The name of the avogadro number is. Avogadro's law in chemistry. Calculation of gas volume for normal conditions

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

Law

Joseph Gay-Lussac was the first to study gas reactions in 1808. He formulated the laws of thermal expansion of gases and volumetric relations, obtaining a crystalline substance - NH 4 Cl (ammonium chloride) from hydrogen chloride and ammonia (two gases). 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 remained unused after the reaction.

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

Rice. 1. Amedeo Avogadro.

Avogadro's law has two consequences:

• 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 over the other (denoted by D).

Normal conditions (n.s.) are considered to be 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 divided by its quantity) 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 corollary of the law, we can calculate the amount of a gaseous substance through 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 gas density (ρ). Density is calculated using the formula m/V. If we consider 1 mole of gas, 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 densities 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 you substitute the calculation of density into the formula, you get:

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

The molar volume is reduced and remains

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

Let's consider the practical application of the law using the example of two tasks:

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

Let's solve the first problem first.

n(MgCO 3) = 6 mol

MgCO 3 = MgO+CO 2

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

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

Answer: V(CO 2) = 134.4 l

Solution to the second problem:

• D (H2) CO 2 = M(CO 2) / M(H 2) = 44 g/mol / 2 g/mol = 22;
• D (air) CO 2 = M(CO 2) / M (air) = 44 g/mol / 29 g/mol = 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 are not applicable 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.s.), the value of the molar volume is constant, i.e. V m for gases is always equal to 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 compared to another - the ratio of the molar mass of one gas to the molar mass of the second gas.

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> Avogadro's number

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

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

Learning Objective

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

Main points

• Avogadro proposed that in the case of equal pressure and temperature, equal gas volumes contain the same number of molecules.
• Avogadro's constant is an important factor, since it connects 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), which follows from the ideal gas law. It is obtained from Boltzmann's constant and Avogadro's 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, it is easier to use a unit other than the number of molecules. The mole serves as the basic unit in the international system and conveys a substance containing the same number of atoms as are stored in 12 g of carbon-12. This amount of substance is called Avogadro's number.

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

Avogadro's number represents the number of molecules in one gram of oxygen. Remember that this is an indication of a quantitative characteristic of a substance, and not an independent dimension of measurement. In 1811, Avogadro guessed that the volume of a gas could be proportional to the number of atoms or molecules and this would not be affected by the nature of the gas (the number is universal).

The Nobel Prize in Physics was awarded to Jean Perinne in 1926 for his derivation of Avogadro's constant. So Avogadro's number is 6.02 x 10 23 mol -1.

Scientific significance

Avogadro's constant plays the role of an important link in macro- and microscopic natural observations. It kind of lays a bridge for other physical constants and properties. For example, it establishes a connection between the gas constant (R) and Boltzmann constant (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 .

Calculation of constant

Determining the number affects the calculation of the mass of the atom, which is obtained by dividing the mass of a mole of gas by Avogadro's number. In 1905, Albert Einstein proposed to derive it based on the magnitude of Brownian motion. It was this idea that Jean Perrin tested in 1908.

According to changes in the definitions of the SI base units, it is exactly equal to

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

Avogadro's law

History of constant measurement

Avogadro himself did not estimate the number of molecules in a given volume, but he understood that this was a very large value. The first attempt to find the number of molecules occupying a given volume was made in the year Joseph Loschmidt. From Loschmidt’s calculations it followed that for air the number of molecules per unit volume is 1.81⋅10 18 cm −3, which is approximately 15 times less than the true value. Eight years later, 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 his estimate, 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 was called the Loschmidt number (or constant). Since then, a large number of independent methods for determining Avogadro's number have been developed. The excellent agreement between the obtained values ​​provides strong evidence of the actual number of molecules.

Modern estimates

The value of Avogadro's number, officially adopted in 2010, was measured using two spheres made of silicon-28. The spheres were obtained at the Leibniz Institute for Crystallography and polished at the Australian Center for Precision Optics so smoothly that the height of the 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 Mechanical Engineering Design Bureau in St. Petersburg.

Having such practically ideal objects, it is possible to calculate with high accuracy the number of silicon atoms in the ball and thereby determine Avogadro's number. According to the results obtained, it is equal to 6.02214084(18) 10 23 mol −1 .

Relationship between constants

see also

Comments

Notes

1. Previously it was displayed as the number of molecules in gram-molecule or atoms in gram-atom.
2. Avogadro's constant// Physical encyclopedia / Ch. ed. A. M. Prokhorov. - M.: Soviet Encyclopedia, 1988. - T. 1. - P. 11. - 704 p. - 100,000 copies
3. Unlike N, indicating the number of particles (eng. 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).

