Avogadro's Law: description and biography of the scientist. The most important position in chemistry
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 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 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 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 the same (one molecule at a time), 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 law, discovered in 1811, played a major role in the development of chemistry. First of all, he contributed to the recognition of the atomic-molecular doctrine, formulated for the first time in the middle of the 18th century. M.V. Lomonosov. So, for example, using Avogadro's number:
It turned out to be possible to calculate not only the absolute masses of atoms and molecules, but also the actual linear dimensions these particles. According to Avogadro's law:
“Equal volumes of various gases at constant pressure and temperature contain same number molecules equal to "
A number of important consequences regarding the molar volume and density of gases follow from Avogadro’s law. Thus, it directly follows from Avogadro’s law that the same number of molecules of different gases will occupy the same volume, equal to 22.4 liters. This volume of gases is called molar volume. The opposite is also true - the molar volume of various gases is the same and equal to 22.4 liters:
Indeed, since 1 mole of any substance contains the same number of molecules, equal to , then obviously their volumes in the gaseous state under the same conditions will be the same. Thus, under normal conditions (n.s.), i.e. at pressure 
and temperature, the molar volume of various gases will be 
. The amount of substance, volume and molar volume of gases can be related to each other in the general case by a relationship of the form:
from where, respectively:
In general, normal conditions (n.s.) are distinguished:
Standard conditions include:
In order to convert temperature on the Celsius scale to temperature on the Kelvin scale, use the following relationship:
The mass of the gas itself can be calculated from the value of its density, i.e.
Because as shown above:
then it's obvious:
from where, respectively:
From the above relations of the form:
after substitution into the expression:
it also follows that:
from where, respectively:
and thus we have:
Since under normal conditions 1 mole of anything occupies a volume equal to:
then accordingly:
The relationship obtained in this way is quite important for understanding the 2nd corollary of Avogadro’s law, which in turn is directly related to such a concept as the relative density of gases. In general, the relative density of gases is a value that shows how many times one gas is heavier or lighter than another, i.e. How many times is the density of one gas greater or less than the density of another, i.e. we have a relation of the form:
So, for the first gas we have:
respectively for the second gas:
then it's obvious:
and thus:
In other words, the relative density of a gas is the ratio of the molecular mass of the gas under study to the molecular mass of the gas with which the comparison is made. The relative density of a gas is a dimensionless quantity. Thus, in order to calculate the relative density of one gas from another, it is enough to know the relative molecular masses of these gases. In order to make it clear with which gas the comparison is being made, an index is given. For example, it means that a comparison is made with hydrogen and then they talk about the density of the gas in terms of hydrogen, without using the word “relative”, taking this as if by default. Measurements are carried out similarly, using air as a reference gas. In this case, indicate that the gas under study is compared with air. In this case, the average molecular mass of air is taken to be 29, and since the relative molecular mass and molar mass are numerically the same, then:
The chemical formula of the gas under study is placed next to it in parentheses, for example:
and reads as - the density of chlorine by hydrogen. Knowing the relative density of one gas in relation to another, it is possible to calculate the molecular as well as molar mass of the gas, even if the formula of the substance is unknown. All the above ratios refer to the so-called normal conditions.
2.6. Avogadro's law(A. Avogadro, 1811)
Equal volumes of gases (V) under the same conditions (temperature T and pressure P) contain the same number of molecules.
Corollary to Avogadro's law: one mole of any gas under the same conditions occupies the same volume.
In particular, under normal conditions, i.e. at 0°C (273K) and
101.3 kPa, the volume of 1 mole of gas is 22.4 liters. This volume is called the molar volume of the gas V m.
Thus, under normal conditions (n.s.), the molar volume of any gas V m= 22.4 l/mol.
Avogadro's law is used in calculations for gaseous substances. When recalculating the volume of gas from normal conditions to any other, the combined gas law of Boyle-Mariotte and Gay-Lussac is used:
where P o , V o , T o are pressure, gas volume and temperature under normal conditions (P o = 101.3 kPa, T o = 273 K).
