Avogadro's number: interesting information. Avogadro's constant

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, Avogadro’s number is usually written in this form: 6.02. 10^23.

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

To be precise, I was not involved in counting molecules or atoms in any specific volume. The first who tried to find out how many molecules of gas

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

Subsequently, independent methods were invented on how to determine Avogadro's number, and since the results mostly coincided, this once again spoke in favor of the actual existence of molecules. On this moment the number of methods exceeded 60, but in last years scientists are trying to further improve the accuracy of the estimate to introduce a new definition of the term “kilogram”. So far, the kilogram has been compared to a chosen material standard without any fundamental definition.

However, let's return to our question - why this constant is 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 mole became the basic unit for measuring quantity. According to 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 Avogadro's number is its reciprocal.

For clarity, let's take an example. As is known from the definition of the atomic mass unit, 1 a.u.m. corresponds to one twelfth of the mass of one carbon atom 12C and is 1.66053878.10^(−24) grams. If you multiply 1 amu. by Avogadro's constant, we get 1.000 g/mol. Now let's take some, say, beryllium. According to the table, the mass of one beryllium atom 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 it coincides with the atomic one.

Avogadro's constant was specially chosen so that the molar mass corresponded to an atomic or dimensionless quantity - relative molecular. We can say that Avogadro's number owes its appearance, on the one hand, to the atomic unit of mass, and on the other, to the generally accepted unit for comparing mass - the gram.

A physical quantity equal to the number of structural elements (which are molecules, atoms, etc.) per mole of a substance is called Avogadro's number. Its officially accepted value today is NA = 6.02214084(18)×1023 mol−1, it was approved in 2010. In 2011, the results of new studies were published; they are considered more accurate, but are not officially approved at the moment.

Avogadro's law has great value in the development of chemistry, it made it possible to calculate the weight of bodies that can change state, becoming gaseous or vaporous. It was on the basis of Avogadro's law that its development began atomic-molecular theory, following from the kinetic theory of gases.

Moreover, using Avogadro's law, a method has been developed to obtain the molecular weight of solutes. For this purpose, the laws of ideal gases were extended to dilute solutions, taking as a basis the idea that the solute will be distributed throughout the volume of the solvent, just as a gas is distributed in a vessel. Also, Avogadro's law made it possible to determine the true atomic masses a number of chemical elements.

Practical use of Avogadro's number

The constant is used in calculations chemical formulas and in the process of composing equations chemical reactions. It is used to determine the relative molecular masses of gases and the number of molecules in one mole of any substance.

The universal gas constant is calculated through Avogadro's number; it is obtained by multiplying this constant by Boltzmann's constant. In addition, by multiplying Avogadro's number and the elementary electric charge, one can obtain Faraday's constant.

Using the consequences of Avogadro's law

The first corollary of the law says: “One mole of gas (any), under equal conditions, will occupy one volume.” Thus, in normal conditions the volume of one mole of any gas is equal to 22.4 liters (this value is called the molar volume of a gas), and using the Mendeleev-Clapeyron equation you can determine the volume of a gas at any pressure and temperature.

The second corollary of the law: “The molar mass of the first gas is equal to the product of the molar mass of the second gas times relative density the first gas to the second." In other words, under the same conditions, knowing the ratio of the densities of two gases, one can determine their molar masses.

At the time of Avogadro, his hypothesis was theoretically unprovable, but it made it possible to easily establish experimentally the composition of gas molecules and determine their mass. Over time, a theoretical basis was provided for his experiments, and now Avogadro’s number is used

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 22,41383 . This quantity is known as the molar volume of a gas.

Avogadro himself did not estimate the number of molecules in a given volume, but he understood that this was a very large value. 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. After the name of this scientist, the indicated value was called the Loschmidt number (or constant). Since then it has been developed big number independent methods for determining Avogadro's number. The excellent agreement between the obtained values is convincing evidence of the real existence of the molecules.

Relationship between constants

Through the product of Boltzmann's constant, the Universal gas constant, R=kN A.
Faraday's constant is expressed through the product of the elementary electric charge and Avogadro's number, F=eN A.

Avogadro's law

Avogadro himself did not estimate the number of molecules in a given volume, but he understood that this was a very large value. The first attempt to find the number of molecules occupying a given volume was made in the year J. Loschmidt. From Loschmidt’s calculations it followed that for air the number of molecules per unit volume is 1.81·10 18 cm −3, which is approximately 15 times less than the true value. Eight years later, 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 was called the Loschmidt number (or constant). Since then, a large number of independent methods for determining Avogadro's number have been developed. The excellent agreement between the obtained values provides strong evidence of the actual number of molecules.

Measuring a constant

Data in this article is as of December 2011.

The officially accepted value for 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 for Crystallography and polished at the Australian Center for Precision Optics so smoothly that the heights of the 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 Mechanical Engineering Design Bureau in St. Petersburg.

