> Avogadro's number

Find out what is Avogadro's number in prayers. Study the ratio of the amount of substance of molecules and the Avogadro number, Brownian motion, gas constant and Faraday.

The number of molecules in a mole is called the Avogadro number, which is 6.02 x 10 23 mol -1.

Learning task

• Understand the relationship between Avogadro's number and moles.

Key Points

• Avogadro suggested that in the case of uniform pressure and temperature, equal gas volumes contain the same number of molecules.
• The Avogadro constant is an important factor, as it links other physical constants and properties.
• Albert Einstein believed that this number could be derived from the quantities brownian motion. It was first measured in 1908 by Jean Perrin.

Terms

• The gas constant is the universal constant (R) resulting from the ideal gas law. It is extracted from the Boltzmann constant and the Avogadro number.
• Faraday's constant is the amount of electric charge per mole of electrons.
• Brownian motion is the random displacement of elements formed due to impacts with individual molecules in a liquid.

If you are faced with a change in the amount of a substance, then it is easier to use a unit other than the number of molecules. The mole is the basic unit in the international system and conveys a substance containing as many atoms as is stored in 12 g of carbon-12. This amount of substance is called Avogadro's number.

He managed to establish a relationship between the masses of the same volume of different gases (under conditions of the same temperature and pressure). This contributes to the relationship of their molecular weights

The Avogadro number conveys the number of molecules in one gram of oxygen. Do not forget that this is an indication of the quantitative characteristic of a substance, and not an independent measurement size. In 1811, Avogadro guessed that the volume of a gas can be proportional to the number of atoms or molecules, and this will not be affected by the nature of the gas (the number is universal).

Jean Perinne won the Nobel Prize in Physics in 1926 for deriving Avogadro's constant. So Avogadro's number is 6.02 x 10 23 mol -1.

scientific significance

The Avogadro constant plays the role of an important link in macro- and microscopic natural observations. It kind of builds a bridge for other physical constants and properties. For example, establishes a relationship between the gas constant (R) and Boltzmann (k):

R = kN A = 8.314472 (15) J mol -1 K -1 .

And also between the Faraday constant (F) and the elementary charge (e):

F = N A e = 96485.3383 (83) C mol -1 .

Constant calculation

The definition of the number affects the calculation of the mass of an atom, which is obtained by dividing the mass of a mole of gas by Avogadro's number. In 1905, Albert Einstein suggested deriving it based on the magnitudes of Brownian motion. It was this idea that Jean Perrin tested in 1908.

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 molecules. Later it was shown that this conjecture is a necessary consequence of 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

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

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 constant found, a crater on the Moon was also named after 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 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.

Doctor of Physical and Mathematical Sciences Evgeny Meilikhov

Introduction (abbreviated) to the book: Meilikhov EZ Avogadro's number. How to see an atom. - Dolgoprudny: Publishing House "Intellect", 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. 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 least number of words, would bring most information? I believe that this is the atomic hypothesis: ... all bodies are composed of atoms - small bodies that are in constant motion.
R. Feynman. 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) 10 23 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 (a.e. .m) is equal to 1/12 of 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 \u003d 1 atm and temperature T 0 \u003d 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. 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 than the 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 gives an already 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 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 the Avogadro 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, 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 number of fundamental constants often includes 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 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.

Information about the books of the Publishing House "Intellect" - on the site www.id-intellect.ru

Avogadro's law in chemistry helps to calculate the volume, molar mass, amount of a gaseous substance and the relative density of a gas. The hypothesis was formulated by Amedeo Avogadro in 1811 and was later confirmed experimentally.

Law

Joseph Gay-Lussac was the first to study the reactions of gases in 1808. He formulated the laws of thermal expansion of gases and volumetric ratios, having obtained from hydrogen chloride and ammonia (two gases) a crystalline substance - NH 4 Cl (ammonium chloride). It turned out that to create it, it is necessary to take the same volumes of gases. Moreover, if one gas was in excess, then the “extra” part after the reaction remained unused.

A little later, Avogadro formulated the conclusion that at the same temperatures and pressures, equal volumes of gases contain the same number of molecules. In this case, gases can have different chemical and physical properties.

Rice. 1. Amedeo Avogadro.

Two consequences follow from Avogadro's law:

• first - one mole of gas under equal conditions occupies the same volume;
• second - the ratio of the masses of equal volumes of two gases is equal to the ratio of their molar masses and expresses the relative density of one gas in terms of another (denoted by D).

Normal conditions (n.s.) are pressure P=101.3 kPa (1 atm) and temperature T=273 K (0°C). Under normal conditions, the molar volume of gases (the volume of a substance to its amount) is 22.4 l / mol, i.e. 1 mol of gas (6.02 ∙ 10 23 molecules - constant number Avogadro) occupies a volume of 22.4 liters. Molar volume (V m) is a constant value.

Rice. 2. Normal conditions.

Problem solving

The main significance of the law is the ability to carry out chemical calculations. Based on the first consequence of the law, you can calculate the amount of gaseous matter through the volume using the formula:

where V is the volume of gas, V m is the molar volume, n is the amount of substance, measured in moles.

The second conclusion from Avogadro's law concerns the calculation of the relative density of a gas (ρ). Density is calculated using the m/V formula. If we consider 1 mole of gas, then the density formula will look like this:

ρ (gas) = ​​M/V m ,

where M is the mass of one mole, i.e. molar mass.

To calculate the density of one gas from another gas, it is necessary to know the density of the gases. The general formula for the relative density of a gas is as follows:

D(y)x = ρ(x) / ρ(y),

where ρ(x) is the density of one gas, ρ(y) is the density of the second gas.

If we substitute the density calculation into the formula, we get:

D (y) x \u003d M (x) / V m / M (y) / V m.

The molar volume decreases and remains

D(y)x = M(x) / M(y).

Consider practical use law on the example of two tasks:

• How many liters of CO 2 will be obtained from 6 mol of MgCO 3 in the reaction of decomposition of MgCO 3 into magnesium oxide and carbon dioxide (n.o.)?
• What is the relative density of CO 2 for hydrogen and for air?

Let's solve the first problem first.

n(MgCO 3) = 6 mol

MgCO 3 \u003d MgO + CO 2

The amount of magnesium carbonate and carbon dioxide is the same (one molecule each), therefore n (CO 2) \u003d n (MgCO 3) \u003d 6 mol. From the formula n \u003d V / V m, you can calculate the volume:

V = nV m , i.e. V (CO 2) \u003d n (CO 2) ∙ V m \u003d 6 mol ∙ 22.4 l / mol \u003d 134.4 l

Answer: V (CO 2) \u003d 134.4 l

Solution of the second problem:

• D (H2) CO 2 \u003d M (CO 2) / M (H 2) \u003d 44 g / mol / 2 g / mol \u003d 22;
• D (air) CO 2 \u003d M (CO 2) / M (air) \u003d 44 g / mol / 29 g / mol \u003d 1.52.

Rice. 3. Formulas for the amount of substance by volume and relative density.

The formulas of Avogadro's law only work for gaseous substances. They do not apply to liquids and solids.

What have we learned?

According to the formulation of the law, equal volumes of gases under the same conditions contain the same number of molecules. Under normal conditions (n.c.), the value of the molar volume is constant, i.e. V m for gases is always 22.4 l/mol. It follows from the law that the same number of molecules of different gases under normal conditions occupy the same volume, as well as the relative density of one gas in another - the ratio of the molar mass of one gas to the molar mass of the second gas.

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