If the mass (m) or quantity (n) of a gas is known and it is necessary to calculate its volume, or vice versa, use the Mendeleev-Clapeyron equation: PV = n RT,
where n = m/M is the ratio of the mass of a substance to its molar mass,
R is the universal gas constant equal to 8.31 J/(mol H K).
Another important corollary follows from Avogadro’s law: the ratio of the masses of equal volumes of two gases is a constant value for these gases. This constant value is called the relative density of the gas and is denoted D. Since the molar volumes of all gases are the same (1st consequence of Avogadro’s law), the ratio of the molar masses of any pair of gases is also equal to this constant:
where M 1 and M 2 - molar masses two gaseous substances.
The value of D is determined experimentally as the ratio of the masses of equal volumes of the gas under study (M 1) and a reference gas with a known molecular weight (M 2). Using the values of D and M 2, you can find the molar mass of the gas under study: M 1 = D × M 2.
6. Application of Avogadro's law. Molar volume
Since equal volumes of gas contain the same number of molecules, then the weights of molecules are proportional to the density of gases.
Gas density is the weight of one liter of gas at a temperature of 0°C and a pressure of 760 mmHg (oxygen density is 1.429). By physical methods it can be established very accurately (especially if the molecular weight of a substance that has not yet been studied is determined) in this way: at appropriate pressure and temperature, the volume occupied by a certain weight amount of the test substance is determined; temperature and pressure are recalculated to 0°C and 760 mmHg, and the density of the gas or substance in the gaseous state is calculated from the resulting volume and weight.
If the specific gravity of a gas or substance in a gaseous state is known, then according to the relationship:
calculate that the molecular weight of the test substance is:
i.e. the molecular weight of a gas or substance in the gaseous state is specific gravity gas or substance in a gaseous state multiplied by the number 22.41.
Since this equation is valid in all cases, it follows that the gram molecule or mole of each gas, i.e., the molar volume of each gas
A gram molecule or mole of each gas or substance in the gaseous state occupies the same volume at the same temperature and pressure. Under normal conditions 0°C and 760 mm Hg pressure. Art. this volume is 22.41 liters.
Rice. 5. Under normal conditions (0°C and a pressure of 760 mm Hg, all gases occupy a volume equal to 22.41 liters (molar volume)
Stoichiometric calculations, in which the weights of gases are converted to their volume, are based on the molar volume of a gas and on molecular equations.
Calculate how many liters of oxygen will be obtained by decomposing 250 g HgO and what volume oxygen will occupy under normal conditions(0°C and 760 mm pressure).
To calculate, you need to use the molecular equation, because it indicates the volume ratios:
from 432.32 g HgO you get 32 g of oxygen (22.41 liters)
from 250 g HgO it will be x g oxygen × liters
Avogadro's law examples
Problem solving >> Mol. Avogadro's law. Mole volume of gas
Since 1961, our country has introduced the International System of Units of Measurement (SI). The unit of quantity of a substance is taken to be a mole. Mole is the amount of substance in a system containing as many molecules, atoms, ions, electrons or other structural units as are contained in 0.012 kg of the 12C carbon isotope. The number of structural units contained in 1 mole of the substance N a (Avogadro's number) is determined with great accuracy; in practical calculations it is taken equal to 6.02 * 10 23 molecules (mol-1).
It is easy to show that the mass of 1 mole of a substance (molar mass), expressed in grams, is numerically equal to the relative molecular mass of this substance, expressed in atomic mass units (amu). For example, the relative molecular mass of oxygen (Mg) is 32 amu, and the molar mass (M) is 32 g/mol.
According to Avogadro's law, equal volumes of any gases taken at the same temperature and the same pressure contain the same number of molecules. In other words, the same number of molecules of any gas occupies the same volume under the same conditions. At the same time, 1 mole of any gas contains the same number of molecules. Consequently, under the same conditions, 1 mole of any gas occupies the same volume. This volume is called the molar volume of gas (Vо) and under normal conditions (0 °C = 273 K, pressure 101.325 kPa = 760 mm Hg = 1 atm) is equal to 22.4 dm3. The volume occupied by a gas under these conditions is usually denoted by Vo, and the pressure by Po.
According to the Boyle-Mariotte law, when constant temperature The pressure produced by a given mass of gas is inversely proportional to the volume of gas:
Po / P 1 = V 1 / Vo, or PV = const.
