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
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
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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 ...
> 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 of 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.
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 smallest number of words, would bring the 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), which, when expressed in grams, is numerically equal to the molecular weight of this 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, 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 \u003d 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
Amount of substanceν is equal to the ratio of the number of molecules in a given body to the number of atoms in 0.012 kg of carbon, that is, the number of molecules in 1 mole of a substance.
ν = N / N A
where N is the number of molecules in a given body, N A is the number of molecules in 1 mole of the substance that makes up the body. N A is Avogadro's constant. The amount of a substance is measured in moles. Avogadro constant is the number of molecules or atoms in 1 mole of a substance. This constant got its name in honor of the Italian chemist and physicist Amedeo Avogadro(1776 - 1856). 1 mole of any substance contains the same number of particles.
N A \u003d 6.02 * 10 23 mol -1 Molar mass is the mass of a substance taken in the amount of one mole:
μ = m 0 * N A
where m 0 is the mass of the molecule. Molar mass is expressed in kilograms per mole (kg/mol = kg*mol -1). Molar mass is related to relative molecular mass by the relationship:
μ \u003d 10 -3 * M r [kg * mol -1]
The mass of any amount of substance m is equal to the product of the mass of one molecule m 0 by the number of molecules:
m = m 0 N = m 0 N A ν = μν
The amount of a substance is equal to the ratio of the mass of the substance to its molar mass:
ν = m / μ
The mass of one molecule of a substance can be found if the molar mass and the Avogadro constant are known:
m 0 = m / N = m / νN A = μ / N A
Ideal gas- a mathematical model of a gas, in which it is assumed that the potential energy of the interaction of molecules can be neglected in comparison with their kinetic energy. There are no forces of attraction or repulsion between molecules, the collisions of particles between themselves and with the walls of the vessel are absolutely elastic, and the time of interaction between molecules is negligibly small compared to the average time between collisions. In the extended model of an ideal gas, the particles of which it is composed also have a shape in the form of elastic spheres or ellipsoids, which makes it possible to take into account the energy of not only translational, but also rotational-oscillatory motion, as well as not only central, but also non-central collisions of particles, etc. .)
