Finding the Avogadro Number. Atomic mass unit

We know from a school chemistry course that if we take one mole of any substance, then it will contain 6.02214084(18).10^23 atoms or other structural elements (molecules, ions, etc.). For convenience, the Avogadro number is usually written in this form: 6.02. 10^23.

However, why is the Avogadro constant (in Ukrainian “became Avogadro”) equal to this value? There is no answer to this question in textbooks, and chemistry historians offer a variety of versions. It seems that Avogadro's number has some secret meaning. After all, there are magic numbers, where some include the number "pi", fibonacci numbers, seven (eight in the east), 13, etc. We will fight the information vacuum. We will not talk about who Amedeo Avogadro is, and why, in addition to the law he formulated, the found constant was also named in honor of this scientist. Many articles have already been written about this.

To be precise, I did not count molecules or atoms in any particular volume. The first person to try to figure out how many gas molecules

contained in a given volume at the same pressure and temperature, was Josef Loschmidt, and that was in 1865. As a result of his experiments, Loschmidt came to the conclusion that in one cubic centimeter of any gas under normal conditions there is 2.68675. 10^19 molecules.

Subsequently, independent methods were invented on how to determine the Avogadro number, and since the results for the most part coincided, this once again spoke in favor of the actual existence of molecules. At the moment, the number of methods has exceeded 60, but in recent years, scientists have been trying to further improve the accuracy of the estimate in order to introduce a new definition of the term “kilogram”. So far, the kilogram is compared with the chosen material standard without any fundamental definition.

However, back to our question - why is this constant equal to 6.022 . 10^23?

In chemistry, in 1973, for convenience in calculations, it was proposed to introduce such a concept as "amount of substance." The basic unit for measuring quantity was the mole. According to the IUPAC recommendations, the amount of any substance is proportional to the number of its specific elementary particles. The proportionality coefficient does not depend on the type of substance, and the Avogadro number is its reciprocal.

To illustrate, let's take an example. As is known from the definition of the atomic mass unit, 1 a.m.u. corresponds to one twelfth of the mass of one carbon atom 12C and is 1.66053878.10^(−24) grams. If you multiply 1 a.m.u. by the Avogadro constant, you get 1.000 g/mol. Now let's take some, say, beryllium. According to the table, the mass of one atom of beryllium is 9.01 amu. Let's calculate what one mole of atoms of this element is equal to:

6.02 x 10^23 mol-1 * 1.66053878x10^(−24) grams * 9.01 = 9.01 grams/mol.

Thus, it turns out that numerically coincides with the atomic.

The Avogadro constant was specially chosen so that the molar mass corresponded to an atomic or dimensionless value - a relative molecular one.

Avogadro's law

At the dawn of the development of atomic theory (), A. Avogadro put forward a hypothesis according to which, at the same temperature and pressure, equal volumes of ideal gases contain the same number of molecules. This hypothesis was later shown to be a necessary consequence of the kinetic theory, and is now known as Avogadro's law. It can be formulated as follows: one mole of any gas at the same temperature and pressure occupies the same volume, under normal conditions equal to 22,41383 . This quantity is known as the molar volume of the gas.

Avogadro himself did not make estimates of the number of molecules in a given volume, but he understood that this is a very large value. The first attempt to find the number of molecules occupying a given volume was made in the year J. Loschmidt. It followed from Loschmidt's calculations that for air the number of molecules per unit volume is 1.81·10 18 cm −3, which is about 15 times less than the true value. After 8 years, Maxwell gave a much closer estimate of "about 19 million million million" molecules per cubic centimeter, or 1.9·10 19 cm −3 . In fact, 1 cm³ of an ideal gas under normal conditions contains 2.68675·10 19 molecules. This quantity has been called the Loschmidt number (or constant). Since then, a large number of independent methods for determining the Avogadro number have been developed. The excellent agreement of the obtained values ​​is a convincing evidence of the real number of molecules.

Constant measurement

Data in this article is current as of December 2011.

The officially accepted value of Avogadro's number today was measured in 2010. For this, two spheres made of silicon-28 were used. The spheres were obtained at the Leibniz Institute of Crystallography and polished at the Australian Center for High Precision Optics so smoothly that the heights of protrusions on their surface did not exceed 98 nm. For their production, high-purity silicon-28 was used, isolated at the Nizhny Novgorod Institute of Chemistry of High-Purity Substances of the Russian Academy of Sciences from silicon tetrafluoride highly enriched in silicon-28, obtained at the Central Design Bureau of Mechanical Engineering in St. Petersburg.