According to Gay-Lussac's law, at constant pressure, the volume of a gas changes in direct proportion to the absolute temperature (T):
V 1 / T 1 = Vo / To or V / T = const.
The relationship between gas volume, pressure and temperature can be expressed general equation, combining the Boyle-Mariotte and Gay-Lussac laws:
PV / T = PoVo / To, (*)
where P and V are the pressure and volume of gas at a given temperature T; Po and Vo are the pressure and volume of gas under normal conditions (norm). The above equation allows you to find any of the indicated quantities if the others are known.
At 25 °C and a pressure of 99.3 kPa (745 mm Hg), a certain gas occupies a volume of 152 cm3. Find what volume the same gas will occupy at 0 °C and a pressure of 101.33 kPa?
Substituting these problems into equation (*) we obtain: Vo = PVTo / ТPo = 99.3*152*273 / 101.33*298 = 136.5 cm3.
Express the mass of one CO2 molecule in grams.
The molecular weight of CO2 is 44.0 amu. Therefore, the molar mass of CO2 is 44.0 g/mol. 1 mole of CO2 contains 6.02 * 10 23 molecules. From here we find the mass of one molecule: m = 44.0 / 6.02-1023 = 7.31 * 10 -23 g.
Determine the volume that nitrogen weighing 5.25 g will occupy at 26 °C and a pressure of 98.9 kPa (742 mm Hg).
We determine the amount of N2 contained in 5.25 g: 5.25 / 28 = 0.1875 mol, V = 0.1875 * 22.4 = 4.20 dm3. Then we bring the resulting volume to the conditions specified in the problem: V = PoVoT / PTo = 101.3 * 4.20 * 299 / 98.9 * 273 = 4.71 dm3.
Avogadro's law
In 1811, Avogadro put forward the hypothesis that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. This hypothesis later became known as Avogadro's law.
Amedeo Avogadro (1776-1856) - Italian physicist and chemist. His greatest achievements are that he: established that water has the chemical formula H2O, and not H O, as previously thought; began to distinguish between atoms and molecules (indeed, he introduced the term “molecule”) and between atomic “weight” and molecular “weight”; formulated his famous hypothesis (law).
The number of molecules in one mole of any gas is 6.022 -10″. This number is called Avogadro's constant and is denoted by the symbol A. (Strictly speaking, it is not a dimensionless numerical value, but a physical constant with the dimension of a mole."1) Avogadro's constant is simply the name of the number 6.022-1023 (of any particles - atoms, molecules, ions, electrodes, even chemical bonds or chemical equations).
Since one mole of any gas always contains the same number of molecules, it follows from Avogadro's law that one mole of any gas always occupies the same volume. This volume for normal conditions can be calculated using the equation of state of an ideal gas (4), setting n = 1 and substituting into it the values of the gas constant R and standard temperature and pressure in SI units. This calculation shows that a mole of any gas under normal conditions has a volume of 22.4 dm3. This quantity is called molar volume.
Gas density. Since one mole of any gas under normal conditions occupies a volume of 22.4 dm3, it is not difficult to calculate the density of the gas. For example, one mole of CO2 gas (44 g) occupies a volume of 22.4 dm3. It follows that the density of CO2 under normal conditions is equal to
It should be noted that this calculation is based on two assumptions, namely: a) CO2 obeys Avogadro's law under normal conditions and b) CO2 is an ideal gas and therefore obeys the ideal gas equation of state.
Later we will make sure that the property real gases, and CO2 is one of them, under certain conditions it deviates significantly from the properties of an ideal gas.
Hydrogen Density
The first determinations in the history of chemistry of the molecular “weight” of many gases and liquids were based on the experimental determination of gas densities and their comparison with the density of hydrogen. In such definitions, hydrogen was always assigned an atomic “weight” equal to one.
The concepts of atomic weight and molecular weight mean approximately the same thing as the modern terms “relative atomic mass” and, accordingly, “relative molecular weight”.
