He became a real breakthrough in theoretical chemistry and contributed to the fact that hypothetical guesses turned into great discoveries in the field of gas chemistry. The assumptions of chemists have received convincing evidence in the form of mathematical formulas and simple ratios, and the results of experiments now allow far-reaching conclusions to be drawn. In addition, the Italian researcher derived a quantitative characteristic of the number of structural particles of a chemical element. The Avogadro number subsequently became one of the most important constants in modern physics and chemistry.
Law of Volumetric Relations
The honor of being the discoverer of gas reactions belongs to Gay-Lussac, a French scientist at the end of the 18th century. This researcher gave the world a well-known law, which obeys all reactions associated with the expansion of gases. Gay-Lussac measured the volumes of gases before the reaction and the volumes that were obtained as a result of chemical interaction. As a result of the experiment, the scientist made a conclusion known as the law of simple volumetric ratios. Its essence is that the volumes of gases before and after are related to each other as integer small numbers.
For example, when interacting gaseous substances corresponding, for example, to one volume of oxygen and two volumes of hydrogen, two volumes of vaporous water are obtained, and so on.
Gay-Lussac's law is valid if all measurements of volumes occur at the same pressure and temperature. This law turned out to be very important for the Italian physicist Avogadro. Guided by him, he deduced his assumption, which had far-reaching consequences in the chemistry and physics of gases, and calculated Avogadro's number.
Italian scientist
Avogadro's law
In 1811, Avogadro came to the realization that equal volumes of arbitrary gases at constant temperatures and pressures contained the same number of molecules.
This law, later named after the Italian scientist, introduced into science the concept of the smallest particles of matter - molecules. Chemistry split into the empirical science that it was and the quantitative science that it became. Avogadro especially emphasized the point that atoms and molecules are not the same, and that atoms are the building blocks of all molecules.
The law of the Italian researcher made it possible to come to the conclusion about the number of atoms in the molecules of various gases. For example, after the derivation of Avogadro's law, he confirmed the assumption that the molecules of gases such as oxygen, hydrogen, chlorine, nitrogen, consist of two atoms. It also became possible to establish the atomic masses and molecular masses of elements consisting of different atoms.
Atomic and molecular weights
When calculating the atomic weight of an element, the mass of hydrogen, as the lightest chemical substance, was initially taken as a unit of measurement. But the atomic masses of many chemicals are calculated as the ratio of their oxygen compounds, that is, the ratio of oxygen and hydrogen was taken as 16:1. This formula was somewhat inconvenient for measurements, so the mass of the carbon isotope, the most common substance on earth, was taken as the standard of atomic mass.
On the basis of Avogadro's law, the principle of determining the masses of various gaseous substances in molecular equivalent is based. In 1961, a unified reference system for relative atomic quantities was adopted, which was based on a conventional unit equal to 1/12 of the mass of one carbon isotope 12 C. The abbreviated name of the atomic mass unit is amu. According to this scale, the atomic mass of oxygen is 15.999 amu, and carbon is 1.0079 amu. So a new definition arose: the relative atomic mass is the mass of an atom of a substance, expressed in amu.
Mass of a substance molecule
Any substance is made up of molecules. The mass of such a molecule is expressed in amu, this value is equal to the sum of all the atoms that make up its composition. For example, a hydrogen molecule has a mass of 2.0158 amu, that is, 1.0079 x 2, and the molecular weight of water can be calculated from its chemical formula H 2 O. Two hydrogen atoms and a single oxygen atom add up to 18 .0152 amu
The value of the atomic mass for each substance is usually called the relative molecular weight.
Until recently, instead of the concept of "atomic mass" the phrase "atomic weight" was used. It is not currently used, but is still found in old textbooks and scientific papers.
Unit of quantity of a substance
Together with units of volume and mass in chemistry, a special measure of the amount of a substance, called a mole, is used. This unit shows the amount of a substance that contains as many molecules, atoms and other structural particles as they are contained in 12 g of carbon of the 12 C isotope. , atoms or molecules. For example, a mole of H + ions and H 2 molecules are completely different measures.
At present, the amount of a substance in a mole of a substance has been measured with great accuracy.
Practical calculations show that the number of structural units in a mole is 6.02 x 10 23 . This constant is called "Avogadro's number". Named after an Italian scientist, this chemical quantity indicates the number of structural units in a mole of any substance, regardless of its internal structure, composition and origin.
molar mass
The mass of one mole of a substance in chemistry is called "molar mass", this unit is expressed by the ratio g / mol. Applying the value of the molar mass in practice, it can be seen that the molar mass of hydrogen is 2.02158 g/mol, oxygen is 1.0079 g/mol, and so on.