Having such practically ideal objects, it is possible to count with high accuracy the number of silicon atoms in the ball and thereby determine the Avogadro number. According to the results obtained, it is equal to 6.02214084(18)×10 23 mol −1 .

Relationship between constants

  • Through the product of the Boltzmann constant, the Universal gas constant, R=kN A.
  • Through the product of an elementary electric charge and the Avogadro number, the Faraday constant is expressed, F=en A.

see also

Notes

Literature

  • Avogadro's number // Great Soviet Encyclopedia

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See what "Avogadro's Number" is in other dictionaries:

    - (Avogadro's constant, symbol L), a constant equal to 6.022231023, corresponds to the number of atoms or molecules contained in one MOL of a substance ... Scientific and technical encyclopedic dictionary

    Avogadro's number- Avogadro konstanta statusas T sritis chemija apibrėžtis Dalelių (atomų, molekulių, jonų) skaičius viename medžiagos molyje, lygus (6.02204 ± 0.000031) 10²³ mol⁻¹. santrumpa(os) Santrumpą žr. priede. priedas(ai) Grafinis formatas atitikmenys:… … Chemijos terminų aiskinamasis žodynas

    Avogadro's number- Avogadro konstanta statusas T sritis fizika atitikmenys: engl. Avogadro's constant; Avogadro's number vok. Avogadro Konstante, f; Avogadrosche Konstante, f rus. Avogadro's constant, f; Avogadro's number, n pranc. constante d'Avogadro, f; nombre… … Fizikos terminų žodynas

    Avogadro constant (Avogadro number)- the number of particles (atoms, molecules, ions) in 1 mole of a substance (a mole is the amount of a substance that contains as many particles as there are atoms in exactly 12 grams of the carbon 12 isotope), denoted by the symbol N = 6.023 1023. One of ... ... Beginnings of modern natural science

    - (Avogadro's number), the number of structural elements (atoms, molecules, ions or other h c) in units. count va to va (in one mole). Named after A. Avogadro, designated NA. A. p. one of the fundamental physical constants, essential for determining many ... Physical Encyclopedia

    - (Avogadro's number; denoted by NA), the number of molecules or atoms in 1 mole of a substance, NA \u003d 6.022045 (31) x 1023 mol 1; name named A. Avogadro ... Natural science. encyclopedic Dictionary

    - (Avogadro's number), the number of particles (atoms, molecules, ions) in 1 mole in VA. Denoted NA and equal to (6.022045 ... Chemical Encyclopedia

    Na \u003d (6.022045 ± 0.000031) * 10 23 the number of molecules in a mole of any substance or the number of atoms in a mole of a simple substance. One of the fundamental constants, with which you can determine such quantities as, for example, the mass of an atom or molecule (see ... ... Collier Encyclopedia

Mole - the amount of a substance that contains as many structural elements as there are atoms in 12 g 12 C, and the structural elements are usually atoms, molecules, ions, etc. The mass of 1 mol of a substance, expressed in grams, is numerically equal to its mol. mass. So, 1 mole of sodium has a mass of 22.9898 g and contains 6.02 10 23 atoms; 1 mol of calcium fluoride CaF 2 has a mass of (40.08 + 2 18.998) = 78.076 g and contains 6.02 10 23 molecules, like 1 mol of carbon tetrachloride CCl 4 , whose mass is (12.011 + 4 35.453) = 153.823 g etc.

Avogadro's law.

At the dawn of the development of atomic theory (1811), A. Avogadro put forward a hypothesis according to which, at the same temperature and pressure, equal volumes of ideal gases contain the same number of molecules. This hypothesis was later shown to be a necessary consequence of the kinetic theory, and is now known as Avogadro's law. It can be formulated as follows: one mole of any gas at the same temperature and pressure occupies the same volume, at standard temperature and pressure (0 ° C, 1.01×10 5 Pa) equal to 22.41383 liters. This quantity is known as the molar volume of the gas.

Avogadro himself did not make estimates of the number of molecules in a given volume, but he understood that this was a very large quantity. The first attempt to find the number of molecules occupying a given volume was made in 1865 by J. Loschmidt; it was found that 1 cm 3 of an ideal gas under normal (standard) conditions contains 2.68675×10 19 molecules. By the name of this scientist, the specified value was called the Loschmidt number (or constant). Since then, a large number of independent methods for determining the Avogadro number have been developed. The excellent agreement of the obtained values ​​is a convincing evidence of the real existence of molecules.

