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. Avogadro's law also made it possible to determine the true atomic masses of a number of chemical elements.
Practical use of Avogadro's number
The constant is used in the calculation of chemical formulas and in the process of drawing up equations of chemical reactions. It is used to determine the relative molecular masses of 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, the volume of a gas can be determined 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 being used
January 21, 2017Knowing the amount of a substance in moles and Avogadro's number, it is very easy to calculate how many molecules are contained in this substance. Simply multiply Avogadro's number by the amount of substance.
N=N A *ν
And if you come to the clinic to take tests, let’s say, blood sugar, knowing Avogadro’s number, you can easily count the number of sugar molecules in your blood. Well, for example, the analysis showed 5 mol. Let's 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 stopped measuring molecules in pieces and began measuring 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 may arise here is: “what is molar mass?” No, this is not a mass of painter, as it might 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 m 0 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 it’s known, but what if it’s not? We will have to calculate the mass of one molecule m 0 . But this is 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 very large, then the mass of one molecule m0, on the contrary, is very small. Therefore, for the convenience of calculations, we introduced relative molecular mass (M r). 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 this 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 atoms included in the molecule. Relative molecular weight is measured in atomic mass units (a.u.m), 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 = 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 mass.
Let us recall the formula for finding the molar mass:
M=m 0 *N A .
Because m 0 = M r * 1.67 10 -27, we can express molar mass as:
M=M r *N A *1.67 10 -27 .
Now if we multiply Avogadro's 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 mass by 10 -3.
M=M r *10 -3
But don’t 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 the molecule m 0, we get the number of molecules in this substance.
N=m / m 0
Of course, it is a thankless task to count molecules; not only are they small, they are also constantly moving. Just in case you get lost, you'll have to count again. But in science, as in the army, there is such a word “must”, and therefore even atoms and molecules were counted...
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 it, 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.
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 and 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 fundamental law for ideal gases.
Avogadro's law formula
The discoverer of the law himself believed that the physical constant was a large quantity, but he did not know which one. After his death, in the course of numerous experiments, the exact number of atoms contained in 12 g of carbon (precisely 12 g is the atomic mass unit of carbon) or in a 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 of 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 the substance to its molar mass; VM is the 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.
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 to another - the ratio of the molar mass of one gas to the molar mass of the second gas.
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