How to find a constant avogadro. Avogadro's number: interesting information
Avogadro's law was formulated by the Italian chemist Amadeo Avogadro in 1811 and was of great importance for the development of chemistry at that time. However, even today it has not lost its relevance and significance. Let's try to formulate Avogadro's law, it will sound something like this.
Formulation of Avogadro's Law
So, Avogadro's law states that at the same temperatures and in equal volumes of gases, the same number of molecules will be contained, regardless of both their chemical nature and physical properties. This number is a certain physical constant, equal to the number of molecules, ions contained in one mole.
Initially, Avogadro's law was only a scientist's hypothesis, but later this hypothesis was confirmed by a large number of experiments, after which it entered science under the name "Avogadro's law", which was destined to become the basic law for ideal gases.
Avogadro's law formula
The discoverer of the law himself believed that the physical constant is a large quantity, but he did not know which one. Already after his death, in the course of numerous experiments, the exact number of atoms contained in 12 g of carbon (namely, 12 g is the atomic mass unit of carbon) or in the molar volume of gas equal to 22.41 liters was established. This constant was named “Avogadro's number” in honor of the scientist, it is designated as NA, less often L and it is equal to 6.022*10 23 . In other words, the number of molecules of any gas in a volume of 22.41 liters will be the same for both light and heavy gases.
The mathematical formula for Avogadro's law can be written as follows:
Where, V is the volume of gas; n is the amount of a substance, which is the ratio of the mass of a substance to its molar mass; VM is a constant of proportionality or molar volume.
Application of Avogadro's Law
Further practical application of Avogadro's law greatly helped chemists to determine the chemical formulas of many compounds.
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).
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 mole of gas (6.02 ∙ 10 23 molecules - Avogadro's constant number) 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 the practical application of the law on the example of two problems:
- 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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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 this is the atomic hypothesis:<...>all bodies are made up of atoms - small bodies that are in constant motion.
R. Feynman, "The 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) 1023 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 (amu) is 1/12 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 = 1 atm and temperature T 0 = 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. It followed from his calculations 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 an estimate much closer to the truth - 1.9 · 10 19 cm −3 . Finally, in 1908, Perrin gives an already acceptable assessment: 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 Avogadro's 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= 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, which 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.
Introduction (abbreviated) to the book: Meilikhov EZ Avogadro's number. How to see an atom. - Dolgoprudny: Publishing House "Intellect", 2017.
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. .)