Loschmidt method

is of historical interest only. It is based on the assumption that liquefied gas consists of close-packed spherical molecules. By measuring the volume of liquid that was formed from a given volume of gas, and knowing approximately the volume of gas molecules (this volume could be represented based on some properties of the gas, such as viscosity), Loschmidt obtained an estimate of the Avogadro number ~10 22 .

Definition based on the measurement of the charge of an electron.

The unit of quantity of electricity known as the Faraday number F, is the charge carried by one mole of electrons, i.e. F = Ne, where e is the charge of an electron, N- the number of electrons in 1 mol of electrons (i.e. Avogadro's number). The Faraday number can be determined by measuring the amount of electricity required to dissolve or precipitate 1 mole of silver. Careful measurements made by the US National Bureau of Standards gave the value F\u003d 96490.0 C, and the electron charge measured by various methods (in particular, in the experiments of R. Milliken) is 1.602×10 -19 C. From here you can find N. This method of determining the Avogadro number appears to be one of the most accurate.

Perrin's experiments.

Based on the kinetic theory, an expression involving the Avogadro number was obtained that describes the decrease in the density of a gas (for example, air) with the height of the column of this gas. If we could calculate the number of molecules in 1 cm 3 of gas at two different heights, then, using the indicated expression, we could find N. Unfortunately, this cannot be done, since the molecules are invisible. However, in 1910, J. Perrin showed that the above expression is also valid for suspensions of colloidal particles, which are visible under a microscope. Counting the number of particles at different heights in the suspension column gave an Avogadro number of 6.82 x 10 23 . From another series of experiments in which the root-mean-square displacement of colloidal particles as a result of their Brownian motion was measured, Perrin obtained the value N\u003d 6.86 × 10 23. Subsequently, other researchers repeated some of Perrin's experiments and obtained values ​​that are in good agreement with those currently accepted. It should be noted that Perrin's experiments became a turning point in the attitude of scientists to the atomic theory of matter - earlier, some scientists considered it as a hypothesis. W. Ostwald, an outstanding chemist of that time, expressed this change in his views in the following way: “The correspondence of the Brownian motion to the requirements of the kinetic hypothesis ... forced even the most pessimistic scientists to talk about the experimental proof of the atomic theory.”

Calculations using the Avogadro number.

With the help of the Avogadro number, the exact masses of atoms and molecules of many substances were obtained: sodium, 3.819×10 -23 g (22.9898 g / 6.02×10 23), carbon tetrachloride, 25.54×10 -23 g, etc. It can also be shown that 1 g of sodium should contain approximately 3×10 22 atoms of this element.
see also

N A = 6.022 141 79(30)×10 23 mol −1 .

Avogadro's law

At the dawn of the development of atomic theory (), A. Avogadro put forward a hypothesis according to which, at the same temperature and pressure, equal volumes of ideal gases contain the same number of molecules. This hypothesis was later shown to be a necessary consequence of the kinetic theory, and is now known as Avogadro's law. It can be formulated as follows: one mole of any gas at the same temperature and pressure occupies the same volume, under normal conditions equal to 22,41383 . This quantity is known as the molar volume of the gas.

Avogadro himself did not make estimates of the number of molecules in a given volume, but he understood that this was a very large quantity. The first attempt to find the number of molecules occupying a given volume was made by J. Loschmidt; it was found that 1 cm³ of an ideal gas under normal conditions contains 2.68675 10 19 molecules. By the name of this scientist, the indicated value was called the Loschmidt number (or constant). Since then, a large number of independent methods for determining the Avogadro number have been developed. The excellent agreement of the obtained values ​​is a convincing evidence of the real existence of molecules.

Relationship between constants

  • Through the product of the Boltzmann constant, the Universal gas constant, R=kN A.
  • Through the product of an elementary electric charge and the Avogadro number, the Faraday constant is expressed, F=en A.

see also

Wikimedia Foundation. 2010 .