Consequences of Avogadro's Law
Avogadro's law is quite applicable for determining the amount of a substance when calculating the volume of a gas. The same number of molecules of any gaseous substance under constant conditions occupies an equal volume. On the other hand, 1 mole of any substance contains the same number of molecules. The conclusion suggests itself: at constant temperature and pressure, one mole of a gaseous substance occupies a constant volume and contains an equal number of molecules. The Avogadro number states that there are 6.02 x 10 23 molecules in the volume of 1 mole of gas.
Calculation of gas volume for normal conditions
Normal conditions in chemistry are atmospheric pressure of 760 mm Hg. Art. and a temperature of 0 ° C. With these parameters, it has been experimentally established that the mass of one liter of oxygen is 1.43 kg. Therefore, the volume of one mole of oxygen is 22.4 liters. When calculating the volume of any gas, the results showed the same value. So the Avogadro constant made another conclusion regarding the volumes of various gaseous substances: under normal conditions, one mole of any gaseous element occupies 22.4 liters. This constant is called the molar volume of the gas.
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 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.
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 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 was obtained that includes the Avogadro number and 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
Knowing the amount of a substance in moles and the Avogadro number, it is very easy to calculate how many molecules are contained in this substance. Simply multiply Avogadro's number by the amount of the substance.
N=N A *ν
And if you came to the clinic to take tests, well, say, blood for sugar, knowing the Avogadro number, you can easily calculate the number of sugar molecules in your blood. Well, for example, the analysis showed 5 mol. We multiply this result by Avogadro's number and get 3,010,000,000,000,000,000,000,000 pieces. Looking at this figure, it becomes clear why they refused to measure molecules in pieces, and began to measure them in moles.
Molar mass (M).
If the amount of a substance is unknown, then it can be found by dividing the mass of the substance by its molar mass.
N=N A * m / M .
The only question that can arise here is: “what is the molar mass?” No, this is not the mass of the painter, as it may seem!!! Molar mass is the mass of one mole of a substance. Everything is simple here, if one mole contains N A particles (i.e. equal to Avogadro's number), then, multiplying the mass of one such particle m0 by Avogadro's number, we get the molar mass.
M=m 0 *N A .
Molar mass is the mass of one mole of a substance.
And it's good if she is known, but if not? We'll have to calculate the mass of one molecule m 0 . But that's not a problem either. You only need to know its chemical formula and have the periodic table at hand.
Relative molecular weight (Mr).
If the number of molecules in a substance is a very large value, then the mass of one molecule m0, on the contrary, is a very small value. Therefore, for the convenience of calculations, we introduced relative molecular weight (Mr). This is the ratio of the mass of one molecule or atom of a substance to 1/12 of the mass of a carbon atom. But don't let that scare you, for atoms it is indicated in the periodic table, and for molecules it is calculated as the sum of the relative molecular masses of all the atoms that make up the molecule. Relative molecular weight is measured in atomic mass units (a.m.u.), in terms of kilograms 1 amu = 1.67 10 -27 kg. Knowing this, we can easily determine the mass of one molecule by multiplying the relative molecular mass by 1.67 10 -27 .
m 0 \u003d M r * 1.67 * 10 -27.
Relative molecular weight- the ratio of the mass of one molecule or atom of a substance, to 1/12 of the mass of a carbon atom.
Relationship between molar and molecular weights.
Recall the formula for finding the molar mass:
M=m 0 *N A .
Because m 0 \u003d M r * 1.67 10 -27, we can express the molar mass as:
M=M r *N A *1.67 10 -27 .
Now, if we multiply the Avogadro number N A by 1.67 10 -27, we get 10 -3, that is, to find out the molar mass of a substance, it is enough just to multiply its molecular weight by 10 -3.
M=M r *10 -3
But do not rush to do all this by calculating the number of molecules. If we know the mass of a substance m, then dividing it by the mass of a molecule m 0, we get the number of molecules in this substance.
N=m / m0
Of course, it is a thankless task for molecules to count, not only are they small, they are also constantly moving. That and look you will get lost, and you will have to count again. But in science, as in the army, there is such a word “necessary”, and therefore even atoms and molecules were counted ...
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) 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, 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 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
