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 historians from chemistry offer the most different 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 in normal conditions 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 last years scientists are 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 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.
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 brought quantitative characteristic number of structural particles 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 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 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 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, adopted one system reference of relative atomic quantities, which was based on a conventional unit equal to 1/12 of the mass of one isotope of carbon 12 C. The abbreviated name of the atomic mass unit is amu. According to this scale, atomic mass 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 a value of 18.0152 a.m.u.
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, special measure amount of a substance, called a mole. 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 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, 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: at normal conditions one mole of any gaseous element occupies 22.4 liters. This constant is called the molar volume of the gas.
> Avogadro's number
Find out what is Avogadro's number in prayers. Study the ratio of the amount of substance of molecules and the Avogadro number, Brownian motion, gas constant and Faraday.
The number of molecules in a mole is called the Avogadro number, which is 6.02 x 10 23 mol -1.
Learning task
- Understand the relationship between Avogadro's number and moles.
Key Points
- Avogadro suggested that in the case of uniform pressure and temperature, equal gas volumes contain the same number of molecules.
- The Avogadro constant is an important factor, as it links other physical constants and properties.
- Albert Einstein believed that this number could be derived from the quantities brownian motion. It was first measured in 1908 by Jean Perrin.
Terms
- The gas constant is the universal constant (R) resulting from the ideal gas law. It is extracted from the Boltzmann constant and the Avogadro 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, then it is easier to use a unit other than the number of molecules. The mole is the basic unit in the international system and conveys a substance containing as many atoms as is stored in 12 g of carbon-12. This amount of substance is called Avogadro's number.
He managed to establish a relationship between the masses of the same volume of different gases (under conditions of the same temperature and pressure). This contributes to the relationship of their molecular weights
The Avogadro number conveys the number of molecules in one gram of oxygen. Do not forget that this is an indication of the quantitative characteristic of a substance, and not an independent measurement size. In 1811, Avogadro guessed that the volume of a gas can be proportional to the number of atoms or molecules, and this will not be affected by the nature of the gas (the number is universal).
Jean Perinne won the Nobel Prize in Physics in 1926 for deriving Avogadro's constant. So Avogadro's number is 6.02 x 10 23 mol -1.
scientific significance
The Avogadro constant plays the role of an important link in macro- and microscopic natural observations. It kind of builds a bridge for other physical constants and properties. For example, establishes a relationship between the gas constant (R) and Boltzmann (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 .
Constant calculation
The definition of the number affects the calculation of the mass of an atom, which is obtained by dividing the mass of a mole of gas by Avogadro's number. In 1905, Albert Einstein suggested deriving it based on the magnitudes of Brownian motion. It was this idea that Jean Perrin tested in 1908.
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 development 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 it has been developed big number independent methods for determining the Avogadro number. 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 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 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 involving the Avogadro 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 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
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) 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 mol of gas (6.02 ∙ 10 23 molecules - constant number Avogadro) occupies a volume of 22.4 liters. Molar volume (V m) is a constant value.
Rice. 2. Normal conditions.
Problem solving
The main meaning 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. General formula relative density of the 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 practical use law on the example of two tasks:
- 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 the same way (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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