See what the "Avogadro constant" is in other dictionaries:

    Avogadro's constant- Avogadro konstanta statusas T sritis Standartizacija ir metrologija apibrėžtis Apibrėžtį žr. priede. priedas(ai) Grafinis formatas atitikmenys: engl. Avogadro constant vok. Avogadro Konstante, f; Avogadrosche Konstante, f rus. Avogadro's constant... Penkiakalbis aiskinamasis metrologijos terminų žodynas

    Avogadro's constant- Avogadro konstanta statusas T sritis fizika atitikmenys: engl. Avogadro's constant; Avogadro's number vok. Avogadro Konstante, f; Avogadrosche Konstante, f rus. Avogadro's constant, f; Avogadro's number, n pranc. constante d'Avogadro, f; nombre… … Fizikos terminų žodynas

    Avogadro's constant- Avogadro konstanta statusas T sritis Energetika apibrėžtis Apibrėžtį žr. priede. priedas(ai) MS Word formatas atitikmenys: engl. Avogadro's constant vok. Avogadro Konstante, f; Avogadrosche Konstante, f rus. Avogadro's constant, f; constant... ... Aiškinamasis šiluminės ir branduolinės technikos terminų žodynas

    - (Avogadro number) (NA), the number of molecules or atoms in 1 mole of a substance; NA \u003d 6.022? 1023 mol 1. Named after A. Avogadro ... Modern Encyclopedia

    Avogadro constant- (Avogadro number) (NA), the number of molecules or atoms in 1 mole of a substance; NA=6.022´1023 mol 1. Named after A. Avogadro. … Illustrated Encyclopedic Dictionary

    Avogadro Amedeo (08/09/1776, ‒ 07/09/1856, ibid.), Italian physicist and chemist. He received a law degree, then studied physics and mathematics. Corresponding member (1804), ordinary academician (1819), and then director of the department ... ...

    - (Avogadro) Amedeo (08/09/1776, Turin, 07/09/1856, ibid.), Italian physicist and chemist. He received a law degree, then studied physics and mathematics. Corresponding member (1804), ordinary academician (1819), and then director of the department of physics ... ... Great Soviet Encyclopedia

    The fine structure constant, usually denoted as, is a fundamental physical constant that characterizes the strength of the electromagnetic interaction. It was introduced in 1916 by the German physicist Arnold Sommerfeld as a measure ... ... Wikipedia

    - (Avogadro's number), the number of structural elements (atoms, molecules, ions or other h c) in units. count va to va (in one mole). Named after A. Avogadro, designated NA. A. p. one of the fundamental physical constants, essential for determining many ... Physical Encyclopedia

    CONSTANT- a value that has a constant value in the area of ​​its use; (1) P. Avogadro is the same as Avogadro (see); (2) P. Boltzmann is a universal thermodynamic quantity that connects the energy of an elementary particle with its temperature; denoted by k,… … Great Polytechnic Encyclopedia

Books

  • Biographies of physical constants. Fascinating stories about universal physical constants. Issue 46
  • Biographies of physical constants. Fascinating stories about universal physical constants, O. P. Spiridonov. This book is devoted to the consideration of universal physical constants and their important role in the development of physics. The task of the book is to tell in a popular form about the appearance in the history of physics ...

The Italian scientist Amedeo Avogadro, a contemporary of A. S. Pushkin, was the first to understand that the number of atoms (molecules) in one gram-atom (mole) of a substance is the same for all substances. Knowledge of this number opens the way to estimating the size of atoms (molecules). During the life of Avogadro, his hypothesis did not receive due recognition. The history of the Avogadro number is the subject of a new book by Evgeny Zalmanovich Meilikhov, professor at the Moscow Institute of Physics and Technology, chief researcher at the National Research Center "Kurchatov Institute".

If, as a result of some world catastrophe, all the accumulated knowledge would be destroyed and only one phrase would come to the future generations of living beings, then what statement, composed of the smallest number of words, would bring the most information? I believe this is the atomic hypothesis:<...>all bodies are made up of atoms - small bodies that are in constant motion.

R. Feynman, "The Feynman Lectures on Physics"

The Avogadro number (Avogadro's constant, Avogadro's constant) is defined as the number of atoms in 12 grams of the pure isotope carbon-12 (12 C). It is usually denoted as N A, less often L. The value of the Avogadro number recommended by CODATA (working group on fundamental constants) in 2015: N A = 6.02214082(11) 1023 mol −1 . A mole is the amount of a substance that contains N A structural elements (that is, as many elements as there are atoms in 12 g 12 C), and the structural elements are usually atoms, molecules, ions, etc. By definition, the atomic mass unit (amu) is 1/12 the mass of a 12 C atom. One mole (gram-mol) of a substance has a mass (molar mass) that, when expressed in grams, is numerically equal to the molecular weight of that substance (expressed in atomic mass units). For example: 1 mol of sodium has a mass of 22.9898 g and contains (approximately) 6.02 10 23 atoms, 1 mol of calcium fluoride CaF 2 has a mass of (40.08 + 2 18.998) = 78.076 g and contains (approximately) 6 .02 10 23 molecules.

