known as universal gas constant, usually denoted by symbol R) is the constant occurring in the universal gas equation, i. ... Ludwig Boltzmann The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... Molar gas constant (also known as universal gas constant, usually denoted by symbol R) is the constant occurring in the universal gas equation, i. ... Ludwig Boltzmann The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... In physics and chemistry, the Faraday constant is the amount of electric charge of one mole of electrons. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... In physics and chemistry, the Faraday constant is the amount of electric charge of one mole of electrons. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ...

## Numerical value

At present it is not technologically feasible to count the exact number of atoms in 12 g of carbon-12, so the precise value of Avogadro's number is unknown. The 2002 CODATA recommended value for Avogadro's number is CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ...

$N_{rm A} = 6.022,1415 times 10^{23} pm 0.000,0010 times 10^{23} mathrm{mol}^{-1}$.

A number of methods can be used to measure Avogadro's number. One modern method is to calculate Avogadro's number from the density of a crystal, the relative atomic mass, and the unit cell length determined from x-ray crystallography. Very accurate values of these quantities for silicon have been measured at the National Institute of Standards and Technology (NIST) and used to obtain the value of Avogadro's number. X-ray crystallography is a technique in crystallography in which the pattern produced by the diffraction of X-rays through the closely spaced lattice of atoms in a crystal is recorded and then analyzed to reveal the nature of that lattice. ... NIST logo The National Institute of Standards and Technology (NIST, formerly known as The National Bureau of Standards) is a non-regulatory agency of the United States Department of Commerceâ€™s Technology Administration. ...

## Connection to masses of protons and neutrons

A carbon-12 atom consists of 6 protons and 6 neutrons (which have approximately the same mass) and 6 electrons (whose mass is negligible as a first approximation, being about 11840 of the mass of the proton). One could therefore think that NA is the number of protons or neutrons that have a mass of 1 gram. While this is approximately correct, the mass of a free proton is 1.00727 amu, so a mole of protons would actually have a mass of 1.00727 g. Similarly, a mole of neutrons has a mass of 1.00866 g. Clearly, 6 moles of protons combined with six moles of neutrons would have a mass greater than 12 g. So it would appear that one mole of carbon-12 atoms, which should consist of 6 moles each of protons, neutrons, and electrons would have a mass greater than 12 g. The discrepancy or mass defect (as it is known) is related to the equivalence of matter and energy discovered by Albert Einstein as part of the theory of special relativity. When an atom is formed, the protons and neutrons in the nucleus are bound together by the strong nuclear force. This binding results in the formation of a low energy state and is accompanied by a large release of energy. Since energy is equivalent to mass (which means that all energy has mass), the released energy has mass and carries away the loss in the mass of the nucleus relative to that of the separated protons and neutrons (note that mass is conserved in this process just as energy is). Thus, protons and neutrons in the nucleus have masses that are less (about 0.7 percent less) than those of free protons and neutrons. The precise amount of mass loss is related to the binding energy of the nucleus and varies depending on the type of atom. Properties [1][2] In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... This article or section does not cite its references or sources. ... The electron is a fundamental subatomic particle that carries an electric charge. ... Binding energy is the energy required to disassemble a whole into separate parts. ... Mass-energy equivalence is where mass has an energy equivalence, and energy has a mass equivalence. ... Einstein redirects here. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ...

One may therefore say that NA is approximately the number of nuclear neutrons or protons (nucleons) that have a mass of 1 gram. This is approximate because the precise mass of a nuclear proton or neutron depends on the composition of the nucleus, as explained above. For example, iron nucleons will have a significantly lower mass than those in hydrogen or plutonium. General Name, Symbol, Number iron, Fe, 26 Chemical series transition metals Group, Period, Block 8, 4, d Appearance lustrous metallic with a grayish tinge Atomic mass 55. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... General Name, Symbol, Number plutonium, Pu, 94 Chemical series actinides Group, Period, Block n/a, 7, f Appearance silvery white Atomic mass (244) g/mol Electron configuration [Rn] 5f6 7s2 Electrons per shell 2, 8, 18, 32, 24, 8, 2 Physical properties Phase solid Density (near r. ...

Avogadro's number may also yield practical reasonings in real life. For example, the fact that a known number of atoms are in a given amount of a substance is one reason for scientific criticism of homeopathy, in which medicinal substances are often diluted to the extent that a single molecule appears in only one dose amongst the hundreds or thousands prepared, as a simple calculation involving Avogadro's number will reveal. It has been suggested that Classical homeopathy be merged into this article or section. ...

Another common sense application shows that without determining the actual weight of a substance, a good rule of thumb to use is that a cubic centimeter of solid matter contains about 1024 atoms [5].

Portrait of Amedeo Avogadro Count Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e Cerreto (August 9, 1776â€“July 9, 1856) was an Italian chemist, most noted for his contributions to the theory of molarity and molecular weight. ... For information on how large numbers are named in English, see names of large numbers. ... The mole and its simple conversions into different units of measurements. ... Mole Day is an unofficial holiday celebrated among chemists in North America on October 23, between 6:02 AM and 6:02 PM, making the date 6:02 10/23 in the American style of writing dates. ...

• Journal of Physical and Chemical Reference Data, 28 (1999) 1713.

Results from FactBites:

 PlanetPapers - Avogadros Number (1045 words) Avogadros number is the number 6.0221367 x 10^23, commonly rounded to just three significant digits: 6.02 x 10^23, and is the number of representative particles in a mole. Avogadros number is commonly used to compute the quantities of substances involved in chemical reactions, called stoichiometry, and is one of the most important and versatile components of modern chemistry. Avogadros number relates the mass of a mole of a substance to the mass of a single molecule.
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