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Weight of avogadro. Avogadro's law in chemistry




According to changes in the definitions of the SI base units, exactly equals

N A= 6.022 140 76⋅10 23 mol −1.

Sometimes in the literature a distinction is made between constant Avogadro N A , which has the dimension mol −1 , and numerically equal to it dimensionless Avogadro's number BUT .

Avogadro's law

History of constant measurement

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 Josef 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 . According to him, Avogadro's number was approximately 10 22 (\displaystyle 10^(22)).

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.

Contemporary estimates

Officially adopted in 2010, the value of Avogadro's number was measured using two spheres made of silicon-28. 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 in Nizhny Novgorod 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 .

N A= 6.022 141 29(27)⋅10 23 mol −1. N A= 6.022 140 857(74)⋅10 23 mol −1

Relationship between constants

see also

Comments

Notes

  1. Previously expressed as the number of molecules in gram-molecule or atoms in gram-atom.
  2. Avogadro constant// Physical Encyclopedia / Ch. ed. A. M. Prokhorov. - M.: Soviet Encyclopedia, 1988. - T. 1. - S. 11. - 704 p. - 100,000 copies
  3. Unlike N, denoting the number of particles (English. particle number)
  4. http://www.iupac.org/publications/books/gbook/green_book_2ed.pdf
  5. , With. 22-23.
  6. , With. 23.
  7. On the possible future revision of the International System of Units, the SI. Resolution 1 of the 24th meeting of the CGPM (2011).

Matter is made up of molecules. By a molecule we mean the smallest particle of a given substance that retains the chemical properties of the given substance.

Reader: And in what units is the mass of molecules measured?

Author: The mass of a molecule can be measured in any unit of mass, for example, in tons, but since the masses of molecules are very small: ~ 10 -23 g, then for convenience introduced a special unit atomic mass unit(a.u.m.).

atomic mass unitcalled a value equal to the -th mass of a carbon atom 6 C 12 .

Record 6 C 12 means: a carbon atom having a mass of 12 a.m.u. and the charge of the nucleus is 6 elementary charges. Similarly, 92 U 235 is a uranium atom with a mass of 235 a.m.u. and the charge of the nucleus is 92 elementary charges, 8 O 16 is an oxygen atom with a mass of 16 amu and the charge of the nucleus is 8 elementary charges, etc.

Reader: Why was it taken as the atomic unit of mass (but not or ) part of the mass of an atom and precisely carbon, and not oxygen or plutonium?

It has been experimentally established that 1 g » 6.02×10 23 a.m.u.

The number showing how many times the mass of 1 g is greater than 1 amu is called Avogadro's number:N A = 6.02×10 23 .

From here

N A × (1 amu) = 1 g. (5.1)

Neglecting the mass of electrons and the difference in the masses of the proton and neutron, we can say that the Avogadro number approximately shows how many protons (or, which is almost the same, hydrogen atoms) must be taken to form a mass of 1 g (Fig. 5.1).

mole

The mass of a molecule expressed in atomic mass units is called relative molecular weight .

Denoted M r(r- from relative - relative), for example:

12 amu = 235 amu

A portion of a substance that contains as many grams of a given substance as atomic mass units contains a molecule of a given substance is called molem(1 mol).

For example: 1) the relative molecular weight of hydrogen H 2: therefore, 1 mol of hydrogen has a mass of 2 g;

2) relative molecular weight of carbon dioxide CO 2:

12 amu + 2×16 amu = 44 amu

therefore, 1 mole of CO 2 has a mass of 44 g.

Statement. One mole of any substance contains the same number of molecules: N A \u003d 6.02 × 10 23 pcs.

Proof. Let the relative molecular weight of the substance M r(a.m.u.) = M r× (1 amu). Then, according to the definition, 1 mole of a given substance has a mass M r(d) = M r×(1 g). Let N is the number of molecules in one mole, then

N×(mass of one molecule) = (mass of one mole),

The mole is the basic SI unit of measure.