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Avogadro's law
Formulation of Avogadro's law
This law was formulated by the Italian scientist Amedeo Avogadro in 1811 as a hypothesis, and then received experimental confirmation. This law can also be derived from the basic equation of molecular kinetic theory:
Considering that the concentration:
From the last expression, the number of gas molecules:
Obviously, under the same conditions (the same pressure and temperature) in equal volumes, the number of molecules will be the same.
Corollaries from Avogadro's law
Two important consequences follow from Avogadro's law.
Corollary 1 from Avogadro's law. One mole of any gas under the same conditions occupies the same volume.
In particular, under normal conditions, the volume of one mole of an ideal gas is 22.4 liters. This volume is called molar volume :
Corollary 2 from Avogadro's law. The ratio of the masses of equal volumes of two gases is a constant value for these gases. This quantity is called relative density.
Let the temperature be constant (\(T=const \)), the pressure not change (\(p=const \)), the volume constant \((V=const) \) : \((N) \) - the number of particles (molecules ) of any ideal gas is a constant value. This statement is called Avogadro's law.
Avogadro's law goes like this:
Equal volumes of gases (V) under the same conditions (temperature T and pressure P) contain the same number of molecules.
Avogadro's Law was discovered in 1811 by Amedeo Avogadro. The prerequisite for this was the rule of multiple ratios: under the same conditions, the volumes of gases entering the reaction are in simple ratios, such as 1:1, 1:2, 1:3, etc.
French scientist J.L. Gay-Lussac established the law of volumetric relations:
The volumes of reacting gases under the same conditions (temperature and pressure) are related to each other as simple integers.
For example, 1 liter of chlorine combines with 1 liter of hydrogen to form 2 liters of hydrogen chloride; 2 liters of sulfur (IV) oxide combine with 1 liter of oxygen to form 1 liter of sulfur (VI) oxide.
Real gases, as a rule, are a mixture of pure gases - oxygen, hydrogen, nitrogen, helium, etc. For example, air consists of 77% nitrogen, 21% oxygen, 1% hydrogen, the rest are inert and other gases. Each of them creates pressure on the walls of the vessel in which it is located.
Partial pressure The pressure that each gas creates separately in a mixture of gases, as if it alone occupied the entire volume, is called partial pressure(from Latin partialis - partial)
Normal conditions: p = 760 mm Hg. Art. or 101,325 Pa, t = 0 °C or 273 K.
Corollaries from Avogadro's law
Corollary 1 from Avogadro's law One mole of any gas under the same conditions occupies the same volume. In particular, under normal conditions, the volume of one mole of an ideal gas is 22.4 liters. This volume is called molar volume\(V_(\mu)\)
where \(V_(\mu)\) is the molar volume of gas (dimension l/mol); \(V\) - volume of matter of the system; \(n\) - the amount of substance in the system. Example entry: \(V_(\mu)\) gas (n.s.) = 22.4 l/mol.
Corollary 2 from Avogadro's law The ratio of the masses of equal volumes of two gases is a constant value for these gases. This quantity is called relative density\(D\)
where \(m_1\) and \(m_2\) are the molar masses of two gaseous substances.
The value \(D\) is determined experimentally as the ratio of the masses of equal volumes of the gas under study \(m_1\) and a reference gas with a known molecular mass (M2). From the values of \(D\) and \(m_2\) you can find the molar mass of the gas under study: \(m_1 = D\cdot m_2\)
Thus, under normal conditions (n.s.), the molar volume of any gas is \(V_(\mu) = 22.4\) l/mol.
Relative density is most often calculated in relation to air or hydrogen, using the molar masses of hydrogen and air to be known and equal, respectively:
\[ (\mu )_(H_2)=2\cdot (10)^(-3)\frac(kg)(mol) \]
\[ (\mu )_(vozd)=29\cdot (10)^(-3)\frac(kg)(mol) \]
Very often, when solving problems, it is used that under normal conditions (n.s.) (pressure of one atmosphere or, which is the same \(p=(10)^5Pa=760\ mm\ Hg,\ t=0^o C \)) molar volume of any ideal gas:
\[ \frac(RT)(p)=V_(\mu )=22.4\cdot (10)^(-3)\frac(m^3)(mol)=22.4\frac(l)( mole)\ . \]
Concentration of ideal gas molecules under normal conditions:
\[ n_L=\frac(N_A)(V_(\mu ))=2.686754\cdot (10)^(25)m^(-3)\ , \]
called the Loschmidt number.