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

Relationship between constants

Through the product of Boltzmann's constant, the Universal gas constant, R=kN A.
Faraday's constant is expressed through the product of the elementary electric charge and Avogadro's number, F=eN A.

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 MOLE 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 aiškinamasis žodynas

Avogadro's number- Avogadro konstanta statusas T sritis fizika atitikmenys: engl. Avogadro's constant; Avogadro's number vok. Avogadro Constante, 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's number)- the number of particles (atoms, molecules, ions) in 1 mole of a substance (a mole is the amount of substance that contains the same number of particles as there are atoms in exactly 12 grams of the carbon isotope 12), denoted by the symbol N = 6.023 1023. One of ... ... The beginnings of modern natural science

- (Avogadro’s number; denoted by NA), the number of molecules or atoms in 1 mole of a substance, NA = 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. It is designated NA and is equal to (6.022045 ... Chemical encyclopedia

Na = (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 the help of which you can determine quantities such as, for example, the mass of an atom or molecule (see... ... Collier's Encyclopedia

Doctor of Physical and Mathematical Sciences Evgeniy Meilikhov

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

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. Knowing this number opens the way to estimating the sizes of atoms (molecules). During Avogadro's lifetime, his hypothesis did not receive due recognition.

A new book by Evgeny Zalmanovich Meilikhov, professor at MIPT, chief researcher at the National Research Center Kurchatov Institute, is dedicated to the history of Avogadro’s number.

If, as a result of some global catastrophe, all accumulated knowledge were destroyed and only one phrase came to future generations of living beings, then which statement, composed of the fewest words, would bring the most information? I believe that this is the atomic hypothesis: ...all bodies consist of atoms - small bodies in continuous motion.
R. Feynman. Feynman lectures on physics

Avogadro's 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 designated as N A, less often L. The value of Avogadro’s number recommended by CODATA ( working group according to fundamental constants) in 2015: N A = 6.02214082(11)·10 23 mol -1. A mole is the amount of a substance that contains N A structural elements (that is, the same number of elements as there are atoms contained in 12 g of 12 C), and the structural elements are usually atoms, molecules, ions, etc. By definition, an atomic mass unit (a.u. .m.) is equal to 1/12 of the mass of an atom of 12 C. One mole (gram-mol) of a substance has a mass (molar mass), which, when expressed in grams, is numerically equal to the molecular mass of this substance (expressed in atomic mass units). For example: 1 mole of sodium has a mass of 22.9898 g and contains (approximately) 6.02 10 23 atoms, 1 mole 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 the future version of the International System of Units (SI) in such a way as to avoid its connection with the definition of gram. It is expected 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 results of measurements recommended by CODATA. In the meantime, Avogadro’s number is not an accepted value, but a measurable 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 a gas.

The first attempt to find the number of molecules occupying a given volume was made in 1865 by J. Loschmidt. From his calculations it followed 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 correct value. Eight years later, J. Maxwell gave a much closer estimate to the truth - 1.9·10 19 cm -3. Finally, in 1908, Perrin gave an acceptable estimate: 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 for determining Avogadro's number have been developed, and more accurate measurements have shown that in fact 1 cm 3 of an ideal gas under normal conditions contains (approximately) 2.69 10 19 molecules. 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 a large role in the development natural sciences. But is it a “universal (fundamental) physical constant”? The term itself is undefined and is usually associated with a more or less detailed table of numerical values of physical constants that should be used in solving problems. In this regard, fundamental physical constants are often considered to be those quantities that are not constants of nature and owe their existence only to a chosen system of units (such as the magnetic and electric constants of vacuum) or conventional international agreements (such as the atomic mass unit) . 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 that were chosen only for reasons of convenience (pressure 1 atm and temperature 273.15 K). From this point of view, Avogadro's number is a truly fundamental constant.

This book is devoted to the history and development of methods for determining this number. The epic lasted about 200 years and at different stages was associated with diverse 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 - just name A. Avogadro, J. Loschmidt, J. Maxwell, J. Perrin, A. Einstein, M. Smoluchowski. The list could go on...

The author must admit that the idea of the book belongs not to him, but to Lev Fedorovich Soloveichik, his classmate at the Moscow Institute of Physics and Technology, a man who studied applied research and developments, but at heart he remained a romantic physicist. This is a person who (one of the few) continues “even in our cruel age” to fight for a real “higher” physics education in Russia, appreciates and, to the best of his ability, promotes the beauty and grace of physical ideas. It is known that from the plot that A. S. Pushkin gave to N. V. Gogol, a brilliant comedy arose. Of course, this is not the case here, but maybe this book will also seem 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 fairly 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 keen on 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.

Information about books from the Intellect Publishing House is on the website www.id-intellect.ru

Avogadro's number: interesting information. Avogadro's constant

Practical use of Avogadro's number

Using the consequences of Avogadro's law

Avogadro's law

Relationship between constants

see also

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

Books

Avogadro's law

Measuring a constant

Relationship between constants

see also

Notes

Literature

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