At the end of 2011, at the XXIV General Conference on Weights and Measures, a proposal was unanimously adopted to define the mole in a future version of the International System of Units (SI) in such a way as to avoid its linkage to the definition of the gram. It is assumed that in 2018 the mole will be determined directly by the Avogadro number, which will be assigned an exact (without error) value based on the measurement results recommended by CODATA. So far, the Avogadro number is not accepted by definition, but a measured value.

This constant is named after the famous Italian chemist Amedeo Avogadro (1776–1856), who, although he himself did not know this number, understood that it was a very large value. At the dawn of the development of atomic theory, Avogadro put forward a hypothesis (1811), according to which, at the same temperature and pressure, equal volumes of ideal gases contain the same number of molecules. This hypothesis was later shown to be a consequence of the kinetic theory of gases, and is now known as Avogadro's law. It can be formulated as follows: one mole of any gas at the same temperature and pressure occupies the same volume, under normal conditions equal to 22.41383 liters (normal conditions correspond to pressure P 0 = 1 atm and temperature T 0 = 273.15 K). This quantity is known as the molar volume of the gas.

The first attempt to find the number of molecules occupying a given volume was made in 1865 by J. Loschmidt. It followed from his calculations that the number of molecules per unit volume of air is 1.8 10 18 cm −3 , which, as it turned out, is about 15 times less than the correct value. Eight years later, J. Maxwell gave an estimate much closer to the truth - 1.9 · 10 19 cm −3 . Finally, in 1908, Perrin gives an already acceptable assessment: N A = 6.8 10 23 mol −1 Avogadro's number, found from experiments on Brownian motion.

Since then, a large number of independent methods have been developed to determine the Avogadro number, and more accurate measurements have shown that in reality there are (approximately) 2.69 x 10 19 molecules in 1 cm 3 of an ideal gas under normal conditions. This quantity is called the Loschmidt number (or constant). It corresponds to Avogadro's number N A ≈ 6.02 10 23 .

Avogadro's number is one of the important physical constants that played an important role in the development of the natural sciences. But is it a "universal (fundamental) physical constant"? The term itself is not defined and is usually associated with a more or less detailed table of the numerical values ​​of physical constants that should be used in solving problems. In this regard, the fundamental physical constants are often considered those quantities that are not constants of nature and owe their existence only to the chosen system of units (such, for example, the magnetic and electric vacuum constants) or conditional international agreements (such, for example, the atomic mass unit) . The fundamental constants often include many derived quantities (for example, the gas constant R, the classical electron radius r e= e 2 / m e c 2 etc.) or, as in the case of molar volume, the value of some physical parameter related to specific experimental conditions, which are chosen only for reasons of convenience (pressure 1 atm and temperature 273.15 K). From this point of view, the Avogadro number is a truly fundamental constant.

This book is devoted to the history and development of methods for determining this number. The epic lasted for about 200 years and at different stages was associated with a variety of physical models and theories, many of which have not lost their relevance to this day. The brightest scientific minds had a hand in this story - suffice it to name A. Avogadro, J. Loschmidt, J. Maxwell, J. Perrin, A. Einstein, M. Smoluchovsky. The list could go on and on...

The author must admit that the idea of ​​the book does not belong to him, but to Lev Fedorovich Soloveichik, his classmate at the Moscow Institute of Physics and Technology, a man who was engaged in applied research and development, but remained a romantic physicist at heart. This is a person who (one of the few) continues “even in our cruel age” to fight for a real “higher” physical education in Russia, appreciates and, to the best of his ability, promotes the beauty and elegance of physical ideas. It is known that from the plot, which A. S. Pushkin presented to N. V. Gogol, a brilliant comedy arose. Of course, this is not the case here, but perhaps this book will also be useful to someone.

This book is not a "popular science" work, although it may seem so at first glance. It discusses serious physics against some historical background, uses serious mathematics, and discusses rather complex scientific models. In fact, the book consists of two (not always sharply demarcated) parts, designed for different readers - some may find it interesting from a historical and chemical point of view, while others may focus on the physical and mathematical side of the problem. The author had in mind an inquisitive reader - a student of the Faculty of Physics or Chemistry, not alien to mathematics and passionate about the history of science. Are there such students? The author does not know the exact answer to this question, but, based on his own experience, he hopes that there is.

Introduction (abbreviated) to the book: Meilikhov EZ Avogadro's number. How to see an atom. - Dolgoprudny: Publishing House "Intellect", 2017.

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