Atomic mass unit. Avogadro's number

Matter consists of molecules. By molecule we will mean smallest particle of this substance, preserving Chemical properties of this substance.

Reader: In what units is the mass of molecules measured?

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

Atomic mass unitis called a value equal to the th mass of the carbon atom 6 C 12.

The notation 6 C 12 means: a carbon atom having a mass of 12 amu. and the nuclear charge is 6 elementary charges. Similarly, 92 U 235 is a uranium atom with a mass of 235 amu. 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 chosen as the atomic unit of mass? (but not or ) part of the mass of an atom and specifically carbon, and not oxygen or plutonium?

It has been experimentally established that 1 g » 6.02×10 23 amu.

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 a proton and a neutron, we can say that Avogadro’s number approximately shows how many protons (or, which is almost the same thing, 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 .

Designated M r(r– from relative – relative), for example:

12 a.m.u. = 235 a.m.u.

A portion of a substance that contains the same number of grams of a given substance as the number of atomic mass units contained in a molecule of a given substance is called pray(1 mol).

For example: 1) relative molecular weight of hydrogen H2: therefore, 1 mole of hydrogen has a mass of 2 g;

2) relative molecular weight of carbon dioxide CO 2:

12 amu + 2×16 a.m.u. = 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 = 6.02×10 23 pcs.

Proof. Let the relative molecular mass of a substance M r(a.m.) = M r× (1 amu). Then, according to the definition, 1 mole of a given substance has a mass M r(g) = 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 SI base unit of measurement.

Comment. A mole can be defined differently: 1 mole is N A = = 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.u.m.), 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 you take the mass T of some substance whose molar mass is m, then how many moles will it be?

Let's remember:

Reader: In what SI units should m be measured?

, [m] = kg/mol.

For example, the molar mass of hydrogen

From school course In chemistry, we know 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 the most different versions. It seems that Avogadro's number has a certain secret meaning. After all, there is magic numbers, where some include the number “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 a crater on the Moon was also named in honor of this scientist, in addition to the law he formulated and the constant he found. Many articles have already been written about this.

To be precise, I was not involved in counting molecules or atoms in any a certain 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 were mostly the same, then this once again spoke in favor of the actual existence of molecules. On this moment the number of methods exceeded 60, but in last years scientists are trying to further improve the accuracy of the estimate 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.

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 thermal expansion gases and volume ratios, obtaining 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 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 - constant number Avogadro) takes up 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 practical use law using the example of two problems:

• 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.

Avogadro's law formulas 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 to another - the ratio molar mass one gas to the molar mass of the second gas.

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Mole is the amount of a substance that contains the same number of structural elements as there are atoms contained in 12 g of 12 C, and the structural elements are usually atoms, molecules, ions, etc. The mass of 1 mole of a substance, expressed in grams, is numerically equal to its mole. mass. Thus, 1 mole of sodium has a mass of 22.9898 g and contains 6.02·10 23 atoms; 1 mole of calcium fluoride CaF 2 has a mass of (40.08 + 2 18.998) = 78.076 g and contains 6.02 10 23 molecules, as does 1 mole of carbon tetrachloride CCl 4, the mass of which 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 in equal volumes ideal gases contained same number molecules. Later it was shown that this hypothesis is a necessary consequence 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 a gas.

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 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. After 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 Avogadro's number have been developed. The excellent agreement between the obtained values ​​is convincing evidence of the real existence of the 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 Avogadro's number ~10 22.

Determination based on measuring the charge of an electron.

A 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– electron charge, N– the number of electrons in 1 mole 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 carried out by the US National Bureau of Standards gave the value F= 96490.0 C, and the electron charge, measured different methods(in particular, in the experiments of R. Millikan), is equal to 1.602×10 –19 C. From here you can find N. This method of determining Avogadro's number appears to be one of the most accurate.

Perrin's experiments.

Based on kinetic theory, an expression including Avogadro's 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 above expression, we could find N. Unfortunately, this is impossible to do because molecules are invisible. However, in 1910 J. Perrin showed that the mentioned expression is also valid for suspensions of colloidal particles that are visible in a microscope. Counting the number of particles located at different heights in the suspension column gave Avogadro's number 6.82×10 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= 6.86Х10 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 marked a turning point in the attitude of scientists to the atomic theory of matter - previously, some scientists considered it as a hypothesis. W. Ostwald, an outstanding chemist of that time, expressed this change in views this way: “The correspondence of Brownian motion to the requirements of the kinetic hypothesis... forced even the most pessimistic scientists to talk about experimental proof of the atomic theory.”

Calculations using Avogadro's number.

Using Avogadro's number, exact values ​​of the mass 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 3x1022 atoms of this element.
see also

A physical quantity equal to the number of structural elements (which are molecules, atoms, etc.) per mole of a substance is called Avogadro's number. Its officially accepted value today is NA = 6.02214084(18)×1023 mol−1, it was approved in 2010. In 2011, the results of new studies were published; they are considered more accurate, but are not officially approved at the moment.

Avogadro's law is of great importance in the development of chemistry; it made it possible to calculate the weight of bodies that can change state, becoming gaseous or vaporous. It was on the basis of Avogadro's law that the atomic-molecular theory, which follows from the kinetic theory of gases, began its development.

Moreover, using Avogadro's law, a method has been developed to obtain the molecular weight of solutes. For this purpose, the laws of ideal gases were extended to dilute solutions, taking as a basis the idea that the solute will be distributed throughout the volume of the solvent, just as a gas is distributed in a vessel. Also, Avogadro's law made it possible to determine the true atomic masses a number of chemical elements.

Practical use of Avogadro's number

The constant is used in calculations chemical formulas and in the process of composing equations chemical reactions. It is used to determine relative molecular weights gases and the number of molecules in one mole of any substance.

The universal gas constant is calculated through Avogadro's number; it is obtained by multiplying this constant by Boltzmann's constant. In addition, by multiplying Avogadro's number and the elementary electric charge, one can obtain Faraday's constant.

Using the consequences of Avogadro's law

The first corollary of the law says: “One mole of gas (any), under equal conditions, will occupy one volume.” Thus, under normal conditions, the volume of one mole of any gas is equal to 22.4 liters (this value is called the molar volume of a gas), and using the Mendeleev-Clapeyron equation, you can determine the volume of a gas at any pressure and temperature.

The second corollary of the law: “The molar mass of the first gas is equal to the product of the molar mass of the second gas and the relative density of the first gas to the second.” In other words, under the same conditions, knowing the ratio of the densities of two gases, one can determine their molar masses.

At the time of Avogadro, his hypothesis was theoretically unprovable, but it made it possible to easily establish experimentally the composition of gas molecules and determine their mass. Over time, a theoretical basis was provided for his experiments, and now Avogadro’s number is used