Comment. Mole can be defined differently: 1 mole is N A \u003d \u003d 6.02 × 10 23 molecules of this substance. Then it is easy to understand that the mass of 1 mole is equal to M r(G). Indeed, one molecule has a mass M r(a.m.u.), i.e.

(mass of one molecule) = M r× (1 amu),

(mass of one mole) = N A × (mass of one molecule) =

= N A × M r× (1 amu) = .

The mass of 1 mole is called molar mass of this substance.

Reader: If we take the mass t some substance, the molar mass of which is equal to m, then how many moles will it be?

Let's remember:

Reader: And in what units in the SI system should m be measured?

, [m] = kg/mol.

For example, the molar mass of hydrogen

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

Wikimedia Foundation. 2010 .

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

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    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

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    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

The remarkable work of Perrin, which played an exceptional role in the establishment of molecular concepts, is connected with the use of the barometric formula obtained above. The main idea of ​​Perrin's experiments boiled down to the assumption that the laws of molecular kinetic theory determine the behavior not only of atoms and molecules, but also of much larger particles, consisting of many thousands of molecules. Based on very general considerations, which will not be considered here, it can be assumed that the average kinetic energies of very small particles that perform Brownian motion in a liquid coincide with the average kinetic energies of gas molecules, provided that the temperature of the liquid and the temperature of the gas are the same. Similarly, the height distribution of particles suspended in a liquid obeys the same law as the height distribution of gas molecules. Such a conclusion is very important, since on the basis of it a quantitative verification of the law of distribution is possible. The check can be carried out by directly counting the number of suspended particles in the liquid at different heights using a microscope.

Equation (36) for particle height distribution

it is convenient in this case to rewrite, dividing the numerator and denominator of the fraction on the right side of the equation by the Avogadro number

It should be noted that the ratio - corresponds to the mass of the particle and the ratio is equal to the average kinetic energy of the particle [compare equation (28)]. Introducing these notations, we get:

If we now empirically determine the number of particles and corresponding to two different values, then it will be possible to write:

Subtracting the second equation from the first equation, we find:

From this relation it is possible to determine if only the mass of the particle is known

Despite the simplicity and clarity of the main idea, Perrin's experiments were associated with overcoming great difficulties. As an object of study, he chose aqueous emulsions of mastic and gum, which were subjected to centrifugation to obtain emulsions consisting of grains of the same size. The size of the grains, which were considered balls, was determined by the rate of their settling. It was impossible to follow the movement of an individual grain, and therefore the rate of settling of the upper boundary of the emulsion, i.e., the average settling rate of many thousands of grains, was observed. Knowing the density of the emulsified substance and determining the size of the grains of the emulsion, it was possible to calculate their masses. Next, it was necessary to determine the numbers. To this end, Perrin glued a second glass with a round hole drilled in it to a glass slide for microscopic observations, so that a cylindrical transparent cuvette was formed. By placing a drop of emulsion in a cuvette and closing the cuvette with a cover slip to prevent evaporation, it was possible to observe emulsion grains with a microscope. If you use a lens with a shallow depth of field, then only grains located in a very thin layer of liquid will be visible in the microscope. In practice, in these experiments, only a small number of grains can be counted, since their number is constantly changing. To overcome this difficulty in the focal

an opaque screen with a small round hole was placed in the plane of the eyepiece. Due to this, the field of view of the microscope was greatly reduced, and the observer could immediately determine how many grains were currently in the field of view (Fig. 12).

By repeating such observations at regular intervals, recording the observed number of grains, and averaging the data obtained, Perrin showed that the average number of grains at a given level tends to some definite limit corresponding to the density of the emulsion at that level. In order to illustrate the complexity of these experiments, it can be pointed out that in order to obtain an accurate result, it was necessary to make several thousand measurements.

Rice. 12. Distribution of emulsion grains.

Having determined the density of the emulsion at a certain level with the desired degree of accuracy, Perrin moved the microscope in a vertical direction and measured the density of the emulsion at the second level. Carefully performed measurements showed that the distribution of emulsion grains in height obeys the barometric formula (equation 37).