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The principle, which was formulated in 1811 by the Italian chemist Amadeo Avogadro (1776-1856), states: at the same temperature and pressure, equal volumes of gases will contain the same number of molecules, regardless of their chemical nature And physical properties. This number is a physical constant, numerically equal to the amount molecules, atoms, electrons, ions, or other particles contained in a single mole. Avogadro's hypothesis was later confirmed a large number experiments, began to be considered one of the fundamental laws, included in science under the name Avogadro's law, and its consequences are all based on the statement that a mole of any gas, under the same conditions, will occupy the same volume, called molar.
Amadeo Avogadro himself assumed that the physical constant is a very large value, but only many independent methods, after the death of the scientist, made it possible to experimentally establish the number of atoms contained in 12 g (which is the atomic mass unit of carbon) or in a molar volume of gas (at T = 273.15 K and p = 101.32 kPa), equal to 22.41 l. The constant is usually denoted as NA or less commonly L. It is named after the scientist - Avogadro's number, and it is approximately 6.022. 1023. This is the number of molecules of any gas located in a volume of 22.41 liters, it is the same for both light gases (hydrogen) and heavy gases Avogadro’s Law can be expressed mathematically: V / n = VM, 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.
He belonged to a noble family living in the northern part of Italy. He was born on 08/09/1776 in Turin. His father, Filippo Avogadro, was an employee of the judicial department. The surname in Venetian medieval dialect meant a lawyer or official who interacted with people. According to the tradition that existed in those days, positions and professions were inherited. Therefore, at the age of 20, Amadeo Avogadro received his degree, becoming a doctor of jurisprudence (ecclesiastical). He began studying physics and mathematics on his own at the age of 25. In his scientific activity engaged in study and research in the field of electrochemistry. However, Avogadro entered the history of science by making a very important addition to the atomic theory: he introduced the concept of the smallest particle of matter (molecule) capable of existing independently. This was important for explaining simple volumetric relationships between reacting gases, and Avogadro's law came to have great importance for the development of science and widely used in practice.
But this did not happen right away. Avogadro's law was recognized by some chemists decades later. The Italian physics professor's opponents included such famous and recognized scientific authorities as Berzelius, Dalton, and Davy. Their misconceptions led to many years of controversy about chemical formula water molecules, since there was an opinion that it should be written not as H2O, but as HO or H2O2. And only Avogadro’s law helped to establish the composition of other simple and complex substances. Amadeo Avogadro argued that the molecules of simple elements consist of two atoms: O2, H2, Cl2, N2. From which it followed that the reaction between hydrogen and chlorine, as a result of which hydrogen chloride will be formed, can be written in the form: Cl2 + H2 → 2HCl. When one Cl2 molecule interacts with one H2 molecule, two HCl molecules are formed. The volume that HCl will occupy must be twice the volume of each of the components involved in this reaction, that is, it must be equal to their total volume. Only starting in 1860, Avogadro’s law began to be actively applied, and its consequences made it possible to establish the true values of the atomic masses of some chemical elements.
One of the main conclusions drawn on its basis was the equation describing the state of an ideal gas: p.VM = R. T, where:
- VM—molar volume;
- p—gas pressure;
- T—absolute temperature, K;
- R is the universal gas constant.
United is also a consequence of Avogadro's law. At constant mass of the substance it looks like (p. V) / T = n. R = const, and its notation: (p1 . V1) / T1 = (p2 . V2) / T2 allows you to make calculations when a gas transitions from one state (indicated by index 1) to another (with index 2).
Avogadro's law made it possible to draw a second important conclusion, which opened the way for the experimental determination of those substances that do not decompose when they pass into a gaseous state. M1 = M2. D1, where:
- M1—molar mass for the first gas;
- M2 is the molar mass for the second gas;
- D1 is the relative density of the first gas, which is set for hydrogen or air (for hydrogen: D1 = M1 / 2, for air D1 = M1 / 29, where 2 and 29 are the molar masses of hydrogen and air, respectively).