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 chemists' assumptions received convincing evidence in the form of mathematical formulas and simple relationships, and the results of experiments now made it possible to draw far-reaching conclusions. In addition, the Italian researcher derived a quantitative characteristic of the number of structural particles of a chemical element. Avogadro's 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 of the late 18th century. This researcher gave the world a well-known law that governs all reactions associated with the expansion of gases. Gay-Lussac measured the volumes of gases before the reaction and the volumes that resulted from the chemical interaction. As a result of the experiment, the scientist came to a conclusion known as the law of simple volumetric relations. Its essence is that the volumes of gases before and after are related to each other as small whole numbers.

For example, when gaseous substances interact, 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 volume measurements occur at the same pressure and temperature. This law turned out to be very important for the Italian physicist Avogadro. Guided by him, he derived his hypothesis, 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 understanding that equal volumes of arbitrary gases at constant temperatures and pressures contain the same number of molecules.

This law, later named after the Italian scientist, introduced into science the idea of ​​the smallest particles of matter - molecules. Chemistry was divided into the empirical science it was and the quantitative science it became. Avogadro especially emphasized the point that atoms and molecules are not the same thing, and that atoms are the building blocks of all molecules.

The law of the Italian researcher allowed him to come to the conclusion about the number of atoms in the molecules of various gases. For example, after deducing 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 masses

When calculating the atomic weight of an element, the mass of hydrogen, as the lightest chemical substance, was initially taken as the unit of measurement. But the atomic masses of many chemical substances 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 isotope of carbon, the most common substance on earth, was taken as the standard of atomic mass.

The principle of determining the masses of various gaseous substances in molecular equivalent is based on Avogadro's law. In 1961, a unified system of reference 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 for the atomic mass unit is a.m.u. According to this scale, the atomic mass of oxygen is 15.999 amu, and carbon is 1.0079 amu. This is how a new definition arose: relative atomic mass is the mass of an atom of a substance, expressed in amu.

Mass of a molecule of a substance

Any substance consists 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 mass 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 atomic mass value for each substance is usually called relative molecular mass.

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 works.

Unit of quantity of substance

Together with units of volume and mass, chemistry uses a special measure of the amount of a substance called the mole. This unit shows the amount of a substance that contains as many molecules, atoms and other structural particles as are contained in 12 g of carbon isotope 12 C. In the practical application of a mole of a substance, one should take into account which particles of elements are meant - ions , atoms or molecules. For example, moles of H + ions and moles of H 2 molecules are completely different measures.

Currently, the amount of substance per mole of substance is 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 the Italian scientist, this chemical quantity shows 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 as the ratio g/mol. Using the molar mass value in practice, we can see 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 to determine 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 a constant 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. Avogadro's number states that 1 mole of gas contains 6.02 x 1023 molecules.

Calculation of gas volume for normal conditions

Normal conditions in chemistry are atmospheric pressure of 760 mm Hg. Art. and temperature 0 o 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. Thus, Avogadro’s 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 value 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, Avogadro’s number is usually written in this form: 6.02. 10^23.

However, why is Avogadro’s constant (in Ukrainian “became Avogadro”) equal to exactly this value? There is no answer to this question in textbooks, and historians of chemistry offer a variety of versions. It seems that Avogadro's number has some secret meaning. After all, there are magic numbers, which some include pi, Fibonacci numbers, seven (in the east eight), 13, etc. We will fight the information vacuum. We will not talk about who Amedeo Avogadro is, and why in honor of this scientist, in addition to the law he formulated, the found constant was also named. Many articles have already been written about this.

To be precise, I was not involved in counting molecules or atoms in any specific volume. The first who tried to find out how many molecules of gas

contained in a given volume at the same pressure and temperature, was Joseph Loschmidt, and this 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 Avogadro's number, and since the results mostly 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 has been compared to a chosen material standard without any fundamental definition.

However, let's return to our question - why this constant is 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 mole became the basic unit for measuring quantity. 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 Avogadro's number is its reciprocal.

For clarity, let's take an example. As is known from the definition of the atomic mass unit, 1 a.u.m. corresponds to one twelfth of the mass of one carbon atom 12C and is 1.66053878.10^(−24) grams. If you multiply 1 amu. by Avogadro's constant, we get 1.000 g/mol. Now let's take some, say, beryllium. According to the table, the mass of one beryllium atom 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 it coincides with the atomic one.

Avogadro's constant was specially chosen so that the molar mass corresponded to an atomic or dimensionless quantity - relative molecular. We can say that Avogadro's number owes its appearance, on the one hand, to the atomic unit of mass, and on the other, to the generally accepted unit for comparing mass - the gram.